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GOTTFRIED WILHELM LEIBNIZ PHILOSOPHICAL PAPERS AND LETTERS
The New Synthese Historical Library Texts and Studies in the History of Philosophy VOLUME 2 Managing Editor: SIMO KNUUTIILA, University of Helsinki Associate Editors: DANIEL ELLIOT GARBER, University of Chicago RICHARD SORABJI, University of London Editorial Consultants: JAN A. AERTSEN, Free University, Amsterdam ROGER ARIEw, Virginia Polytechnic Institute E. JENNIFER ASHWORTH, University of Waterloo MICHAEL AYERS, Wadham College, Oxford GAIL FINE, Cornell University R. J. HANKINSON, University of Texas JAAKKO HINTIKKA, Boston University, Finnish Academy PAUL HOFFMAN, University of California, Riverside DAVID KONSTAN, Brown University RICHARD H. KRAUT, University of Illinois, Chicago ALAIN DE LIBERA, Ecole Pratique des Hautes Etudes, Sorbonne JOHN E. MURDOCH, Harvard University DAVID FATE NORTON, McGill University LUCA OBERTELLO, Universita degli Studi di Genova ELEONORE STUMP, St. Louis University ALLEN WOOD, Cornell University The titles published in this series are listed at the end of this volume.
GOTTFRIED WILHELM LEIBNIZ PHILOSOPHICAL PAPERS AND LETTERS A Selection Translated and Edited, with an Introduction by LEROY E. LOEMKER SECOND EDITION KLUWER ACADEMIC PUBLISHERS DORDRECHT ! BOSTON ! LONDON
ISBN-13: 978-90-277-0693-5 DOl: 10.1007/978-94-0 I 0-1426-7 e-ISBN-13: 978-94-010-1426-7 Published by Kluwer Academic Publishers, P.O. Box 17,3300 AA Dordrecht, The Netherlands. Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, The Nethcrlands. First edition: 1956 by Chicago University Press, Chicago Second edition: 1969 by D. Reidel Publishing Co., Dordrecht Second edition/second print: 1989 by Kluwer Academic Publishers printed Oil acidfi'ec paper All Rights Reserved © 1989 by Kluwer Academic Publishers Softcover reprint of the hardcover I st Edition 1989 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
To Priscilla
PREFACE TO THE FIRST EDITION The selections contained in these volumes from the papers and letters of Leibniz are intended to serve the student in two ways: first, by providing a more adequate and balanced conception of the full range and penetration of Leibniz's creative intellectual powers; second, by inviting a fresher approach to his intellectual growth and a clearer perception of the internal strains in his thinking, through a chronological arrangement. Much confusion has arisen in the past through a neglect of the development of Leibniz's ideas, and Couturat's impressive plea, in his edition of the Opuscu/es et fragments (p. xii), for such an arrangement is valid even for incomplete editions. The beginning student will do well, however, to read the maturer writings of Parts II, III, and IV first, leaving Part I, from a period too largely neglected by Leibniz criticism, for a later study of the still obscure sources and motives of his thought. The Introduction aims primarily to provide cultural orientation and an exposition of the structure and the underlying assumptions of the philosophical system rather than a critical evaluation. I hope that together with the notes and the Index, it will provide those aids to the understanding which the originality of Leibniz's scientific, ethical, and metaphysical efforts deserve. My indebtedness to all who have in some measure aided me in the preparation of the translations and interpretations is so extensive as to forbid detailed acknowledgment. Professor Paul Schrecker, whose knowledge of the thought forms and relations of Leibniz, and indeed, of seventeenth century thought in general, is unsurpassed, has read and corrected a large number of the translations, particularly in Volume I, and should be credited with setting norms for accuracy and adequacy. Professor Elizabeth DeLacey has exercised extensive editorial supervision, caught many defects, and suggested changes which have consistently improved the work. Beyond the extensive work of these, there are many others who deserve my gratitude for help rendered. A fellowship of the Rosenwald Foundation in 1938 and a grant from an anonymous source in 1951 enabled me to begin a detailed study of Leibniz, to make use of the Hanover manuscripts, and to confer with European scholars. The editors of the Prussian Academy edition, and the directors of the Hanover Landesbibliothek, gave generous advice and opportunities for study. Professor Helmut Kuhn, now of the University of Munich, checked the translations. For detailed answers to many questions I am indebted to more friends and colleagues than I can conveniently name. Publication was subsidized in part by a grant from the Research Committee of the University Center in Georgia, generously enlarged by Emory University. More important even than this, however, has been the climate of study provided by Emory University and its administration during troubled years of war and of uncertain peace.
viii PREFACE To acknowledge with gratitude the social co-operation required in such work is a pleasure which does not, however, remove the uneasy recognition that the responsibility for errors and other blights on the usefulness of these translations, being the fruits of solitary decision, must be borne by the translator and editor himself. All parentheses in the text are Leibniz's own, though some of his parentheses have been removed. All editorial interpolations are in brackets. Leibniz's own underscoring has been retained except when he used it to indicate direct quotation. The keys used throughout in references to the editions of Leibniz and related works may be identified in the Bibliography. Emory University. Georgia The appearance of a corrected edition of these Leibniz translations provides an opportunity to thank many who have suggested improvements in the text, and in particular Professor L. J. Russell of Birmingham and Professor G. H. R. Parkinson of Reading for their numerous corrections. I must also acknowledge gratfully the help given by Mrs. Linda Cornett, Mrs. Margaret Wood, and Mr. J. Brooke Hamilton in making the textual changes involved, and that of Mr. Grant Luckhardt in revising the Index. L.E.L. Emory University, 1969
T ABLE OF CONTENTS Preface vii Introduction: Leibniz as Philosopher I. The 17th Century II. Leibniz's Life and Work III. The Metaphysical Pattern IV. Leibniz's Method V. Logic and the Principles of Truth and Reality VI. Mathematics and Philosophy VII. Physics and the Realm of Nature VIII. Biology IX. Psychology X. Theory of Knowledge XI. Summary: Structure and Purpose XII. Ethics and Social Thought XIII. Theology XIV. Leibniz's Consistency and Influence 1 2 4 13 19 23 28 31 35 37 41 44 46 49 54 Bibliography 63 PART I. MAINZ AND PARIS, 1666-76 1. Dissertation on the Art of Combinations, 1666 (Selections) I. Demonstration of the Existence of God II. Corollaries for Disputation III. Cum Deo! Definitions Problems 2. A New Method for Learning and Teaching Jurisprudence, 1667 (Selections from Part I) Part I. General and Common to All Faculties: on a Basis for Studies in General 3. Letter to Jacob Thomasius, 1669 4. Letter to Thomas Hobbes, 1670 5. Theological Writings Related to the Catholic Demonstrations, 1668-70 I. The Confession of Nature against Atheists, 1669 II. A Fragment on Dreams III. On Transubstantiation, 1668(?) Supplement: Notes on the Eucharist, 1668 6. Preface to an Edition of Nizolius, 1670 (Selections) 71 73 73 74 76 77 78 85 85 93 105 109 109 113 115 118 121
x T ABLE OF CONTENTS 7. Elements of Natural Law, 1670-71 131 8. Studies in Physics and the Nature of Body, 1671 139 I. The Theory of Abstract Motion: Fundamental Principles 139 II. An Example of Demonstrations about the Nature of Corporeal Things Drawn from Phenomena 142 9. Letter to Magnus Wedderkopf, 1671 146 10. Letter to Antoine Arnauld, 1671 (Selection) 148 11. Letter to Simon Foucher, with Notes on Foucher's Reply to Des Gabets, 1675 151 12. Selections from the Paris Notes, 1676 157 13. Letter to Henry Oldenburg, 1675 165 14. Two Notations for Discussion with Spinoza, 1676 167 PART II. HANOVER TO THE ITALIAN JOURNEY, 1676-87 15. On a Method of Arriving at a True Analysis of Bodies and the Causes of Natural Things, 1677 16. Letter to Arnold Eckhard, 1677 17. Dialogue, 1677 18. Letter to Herman Conring, 1678 19. Letter to WaIter von Tschirnhaus, 1678 20. On the Ethics of Benedict de Spinoza, 1678 Part I. On God 21. What is an Idea? 1678 22. Letters to Nicolas Malebranche, 1679 (Selections) 23. Two Dialogues on Religion, ca. 1678 (Selections) I. Dialogue between Poliander and Theophile II. Dialogue between Polidore and Theophile 24. On the General Characteristic, ca. 1679 25. On Universal Synthesis and Analysis, or the Art of Discovery and Judgment, 1679(?) 26. Two Studies in the Logical Calculus, 1679 I. Elements of Calculus II. Specimen of Universal Calculus 27. Studies in a Geometry of Situation, 1679 I. Letter to Christian Huygens, 1679 II. Supplement III. On Analysis Situs 28. Letter to John Frederick, Duke of Brunswick-Hanover, 1679 29. On Freedom, ca. 1679 30. "First Truths", ca. 1680-84 31. Selections from Leibniz's Correspondence, 1679-84 I. To Christian Philipp, 1679 II. To Philipp, 1680 III. To Frantyois de la Chaise, 1680 IV. To Veit Ludwig von Seckendorf, 1683 V. To Walter von Tschirnhaus, 1684 171 173 177 182 186 192 196 196 207 209 213 213 216 221 229 235 235 240 248 248 249 254 259 263 267 272 272 273 273 275 275
xi TABLE OF CONTENTS 32. On the Elements of Natural Science, ca. 1682-84 I. The Plan of the Book II. An Introduction on the Value and Method of Natural Science 33. Meditations on Knowledge, Truth, and Ideas, 1684 34. A Brief Demonstration of a Notable Error of Descartes and Others Concerning a Natural Law, 1686 35. "Discourse on Metaphysics", 1686 36. Correspondence with Arnauld, 1686-87 (Selections) 37. Letter of Mr. Leibniz on a General Principle Useful in Explaining the Laws of Nature through a Consideration of the Divine Wisdom; to Serve as a Reply to the Response of the Rev. Father Malebranche, 1687 Introduction to Parts III and IV PART III. HANOVER TO THE DEATH OF ERNEST AUGUST, 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 1690-98 Letter to Arnauld, 1690 On the Method of Distinguishing Real from Imaginary Phenomena On the True The%gia Mystica, ca. 1690(?) A Study in the Logical Calculus Critical Thoughts on the General Part of the Principles of Descartes, 1692 On Part I On Part II Correspondence with Huygens, 1692-94 (Selections) From the Ethical and Legal Writings, 1693-1700 I. From the Preface of the 'Codex Juris Gentium Diplomaticus' II. From the Preface to the Mantissa Codicis Juris Gentium III. On Wisdom IV. On Natural Law A Classification of Societies or Communities On the Correction of Metaphysics and the Concept of Substance, 1694 Specimen Dynamicum, 1695 I. A New System of the Nature and the Communication of Substances, as weIl as the Union between the Soul and the Body, 1695 II. "Second Explanation of the New System", 1696 Letter to Gabriel Wagner on the Value of Logic, 1696 Letters to Des Billettes, 1696-97 Tentamen Anagogicum: An Anagogical Essay in the Investigation of Causes, ca. 1696 On the Radical Origination of Things, 1697 Clarification of the Difficulties which Mr. Bayle has found in the New System of the Union of Soul and Body, 1698 On Nature Itself, or on the Inherent Force and Actions of Created Things, 1698 PART IV. HANOVER UNDER GEORGE LOUIS, 54. Correspondence with John Bernoulli, 1698-99 1698-1716 277 277 280 291 296 303 331 351 355 357 359 363 367 371 383 383 391 413 421 421 424 425 428 429 432 435 453 459 462 472 477 486 492 498 509 511
xii TABLE OF CONTENTS 55. Correspondence with De Voider, 1699-1706 56. Letter to Varignon, with a Note on the 'Justification of the Infinitesimal Calculus by That of Ordinary Algebra', 1702 I. Letter to Varignon, February 2, 1702 II. Justification of the Infinitesimal Calculus by That of Ordinary Algebra, 1701 57. On What is Independent of Sense and of Matter, 1702 58. Reflections on the Doctrine of a Single Universal Spirit, 1702 59. Reflections on the Common Concept of Justice, 1702(?) 60. Reply to the Thoughts on the System of Pre-Established Harmony contained in the Second Edition of Mr. Bayle's Critical Dictionary, Article Rorarius 1702 61. Considerations on Vital Principles and Plastic Natures, by the Author of the System of Pre-Established Harmony, 1705 62. Letter to Hansch on the Platonic Philosophy or on Platonic Enthusiasm, 1707 63. Correspondence with Des Bosses, 1709-15 64. Conversation of Philarete and Ariste, following a Conversation of Ariste and Theodore, ca. 1711 65. Remarks on the three Volumes Entitled Characteristics of Men, Manners, Opinions, Times, ... 1711, 1712 66. The Principles of Nature and of Grace, based on Reason, 1714 67. "The Monadology", 1714 68. Letters to Nicolas Remond, 1714-15 69. Letters to Louis Bourguet, 1714-15 70. The Metaphysical Foundations of Mathematics, after 1714 71. The Controversy between Leibniz and Clarke, 1715-16 Index 515 542 542 545 547 554 561 574 586 592 596 618 629 636 643 654 661 666 675 722
INTRODUCTION: LEIBNIZ AS PHILOSOPHER The 300th birthday of Gottfried Wilhelm Leibniz was widely observed in 1946 but nowhere more appropriately, though unintentionally, than in the complex ritual of exploding the fourth atomic bomb at Bikini on the exact anniversary day, July I,1 It is not only that he was the first to argue that force is the essence of matter. It is rather that, second to none is his faith in science, and a forger of its new mathematical tools and social instruments, the academies, he was also vigorous in opposing the divorce between truth and action, and between power and its moral controls, which was already weakening the Western will. No event could better have reminded the thoughtful of the power released by modern science and of the failures of modern wisdom. It was the 17th century whose great achievements and crucial decisions led to our own cultural conflicts, but it was the wise men of that century, too, who first saw the dangers and sought ways of avoiding them. And among these Leibniz was one of the last to offer a unified and inclusive answer for the problems of European life. Our century can appreciate a man whose motto was "Pars vitae, quoties perditur hora, perit", and who expressed his sense of the dynamic in such maxims as "Aus Taten werden Leute".2 Not only have we verified his conviction that substance is activity. We are still working to achieve his dream of a universal grammar and strategy of science. We have rediscovered the value of his idea of an 'art of symbols' to standardize mathematical operations, mechanical assemblies, and orderly procedures of all kinds. The great calculators which we have constructed are more perfect applications of a conception which Leibniz applied to the complicated little mathematical machines on which he spent his income for so many decades. We have overtaken and surpassed his insights into mathematics, logic, and psychology. But our greatest unsolved problem is still, in essence, that whose solution served as a unifying goal of his efforts - a scientific, legal, religious, and moral basis for social order. It is timelessness rather than timeliness, however, that justifies the study of a philosopher. The fascination which Leibniz's insights have aroused in so many minds is due less to his relation to his own times - or to ours - than to the breadth and substance of his thought. Though he never philosophized in a vacuum, the range of problems upon which he worked creatively was wider than that of any other modern thinker; it covered the entire intellectual enterprise from mathematics and logic through the sciences to ethics, law, and theology. He was continuously engaged with these problems for over 50 years, sometimes attaining clarity and sometimes not, but always striving for coherence and harmony through the formulation of first principles. His spirit was at once creative and conciliatory, a rare combination which Bertrand Russell and others have held destroyed his integrity as a thinker. Most important of all, the principles of method in terms of which he sought to harmonize all truth form one of the enduring types of philosophy, and those who approach speculation from logic, or mathematics, or science, or religion have repeatedly been impelled to return to them. For references see p. 58
2 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS He himself defined the grounds which, paraphrased, justify a more extensive translation of his works; in preparing an edition of Marius Nizolius, an obscure rhetorician of the century preceding, he gave as his reasons "a basis for discourse, and the time ofthe author; a basis for discourse, because it is worthy of a philosopher, and the time of the author because he is worthy of our own" (G., IV, 138; cf. No.8, below). I. THE 17TH CENTURY The time of the author is the clue to his motives as philosopher. The 17th century stirred with decisions - and with a growing fear of crisis. The heir of the Renaissance, it felt the spirit of freedom and mastery but also the rude shocks and clashes which marked the collapse of those medieval controls upon which it stilI depended in government, law, education, and religion. The Treaty of Westphalia, ending Europe's most devastating war - until our own days - had finally destroyed Europe's devotion to the old bases of peace and unity and had substituted the principle of nationalism sanctioned by religion and buttressed by power politics. The interests of royal families, different languages, and separate traditions of law and culture were spurs to political pluralism; but a much-altered Corpus Juris Civilis, the Turkish danger, a Pan-European educational system surviving from the Middle Ages, and the new science provided some impetus toward political and cultural unity. Between the opposing forces of unity and disintegration, of conservation and innovation, were diplomacy and the churches. The balance of power shifted as adroit statesmen countered the dangers of concentrated power. Of the old Holy Roman Empire there remained but the titles and trappings and an aggregation of states whose self-interest often conflicted with their loyalty to the remaining focus of the empire in Austria. France, now unified, became the center of European power and the symbol of its culture. In England and Holland political revolution was determining the principles of modern liberalism, and its human type as well - the citizen-patriot-merchant. The small courts of northern and western Europe became unduly powerful through their bargaining strength in the great game of war potentials; Mainz, Hanover, and Berlin, to mention only three with which Leibniz was intimately involved, were not second in political astuteness even to Paris, London, and Vienna. The economic patterns of the Renaissance had made possible the accumulation of new wealth; explorer and entrepreneur provided new materials and new crafts for the enrichment of the new nations. However slow by modern standards, commerce and communication 3 were creating a European taste. Modem economic theory and practice were evolving and being fixed, partly in the cabinets of monarchs, partly in the counting-houses of merchants; capitalism and the beginnings of state socialism thus developed side by side, until the destruction of absolutism in government facilitated the triumph of private enterprise. Divided against itself, Christianity too became the tool of power. Having failed to control the new forces of nationalism and capitalism by imposing a unitary moral order upon them 4, the church now became involved in an effort to revive its own spiritual power. Theological controversy was the inevitable intellectual deposit from this effort; the problem of divine grace and its relation to man's freedom engaged Catholic and Protestant alike, with the mystics adding the force of living experience, but confusion as well. Jesuits were viewed with distrust because their compromises and strategy
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 3 fitted the new spirit of freedom too well; Jansenists were condemned for their misgivings about this same freedom. Since the fall of Rome, Christianity had never been more self-critical, and theological argument had become the tool of this critical reexamination. Most unifying and productive, however, seemed the rapid advance of science and technology. The 17th century felt a simple awe at the wonderful harmonies of nature which science was revealing and at man's power in creating tools for discovering them. With a rapidity that may seem appalling in retrospect, the age permitted a breach to widen between the humanistic and the scientific interests of the Renaissance. Early in the century scientists had developed both a permanent method and a social aim. The method was at once experimental and mathematical, Kepler and Galileo having shown with what advantage the two might be combined. The aim was universal well-being; Bacon had popularized the human worth of the new science. Yet the tendency to reduce human ends to such as could be attained by scientific discovery and control alone soon followed. Before the century closed, Leibniz himself could write to his friend Thomas Burnet as follows, despite his high esteem for Yergil, whom he once called his Leibbuch second only to the Bible. I do not begrudge the excellent Mr. Dryden the fact that his Vergil has won more than a thousand pounds sterling for him; this is the least that he deserved. But I wish that Mr. Halley might gain four times as much, at least, to make his voyage around the world and discover for us the secret of magnetic declination, and that Mr. Newton might gain this tenfold, and even more, to continue his profound studies without interruption. I am distressed at the destruction of Holbein's pictures, which were burned at Whitehall; yet I am a little in the sentiment of the Czar of Muscovy, who, I have been told, admired certain ingenious machines more than all of the pictures which he was shown in the royal palace [1698; G., III, 222-23]. Curiosite came to rank high among the courtier's virtues, as every man of intellectual pretensions became also a scientific dilettante. While universities, with notable exceptions, still sought to admit humanistic learning without ceasing to be strongholds of Scholasticism, the new science was forming its own social instruments independently, in the scientific academies andjoumals. In spite of the promise of scientific universalism, however, the age of Leibniz felt within itself the beginnings of tragedy, sensing its failure to perfect its social and moral controls. This sense of conflict and impending collapse appeared in the ethical problem of the nature of the just and the free man. The English Revolution was a revolution of Puritans, that is to say, Augustinian Platonists. Beginning as a revolt against tyrants in the interest of law, it implied a new conception of the individual- one essential to a century preferring order to freedom. Whatever their other differences, few of his critics disagreed with Leibniz's own conviction that true freedom must be consistent with universal harmony. Most of them, like him, feared another revolution, in which the libertine, the esprit jort, threatened to replace the man of honor (homo honestatis, homme honnete). 5 The latter was the courtier, who found his true freedom in exemplary obedience to the law of his sovereign and his court. The libertine, in contrast, demanded a freedom independent of external law and order, seeking to create his own law from within. The literature of the century abounded in praise for the one but showed a persistent distrust for the other. The crisis of the European consiciousness, which Paul Hazard has placed in the years of Leibniz's mature activity 6, was the crisis of the For references see p. 58
4 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS honorable man, who must either give way to the libertine or find an object of allegiance more permanent and universal than that of earthly ruler and law. It is in this crisis that Leibniz takes his stand with the honorable man, and it is through his eyes that he seeks an intellectual basis for Europe's futUIe. Science, law, and religion are to be grounded on universal order and a universal monarch, the ruler of the inseparably interwoven kingdoms of nature and of grace. It is only by allegiance to such an order that the man of honor, his honnetete enlarged by the cardinal virtues of curiosite in science, charite in human relations, andpiete toward the supreme ruler, can preserve himself and Europe. II. LEIBNIZ'S LIFE AND WORK Leibniz was 2 years old when the Thirty Years' War ended, having been born in the old Protestant university town of Leipzig in 1646. His childhood and youth were spent in an academic atmosphere, for both parents belonged to families esteemed for their connection with the university and the legal profession. His intellectual growth was precocious, though perhaps not so much as he later recalled it to be, and the autodidacticism of which he later boasted seems to have consisted chiefly in a certain independence and originality in pursuing studies which interested him beyond his school work - first Latin and history, then the Church Fathers, and later the logical structure of propositions and syllogisms. More significant, perhaps, is the sense of a call with which his father, impressed by certain omens of divine favor toward the young child, may have imbued him before he died in Leibniz's 6th year. One of the pen names under which the great projects for the unification of science and religion were later planned was partly translation and partly transliteration of his own name, Gottfried Leibniz, into Pacidius Lubentianus, a form expressive of the religious virtues of peace and good will which he sought to nurture. Leibniz's university training, which pointed toward legal scholarship, was not outstanding. Except for a semester at Jena, where he heard the lectUIes of the erudite and imaginative Erhard Weigel, reconciler of Plato, Aristotle, and Euclid, his studies were completed in the still strongly Scholastic tradition of his home university. Instruction served to develop the weighty learnedness which his early works display, but of his teachers only Jacob Thomasius seems to have stirred him to an active will to engage in the living issues of thought (No.3). It was probably in 1664, after 3 university years, and not at the age of 15, as he himself later recalled, that he walked in the Rosenthal, trying to decide between the old philosophy of substantial forms and the new of atomism and the machine, and at length cast his vote for the new, yet without ever really rejecting the essentials of the old. His early writings indicate that, aside from Bacon, he knew the modems only by hearsay or through the compendious summaries of his textbooks; he began the serious study of Hobbes several years later and of Descartes only during his years in Paris after 1672. With little mathematics beyond Euclid, but with a thorough knowledge of traditional philosophical and theological issues, he went into the study oflaw, succeeding, as he later says, in mixing some practical experience with his theoretical learning. For unclear reasons, apparently related to a failure to receive priority for a subordinate post in the law facuity, he withdrew to the University of Altdorf after completing his baccalaureate in law, and there he received a doctorate and was eventually offered a university position.
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 5 Four academic writings contain the beginnings of Leibniz's own thought, but with one exception their importance for the student of his philosophy is only indirect. This exception is the Dissertation on the Art of Combinations, published in 1666 as the first fruit of his logical studies. It points to a program for arriving at an exhaustive inventory and arrangement of human knowledge by means of a method of analysis and synthesis, using principles of permutation or combination as the basis of its enumerations - a refinement of the old Lullian art. Leibniz's later conception of a universal calculus was to grow out of the position developed in this work (No.1). Of the other three, the earliest is a display piece in traditional Scholastic form, the Metaphysical Disputation on the Principle of Individuality (1663), important only because it concerns one of his basic philosophic emphases; the others are studies in legal casuistry, applying probability to the settlement of doubtful cases in the law. They have some bearing on the development of his later ideas about truths of fact. In Niirnberg, however, a center in which the new sciences were beginning to flourish and where he himself was inducted into the Rosicrucian Society, his mind seems to have teemed with projects to be achieved at courts, not in universities - projects for the reform of law and of education for the law; for academies, libraries, and other agencies for advancing science; for the strategy of European politics. A chance meeting with the Baron John Christian von Boineburg, brilliant diplomat and statesman, led him to seek an appointment at the court of the Bishop Elector of Mainz, John Philip of Sch6nborn, and academic robes were laid aside permanently for the more modish raiment of the courtier. Except for 4 years in Paris from 1672 to 1676, the rest of his life was spent in residence at courts - at Mainz until 1672 and at Hanover, with frequent and long absences at Berlin and Vienna, in Italy, and elsewhere, from 1676 until his death in 1716. It is with this decision that the motives of Leibniz's activities and thought merge with the needs of European order. It may be said that his life was henceforth impelled in two opposite directions; the man of action and the scholar found it hard to achieve their aims within a single lifetime. On the one hand, there was the diplomat, counselor, unofficial historian, and tutor of princes and princesses; the adviser of statesmen, kings, and emperors. The rapidly changing map of Europe, which resulted from nine great wars and as many peace settlements in his lifetime, made it inevitable that much of his official activity should be devoted to the transient play of power politics - to restricting the power of France and maintaining that of the crumbling empire, to advancing the influence of the smaller states, particularly of Hanover, whose house he helped elevate to an imperial electorate and then to the throne of England. His political realism is well shown in an analysis of the European situation written in 1670, in which he described the causes of political tension and proposed a plan for federation and collective military security to maintain peace. 7 The elaborate proposal which he and Boineburg drew up the next year for a French crusade against Egypt, and which he carried to Paris in 1672, failed to divert Louis XIV's military ambitions from Europe, for the Sun King had already laid his plans for the invasion of the Low Countries. But the plan reveals an early understanding of the geographic, economic, and cultural factors in political strategy which later years sharpened, so that Leibniz's services as counselor were sought after by Prussia, Austria, Russia, and even the Vatican; with Peter the Great he had three conferences and an extended correspondence looking toward the modernization of Russia. For references see p. 58
6 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Yet his hopes for Europe rested upon deeper and more enduring plans, and it is with the promotion of these more permanent cultural goals that his long-term intellectual efforts were concerned. Four lifelong projects, anyone of which might have absorbed the full energies of a man without success - and in none of which, it may be added, Leibniz himself succeeded - occupied the leisure he was able to find for them. (1) Of these plans, the first in time concerned legal reform. His academic studies of doubtful cases in the law had convinced him of the need of a stricter and more universal method in legal rules and decisions. John Althus' suggestion that the confused state of European law could be simplified by finding more logical classifications than those of the Roman Corpus Juris had early impressed him 8, and the small work which helped him to secure his first appointment, the New Method/or Learning and Teaching Jurisprudence (No.2; cf. No. 4), proposed a psychological and a logical basis for simplifying law, together with a philosophical grounding of the law of nature. At Mainz, where he assisted Herman Lasser in a project of recodification, he undertook to prepare the general parts of a work on Rational Jurisprudence, only incomplete studies for which were ever written (No.6). Leibniz expected great values to develop from his work; in a letter to John Philip on March 27, 1669, he claimed to have prepared, among other things, a table, comparable in size to a map, which uses a unique arrangement and method to present the entire common private law of the Empire today, with all of its fundamental rules and propositions, and reduces them to first principles so that anyone who understands this table, or has it lying before him, can decide any fact or case of private law, and at once put his finger on the basis for the decision in the table itself [Guh. L., J, Anhang, 9-10). The work of Hugo Grotius had fastened in his mind the need of European peace as the practical goal of legal reform 9; his own logical and philosophical interests made him seek the principles of logic and ethics upon which a normative system of law and justice must rest. 10 His efforts to reduce the law to its primitive notions were therefore but one application of the universal method of analysis and synthesis, or of judgment and invention, which was one of the poles of his philosophical work. This jn turn required a new science, the universal characteristic and logical calculus, for its perfection. The metaphysical foundations of the law, on the other hand, he found in a Platonic theory of ideas, which was in turn supported by his mathematical, logical, and theological studies and became one of the permanent components of his system (Nos. 5, 6, and 9). With this foundation he was able to find a common theoretical bond between theology and law, which his more empirical investigations in physics and psychology were intended to support. (2) More persistent, however, than his efforts to establish a basis for European order through legal reform were his projects in religious unification. Leibniz was well aware that the religious controversies of the century were often cloaks for more earthly designs: in 1683, for instance, he wrote a skilful satire, the Mars Christianissimus, attacking the pious pretensions of Louis XIV. Recognizing that the divisions of religion, closely related to those of political power into states, intensified religious conflict, he made vigorous efforts to bring first Roman Catholics and Protestants, and later the Lutheran and Reformed wings of Protestantism, into agreement on church polity and doctrine - efforts which involved much theological writing and hundreds of letters to such leaders as Bossuet, Arnauld, PelIisson, and the Abbess of Maubisson
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 7 and her secretary, Mme de Brignon. In this enterprise Leibniz was not moved merely by political motives, as some interpreters have held, but by religious conviction and an interest in the validity as well as the social effectiveness of the Christian faith (Nos. 5, 23, 28, and 40). Indeed, his interest in religion, like his historical and political interests, extended beyond Europe; the American Indians, about whom he had direct information from the Baron de la Hontan and others, impressed him with a natural Adamic piety and morality, while the morality of China, on whose language and culture the Jesuit missionaries kept him informed, contrasted so favorably with Europe's that he suggested that "considering the rapidly growing decline of manners in Europe it is almost necessary for the Chinese to send missionaries to teach us the purpose and practice of natural theology, as we send missionaries to instruct them in revealed theology" [Dut., IV, 280]. For Leibniz and his contemporaries, ecclesiastical unity meant theological unity and was therefore to be attained through Christian apologetics and an authoritative agreement on church polity. Early in his career (1669) Leibniz outlined a work entitled Catholic Demonstrations, an apologetic study which was to be based on philosophical principles and to be absolutely conclusive - a sound basis for European unity and the immediate evangelization of the world (No.5). Many studies were prepared, but the work was left incomplete. Soon after he came to Hanover he revived the project with the hope of getting the Catholic Duke John Frederick to support it (No. 28); after the death of that patron in 1679, he interested Count Ernest of Hesse-Rheinfels in his plan. Here, as in his other grandiose schemes, he became absorbed in the parts and never completed the whole. But the "little discourse in metaphysics" which provided the basis for his long philosophical correspondence with Arnauld (Nos. 35, 36, and 38) may well have been written as a part of the philosophical introduction for the Catholic Demonstrations; in any case, it is significant that not only Leibniz's metaphysics but his logic and physics were developed as a foundation for his theology (Nos. 5, 8, and 10). Though the extensive writings on dynamics in the 1690's (No. 46) arose as an independent interest, he always insisted upon their theological bearing (No. 50). It has often been pointed out that Leibniz philosophized best in controversy with others and also that his spirit in such controversy was irenic and conciliatory. It has not been sufficiently emphasized, in reply to those who find two thinkers in Leibniz - a good logician and a bad theologian - that his philosophical controversies, whether with the Jansenist Arnauld or the skeptic Bayle, with the Cartesian De Voider or the Jesuit Des Bosses, are irenic because they are always concerned with theological issues as well. The most important problem was logical, metaphysical, and theological all together; it was the problem of the relation of individual to universal, of concrete subject to its predicates, of man to nature, of human freedom to divine grace. His criticism of men like Spinoza, Sturm, and even Malebranche was that they denied power, and therefore existence, to individuals; on the other hand, Hobbes, Bayle, and Newton (as interpreted by Clarke) encouraged naturalism and the complete independence of the individual - in short, Iibertinism. (3) If religion and law were to provide the pattern and motive of European harmony, the advancement of science and technology was to supply the tools. It was high time, Leibniz felt, for Bacon's vision of the advancement of learning to bear fruit in a program of organized research, Pan-European in scope and universal in content. His letters reveal the ardor with which he drove forward his own investigations and chalFor references see p. 58
8 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS lenged the co-operation of others. When he went to Paris in 1672, he was ignorant of mathematics beyond Euclid and some ideas of Cavalieri; he had discovered the essential processes of the calculus before he left 4 years later. 11 The notion of mathematical function and the symbolic and operational tools which he built upon it for the physical sciences were for him an outstanding instance of his more general science of symbols and a clue to the philosophic interpretation of individuality and process. The mathematical principles of continuity and equivalence he used as effective tools in physical analysis, and he showed the necessity of the notion of vis viva and its conservation in closed systems. Not all his inventions and discoveries were capable of arousing the interest of his contemporaries, as did his calculating machine and the new mechanical devices which it embodied; his proposal for a geometry of situation (No. 27) failed to interest even his friend and mentor Huygens, and his logical studies were so far beyond his contemporaries in sharpness if not in conception (for related projects had been made public by LuIIus, Wilkins, Kircher, and others) that publication was out of the question. 12 Leibniz's letters and papers are a rich mine of information about the arts and crafts of the century. No new mechanical principle or natural discovery was too trivial for his attention, and few of the achievements of the day can be named in which he did not have a hand: the discovery of phosphorus and its manufacture as a weapon of war (No. 27, I) (here, again, it remained for the 20th century to execute his purpose); the discovery of European porcelain; the use of microscopes in research; Papin's steam engine, for which he proposed a self-regulating mechanism and the re-use of the expended steam; the principle of the aneroid barometer (No. 49); machinery for the uniform distribution of power in pumps, which he himself devised in his unsuccessful efforts to rid the silver mines of the Harz of superfluous water; and proposals for improving clocks, navigation, and coinage and the economic theory on which it rested. He was an innovator and discoverer in the field of the social sciences as well. The significance of his historical methods and results has been exaggerated 13, but his collection of political documents from the Middle Ages, published in 1693 and 1700 (No. 44, I and II), is one of the beginnings of the modern collection of sources; and his history of the House of Brunswick, which turned into an exhaustive study of the Middle Ages and was later used by Gibbon, emphasized the creative and enlightened character of the 11 th and 12th centuries in contrast to the darkness which preceded and followed them. Meanwhile he prefaced his history with the Protogaea, an account of the development of the earth and life upon it, for he believed that we must first understand the earth if we are to understand the people who inhabit it. 14 The science of linguistics began in his efforts to prepare a comprehensive comparative dictionary of the common terms of all known languages, a project preliminary to the more general one of developing a universal language; this in turn was an aspect of his universal characteristic or science of symbols. He succeeded to a degree in tracing the great migrations from the local names they deposited throughout Europe and discovered some of the rules for the evolution of language. His interest in education is shown in many letters and papers (N o. 2). But though himself a genius, Leibniz considered scientific advance as the work not of individual geniuses but of scholarly co-operation. Hence he commonly used his own studies to build and strengthen co-operative work in science. A member of the British Royal Society and the French Academy, he himself planned the organization
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 9 of the Prussian Academy on broader intellectual bases and drew up plans for similar academies in Mainz, Hanover, Vienna, Dresden, and St. Petersburg, though the continuation of political conflicts kept these from being founded. The church, too, was to support research; monasteries were to be reorganized into institutions for scientific and technological advance, and he suggested an Order of God-lovers (Ordo Theophiforum) or an Ordo Carita tis Pacidianorum 15, whose members were to prepare a universal language and encyclopedia and then serve as missionaries to use this newly organized knowledge in the improvement of the well-being of all peoples. It is in his proposals for a unified method and apparatus for this uncovering of the foundations of the sciences and ordering their results that Leibniz's scientific interests, in their turn, pass over into philosophy. The general tool for investigation was to include a universal language for spoken and written communication, another language of symbols for scientific analysis and synthesis (the universal characteristic), a calculus for using them in discovery and analysis, and a universal encyclopedia based on this characteristic and logic. To the several parts of this project he returned at regular intervals in his life, particularly at the periods centering in 1670, 1679, and 1690, and he never abandoned it (see Nos. 1, 10, 13, 19,24,25,26, and 41). (4) In these efforts at scientific, religious, and legal reform, Leibniz never lost sight, however, of the basic motive, which was the well-being of man and his happiness. In his humanitarian hopes he was a true individualist and internationalist; at the same time that he urged a sound patriotic interest in the German language and culture upon his countrymen he was planning similar developments in Russia. To Count Golofkin he wrote: In this I make no distinction of nation or party, and I should prefer to see the sciences made flourishing in Russia rather than given only mediocre cultivation in Germany. The country which does this best will be the country dearest to me, since the Whole human race will always profit from it [1712; Foucher de Careil, Oeuvres de Leibniz, VII, 503]. And to Des Billettes he said, in dicussing the restoration of the French Academy's work after the Peace of Ryswick: Provided that something of consequence is achieved, I am indifferent whether it is done in Germany or in France, for I seek the good of mankind. I am neither a phil-Hellene nor a philo-Roman, but a phil-anthropos [1697; G., VII, 456]. All Leibniz's projects meet, therefore, in the need for a philosophy and, specifically, an ethics for the man of honor. True piety is to be identified with charity. The basic need of the century is the commitment of honorable men to the universal rather than to the relative and particular. Leibniz was no democrat l6 , though he was within limits a hedonist, a liberal, and an individualist. He was a friend of princes and looked for leadership in advancing man's well-being to "those great men in whom alone there is hope of improvement in this greatest of centuries". Such men must be brought to a philosophia perennis, the synthesis of what is good in all systems. They must be brought to understand what is truly universal and how moral individuality is related to it. Clearness and distinctness of ideas are the first requisites of true honor, for it is only reason, and the creative will based on it, that man and the supreme monarch have in common. The honorable man must live on the highest level of the law, above strict faw and equity (Nos. 6, 44, and 59), and therefore above merely positive law. His great For references see p. 58
10 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS principle is that "of justice and true piety as well, for to contribute to the public good and to the glory of God is the same thing" (G., III, 261). He must be a member of the realm of grace; and the relation of this realm to the individual and to the realm of nature, it is the purpose of Leibniz's philosophy to make clear. Of course he failed. Part of his failure was the result of his own many-sidedness; he either did not see or was not free to apply Goethe's later wisdom: "In der Beschdinkung zeigt sich erst der Meister."17 Part of it lay in the inherent difficulties, not to mention impossibilities, in his plans. But some of the failure was not his but his century's, for it followed other guides and made other choices; going further and further along the way of pluralism and individualism, it retained his faith in science and technology but rejected his quest for moral, religious, and legal unity. The suddenness of the change and the quickness with which the molds of modern Europe were set are still strange to contemplate: as Hazard points out, the French people, who were still thinking like Bossuet at the end of the century, were by 1750 thinking like Voltaire. And the problems which arose in Leibniz's own age have become inescapable in ours. In his old age, ordered by George Louis to persist in the task of completing his history of the House of Hanover while the court was settling in London, goading himself to his burden through various counterirritants to the gout, Leibniz predicted the early revolution, yet still sought and encouraged the "great prince" and the man of honor. As vigorous as ever in controversy (No. 71), as friendly and painstaking as ever with correspondents, he died neglected by his master, with his profoundest thoughts unpublished and his many creative dreams buried in a mass of manuscript. Some of the virtues and faults distinctive of Leibniz's philosophy arise from certain peculiarities in his mode of work, which it will be useful to remember in reading him. Fontenelle said that Leibniz bestowed the honor of reading them upon a mass of bad books. His inclination was to read everything, to read it rapidly, and to understand it in relation to the perennial philosophy which he proposed to found. His own insights came most readily in reaction to the view of someone else whom he read or with whom he corresponded or conversed 18; the independent exposition of his own opinions seems to have come hard to him. His own education, except in mathematics" was one by books rather than inspiring teachers - and these books were chiefly texts in the Scholastic manner. Suarez's Disputationes metaphysicae had become the academic standard of doctrine for Protestant and Catholic Europe alike, and a host of smaller works were written further diluting, supplementing, altering, or rejecting his already modified Aristotelianism in favor of Platonism, Ramism, PhiIIipo-Ramism, the modern corpuscular theory, or Cartesianism. To his textbooks Leibniz's reaction was always independent, yet their immediate effect, like that of most texts, was a rapidly acquired show of erudition, sometimes without exact knowledge (see especially No.3), a glib use of terms without, always, a firm grasp of the restrictions imposed by their history, and a body of ready-made opinions without the time to penetrate their implications. Leibniz's active philosophical career thus begins with his general convictions already accumulated (though not yet formed); like the texts he used, he was an eclectic. He was always at home with Scholastic terms, concepts, and problems; the old bottles into which he tried to pour the wine of his new notions of individuality, force, and mathematical function are the medieval categories of substantial form, causality, active and passive intellect, primary and secondary matter, primary and secondary
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 11 power. In spite of inherent difficulties, Leibniz boldly imposed Aristotle's predicables upon his dynamic monadism. Since Scholastic terms, however confused, stilI provided the most general medium of learned discourse, this was not entirely a misfortune. Yet it had the consequence of introducing many misunderstandings of his meaning, both among his contemporaries and later. Some of Leibniz's difficulty is therefore terminological. The 17th century was fixing the language of modern science, and Scholastic terms were proving inadequate for the new discoveries. Leibniz was aware of the importance of fruitful symbols for the pursuit of truth and showed himself a great inventor of such symbols - for example, in the calculus, in logic, and in geometry. He was a connoisseur ofthe apt phrase as well, and the place of analogy in his method made the substitution of the figure for the principle a constant temptation, though his effective popularizations can usually be translated into the more rigorous logical terminology of his critical writings. His several sets of terms - the Scholastic, the mathematico-logjcal, and the popular - may well confuse the interpreter who has failed to establish equivalences among them. This complexity must in turn be accounted for by the universality of the task which Leibniz set for himself. A perennial philosophy requires social co-operation, the criticism of all existing systems, and the inclusion of all the fields of human knowledge and endeavor. Leibniz's main concern was to avoid sectarianism but to invite helpful criticism, and the effort to be all things to all men in order to stimulate their own labors has left its unmistakable mark upon his works. In terms of a distinction which he himself made in the introduction to Nizolius, these include acroamatic and exoteric writings. In the acroamatic everything is demonstrated, in the exoteric some things are said without demonstration, but confirmed by certain fitting and logical quotations, or even demonstrated, though developed only topically and illustrated by examples and analogies. '" In the exoteric portion one is permitted to luxuriate a little, so that even if some certitude is lost, there is lost no clarity - or atleast very little [G., IV, 1461. Among his own papers there are those developed in logical rigor, those in the courtly style with which he sought to interest princes, princesses, and nobles, and those in the personal style of letters to friends. This sense of the diversity of readers also led him to publish his conclusions in different languages and in different journals: Latin in the Acta eruditorum for scholars and Scholastics, French in the Paris Journal des savants for the intellectuals at the courts, as well as in the emigre journals of the Low Countries - Bayle's Nouvelles de la republique des lettres, Basnage's Histoire des ouvrages des savants, Le Clerc's Bibliotheque universelle - for Cartesians and other moderns.19 For a universal philosophy needed to bring into agreement ancients and moderns, Cartesians and Scholastics, mechanists and teleologists, atomists and subjectivists like Foucher. An adequate faith to serve as the basis of confident action demanded the concord of minds, a goal which challenged Leibniz's diplomatic finesse and in the attainment of which he did not always avoid the skilful exploitation of an ambiguity or of the emotional impact of terms. "I hope", he wrote to Clarke late in his life, "that my demonstrations will change the face of philosophy." Though he refused to compromise irresolvable issues, most of his philosophizing was in a conciliatory spirit; he was usually more aware of the similarities which bound his thought to that of others than of the differences. Among his papers, the basic stratum of reading notes, For references see p. 58
12 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS paraphrases, and preliminary sketches contains studies of Plato, Aristotle, Augustine, the Scholastics, Descartes, Hobbes, Grotius, Spinoza, Cudworth, Boyle, Malebranche, Bayle, Locke, Toland, and Shaftesbury, to mention only those of prominent and enduring place in the tradition. Indeed, his two extended philosophical writings are critical comments on the works of others: the Theodicy on Bayle and the New Essays on Locke. 20 A perennial philosophy, however, must involve a synthesis not merely of the truth found in other philosophers but also of all fields of human investigation and activity. This Leibniz sought to achieve through philosophic construction beginning at two poles, that of method and that of metaphysics - a construction in which unity is achieved through the discovery of general principles with specialized applications to the various fields and the granting of metaphysical status to these principles. The long dispute about Leibniz's starting-point is therefore largely futile; his metaphysics is based no more on jurisprudence than on physics, for the same lawgiver is involved in both - and in ethics and theology, in psychology and mathematics, as well. His philosophy seeks the most general principles common to law, theology, and science; whether in logic, psychology, or physics, it seeks the same truths, though under the restrictions of a different set of definitions and symbols, and therefore with more concrete but limited meaning. No other modern thinker has attempted to bring so great a range of subject matter under the rule of so few general principles. The breadth of Leibniz's cultural goals, of which his methodological and metaphysical studies were but instruments, thus helps to explain the fragmentary and incomplete nature of his work, his extreme caution in considering anything ready for publication, and the general pattern in which his efforts advance from grandiose but purely formal plans to the special investigation of particular problems, particularly after 1690. The universal encyclopedia ended in a series of studies for the logical calculus and the general science; the Catholic Demonstrations, in the various metaphysical discourses of the last 3 decades of his life. It is characteristic of Leibniz that until the age of about 45 he worked as much as possible on the parts of his great intellectual projects and that he then found what energies he could save from other duties completely absorbed by his answers to new intellectual challenges, such as the appearance of Locke's Essay, Newton's Principia, and Bayle's Dictionary, the three giants of the approaching revolution. Yet whatever may be said of this distraction of effort, it must be admitted that Leibniz never lost sight of the general issues involved in his detailed philosophical analyses and that his discernment between the important and the trivial was usually accurate. For it was the lack of time, as well as his own inclinations, that kept his philosophy incomplete. His letters reveal how he devoted to philosophical labors time spent on journeys and periods of illness or occasionally of rest. Nothing seemed ready; to Placcius he wrote in 1696, "He who knows only what I have published does not know me" (Dut., VI, 65). Two revisions of the long New Essays exist among his manuscripts, along with criticisms by a number of French correspondents to whom it was submitted, yet Leibniz did not publish it (Bod. LH., pp. 79, 84). He himself described his confusion in many letters. How extremely distracted I am cannot be described. I dig up various things from the archives, examine ancient documents, conquer unpublished manuscripts. From these I strive to throw
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 13 light on the history of Brunswick. I receive and send letters in great number. 21 I have, indeed, so many things in mathematics, so many thoughts in philosophy, so many other literary observations which I do not wish to have perish, that I am often bewildered as to where to begin [to Placcius, 1695; G., IV, 413 n.). It follows that, although many of Leibniz's interpreters have quarreled about the systematic unity of his thought, he himself abandoned such claims. In 1696 he wrote to Des Billettes : My system, about which you express curiosity for some news, is not a complete body of philosophy, and I make no claim to give a reason for everything which others have sought to explain. We must proceed by stages to proceed with firm steps. I begin with principles, and I hope to be able to satisfy most of the doubts like those which have troubled Mr. Bernier [G., VII, 451). In the first decade of the new century, Leibniz's insistence on the incompleteness of his thought increases; to De VoIder, to Locke's patroness Lady Masham, and to others he writes that his philosophy is still merely a hypothesis, though he holds it to be the most intelligible one so far advanced and therefore presumptively true. Completeness and unity are sacrificed to the task of inciting others to share in the common aim. After careful and repeated revision, Leibniz's papers were circulated among his acquaintances for criticism or, in some cases, submitted for publication. The 'Discourse on Metaphysics', for example (No. 35), was intended not for publication but for the criticism of Arnauld and perhaps of others. This was true too of the Critical Thoughts on the General Part of the Principles of Descartes, the Principles of Nature and of Grace, the Monadology (Nos. 42, 66, and 67), and many others. As a final factor, Leibniz's philosophy is affected at different periods by the particular special studies in which he is engaged. Of this, the outstanding example is the fading of the logical interest from first place in his thoughts, after the publication of Newton's Principia and Locke's Essay, and its replacement by the physical studies of the 1690's, his abandonment of the theological projects for church union, and his growing interest in English politics, thought, and culture. Beginning with the Specimen dynamicum (No. 46), the universal harmony is pushed into the background and force to the center, the law of individuality becomes abstract and 'formal', and the actual dynamic process the concrete and real. The claims of demonstration are weakened and the hypothetical nature of his philosophy emphasized. The eternal chain of being gives way, in emphasis, to the temporal order of progress, so that in his last philosophical statements (Nos. 66 and 67) the Platonic doctrine of ideas on which his thought is always based is not explicit, logic is subordinated to epistemology, while psychology, biology, and history are in the foreground. III. THE METAPHYSICAL PATTERN The intellectual strivings of the 17th century find visible reflection in its architectural forms. The great garden at the summer palace of Herrenhausen, north of Hanover, was replanned and extended in 1696 by the Electress Sophia and her garden architect Charbonnier; Leibniz himself served as consultant on the fountains and perhaps on other matters of technology and design. It may have been in its garden theater that the noble actors performed his masque Trimarcion, to the professed scandal of the more For references see p. 58
14 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS ponderously austere court of Berlin. Certainly it was there that he walked with his patroness Sophia and her daughter, Sophie Charlotte, the first queen of Prussia, and discussed the problem of God's plan and man's place in it. It was there that he challenged Herr von Alversleben to find two leaves that were identical in form, yet discernible. In it he found, too, the physical symbols of an adequate metaphysics - universal harmony; individuality without duplication, yet reflecting and re-presenting the order of the whole; dynamism; and to one side the labyrinth, inviting dalliance but never complete understanding. 22 The Herrenhaus(m garden was an enormous rectangle, surrounded on three sides by canals, and carefully subdivided, in strict geometrical fashion, into thirty smaller squares isolated from each other by walks and thick, carefully shaped hedges. Each smaller garden was further planned in formal order but with complete variety; no two gardens were alike, for each had its individual 'principle' and name. Yet so similar was their basic design that, casually observed, they might easily be confused. Complete individuality was fused with universal harmony. The carp ponds were themselves individualized; gazing into them, Leibniz might well imagine "each portion of matter ... conceived as a garden full of plants, and as a pond full of fish. But every branch of each plant, every member of each animal, and every drop of its liquid parts is itself likewise a similar garden or pond" - not one of the more fortunate of his figures. At the intersections of the main boulevards separating the newer gardens were fountains, among them one of the highest on the Continent. The moral order of the honorable man, like the garden, demanded individuality and freedom within the limits of an inviolable order and plan and spontaneity regulated by the universal harmony. Ability, temperament, and environment vary in each individual, determining the limitations in the successive experiences and perspectives in each. But however different, the individual laws of the separate series follow from the universal harmony which science and the social order seek. It is this universal harmony which provides not only the basis for the honorable man's capacities and actions but also the goal of his moral obligations. Both efficient and final causes are imbedded within it. Three conceptions, therefore, and their mutual relations, determine the pattern and the problems of Leibniz's philosophy - universal harmony, individuality, and force and the notions in terms of which he seeks to relate them are mathematical function, representation, and conatus or striving. Universal harmony he derived from the Platonic tradition; individuality from Aristotle and the moderns, but with an idealistic principle of individuation 23; while that of dynamic change is his own, though stimulated by both Aristotle and Hobbes. Thus his success in reconciling the ancients and moderns is bound up in his success in relating these three determining principles. (1) Leibniz first attempts to interpret individuality and process in terms of the universal harmony. The a priori starting-point for his thought is the perfections of God, the universal calculator from whose contemplation and choice of possibilities the world is born. 24 Not the God of Descartes, a Machiavellian prince on cosmic scale, upon whose will the order of logic and of nature depends, but the "region of ideas", the inner necessity of whose perfection requires it to bring the best of all possibilities into existence - this is Leibniz's God and the foundation of his system. God is perfect intellect, and his will is merely "a certain consequence of his intellect" (G., J, 257, No. 16; cf. PA., VI, i, 45). The reality of a harmonious perfection is the first presupposition of Leibniz's philosophy.
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 15 The full meaning of this region of possibilities becomes more apparent only when the nature of an idea is understood. An idea is a structure of meaning, a real definition, based on the law of identity and contradiction, and in close logical dependence upon the other ideas constituting God's mind. As such it is the possibility of existence, and not merely, as Cassirer's Neo-Kantianism leads him often to imply, of experience alone. Every simple idea is a mode of God's perfection and therefore harmonizes with all other such units in the divine intellect. In terms of the mathematical analogy in Leibniz's system, every idea is a particular solution, in terms of one variable, of a complex functional relationship between the infinity of variables which comprises God's understanding. Before Paris, he thinks of number as that category which reveals this harmony; after Paris, he sees the need of an extension of mathematics beyond number or quantity and a universal logic of relations. Beyond such mathematical analogy, this harmony of ideas cannot be described, for human knowledge is merely discursive and in symbols, and all description is therefore already involved in a dualism or polarity which the ideas themselves make possible but which they also escape - the dualism of passive content or symbol and symbolic act or active representation. Yet the structure of this realm of possibility can be represented in symbols, and it is this description which provides the foundation for Leibniz's logic, mathematics, metaphysics, and practical philosophy. The universal harmony and perfection of meaning cannot be proved without a vicious circle, for the principles upon which proof rests are derived from it. But unless it exists, there is no principle of knowledge, no explanation for anything being as it is. Descartes is therefore right in his use of the ontological argument - though his argument collapses with his failure to prove the possibility of such perfection of meaning. This possibility Leibniz, too, never succeeds in establishing, though he makes great efforts, and for a time professes to have done so, before he drops the argument and returns to the cosmological (Nos. 14 and 16). But given the existing series of events, there must be some reason for such a series existing and being as it is rather than otherwise, and the quest for such a reason leads to a realm of possibility whose perfection involves all of creation (No. 51). Three properties of the ideas, which arise from their perfection and plenitude, help Leibniz on with his thinking; he finds in them the basis for logical relations, for process, and for metaphysical individuality. (A) Every true proposition or every relationship, whether existent or merely possible (Leibniz tends to disregard negative propositions, since he considers them as mere denials of the truth of positive propositions), must conform to the law of possibility or of identity and contradiction. If it does not, it is mere words unsupported by any idea. At once, however, two issues arise in the interpretation of propositions: (i) they may be understood to signify either the extension of individual instances or the intension or essential meaning, and (ii) they may be given a relational or a more specific predicative interpretation. Leibniz recognized these alternative possibilities, but his effort to construct a metaphysics of individuality on the Aristotelian-Scholastic pattern made it difficult for him to adopt either a relational or an extensional interpretation. Denotation, being possible only in existence, is therefore logically derivative from the a priori realm of essence and hence also merely the empirical preliminary to the true scientific analysis. Furthermore, the conception that all being derives from the intellect of God provides For references see p. 58
16 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS metaphysical warrant for the Aristotelian principle that "in every true affirmative proposition, the predicate is included in the subject" (predicatum subjecto inest)2S, a principle to which Leibniz looks for support of his conception of individual substance. The reconciliation of this logical and metaphysical point of view is the first difficulty in Leibniz's system. The harmony of ideas is one of systematic interdependence, not of the subordination of predicates to subjects or to the substances which they qualify for Leibniz regards substances as completely analyzable analytic propositions. His logic thus applies the Aristotelian-Stoic categories of substance and property to a field of logical meanings which rather demands the Platonic, mathematical logic of relations. Thus he never clearly relates or sharply distinguishes between forms as attributes of substance and forms as 'formulas' or models, as these are developed in his symbolic calculus. The predicative logic should have been considered as a special case of the more general relational analysis, but Leibniz's concern with traditional conceptions of substance kept him from freeing himself from the Aristotelian position. (B) In the second place, ideas are not merely the basis of logic and its laws; they also have a dynamic quality. "In all essence there is a striving for existence." In the ambiguities of the verbs exigo and conor there lies concealed the secret of the relation of process to structure, power to plan, and will to intellect. It is the fulness and perfection of the ideas which make creative activity necessary; if nothing existed, possibility would not be complete or perfect. Therefore ideas must be powers. And man's internal sense reveals that ideas do in fact have this dynamic quality; human ideas are never separate from the drive to action and perfection. Thus, by analogy, every divine idea tends or strives to exist, except insofar as it is prevented by the striving of other ideas. How the harmonious possible ideas can interfere with each other in their striving toward existence is the second great unanswered problem of Leibniz's thought. He points to the fact of interference and conflict, of evil and the demand for compensation, in the created world; he acknowledges the sources of his conception in older doctrines; but the reason for it, he admits, is unknown to us (G., VII, 195). If man knew this, he would not be bound to truths of fact or contingent judgments but would know as God knows. In its logical and absolute sense, the law of sufficient reason fails man at this point, and the infinite breach appears between truths of fact and of reason. Yet Leibniz's effort to reduce the problem to human ignorance is not completely successful, for the paradox is clear for all to see. A realm of harmonious possibilities, comprising the perfections of God, is nonetheless incapable of being rendered existent because of internal inconsistencies. But, when the best of all possible combinations is chosen, the result is an existing order of compossible events in which complete harmony is again the law of the relationships between monads. In terms of possibilities, existence must be relatively disharmonious; yet in terms of the harmonies of existence, the realm of possibility is itself disharmonious. A partial answer to the paradox is to be found in the nature of time and space. With the dynamic quality of ideas, both of these enter as the new dimensions of existent compossibilities. Here too the mathematical analogy is helpful; a functional law is actualized in a series of particular values, and this series involves infinite and continuous succession. So an idea, or the law of an individual, striving to exist under the
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 17 dual conditions of its fulness and its limitation, achieves the greatest possible perfection through a succession of changes or states. Leibniz boldly appropriates the term 'conatus', which Hobbes had used in a physical sense, for the momentary tendency of a meaning to actualize itself. And actual qualities which, considered as possibilities or essences, would be inconsistent with each other may become consistent when distinguished in space or time. Since space is merely the simultaneity of two or more events, and time is succession, creation requires both in order to achieve the best, or the maximum of possible harmony. (C) Finally, because creation involves plurality and mutual limitation, it involves a duality of activity and passivity. As every idea strives to 'realize' 26 itself in harmony with others, it is distinguishable into a polarity of active forces and of passive content or matter. Within the series of events which result from the ideas as powers, therefore, each existing event is unique yet a part of many wholes, some of them existent, some eternal patterns. Its uniqueness consists of activity, however momentary; its dependence consists in passivity, for which Leibniz revives the controversial term materia prima. In mind this matter is inert content, while the activity is perception, and the differentiation of this activity in successive stages is appetite (conatus). In physical processes the matter is inertia, the activity force. Every individual is thus (i) an idea or law, a part of the divine harmony, (ii) continuously differentiating itself into a series of events which are interrelated (though not interacting) spatially and temporally, (iii) in a succession of impulsions or fulgurations, each of which also involves a passive inert quality reflecting the rest of the world upon which it depends. This passive element constitutes the limitation of the individual or of its 'point of view'. Individuals may thus be viewed as differentiated products of the universal harmony of ideas, and natural and historical change as the creation of an existing order after the best of possible plans. And the understanding of existence should be derivable, therefore, from the eternity of God's perfections. But only God can view the universe adequately from this purely logical starting-point; for finite beings it is impossible except in abstract or 'incomplete' terms, since the ideas are perspectiveless, while we are limited to particular spatial and temporal perspectives. (2) It is therefore more fruitful to shift the emphasis from logical possibility to existence and to view the eternal harmony from the viewpoint of the individual. For both theoretical and practical reasons, it is a primary concern of Leibniz to establish a genuine individuality. Pluralism is required if analysis is valid, for, where there are real aggregates or compounds, there must be ultimate and simple minimal realities, and these cannot be spatial, since spatial analysis is possible beyond any definable limit. The spatial analogue to an individual is a point, but an individual is a 'metaphysical' point, one at which something is going on. Here, again, a more convincing argument for the reality of individuals is man's experience of himself as a selfdetermining and private entity different from others and causally independent of them. Leibniz's emphasis upon individuality and process increases in the later periods of his thought; though the Discourse of 1686 (No. 35) is the first work to develop his mature conception of the individual monad, it is still centered upon God and his providence, while the Principles of Nature and of Grace and the Monadology, both written in 1714, are built upon the argument for individual substance. His criticism of other systems is often aimed at their failure to provide a firm basis for individual For references see p. 58
18 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS existence (Nos. 53 and 58 are examples). Spinoza, of course, fails entirely, since he recognizes no plurality of active principles in nature and hence no created substances. But even Malebranche has failed as well, since he shows no real connection between the active principle in man, which he limits to the will, and the ideas in God. Every individual is thus an idea or law fulfilling itself in a succession of activepassive states. Individuality is therefore not determined by matter but rather determines it; only by basing individuality upon the creative ideas themselves can individual and universal be related. To shift the emphasis from the eternal to the temporal, as Leibniz himself tends at last to do, it is within the nexus of perceptions, modifications, or events within the individual that empirical evidence is to be found for the law or the inclusive idea of his individual nature and for the universal harmony which each event reflects or represents. For every passing state of an individual expresses, represents, or perceives the universe according to the restricted limits of its nature or law, so that a complete understanding of anyone involves the whole harmony. Two important applications of this general principle may be pointed out in passingone to the theory of human knowledge and the other to human values. Knowledge is a special case of the more or less momentary representation of the universe according to a finite point of view. The human mind - man as a body-soul unity is an individual only in a secondary sense - is a true metaphysical unity consisting of a succession of states which fit the harmonious functioning of the many individual unities which comprise his body and, through these, the rest of the universe. The body thus determines the mind's limitations or its finite and imperfect point of view. Any present act of knowledge is related to the past states of mind through the abiding law of the individual given imperfectly in memory; it is also related to the future states of the same mind through purposes determined by the same law. But every present state also consists of some content - sensory, emotional, and on higher levels of knowledge, symbolic - by which the mind represents the universal harmony more or less confusedly, indistinctly, and inadequately. Leibniz holds that in the act of knowing we begin with a double datum and that we never free ourselves from it - the subjective act and the objective content of perception. Hence interpretation must always involve the belief in a greater reality of which I am a part, independent yet inclusive. "Every mind", he says in a fragment from the Paris period, "is omniscient but confused" (Cout. OF., p. 10). Knowledge is thus a representative act whose content is symbolic of an external reality but whose objective truth lies in its structure and rests on the universal harmony in creation or beyond it in the logical realm of possibility. Truth is verified by the quality of thinking which the mind does with its symbols. The case is similar with human values. All human goals are the perception of some aspect of the universal harmony. It may be unclear and indistinct or reflective and critical. Pleasure is the subjective matter accompanying the movement of the mind toward objective harmony; pain, the subjective matter representing disharmony, whether within the mind, its body, or beyond it. Thus "pleasure is harmony in a sentient being", "good is contemplation of the ideas", and "the beatific vision .... is the contemplation of the universal harmony of things, because God or universal mind is nothing but this harmony of things of the principle of beauty in them" (PA., VI, i, 97-98, 474, 496). Value is thus, on the subjective side, based on pleasure, but, since feeling is but the primary matter of an active teleological striving which itself expresses more or less of harmony, value is, on its objective side, a relation to perfection. A
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 19 genuine individualism thus involves a unique restriction of, but also a reaction to, a universal order. (3) The third general principle which distinguishes Leibniz's metaphysics is the dynamic. Leibniz's interest in force and action is supported by his theoretical studies in physics and psychology.27 In contrast to Descartes, he stresses the importance of formal operations even in mathematics. Matter is not merely extended, as Descartes held; it involves resistance and therefore action. Mind is not a substance in the sense of an enduring substratum of modifications; it is a succession of active states conforming to law. Force, it is true, does not emerge clearly as a metaphysical principle until the refutation of Descartes's physics around 1686 and the dynamics of the 1690's, at a time when his social interests are also being deflected from the eternal elements of law to history and from the perfect ideal to the process of gradual perfection. Creation is continuous temporal process, and that which distinguishes truths of fact from truths of reason is the essentially temporal nature of their predicates. Leibniz's dynamism is modern and his own, making him a fruitful innovator, particularly in physics, psychology, and the metaphysics of nature; and it is not misleading to find here the point in which modern thought shifts from a domination by extension to a domination by time. The relation between these three principles - harmonious order, individual substance, and dynamic process - presents the most difficult problems for the student of Leibniz. Interpreters have generally followed their own inclinations in making one or the other central. He himself never reached permanent clarity about them. Bound to the end to the eternal 'chain of being', he never succeeded in fully freeing from it the individual and the changing processes of existence, though his appreciation of them grew with the years. His own choice of Scholastic terms, the intellectual mood of the time, and his conviction that experience involves both the changing and the changeless prevented him from adopting, in the end, either a clear temporalism or eternaIism, a clear pluralism or monism. IV. LEIBNIZ's METHOD Since he thought of philosophy and science as a social enterprise of which his own efforts were but a part, Leibniz's actual method may well seem at odds with the conception of method which he is generally held to have proposed. He did, of course, propose one and made efforts to apply it. The Scholastics had failed through poor concepts, iII defined (Nos. 3 and 6); his own method must include a rigorous test of real definitions as opposed to merely verbal or nominal ones. Descartes and the followers who amplified his rules - even the great Arnauld in his Art 0/ Thinking - had failed to provide criteria for clearness and distinctness; he would derive such criteria from the laws of logic themselves (Nos. 33 and 39). The empiricists, even Locke, had failed to distinguish the problem of a valid method from the description of a psychological process; "the question of the origin of our ideas and principles", he asserted against Locke, "is not the preliminary one in philosophy, and we must have made great progress before we can well answer it" (G., Y., 16). His own method had two phases - the critical analysis of concepts and judgments into their component parts (a judgment being the process of breaking up or building a complex concept) and the constructive synthesis of truth which represents or expresses reality (No. 25). In his Art o/Thinking Arnauld 28 had expounded Descartes's method For references see p. 58
20 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS of analysis and synthesis on the basis of an unpublished manuscript given him by Clerselier; Leibniz identified this method with that of judgment and invention proposed by Ramus. Analysis consists of finding the most simple concepts involved in compound concepts and the most general principles implied in more particular ones; it is therefore equivalent to an internal induction which proceeds from complex given facts or relations to the more general and abstract concepts and principles which are entailed in them. Leibniz generally assumed that the number of primary or most simple notions, once found, would be relatively small and fixed. Synthesis, on the other hand, is constructive, building more concrete truth, possible or existent, out of truths that are simple or accepted as simple. It therefore corresponds in general to deduction, which Leibniz therefore conceived as a process of accretion through new definitions. For truths of reason such a method provides certain truth - provided the principles and notions used are known to be possible, that is, to obey the law of identity and contradiction. For truths of fact, however, possible combinations must be tested and verified by experience, since we lack the power to derive them from completely simple and therefore certain concepts. This is the method of hypothesis. Both analysis and synthesis are thus essential to all knowledge, whether of possibility or of existence; both must begin with facts and principles as well and would ultimately include all facts; both must be in terms of the most fitting symbols available; and both rest upon the same ultimate rational principles; identity, contradiction, and sufficient reason (No. 24, II).29 For man intuitive knowledge is possible only of the most abstract principles of reason and of such self-evident notions as being, of abstract logical systems, and in the realm of existence, of himself as the subject of particular experiences; all other knowledge depends on the discursive methods of reasoning. It has been held by penetrating Leibniz interpreters, notably Couturat and Russell, that Leibniz attempted to found his thought by deduction alone. The view has much to justify it. Couturat found very important, in this connection, the 'First Truths', a study from the years between 1679 and 1684 (No. 30) in which Leibniz professes to deduce most of his basic principles - sufficient reason, the identity of indiscernibles, the internality of denominations, continuity, the analytic nature of propositions, and his concept of individuality in general- from the law of identity. Leibniz held, throughout his career, that all propositions are analytic or that in every true affirmative proposition the predicate is included (intensionally or connotatively) in the subject. 30 Therefore, if the elements of all subjects were given clearly enough, deduction would suffice for philosophic knowledge. Such deduction, however, would itself combine analysis and synthesis, if it were possible for man to carry it out. For it would have to begin with a complete definition of God, which would contain all the simple concepts which are his properties or perfections (G., IV, 425), as well as with the most general principles of thought. Deduction proceeds from identities and definitions, but with the exception of the definition of God as the most perfect being all definition involves analysis and synthesis as well. In short, Leibniz held that for God all knowledge would be deductive, and his judgments completely analytic, since his knowledge always rests on adequate and complete intuition, but that for man such knowledge is limited to those abstract fields of possibility, like mathematics, formal logic, and abstract ontology, which involve no time and contingency. Most human knowledge concerns the temporal and conditional where analysis and synthesis must support each other, whether we proceed
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 21 deductively from established truth or from mere hypotheses. Here analysis is still the essential basis of synthesis, whether the concepts to be analyzed are known and the compatibility of their component concepts is to be shown or whether the notions themselves are unverified and the formal analysis of their definitions leads to verifiable abstract parts, thus verifying the concepts themselves. The unknowns of algebra furnish the outstanding example of such 'dumb reckoning', as Leibniz sometimes calls it; the verification of a scientific hypothesis is an important application. A concept is necessary if it is implied in the analysis of a known truth. If this necessary implication involves causal inference (from effect to cause), it is contingent or physical necessity; if it involves only the laws of logic, it is metaphysical or logical necessity. It is synthesis, however, which is the source of new knowledge on the part of man. Every human judgment - we may now restrict ourselves to judgments of fact - involves two mental functions: representation and reasoning. Representation is the function of symbols or characters in knowledge; it is the relation of expressing or standing for an objective state of things. Reasoning (ratiocinari) consists of the analytic-synthetic defining or 'formulating' of a structure of symbols in such a way that it can be verified as representing the structure of reality. Successful synthesis involves the choice of 'real' characters, symbols qualified by their very structure to reveal the organization of the world in their formulas. Leibniz was aware of the fact that common language contains this 'real' element and was concerned to improve it. But science and technology are in a position to develop their own efficient symbols and operations - the decimal system, the symbols of the calculus, or more recently, the benzene ring are examples of such real characters. It was to develop and to unify these that Leibniz proposed a universal characteristic or science of symbols, toward which the operational symbols he himself developed in logic, geometry, the calculus, and mechanics were but a beginning. Reasoning thus consists in the construction and application to experience of symbols according to an established set of axioms and accepted rules of operation or transformation. Thus the ideal of a general characteristic becomes a general science in which the principles and methods of all the sciences are generalized. The conception of such a science is one of Leibniz's greatest visions. In addition to the characteristic, this would contain the sets of axioms applicable for any particular science and, derived from them and from the definitions of the symbols, the appropriate rules for transforming the symbolic formulas which constitute the methodology of the science. Every science is thus thought of as capable of mathematical organization through a general theory represented in a language by means of an appropriate set of symbols and developed by fitting operations. But the axioms themselves are all special instances of the most general metaphysical principles; for example, geometric similarity and congruence are derivatives, on two distinct levels of completeness, of the law of identity, as are algebraic equations and the principle of the equipollence of cause and effect or the principle of conservation in dynamics.31 Thus the ideal of a general science implies in its turn the ordering of the sciences into a hierarchy in which all are related analogically because all involve the same ultimate principles and rest upon the same harmony. Reality as we know it consists of 'wellfounded' systems of phenomena, each of which is a particular translation of the same unified and ultimate pattern of being. The result is a pattern of analogies, so that physics becomes a phenomenal commentary on metaphysics, the nature of the monad For references see p. 58
22 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS being reflected in the mass and energy of composite bodies. Similarly, physics reflects the same ultimate principles, differently synthesized, as psychology, biology, ethics, and law, all of them (and we should add, though Leibniz did not, theology as well) being partial symbolic representations of the ultimate harmony of being which man can know only abstractly in logic, mathematics, and metaphysics. Philosophy therefore becomes the most general and universal science, seeking the common principles and common structure of being which all other fields represent from a limited point of view. And its problems center in two foci, that of metaphysics and that of the methodology of knowledge. It may be well to remind ourselves, in view of the widespread revival today of Leibniz's vision of a unified science, of the limits which he discovered to its development. Three factors are important for the understanding of his own thought: (1) Human knowledge, Leibniz himself discovered, is more relative and shifting than his conception of method allows. It is true that modern logic does not hold his conviction that, if we could but reach them, the simple notions out of which all being is compounded would be sharply defined, easily enumerable, and all on one level as far as their combination is concerned. His own recognition that in the analysis of existence human efforts to arrive at finality are blocked by man's finiteness points to this conclusion. To anticipate Kant, we may say that such efforts finally confront the antinomies which mark our knowledge of existence - those of finiteness and infinity, plurality and unity, activity and passivity, change and permanence. (2) Leibniz's failure to apply his own method perfectly illustrates this. It is true that his papers contain many successful applications of the method of analysis and synthesis, but except for his logical studies, his approach to philosophical problems was relative to experience and applied the method only within empirically applicable limits. Excellent examples of this are the physical studies in Nos. 15 and 32. Thus he generally uses a twofold method. His dynamics was written from both an a priori and an a posteriori point of view - treating motion, and later force, abstractly and concretely (Nos. 8 and 46). In law he attempted both the casuistic and the formal and normative approach. No part of experience escaped his scrutiny - on the subjective side joy and sorrow, dreams and the confusions of sense, the orderly processes of memory, association, and thought, claims to the beatific vision; on the objective side, everything from stellar relations to the microscopic cells which Leeuwenhoek showed him, and from the impact of colliding bodies to the problems of architecture and other arts, and the hidden harmonies and collisions of social order. Yet his rationalistic assumptions protected him from falling into the empirical confusion between simple enumeration and induction, origin and validity, while his wide interest in facts received at least a formal unity from his search for the general principles of an exact scientific instrument. (3) Finally, metaphysics, though abstract, receives analogical support from one empirical source of knowledge that escapes the symbolic and representational character of the rest. This is man's experience of his own mental processes in reflection or the internal sense, or after 1700, 'apperception'. Self-awareness of this immediate kind is the only concrete intuitive knowledge which man possesses and proves adequate to penetrate into the deepest levels of the soul and to reveal the enduring nature of its thought and desires; if analogies are based on it, it provides the most concrete clue to an explanation of the metaphysical categories or the simple perfections of God.
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 23 In whatever sense they are taken, it is always false to say that all our concepts come from the senses which are called external; for the concepts which I have of myself and of my thoughts, and as a result, of being, of substance, of action, of identity, and of many others, come from an internal experience [1686; No. 35, Sec. 27]. The immediate apperception of our own existence and our thoughts provides us with the first truths a posteriori or of fact, as identical propositions contain first truths a priori or of reason, that is, the first lights. Both are incapable of being proved and can be called immediate, the former because there is immediacy between the understanding and its object, the latter because there is immediacy between the subject and the predicate [after 1704; G., Y, 415]. Thus the nature of the scientist himself, as given in immediate experience, throws a more concrete light upon the metaphysical implications of his work. V. LOGIC AND THE PRINCIPLES OF TRUTH AND REALITY The problem of the relation of Leibniz's logic to his metaphysics is crucial in the criticism of his thought. It does not belittle the excellence of Russell's and Couturat's work to say that their efforts to show that his metaphysics is built upon his logic, though not soundly, have been refuted. 32 Leibniz shared the Aristotelian and Scholastic conviction that logic is a tool of thought, that it is a science of relations only as these are thought, and that it must be grounded in the universal, self-differentiating harmony which is reflected imperfectly in individual substances. His logical studies aimed to provide the instruments by which man can grasp the structure of being in his own symbolic formulas. They were devoted, first, to the perfection and reduction to mathematical form of the Aristotelian logic, which he used most skilfully on occasion, and then to the development of a more universal logic built upon mathematical symbols, operations, and axioms. This logic was to become the instrument of his universal science. As has already been shown, however, there is a difficulty in adjusting Leibniz's logic to his metaphysics, which corresponds to the difficulty he found in adapting Scholastic terminology to functional modes of thought. Its source is to be found in his theory of the proposition. His problem was to generalize a logic of the subordination or inclusion of meanings into a logic of symbolic forms and then to make this fit both metaphysical dynamism and metaphysical pluralism. In none of these tasks was he successful. The structures of classical logic consist of terms, propositions, and syllogisms. Interpreted in terms of symbolic relations, however, these become formulas, relations, and operations - logical entities which are more relative and interchangeable than the traditional concepts. The operations of logic are for Leibniz processes of climbing the scale of being from less adequate and complete to more adequate and complete concepts or constructions or, to use the terminology of 1686, from partial to integral concepts. But with this conception the notion of the proposition with which Leibniz begins is not completely compatible. In his opinion, all knowledge implies the identity of the complete predicate with the complete subject. Identity is therefore the basic principle of possible knowledge, whether of fact or of reason. Operationally, identity is defined by the possibility of substitution; two terms are identical if one can be substituted for the other without For references see p. 58
24 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS distortion of meaning. If they cannot, the reason is either contradiction or inadequacy. Contradiction, therefore, or the principle of impossibility, is implied in identity, and the two are opposite aspects of the same law, which Leibniz sometimes calls the basic law 0/ being. The principles of equality in mathematics, of congruence and similarity in geometry and mechanics, and of equipollence or equivalence in dynamics are particularized special cases of the general law of being upon which all truths of reason and the a priori components of truths offact depend. The principle that the predicate of every affirmative proposition is included in the subject is therefore the most general logical consequence of the law of identity.33 But Leibniz uses it also to express the ontological unity of a substance and its modifications. Since this principle is important for his argument to individual substance, the logical qualifications which he places upon it must be clear. In the first place, the relation between predicate and subject must be understood intensionally, not extensionally. Extensionally the relation would be reversed, and the subject included in the predicate. Leibniz recognized both points of view and even discussed the rules for conversion from one to the other, but his own metaphysics of harmony required the intensional interpretation. 'All A is B' means always that the properties of A, or the simple notions contained in it, include those of B. In the second place, he recognized that there are human judgments with particular subjects of which this is true only implicitly, not explicitly. Thus human judgments are synthetic, taken empirically, though their analytic nature would become explicit if both subject and predicate were further reduced to their simpler components. Thus 'Some A is B' means that there is among the simple notions included in A at least one that itself includes B, so that, calling this C, the particular proposition reduces to the two universal ones: 'All A is C' and 'All B is C'. This fundamental logical principle, which Leibniz had some success in defining for the special cases of universal and particular affirmative categorical propositions, is the logical unit in terms of which he undertook to reveal the structure of meaning and existence. The central issue in Leibniz's metaphysics may be put logically in the question whether an individual substance can be identified with a complete or 'integral' logical subject or whether it is merely 'partial' or incomplete. In Scholastic terms, he correlates the basic logical proposition, predicatum subjecto inest, with the ontological one "All modifications are of subjects" (Modi/icationes sunt suppositorum), both of which he ascribes to Aristotle 34, a correlation which entails the third principle that "there are no purely extrinsic denominations". These three principles converge to support his view that every completely analyzed existential proposition would have an individual substance as subject. But though he introduces a number of devices to support this possibility of logical reduction to substantial individuals, notably the distinction between direct (recto) and oblique logical relations, he does not succeed in showing that, as particular propositions can be analyzed into more inclusive universal propositions, these in tum must be referred to propositions with singular and concrete subjects. His mathematical analogies throw more light upon this metaphysical problem than does his logic. It may be added in passing that, besides the law of identity, the law of sufficient reason is also involved in this theory of the proposition. A reason for every predicate must be found in the complete subject (analytically), and conversely, each predicate serves as partial reason for the complete subject (synthetically). When analysis is
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 25 adequate, logical propositions will have substance as subject and its properties as predicates, or using the mathematical analogy, an individual law as subject and its implications, universal or particular, as predicates. The proposition, therefore, which defines a complete concept or the concept of an individual must, Leibniz believes, have as its subject an individual substance, and as its predicate all the simple notions which determine the concrete individual but which include the universal harmony in which it is based. Definition is thus the logical form in which knowledge most completely expresses the principle of identity and of being. As ideas are a higher form of being than natural processes, definition is a higher form of knowledge, for Leibniz, than scientific law. Since the ideas are dynamic, definition reveals not merely the structure of possibility but the processes of existence as well. In human knowledge definitions are of three kinds; if merely verbal, they are arbitrary and express the relation of symbols to meanings only, and the test of their adequacy is the substitution of definiendum for definitum. In themselves verbal definitions signify nothing about reality, and their use is purely structural within restricted levels of discourse. Leibniz held that Hobbes's logic had failed to establish his metaphysics because he recognized only verbal definitions. Nominal definitions are real, but their predicates contain qualities sufficient to identify their subjects. Descartes's basic argument was vitiated by his failure to establish the possibility of his definition of God by the compatibility of the simple predicates it contained, perfection and being, and his definition remained merely nominal. For a real definition must contain in its predicate those essential concepts which serve to determine all the properties and modifications which are involved in the substance which its composite subject represents; Leibniz sometimes calls these essentials determinants. These are the simple, primary essences or concepts, ultimate perfections of God, out of which concrete substances come into being, since all otber qualities, essential or temporal, arise by combination from them. In this sense a real definition is operational and explains the individual subject in terms of predicates which involve the entire universal harmony in which they are based. Paradoxically, Leibniz himself failed to establish a priori the possibility of that concept on which all the rest depended and to prove which he developed his theory of definition - the concept of a most perfect being. The general logical principles on which Leibniz tries to base his metaphysics are thus Aristotelian. His use of the traditional logic was skilful and in some respects original. He used traditional syllogistic structures most ably in controversy and exposition; two notable examples are his letter on dynamics to Papin in 1691 (GM., VI, 204-11) and the summary of the Theodicy in logical form (G., VI, 376-87). He derived the methods of immediate inference and the valid modes of the categorical syllogism in various ways, notably by his own method of regression (a rebours), later also used by C. S. Peirce, and developed both the Eulerian circles and a linear symbolism for portraying relations in inclusion. He skilfully defended the traditional logic in a letter to Gabriel Wagner (No. 48). But his search for a 'sublimer' logic, more universal and useful, overshadowed these more traditional interests. This was the 'logical calculus' for which so many studies are found among his manuscripts, very inadequately represented in Nos. 24, 26, and 41. For his symbols he turned to mathematics and language. In certain studies he tried to lay the ground for a universal logical language, both oral and written, whose syntax should make correctness For references see p. 58
26 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS of thought inevitable, and which might become an agency for scientific communication and cultural universalism. But the mathematical analogy compelled his deeper interest and more enduring efforts, since the symbols here were not to be merely arbitrary, as in language, but real - in the same sense that real definitions differ from verbal. Like the symbols of the calculus, they were to lead to the operations from which truth should emerge. Of this logical calculus, the methods of ordinary algebra, the new infinitesimal calculus, and the pure geometry of situation (Analysis situs, Nos. 27 and 70), were merely separate and specialized applications. The success of Leibniz's studies in the universal calculus was by no means final but consisted rather in the fruitfulness of his individual insights. He was persistently led to think of numbers or, when the elementary notions were unknown, of letters as logical symbols. Prime numbers were to represent simple or primary notions, compound numbers more complex notions, and the processes of multiplication and division (or addition and subtraction) were to suffice for the construction of logical formulas. As these limited concepts proved inadequate, he extended his understanding of logical operations, but his invention was most fruitful when he abandoned arithmetical operations for the direct relation of inclusion (No. 41). Couturat has studied the phases through which his experiments passed, without, however, developing their relations to his metaphysics. It must be said that the more general and relational Leibniz's logical studies become, the more clearly they appear as abstractions from the universal harmony and system of representations or mathematical functions of which his universe consists and the less they help to determine the individual substances on which he insisted. It is not surprising, therefore, that he was always inclined to move back from the relational and combinatorial logic, which applied both within and between compound substances, to the logic of predication, which he hoped would establish the existence of individual substances. To this point Leibniz's logic is general and applicable to truths of reason and of fact alike or to the realms of both possibility and existence. But except for the formal analyses of mathematics, logic, and metaphysics, human reason is limited to truths of fact, which involve not the enduring essences of substance but its changing accidents. Existence is the result of the restricting creative act of God in choosing the best possible of all possibilities; man's knowledge of existence is limited by his spatial and temporal point of view, with the indistinctness and inadequacy of perception which these involve. One of Leibniz's most distinctive achievements is his effort to adapt his logic and the rationalistic principles on which it rests to the realm of existence and change. He does this by using the concept of infinity to bridge the gap between essence and existence and by reformulating the law of being and the law of sufficient reason to apply to temporal events. The fundamental law of existence is temporality or succession (Cout. OF., pp. 19-20). Judgments of fact involve contradiction, as Parmenides saw, because they involve change. But these contradictions can be removed by reference to time. Applied temporally, the general law of sufficient reason is transformed into the principle of mechanical causality, which Leibniz defends as adequate for existence. Thus for example in the proposition, 'That spruce tree is living but will die', temporal reference resolves the contradiction. 'A hedgehog has girdled or is girdling it': this is a sufficient reason for the death of the tree. Therefore, 'the act of the hedgehog is causing the tree to die'. Mechanical causality is thus temporal in its form, empirical in its content, and ab-
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 27 stract or 'partial' in its result. Such causal judgments are therefore capable of symbolic representation, but since they are contingent, based on selected external relations between events and not on their internal nature, they are merely probable. It is true that if we could analyze all the causal dependences, we should arrive, empirically and analytically, at simple essences and, synthetically, at the laws of the individual series of perceptions (monads) involved and therefore at the mind of God. But this is impossible because there is an infinity of monadic representations, and therefore of contingent relations, involved in the death of the tree, and thus such reduction would involve infinite stages of analysis. Since we cannot free ourselves from the relative and inadequate representations to which we are bound, scientific analysis is an endless task, and the notion of completely analyzed identities or laws of serial order for every individual in the tree and the hedgehog is merely a scientific ideal, not its method. In Leibniz's most active logical thinking, however, he recognizes a mediating form of knowledge between truths of reason and truths of fact. This middle knowledge 3 S is primarily God's; it is the logical process by which a particular order of events actually comes into existence from the order of possibilities in God's mind. To be specific, it involves the logic of the 'subordinate regulations', or the laws of nature, and their relation to the more general logical principles of possibility. This middle knowledge is, of course, infinitely removed from our analyses. But we have a formal analogy to the process in the problem of maxima and minima in calculus, in which optimal and unique principles are determined from among an infinity of ambiguous possibilities by a kind of mathematical economy. As a definite instance of this process Leibniz undertook to derive the laws of refraction and reflection as a problem of maxima and minima (No. 50), a demonstration which led to the celebrated controversy on the principle of least action in the next century. The principle 0/ the best possible is therefore not merely a pious assumption but a principle of mathematical necessity, which provides a telic element in our scientific methods and principles. It rests on the perfection of God and the limitation necessary in a spatial and temporal order. Since not all possibilities can be actualized, the best possible compossibles will exist, that is, the greatest possible perfection with the least qualifying conditions. Its logical formulation is the principle o/parsimony: that explanation is best which produces maximal results with minimal assumptions. The principle 0/ conservation is a physical derivative. Every scientific law or subordinate mechanical regulation is thus the best possible of an infinity of possible rules, and the mechanical causes of nature must be completed, ideally, in the final cause of universal perfection. Similarly every individual cannot contain all possibilities; this would contradict his finite point of view. But he can and does contain the best possible experiences or events, consistent with his dependence upon the order of other existing beings and the universal harmony. This constitutes his purpose. 36 The three levels of knowledge are thus made evident, and the logical principles on which they are based formulated - truths of reason or of possibility, resting on the law of being and of sufficient reason; truths of fact or of contingency, resting upon the principle of individuality, on time and (phenomenally) on mechanical causality; and the middle knowledge, resting on the law of maximal determination or the best possible. Beyond these generalizations, the relations between the levels of being and of knowledge are concealed from man in the two labyrinths - infinity and freedom (No. 29). These are the labyrinths which separate the upper garden of essential truths For references see p. 58
28 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS from the lower of contingent truths. Man's freedom, which consists in his spontaneity, or the logical principle that all his modifications follow from the law of his own essential nature, or that his predicates are included in his essential subject, is freedom from external mechanical contingency only but not from logical determination or from self-compulsion. If our analysis could proceed to infinity, we should see how his inquietude, his appetites and perceptions, his point of view, though logically implicit in his substantial nature, are all rooted in the universal harmony as well. We are free only because the events which constitute our individuality flow from the law of our nature, but both are rooted in the perfect logical necessity of God's plan - our individual law through the principle of the best possible, and our particular perceptions through the functional relations by which they represent the universe. The inadequacy of this notion of freedom will be apparent in the discussion of Leibniz's theory of error and his ethics; he himself sought to render it more acceptable by the practical distinction between an order which necessitates and one which merely inclines. The fundamental difficulty with Leibniz's logic is thus the question of whether it allows a genuine pluralism and individualism or whether logical analysis and synthesis, if carried out completely, can end only in God and his simple perfections. That his final answer must be considered ambiguous and inconclusive may best be shown by a reference to his difficulty with relations. It has become commonplace to interpret his doctrine that there are no merely extrinsic denominations as supporting the internality of relations in one or more of the many meanings of that obscure theory. But denominations, or modifications as observed by the mind, are not relations, though of course they involve relations, and Leibniz himself was inconsistent on the significance of the general relations used in his new calculus. Thus he writes to De VoIder, in April 1702, that "there is no substance which does not involve a relation to all of the perfections of all other substances whatever" (No. 55, V), which, together with his belief that substances are the composites of their modifications, would imply relations internal to the perceiving substance, at least. Yet to Des Bosses, and on many other occasions, he made a distinction like the more recent one between relations and relational predicates: "My judgment about relations is that paternity in David is one thing, sonship in Solomon another, but that the relation common to both is a merely mental thing whose foundation is the modifications of the individuals" (No. 63: letter of April 21, 1714).37 His distinction between duration and extension as attributes of bodies, and space and time as relations perceived outside of things, is similar (see No. 71, the fifth letter to Clarke). We may conclude that Leibniz clung to the predicative viewpoint in logic in the belief that it provides the logical grounds for a plurality of logically composite but metaphysically simple substances, while the more abstract relational position does not, but that he did not succeed in escaping the monistic implications of his own logic. The real motives for his pluralism are to be found rather in physics, psychology, and ethics. VI. MATHEMATICS AND PHILOSOPHY It is psychology and mathematics that provide Leibniz with his chief sources of analogy to the metaphysics of existence. From the former he drew his insight into the internal nature of monads or individual series as perception and appetite. In his own great discoveries in the latter field he found an analogy to the problem of the relation betwee n
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 29 monads, which his logic had not sufficed to make clear, and further light on the nature of individuals. Three concepts essential to his infinitesimal calculus, particularly, provided clues to the relations of individuals, to the universal harmony and to each other. These were the conceptions of mathematical function, continuity, and the infinite. Like other scientists of his century, Leibniz was impressed by the adequacy of mathematical knowledge and was convinced that the achievements of the age confirmed the long tradition that mathematics is the grammar of nature. Particularly after he himself had succeeded, by the invention of proper symbols, in solving both the tangent and the quadrature problems within two weeks of each other 38 , his conviction was clarified that 'real' characters and the formulas based upon them have both operational and representative meaning. Analysis by determinants and the use of series in the solution of transcendental problems in algebra supported his belief that there are hidden but effective symmetries within the apparent wholes of experience. He placed great weight upon the binary number system which he himself invented, not only because it revealed fundamental relationships in the number system, but because it seemed to have value as a symbol of creation - by One out of nothing. The mathematical investigation of probability, then being rapidly developed, also seemed significant to him, not merely for the promise it gave of making casuistry more exact in law and morals, but because it offered hope of extending the functional viewpoint of mathematics from merely formal and a priori considerations to truths of fact and existence. 39 It is not surprising, therefore, that he should not only seek generalized mathematical symbols and operations as the basis for a universal method but also find in mathematics an abstract clue to the solution of the problem of relations and, specifically, the relation of universal to particular. The mathematical analogy results from the concept of mathematical function which Leibniz developed as the basis of his calculus. Though the term itself, in its modern meaning, is late in his writings, the idea is present from the Paris period on and underlies the general theory of expression or representation which he first formulates in this period. 40 Viewed functionally, an equation is a 'formula' or law of order which expresses the continuous dependence of one variable upon one or more others. A variable, in turn, is the symbolic representation of a continuous series of particular values determined by the relationship expressed in the law to corresponding values of the other variables. The same relationship can be expressed or represented geometrically in a curve or other figure, depending on the number of dimensions or variables, and the number of defining relations between them given in equations. If these defining relations are inadequate, there remains a parameter, and the law of the series is incomplete, defining not one case but a family of cases. A functional equation may be solved for anyone of its variables in terms of the rest, and each such solution is a distinct equation defining an individual series in terms of its relations. Every particular value of the dependent variable, moreover, contains a factor determined by the corresponding simultaneous values of the dependent variable; it is thus a unity of abstract relations. But every particular value is also a transition between those preceding and following it in the same series. Thus every functional relationship can be represented by as many laws or equations as there are individual variables and by a complex but harmonious and exactly defined quantitative dependence; each variable expresses all the rest in a series of values following from its equation. The existing universe may by analogy be regarded as a harmonious functional For rejerrmces see p. 58
30 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS relationship between an infinity of variables. Each solution of this complex relationship for one variable constitutes the individual notion or law of the individual series. The individual which it determines, and, indeed, whose primary entelechy it is, consists of a series of values, each of which is a transition between the preceding and succeeding values, and each of which represents the corresponding values of all the other variables or individuals involved in the universal harmony. Individuals are therefore serial processes, the continuous expressions of universal laws, but also continuously expressing the infinity of other individuals bound to them by the general harmony. Leibniz carried the analogy much further, however. Curves are not necessarily linear but have inflections, maxima, and minima. Such inflections from internal causes suggested to him the analogy to internal determination, whether conscious or unconscious. Without such control, action would at every point be linear and tangential. There are levels or depths of functional dependence within any individual series, and these are implicit in every particular value. Thus the differential or rate of change of the variable is a derivative of its idea or law; in physical motion this is quantity of motion or momentum, mv, as opposed to quantity of force or living force, mv 2 ; in mind it is the momentary appetite or affective drive. On the other hand, the integral is the sum of all values within definite limits; in physics this is the total energy of a physical system in motion; in psychology it is the concrete person, in contrast to the law of the individual or the abstract essence of his nature on the one hand, and on the other, his varying modes or experiences. This mathematical analogy obviously breaks down at points. It offers no adequate clue to the finiteness or limitation of individuals - no reason why some individual series reflect the universe only blindly and narrowly, and others more or less materially and more or less unclearly and inadequately. It does not involve the essentially temporal nature of metaphysical individuals or monads; indeed, it is the timelessness of the concept of mathematical function and series that drove Leibniz to emphasize the relative and phenomenal nature of space and time, which are therefore involved only in special and concrete cases of the more general logical nature of logical predicates or modifications. Yet the analogy offered Leibniz his ultimate solution of the problem of physical causality - functional dependence - and particularly of the problem of the mind-body relationship. It is in terms of this functional system that he defined continuity and infinity. The principle of continuity he generally stated in relation to the process of expression or representation existing between two or more series. It is only in this application that the principle can serve as the tool for criticizing mathematical and physical theories. Datis ordinatis, etiam quaesita sunt ordinata. As the known variables are ordered, the unknown variables are also ordered; to every value difference in the independent variable, however small, there corresponds a value of the dependent. This principle becomes Leibniz's criterion for testing mathematical and physical theories (Nos. 34, 37,42, 46, etc.); it also provides the reason why finite knowledge can always approach but never attain the continuously varying processes of existence. For there is within existence a multidimensional infinity. There is the infinity of extension in time and space, which Leibniz generally treats as a fiction, or describes merely as indefinite, insofar as numbers cannot be assigned to it. Likewise he also calls a numerical infinitesimal a fiction (Nos. 54, 56, etc.). But there is also the infinite involved in the possi-
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 31 bility of endless analysis of the continuous finite. For every finite series involves infinite differentials; there are differentials of the first, second, and nth order and integrals similarly infinite. So too every perception involves an infinity of representative elements corresponding to the infinity of God's thoughts and their monadic expressions. Such infinity is a necessary consequence of the law of sufficient reason and the principle of plenitude or perfection, since no reason can be given for any finite limit. He writes in a note for a letter to Des Bosses: There is a syncategorematic infinite or a passive power having parts - namely the possibility of further progression in dividing, multiplying, subtracting, and adding. There is also a hypercategorematic infinite or a potestative infinite, an active power having parts eminently, as it were, not formally or actually. This infinite is God himself. But there is no categorematic infinite, or one actually having infinite parts [September 1, 1706; G., II, 314 n.l. That is to say, Leibniz does not hold that there are real infinites and infinitesimals in existence, as Russell interprets him; they are in existence only as possibilities of analysis and synthesis. Real infinity is only in the realm of possibility and in God, whose thought supports the possibility of endless processes of analysis by which finite minds would have to attain him. Infinity is thus not the simple boundless and undefined of the ancients; it is the eternal quasi-mathematical perfection of God, variously symbolized but never intuited by finite minds. Swift's parody, So naturalists observe, a flea Has smaller fleas that on him prey; And these have smaller still to bite 'em, And so proceed ad infinitum, does indeed reflect the remarks in some of Leibniz's popular expositions of his thoughtBut such phenomenal notions are but analogues to the infinity of process to which mathematics give a purer expression. A better example would have been to imagine a complete logical analysis, beginning with the mechanical, of the complex structure of concepts involved in the benzene ring or in the representation of sodium by a certain set of lines in the spectrum. VII. PHYSICS AND THE REALM OF NATURE If Leibniz's mathematical concepts suggested the answer to the metaphysical problems of the relation of individual to universal and of change to permanence, it is his physics that gave his philosophy the more definitely empirical and temporalistic direction which it assumed toward the end of the seventeenth century. For it is in his physical writings that he first sharply distinguished his own conception offorce from the merely formal power of the Aristotelians (No. 45). Both atomists and Cartesians had been impelled by the new discoveries of science to separate the physical world from the order of spirit - the two realms which both Platonist and Aristotelian had held firmly together by the same principles of organization, the forms or ideas. In his youthful walk in the Rosenthal, Leibniz had decided for the new mechanism, but he probably never rejected the necessity of mind as the source of activity and purpose within nature itself. His first interest in the problems of physics themselves arose in Mainz out of two theological problems: the need to analyze motion For references see p. 58
32 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS to prove the existence of God and the need to analyze corporeal substance to prove trans substantiation. Both motives impelled him to take a realistic view of physical things but to stress the continuity of physical processes with mental and the inseparability of mechanism and purpose (Nos. 3; 5, II; 8; 10). It was the Academic skeptic Foucher at Paris (No. 11) who forced him to consider the claims of phenomenalismclaims which led him eventually to a distinction between 'well-founded' physical phenomena and their metaphysical foundations, to a relativistic interpretation of physical motion, and to the distinction between force and motion. 41 At the same time began his penetrating criticism of Descartes's conception of matter and motion. Finally, it seems to have been Newton's Principia, which reached him in Italy around 1690, that moved him to attempt a systematic formulation of his dynamics (Nos. 42, 43, and 46), and the differences between his views and Newton's are the subject of the correspondence in progress with Samuel Clarke when Leibniz died in 1716 (No. 71), though Clarke's theological interests prevented the argument in these letters from being restricted to physical problems. In this long development the pattern of Leibniz's thinking remains largely the same, though some internal inconsistencies are removed and refinements added. Motion is reducible to conatus or impulsion, and though he at first considered a conatus as momentary motion, he later regarded it as momentary force, which mediates between the metaphysical source and the resulting motion. Corporeal bodies, too, are phenomenal results, not of geometric relations or of mere properties of permanence and impenetrability, but of metaphysical points or centers of force resulting from laws. An inorganic body is but the aggregate of such serial forces, appearing in their interdependence to a perceiving mind as spatial and temporal. Thus the dynamic function of the harmony of ideas appears as physical force; its passive correlate, as mass or resistance. The principle of identity reappears in the equipollence of expended force and work done in a physical transaction or, more generally, in the conservation of force (No. 34, etc.), while the law of sufficient reason becomes the principle of mechanical interpretation. Thus the analogy from metaphysics to physics is in outline complete. Physics is always regarded as a subordinate science which corroborates theology, but one which can be established empirically and independently of metaphysics as well and which concerns a real order of creation, the realm of nature appearing to sentient beings as the physical world. 42 Like space and time, the orders in which man perceives simultaneous and successive events, motion is relative to observation. There is no possibility or need, within physics itself, to establish an absolute space, time, matter, or motion, for no absolutes are found in the quantitative relations of force, and the result is always the same when a system of bodies in motion is measured, regardless of which particular body is chosen as point of reference. Measurements of motion are exactly analogous to real definitions; just as different real definitions of the same subject are possible until ultimate simple notions are reached by analysis, so many different measures of motion are valid, and that system of reference is to be chosen which is best fitted to the particular problem being investigated. 43 Yet, whatever system is chosen, the quantitative relations will be the same, for physical invariants are not material but mathematical and logical. The reals in physics are functional relations of force, and these appear to our reason absolutely when we have adequate ideas, while bodies and observed motions are relative and variable.
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 33 It is at this point that the Leibnizian and Newtonian conceptions are at greatest variance. Russell has rightly pointed out that Leibniz himself obscured the issue between them by confusing the problem of the absoluteness of matter and motion with that of action at a distance, which, like the Cartesians, he rejected as a miracle, though it was probably more compatible with his own theory of physical relations than with Newton's materialism. In any case, the difficulties in both opinions are still real, and physicists have by no means become unanimous in their approval of one or the other, though the mathematical harmonies developed by recent microphysics, on an energistic and relativistic basis, seem to support Leibniz rather than his distinguished adversary. Leibniz's further analysis of force must be traced in the writings of the 1690's in which his most advanced thoughts were developed. As derivative force, it is the physical correlative of the impulsion of the ideas to act and is thus 'better founded' than motion, and certainly than the merely phenomenal properties of inertia and impenetrability manifested by bodies. The dual aspect of the ideas, active and passive, is therefore conveniently reflected in force, which manifests itself actively in different integrations as solicitation, conatus, momentum, and vis viva (ma, mv, and mv 2 in aggregate bodies), while its passive pole, materia prima, appears as inertia and impenetrability in an aggregate body. Both active and passive force, in turn, therefore appear as primitive and derivative forms, and it is their derivative or secondary aspects which are manifested in physical phenomena as impulsion and matter respectively. Active primitive force or power is metaphysical; Leibniz also calls it entelechy, substantial form, and soul. Its basis, however, is ultimately the idea, the law of the individual series, or the possibility which determines a particular series of impulsions. Primary passive force, on the other hand, is materia prima, the momentary inertia of any unitary being as acted upon, which, when found in a composite body, becomes secondary matter or derivative passive force - the properties of inertia and resistance in the impact of bodies. From these fundamental relations, together with the principle of the conservation of force - that in any system of moving bodies the sum of mv 2 is a constant - there arise three further principles of conservation in colliding bodies. If a and b are bodies whose velocities before collision are v and y respectively, and after collision x and z respectively, (1) relative velocities are conserved (v+y=z+x); (2) quantity of progress is conserved (av+by=ax+bz); and motive action is conserved (av 2 +by 2=ax 2 +bz 2). These relations, Leibniz holds, can be established a posteriori through experiment but also a priori through derivation from the principles of continuity, sufficient reason, and equipollence. On the nature of physical bodies, however, Leibniz seems never to have achieved an ultimate unambiguous solution. Space and time being the forms of corporeality, a body (as secondary matter) seems on first appearance to be a bounded space filled with homogeneous qualities, which may be at rest or in motion. But such a body is both materially and mathematically divisible and hence not a true individual (at least as far as its temporal and spatial dimensions are concerned) but an aggregate. As the second proposition of the Monadology puts it, "There must be simple substances because there are compound, for the compound is nothing but an aggregate of simples." Such analysis reveals the incorrectness of both Cartesian and atomic conceptions of For references see p. 58
34 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS matter. On the one hand, there is no sufficient reason for stopping such analysis short of what is further indivisible, and such an indivisible part is, mathematically, a fiction, a continuum not composed simply of points. To attempt to stop with indivisible but extended atoms is logically inconsistent and fails to explain cohesion, rigidity, elasticity, and related phenomena, since the concept of an atom presupposes them. Contrary to Descartes's view, again, matter includes more than mere extension, since it may occupy different spaces, may change its situation with respect to the same space, and possesses the properties of impenetrability and inertia. The results of analysis are therefore not merely geometric points but metaphysical points of force, to understand which it is necessary to enter the temporal dimension. The phenomenal body is the continuous representation, not only of momentary simultaneous states, but of successive momentary forces or conatuses. Such units of force explain not merely the continuity of a body, which is phenomenal; they explain also the impenetrability and inertia of apparently rigid composite bodies and their elasticity in impact. Leibniz's proper answer to the question of the unity of a material mass in gross perception is therefore that such unity is phenomenal but is the result of an underlying real harmony offunctional relations between many force-point series or naked monads, perceived indistinctly by a mind. As a spatial and temporal whole, but no more, a body is phenomenal. As a plurality of active forces and their mutual resistances, it is a real creation. On the level of uncreated being it is determined by a harmonious pattern of mathematical laws or ideas. There is therefore no unity in body apart from the laws which produce it; all other unity is imparted by the limited purposes of perceiving minds. This is in fact the explanation with which Leibniz contents himself in his compact expositions to Cartesians and courtly friends. But from the very beginning of his thought, this explanation is supplemented - and some would hold, opposed- by another which seeks to avoid the phenomenal nature of bodies and to ascribe a metaphysical bond of unity to them. The motive for such an effort was theological; the doctrine of trans substantiation as formulated by the Council of Trent required a real body (No.5, II). For some years during his stay in Paris, Leibniz seemed inclined to accept the Cartesian dualism, thus retreating from the more advanced position of his physical writings of 1671 (Nos. 8, I, and 10). In the discussion with Arnauld in 1686 and 1687, and frequently later, he seems to think of every body as dominated by a unifying soul or monad; certainly he assigns a body to every monad. But he also frequently holds that only living organisms, including rational animals, have such a dominant monad. And in the discussion with the Jesuit Des Bosses (No. 63) he returns to the late Scholastic notion of a substantial chain (vinculum substantiale) binding the monads of a body together. This theory has been explained away as an effort on his part to adjust his theories to Jesuit thought by a conception which he himself did not accept, and the tentative quality of his language does much to support this interpretation. 44 It has also been interpreted as a definite movement of Leibniz's thoughts back to realism and to Scholastic sources. 4S As the correspondence develops, the substantial chain appears to be both an active and a passive principle, added to the monads yet inseparable from them, subject to natural law yet above it, like a ruling monad yet not monadic in structure, and at length a law of organization. Finally (August 19, 1715), Leibniz states his own preference for a phenomenal view of body. Appearing at a time when he is concerned with the individual rather than the universal, with change rather than eternity, and with freedom rather than logical necessity, the
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 35 notion of a substantial chain may well express his own desire to provide a realistic interpretation of naive experience. But the interpretation most consistent with his system must regard the substantial chain as a principle of organization, a lesser harmony or secondary complex of individual laws, as it were, within the greater harmony of God's creative plan. That the mechanical laws of physics can be shown to be special temporalizations of the eternal laws of possibility46 is, for Leibniz, another evidence that the realm of nature or of mechanical necessity can be fully understood only through its relation to the realm of grace or of purpose. This, again, is the field of the middle knowledge, to show, so far as human knowledge can, that natural laws are the best possible or most determined instances of universal logical laws. In spite of the limits of our understanding, physics serves to support two important metaphysical principles: first, that the force of every real individual is private to itself, since it follows from its own law, and second, that the realm of existence receives its purpose and value from the realm of essence, so that the mechanical order is subordinate to a spiritual realm which has its being in the relation between the two. Physics is thus a special application of the most general principles of metaphysics on the level of well-founded phenomena, naively perceived - and therefore indistinctly and inadequately - as things in space and time, but adequately understood by the scientist as energetic series functioning in a responsive intercourse. Always more concerned than Newton with its relation to metaphysics and theology, Leibniz foresees the advance of physics beyond the stage of its naive analogies of bouncing billiard balls and pelting hailstones to the subtler mathematical and dynamic analogies of fields of force. VIII. BIOLOGY It is in Leibniz's biological views, stimulated by the stirring dicoveries of his age in that field, that he finds a compelling confirmation of his organic theory of the individual. Even within the realm of nature, mechanism is not a simple linear concatenation of impulsion and motion; it is merely an abstraction from the complex interwoven temporal progression of representation or expression. Every causal connection among phenomena rests upon this relationship and therefore upon a part-whole structure of the simplest order. For representation is itself the expression of many in one; a single perception is for Leibniz a whole composed of many contributing relations and is itself a member of a more inclusive whole, the individual monad whose law it expresses. Mechanical causality is but a phenomenal abstraction from such concrete representational unities, for when two beings are in a representative relationship, the one whose expression is the more clear and distinct is regarded as the cause, and the one whose perception is less distinct as the effect (No. 34, Sec. 15). The determination of parts by wholes, that is, the determination of the activities ingredient in a functional system by the individual monads and transmonadic harmonies, is thus more ultimate than mechanism for Leibniz's metaphysics of existence. Not only the individual actualized monad is a whole which determines its particular perceptions in this sense; the unity of mind and body, a plurality of monads functioning organically under the dominance of a central soul or spirit monad, is also a genuine purposive whole, even though it is not a metaphysical individual. Leibniz's vitalism is thus one of organization and function rather than of substance, and the continuity of For references see p. 58
36 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS the organism and its processes rests on functional laws and the series of events which they determine, rather than upon material unity. Leibniz developed this vitalistic biology in direct criticism of Descartes's mechanism and in support of the remarkable discoveries which the microscope was making possible. Hobbes and the atomists, who interested him early, seemed to support Descartes, but Leeuwenhoek's discovery of cells and spermatozoa seemed to him to answer so many questions left open by mechanism that he not only remained a vitalist but stressed the continuity of plant and animal life (letter to Bourguet; No. 69, II) and the permanence of the animal organism, subject only to processes of evolution and of 'envelopment' or the loss of structures and functions. He agreed that animal behavior has its mechanical parallels and may therefore be considered as a most complex machine. But its essential nature can be understood only through a very complex soul monad, with perceptions clear enough to be considered as causes of bodily movements, and expressing higher laws in the sequence of its perceptions than do inorganic monads - the laws enabling habituation, memory within limits, the pseudoreasoning or 'empirical consecutions' resulting from association or conditionedresponses without reflection or ratiocination. Plant and animal souls are thus monads on a higher level of organization than physical force but with energy built into the bodily structures with which they are inseparably united. The unity of the soul is in part a reflection or representation of the body, for it consists, on one level, of sensory and affective content of great complexity 'caused' by the body. On the active level, however, the soul consists of the greater continuity of purpose which its power of habituation and memory, however fragmentary, makes possible. The internal causal unity of the complex purposes within an animal organism is therefore to be conceived as itself a monad, and even, within limits, a conscious monad, in functional interdependence with the naked monads which together comprise its body. At this point Leibniz's mathematical functionalism is well adapted to support biological functionalism as well, for the stimulus-response arc and the analysis of life as the adjustment of internal to external relations in order to conserve a constancy of energy, fit almost without any translation, into his own thought. The functional unity of body and dominant soul reflects changes in its environment, first of all in the primary matter of the body monads and the resulting readjustment of their expressions, and thus in the feelings and sensibilities of the soul monad, while reactions may be instituted on various levels of bodily organization and the corresponding levels of the soul. The relation of animal soul to body is thus isomorphic, but in such a way that the purposes implicit in body mechanisms become conscious and explicit in the soul. Thus the living organism is a more perfect analogue than the inorganic body or a separate soul to the universe as a whole, where the purposes of nature become explicit in the society of spirits. In his theory of the origin and development of the organism Leibniz was, like the most influential microbiologists of his day, a preformationist. His own theory that each monad is created by God was supported by the victory of the animalculists, following Leeuwenhoek, over the ovulists, following Harvey; the growth of the complex organism from a single cell supported his conception that all change is by internal force and not by the interplay of forces between individual and environment. But his preformationism must not be understood in a naive and materialistic sense.
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 37 Not every organ already exists in miniature in the original cell; rather the function of every organ is already determined in the laws of the changes of the original living unity. Bodies grow by aggregation, but the processes of growth are determined by the laws involved in the general harmony. In short, Leibniz is Weismannian rather than Spencerian. Though he seems not to have seen the possibility of mechanisms of heredity, his interpretation of bodily growth and depletion provides for a law of development into which surrounding conditions can introduce no new factors. Preformation involves transformation. The soul may expand with a more complex body, or suffer depletion and reduction in death, but it cannot be destroyed by nature, and all its changes are involved in its law of organization, while they evolve in harmony with a changing and enlarging environment. It is tempting to think of Leibniz as an evolutionist. His law of continuity stimulated later theories, and he suggested a 'natural evolution' within the individual organism (G., II, 399, 403). His Protogaea outlined the development of the earth and the solar system. In the later decades of his life his inclination to break the great chain of being, or at least to talk as though it did not exist, became more pronounced. But though he recognized novelties in the experience of men, both within themselves and in the external order of nature, there is nothing which is not determined by the plan of God, who creates not only individual souls but the classes to which they belong. Leibniz's tendency to emphasize progress is generally restricted to man, human history, and the realm of grace. It was characteristic of the closing century to think of continuous progress toward perfection; it was not yet within the intellectual climate to think of nature in terms of the emergence of new structures. Leibniz's theory of preformation (a special case of his logical determinism) precluded his advance to a conception of the unfolding of the forms of life, as genetic determinism still conflicts with evolution. Nor had Linnaeus yet shown the way, as he did to Kant. IX. PSYCHOLOGY It is psychology rather than biology which provides Leibniz with his most concrete metaphysical analogies, as mathematics provided him with the analogies to the universal harmony. The human situation is such that we ourselves are metaphysical individuals of high order and possessed of a unique ability to observe ourselves and thus to know one monad, at least, intimately and directly without the intervention of symbols, and therefore not as mere appearance. Psychology 47 had been a central interest of Leibniz since his student days, when he outlined a functional account of mind, of Aristotelian pattern and without an analysis of subjective content, in a long note amplifying the ethics of Thomasius. 48 At Mainz he noted Hobbes's need of a philosophy of mind and proposed to write an Elementa de mente (Nos. 4 and 10). His general method was to find application here as well as in physics; mind was to be approached both a priori and a posteriori, both from general priciples and from direct observation. In the latter method Leibniz showed great skill, particularly in studying dream processes (No.5, III), memory, states of extreme fatigue and introversion (No. 13), and the like. His empirical psychology had as its object the mind, not the body, though he sometimes made skilful use of Hobbes's theory of physiological traces and found important analogies in animal behavior and animal drives to the organization of the human mind on levels below that of reason For references see p. 58
38 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS (No.2). His analyses of mental growth, of the motives and processes of human learning and even of the laws of association are thoroughly functional. Even his theory of the unconscious, though demanded by the structure of his thinking, was given support by the empirical facts of human responses. The a priori approach to mind, on the other hand, consisted in the use of definitions to adapt the general analysis of individuality to the psychological subject. Here it was terms that made trouble for Leibniz; his difficulty was that of all introspective psychology - the illumination of inner experience through words which must be used in an analogical sense. Beginning with Aristotle and the Scholastics, he turned to Augustine's theory of memory and reflection, followed Descartes in his inclusive use of cogito, and at length settled upon the simple and revealing notions of appetite and perception, which become will and apperception when lighted by the internal sense, as the most fitting to unite the empirical and rationalistic approaches to mind. Like all other individuals, then, the soul is a substance with modes, but only in the sense that the individual laws are the substantial sources from which the force of existing series and their changes arise. The soul is, first of all, a complete idea rooted in the universal harmony, and the very complex serial and dynamic process fulfilling that idea in continuous relationship to its environment and to its own preceding and subsequent states; it is also the actual sum or integral of these states or series of acts, combined by their interdependence into one subject. There are many strata, therefore, in the human soul throughout its temporal and spatial dimensions. The deepest is that of the law of the individual series, complex enough to be abstracted into many separate laws, and the source of the innate ideas or logical principles according to which experience is ordered. Upon it are built the impulsions or conations experienced as a basic inquietude 49 , from which appetites and desires arise. On it rest also the petites perceptions, which are innumerable in every conscious perception. The intricate continuity of perceptions and appetites which makes up the existing soul has its active representative and its passive material aspects and thus consists of an, inert qualitative content expressive of the simultaneous, preceding, and consequent states of the universe. On the human level this may rise to the level of thought and will. Finally, there is the highest level, reflection or the internal sense, which penetrates into the soul itself to varying degrees, illuminating its contents, its actions, and even in part its innate law, but also always leaving an infinity of perceptions and laws dark and beyond its scrutiny. Upon this reflective power memory and reasoning depend. Leibniz's theory of sensation and feeling provides the basis for his interpretation of the interdependence of body and mind. There is an active representation of a bodily condition by the mind, on the one hand, and a 'causal' relation between an indistinct and confused mental quality (or 'matter') and its more distinct bodily cause, on the other. Leibniz rejects at once any physical interpretation of sense experience (No. 71, fifth letter to Clarke, Sec. 84). A sensation is a passive quality of the soul representative of a complex bodily process; in the Paris notes and elsewhere Leibniz suggests that it expresses action and resistance in the body. No sensation is simple, for it already involves a complex of unfelt impressions, as well as memory and attention. The case of feeling is similar, though feelings are the material and qualitative aspects of the temporal transitions of the soul - the momentary impulsions from one perception to the next. Upon a permanent undercurrent of inquietude there arise the basic feelings of pleasure and pain, which are themselves, like sensations, imperfect expressions of
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 39 basic harmonies - though in this case the harmonies and disharmonies of the varied impulsions are in the body and the soul itself. But it is the unique capacity of the mind to turn upon its own acts and observe them that distinguishes it from individuals of lower order. Reflection is not self-awareness in the sense of the awareness of an ego, actor, or personal unity at every moment of experience; it is always associated with a kind of momentary memory and attention, in which the immediately past state is carried over into the present. As reflection is supported by analysis and synthesis, however, it extends beyond the awareness of immediate but confused states of mind to an awareness of the mind's processes, and eventually to its structure or law. The ce moi or ego of which he repeatedly speaks as the source of profoundest metaphysical insights is indeed implicit in the acts and processes of the mind but is distinctly perceived only in an advanced level of reflection. Self-consciousness is thus not a part of every mental act; the datum of mind is its passive content or primary matter. But reflection is the condition of all consciousness more enduring than momentary felt impulses and sensory qualities. Only through reflection can perception become apperception 50, and appetite will, so that a clearly and distinctly perceived unity of purpose may emerge. From 1670 on Leibniz thinks of reflection as the source of the felt unity of consciousness (Nos. 8, I; 10; 13; etc.). But such growing experience of self, still intermittent and confused, is not yet self-knowledge. To know one's self is to perceive clearly the real unity from which the manifoldly changing states emerge, and this is possible only when critical thought has discovered the permanent law of the individual series. Personal identity resides not merely in self-consciousness but in the law according to which the series of one's experience develops. Leibniz did not, of course, anticipate the efforts of modern differential psychologists to approximate such a law of individuality, whether as psychic profile or as typical structure. His conception of method, however, would have led him to recognize the value, however limited and abstract, of both. In the law of every individual there is expressed a distinctive point of view or perspective, not only of space and time in sense perception, but of Anlage or temperament in the deepest affective and appetitive levels of the soul. For mind is made up of many strands or minor motor-affective-perceptive series corresponding to the various functions of the body, out of the interactions of which the dominant purposes of the individual arise in conformity to his individual law. Though beasts lack this reflection, they are capable of habituation on the basis of similar responses to similar or connected sense impressions and appetites. Such pseudoreasoning or 'empirical consecution' occurs according to the laws of association, and all animals learn by this means, men certainly not least of all. 51 But such associations are not to be confused with reasoning, or the analysis and synthesis of symbolic truth, which applies to experience entirely different principles from those of association. Thus reflection or apperception, accompanying all consciousness beyond the most confused qualities of feeling, makes human intelligence possible and determines the threshold between consciousness and the unconscious. Personality is for Leibniz essentially a moral concept. It implies apperception, for our person is "the memory and knowledge of what we are". But Leibniz is moved by the legal conception of person to find its essence in moral responsibility, thus providing the psychological unit upon which his social philosophy is built. S2 Of the remaining metaphysical problems related to Leibniz's psychology, the most For references see p. 58
40 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS controversial are the mind-body relation and human freedom. A school of interpreters, of whom Kuno Fischer is the most prominent, has held that the spirit monad is a mind-body unity in the Aristotelian sense, mind being but the form of the body though Leibniz called it substantial form - and body merely the matter of the mind. It must be admitted that Leibniz's own utterances are both ambiguous and contradictory on this problem; his complete view is not often stated clearly. Both materia prima and body are used in ambiguous senses, which confuse the reader. But the most coherent interpretation, clearly expressed in the correspondence with De VoIder and elsewhere, ascribes a matter to the soul itself, but a soul to living and conscious bodies only, though the ingredient monads in a body are analogous to souls (No. 54, letter of June 20, 1703). The body is that organized part of creation which spirit represents or expresses most continuously and adequately, and therefore 'dominates'; the body, conversely, 'causes' the material content of the soul and corresponds to its activities. If cause be understood in the descriptive sense of Bume and his successors, or in the functional sense in which Leibniz defined it to Arnauld, he recognizes a causal relationship between mind and body. But efficient causality is internal to the series of events by which each monad proceeds from its law, that is, from God. In repudiating interactionism, Leibniz, like the Cartesians, was still refuting the crude theory of a physical influx which Suarez had popularized throughout Europe. Be himself frequently used the language of interaction and even, in medical discussions, of psychological materialism. Ultimately he was a parallelist, not in the obvious sense of Spinoza, whose view he criticized even before he had read the Ethics (No. 12), but rather in the sense of contemporary isomorphism. As we have already implied, Leibniz's theory of the unconscious was necessitated by his opinion that mind represents the entire universe and therefore contains levels of psychic content and organization into which the light of attention and reflection does not penetrate. The theory is not new with him, as it had arisen whenever a similar distinction was made between mens and animus or between perception and reflection. 53 The notions of repression, sublimation, hysteria-mechanisms, and the censor have been found in Leibniz, and the technique of reconstructing reactions through association as well. 54 But the unconscious serves Leibniz primarily as a bridge between his psychology and his epistemology and between a finite individual who perceives imperfectly and an infinite God and his universe. The deepest level of spirit is God himself, who "belongs to me more closely than my body" (No. 40), and who provides the norms and principles which are my guide and determine my duty. The problem of freedom is not a psychological one for Leibniz. Yet he frequently approaches it from an empirical analysis, especially in his reply to Locke. Like him, he rejects a liberty of indifference and finds the clue to the analysis of choice in the relative strength of man's conflicting appetites and the feeling of inquietude which expresses this. Scientific and theological considerations unite to incline Leibniz, like most of the orthodox thinkers of his age, to a basic determinism of law, though a determinism of great complexity, and one which in his case is restricted to the efficient causality within the individual himself. Leibniz could never show the difference between God merely inclining me to certain actions and God necessitating me; all he could show was the difference between a necessity arising out of logical laws, which were not enough to determine a concrete existing world, and the necessity arising out of God's choice of the best, or the principle of least action, which does suffice to deter-
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 41 mine it. The element of probability which enters into our knowledge of our own actions is exactly the kind which enters into our knowledge of physical processes, save that the necessity which it fails to measure is within rather than without us. Leibniz identifies freedom with spontaneity, but this is merely the determined order in which the soul's active modifications proceed from its law . .In contrast to the metaphysical constructions which create these difficulties in Leibniz's psychology, however, his perceptive insights into the depths of the mind and its complex activities have proved to be suggestive to the psychologists who followed him, and the development of mentalistic psychology from Herbart's and Wundt's theories of apperception to later theories of the unconscious may be interpreted as an increasingly anti-intellectualistic and voluntaristic version of some of his views. Even today, his notions of an individual law, of an only infrequently and imperfectly organizing and guiding agent, and of the sharp difference between conditioned response and thought are guiding principles which theories of mind must take seriously. X. THEORY OF KNOWLEDGE Knowledge is a special case, but a unique one (since the monad is itself the knower), of the general process in which a metaphysical individual is related to the order of universal harmony and to the existing world involving that order. Metaphysics is therefore prior to epistemology in Leibniz's thought; knowledge is of a real world order greater than ourselves, in which both the objects known and the principles involved in our knowing them are grounded. From his early years Leibniz supplemented Descartes's primary proposition as follows: I think, therefore I am; but I also have a diversity of thoughts, and, since a sufficient reason is needed for these being as they are, there is an existing world (No. 11). Knowledge is neither simple apprehension of being nor merely the mental creation of an order of experience. It is the revelation of independent reality under the limitations of finite representation. Man's individuality, his dependence on a point of view, and the passive elements of sense and feeling in his nature prevent pan-objectivism; the universal harmony revealed with our experience prevents a solipsism, even in the false pluralistic sense that each of us creates his private world (No. 35, I). The universal orders of possibility, nature, and grace are worlds known in common, though the point of view of each mind is different. Knowledge therefore, whether merely theoretical or involving the will, is always, insofar as it is true, a perception of the universal harmony or of its operation in existence; but, insofar as it is mediated by sensory and symbolic content, it is relative and phenomenal. Except in reflection, however, we do not perceive the subjective content of our minds; we perceive an independent reality. Human knowledge is thus a special case of the process of perception by which the harmony between existing individuals is maintained. 55 Each perception, following the mathematical analogy, is the expression of a plurality of relations in a simple unity of content, and each perception is related purposively to the preceding and succeeding events within the mind by the law of the individual. Perceptions are not ideas. An idea is the possibility, the pattern, of a perception; it is an ingredient in the individual law which, when actualized, becomes a perception. Thus every perception has an internal meaning related to the purposes of the individual and an external meaning representative of the universe. For references see p. 58
42 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS It is with this dual reference of human knowledge that Leibniz's logic begins, as we have already seen. When reflection opens the mind's processes and content to itself, and thus makes thought possible, the internal structure of perceptual patterns becomes reasoning (ratiocinari), the external becomes symbolic reference. And to these two aspects of knowledge the universal calculus and the universal characteristic correspond as instruments for the logical perfection of truth. With Descartes's criterion of clear and distinct knowledge Leibniz was never satisfied, and he insisted that later Cartesians had done little to improve it. His own analysis of the stages of truth and their corresponding criteria was worked out under the stimulus of the celebrated controversy between Arnauld and Malebranche over the nature of ideas and of representation, in a paper which, to judge the frequency with which he later cited it, he considered adequate and decisive for his thought. This is the Meditations on Knowledge. Truth. and Ideas (No. 33), which he published in 1684, the first of his strictly philosophical writings. Knowledge is obscure if it fails to give recognition of the thing represented or to distinguish it from adjoining things. It is clear when it suffices for such identification. Clear knowledge, furthermore, is confused when one cannot enumerate the essential marks or determinants of the thing represented or, in short, define it; it is distinct if these marks can be enumerated. Such enumeration is a nominal definition. Distinct knowledge, again, is inadequate if a real definition can be given in terms of the determinants essential to it, so that the possibility of the concept is established; but these separate determinant notions cannot themselves be thus defined. When this can be done, however, so that the concept of the thing known has been analyzed completely into primary notions and truths, knowledge is adequate. Such knowledge, in tum, is either symbolic (or blind) or intuitive. Man has perfect intuitive knowledge only of primary notions and propositions. God, by contrast, has intuitive knowledge of the entire field of possibility and existence, past, present, and future. The lowest and least perfect level of knowledge, which man has even in sleep and shares with animals, consists therefore of obscure and unclear feelings and sensations, without meaning though representative of reality. Pleasure and pain, however, and recognizable sense qualities are clear but confused; we can recognize them and identify them by appropriate symbols, but we cannot give their marks, since they are unanalyzable. Yet they represent forces and resistances in the body and in nature which we can conceive distinctly through analysis on mechanical principles. Animals probably share such clear but confused perceptions with men, for only such perceptions make association possible. But distinct knowledge, being based on analysis, is characteristic of man only, who is capable of distinct but inadequate knowledge in the empirical sciences, but of adequate symbolic knowledge only in the sciences of abstract possibility such as mathematics and logic. Because the serial events which constitute existence are continuous and infinite, the analysis necessary to reduce them to the simple concepts which they involve would, as we have already seen, require an infinity of steps, and is therefore impossible for man. Hence we cannot ever have adequate knowledge about truths offact. Leibniz's epistemology thus supports his logic by adding the psychological dimension. Human knowledge has various levels of certainty and completeness, beginning with the felt certainty of experienced qualities, and ending with the analytic certainty of purely formal reasoning. But in all meaningful facts of experience between these
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 43 extremes man is committed to uncertainty, though analysis and definition may strengthin this into high probability. Reason therefore functions on two planes in human knowledge, within experience to validate it, in truths of fact, and in the realm of the purely possible, apart from concrete particulars, in truths of reason. Upon this distinction, and the principles of method involved in it, rests Leibniz's conception of a hierarchy of empirical sciences, each of which may proceed analytically within its limit notions and with its appropriate symbols, but all of which are rooted, through common laws, in a universal logical order. Truths of reason depend on the laws of logic - identity, contradiction, and sufficient reason - in the sense that animality and rationality are sufficient for humanity. Truths of fact are established through the equivalence of definition and definiendum and the law of sufficient reason in its application to temporal events - in the sense that the bite of anopheles and certain other conditions are sufficient for malaria. Science has as its proper field the construction of symbolic models based on the observed qualities of sense, and serving to analyze them into the relations they imply. Such structures can be tested by their value in discovery and prediction, which assures us that they conform, though only imperfectly and symbolically, with the universal harmony. Leibniz's vision of the future of science was dominated by such algorithms, or mathematical models of natural structures; he himself set them up only in calculus, pure geometry, and a few less prominent mathematical and physical fields, but the wonders of recent quasi-mathematical constructions in chemistry, neurology, and genetics would have abundantly justified the faith which impelled his curiosity in biological and chemical problems. Unlike the more positivistic of modem theories, however, his own interpretation anchored these structures firmly in the universal harmony of being on the one hand, and in the symbolizing individual on the other. The inadequacy of truths of fact requires a criterion of truth less certain and more highly specialized than that of mere possibility. Adequate analysis into compatible primary notions and principles, directly intuited, is a perfect criterion for truths of reason. But the intuition of sense qualities is only psychologically certain, and demonstration cannot be complete; hence we must be content with the 'congruence of meanings' in the realm of time and change. A phenomenon will be coherent when it consists of many phenomena for which a reason can be given either in themselves or by some sufficiently simple hypothesis common to them. It is coherent, furthermore, if it conforms to the customary nature of other phenomena which have repeatedly occurred to us, so that the parts have the same position, order, and outcome in relation to the phenomenon which similar phenomena have had in the past. ... The most valid criterion is by all means consensus with the whole sequence of life, especially if others affirm that their own phenomena are in agreement with it .... But the most powerful criterion of the reality of phenomena, quite sufficient by itself, is success in the prediction of future phenomena from past and present ones .... [No. 39]. The criteria of factual truth are value in prediction, coherence in the strict sense of correspondence in structure with preceding and future experiences of similar nature, and contribution to the wholeness of many separate parts of experience. In the latter connection Leibniz fully recognizes the role of hypothesis and the hypothetical nature of human knowledge offact (Nos. 18 and 32). The virtues of Leibniz's theory of knowledge are to be found in the clarity in which he defines the role of rational principles in establishing the validity of experience, as For references see p. 58
44 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS opposed to Locke's psychological analysis of the genesis of experience. If Descartes may be regarded as stressing the 'distinctification' of knowledge, Locke its 'aggregation' (Grote), Leibniz may be said to have developed the Cartesian analysis into a sharply defined methodological scale in which knowledge moves from vague quality to sharply delineated structure, but without losing either the qualitative or the purposive and dynamic function which is essential to ideas. For as the individual's knowledge grows in distinctness, his valuations, too, must rise from mere egoistic feelings to the just and socialized understanding of perfection which determines his duty. Leibniz's realistic theory of knowledge is completed by his practical conception of man and his idealistic metaphysics. Two difficulties in this theory of knowledge remain to be pointed out. One is the problem of error. In Leibniz's moral system the good man was much clearer on the foundations of truth than on the nature of falsehood. Leibniz himself often discusses the problem in relation to his system (Nos. 13; 35, Sec. 14; 41, I; Theodicy, Prel. Dis., Sec. 44; etc.). Error is the manipulation of symbols or words, for which there is no corresponding idea. It consists of combining words, like 'the greatest of all numbers' and 'the greatest of all circles', whose referents are incompatible. Error is non-sense, fancy unsupported by reality, the synthesis of simple terms into an impossible notion. But how is even such negative error possible? Leibniz's difficulty arises out of his determinism. How can a being whose every action and passive experience follow from the law of his individual nature, that is, from the ideas essential to his nature, set up a combination of symbols and acts to which no idea corresponds and which is therefore expressive of nothing? This would indeed demand a liberty of indifference. Equally difficult is the view in the Discourse that ideas are from God, but the relations between them - the source of error - from us. His own conception of error (and evil) should have forced Leibniz either to set up inconsistent and incoherent ideas as real, which would have destroyed the perfection of God, or to introduce a real indeterminism into man. Though he suggests the latter in his exoteric writings, this is always in violence to the law ofthe individual. The second problem concerns the role of self-experience in providing metaphysical truth. Leibniz frequently says that it is only in reflection that we discover the true meaning of such categories as being, identity, causality, and unity. Does such metaphysical knowledge rest upon analogy or is it direct apprehension of the deepest level 'of man's own nature, where he is bound to God by the law of his individuality? Is Leibniz's meaning to be understood as pointing to an external thing-in-itself analogous to the analyzed structure of our own mind or to an internal transcendental principle of unity or being? Is he confirming the Scholastics or anticipating the post-Kant ian idealists? Both views can be argued from his own words, and commentators have felt obligated to choose one interpretation or the other. But he himself regarded them as reinforcing each other, for is not God the underlying harmony expressed in my own inmost activities but in the external order as well, so that he may be reached, not only by the less certain via externa, but by the less public but more direct via interna as well? XI. SUMMAR Y: STRUCTURE AND PURPOSE With the union of the internal analogy from consciousness and the external analogy from the mathematical-logical structure of existence, Leibniz's metaphysics assumes
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 45 its final form, in terms of which his principles are unified and the various realms of existence and essence harmonized. In the first place, his principles are established and ordered in a scale of universality corresponding to the three orders of being, the possible or essential, the creative, and the existent. On the level of logical necessity these principles are two in number; Leibniz regards both as self-evident, though the former rests in his religious faith. They are the principles of perfection and of identity. The principles of plenitude and of harmony are involved in perfection; the principle of contradiction is involved in identity. The law of sufficient reason itself rests on the perfection of the universe and the possibility of the analysis which is implied in identity. Since perfection implies existence, and therefore plurality with mutual limitation, there must be a creative process, corresponding to the middle knowledge. In this process the 'anagogical principle' of maximal determination or the best possible necessarily follows from the notion of a perfect world order in which the law of identity continues to be valid throughout the limiting choices; every complete substance must still be equivalent to the sum of its predicates. This law of the best possible has its special analogues - the principle of maxima and minima in mathematics, of least action or the extremum in physics, and the law of parsimony in methodology. On the level of existence, finally, the principles of continuity and individual differentiation (the identity of indiscernibles) follow from the law of perfection. And under temporal and spatial conditions which we have already described, sufficient reason becomes mechanical causality, and identity becomes equipollence in its various forms - equality in algebra, congruence and similarity in geometry, equivalence in symbolic logic, and the conservation of force, along with its special derivative forms, in dynamics. Of this structure of principles only the foundation is unproved, for Leibniz succeeded in deriving the others by the deductive process of limiting definitions. But his efforts to establish the existence of perfection itself, in the form of the ontological argument, never succeeded, so that existence was never completely welded to his a priori system of principles. The continuous scale of monads of which existence consists is now also as completely defined as possible for human minds. All monads alike are temporal series of active force and passive content, representative of the universe and striving toward the purposes defined in the individualized law from which they proceed. In his later writings Leibniz preferred to simplify this structure into the two functions of appetite and perception. In the simplest or bare monads, these are without any memory or reflection, so that the harmony of the world is completely external to them and mechanical. Soul monads 56 contain an internality of purpose because perception is accompanied by attention and habituation and is therefore sentient. But spirit monads are possessed of reflection and memory of a kind which enables them to think and unify the purposes implicit in their appetites and perceptions, so that they are capable of "expressing God rather than nature"; the purposes of God are internal to them, so that they become moral persons, citizens of the kingdom of grace. The principle of perfection requires, however, that no two monads be identical but that the greatest variety of value and perfection should exist. So there is a continuous scale of monads, from the simplest to the most complex intelligences, extending far beyond the limitations of man himself. As the immediate source of all monads, exercising a purposive limitation of total possibilities, God himselfmay be called a primitive monad in contrast to created ones. 57 For references see p. 58
46 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Finally, Leibniz's combination of mechanism and purpose is now also complete. Purpose is immanent with every monad, because its law involves its perfection, not as existent but as essential. Since the individual laws all involve each other, the universal harmony is but the most perfect possible integration of individual perfectibilities. Mechanism, on the other hand, is but the phenomenal and abstract universalized description of the relations of representation between the states of individual monads. Contingency within nature therefore provides the basis for the anagogical problem which occupied so great a place in Leibniz's later thinking (Nos. 50 and 51) as the basis for a spiritual interpretation of natural phenomena. In Leibniz's thought it took the form of an argument to a supreme cause on the basis of the maximal fitness of existing laws of contingency. The religious application of this theory is found in the union of the two realms of nature and of grace in every individual substance. Every monad contributes to both realms, since every monad is part of a machine and of a system of purposes. But only self-experiencing monads have intrinsic values to be . achieved in harmony with others, and therefore only spirit monads dwell consciously in the two realms. Grace is the presence of the perfect in the law or our nature, in such a way that we consciously strive toward it. The kingdom of grace is therefore the realm in which essence modifies existence by providing its purpose. It is in this sense that every spirit monad expresses God rather than the world. The kingdom of grace is the arena in which man seeks the good individually and in community with his fellows. Even our confused feelings reflect not merely temporal but eternal harmonies; the value which Leibniz found in luminous instinct and the 'blind' emotional impulses of the soul was largely overlooked by his followers in the Enlightenment but was revived, along with the work in which it is most explicit, by men who sought to found the greatest harmonies upon feeling. 58 Feelings and instincts are themselves confused expressions of harmonies whose structure can be revealed more adequately by reason. It is on this foundation that Leibniz developed his conception of the levels of ethics and the law. XII. ETHICS AND SOCIAL THOUGHT The widespread impression that Leibniz's ethics and value theory are an insignificant and uncritical aspect of his thought rests in part on the fact that his writings in these fields have been neglected and in part on an ad hominem argument from the man's position and temperament. One misses in Leibniz, the courtier, the disregard which Spinoza showed for external circumstances and established opinions as well as Spinoza's sympathetic tolerance with human motives. Yet the burden of his thought was ethical, and value experiences, together with theoretical knowledge, are for him the distinctively human ways of expressing the universal harmony. Unlike his scientific ideas, his practical philosophy was not altered as his thought developed. Though the selections on ethics and the philosophy of law in this volume represent several periods in his work (Nos. 6, 43, and 58), they do not differ in any essentials, for the very good reason that the metaphysical and psychological foundations - universal perfection and man's relatively imperfect perception of it - were laid early. Leibniz's theory of value has been variously described as hedonistic and perfectionistic. It was both, of course, since pleasure and pain are the confused perception of universal harmony or disharmony, and the confused subjective impressions of action
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 47 as well. This harmony or disharmony may be within the physical organism, it may be in the spirit's perceptions and appetites of itself, it may be in the wider realm of creation - grief at the state of others is of this kind, as is love - but in the realm of pure essence there can be only harmony. Thus only the beatific vision of God is unalloyed joy. Even the greatest harmonies may be felt confusedly, as is true in music and art. Yet it is this feeling which determines the value. It is in this sense that Leibniz is a hedonist, though his hedonism is 'well founded' in objective structures, whether existential or possible. He is not only a hedonist but an egoist as well; the argument between Bossuet and Fenelon on the existence of nonmercenary love had already been answered by him in the negative, and he frequently referred to his opinion on this controversy (No. 44, I and II). Feelings are merely the passive aspects of impulsions or appetites, and every human impulse involves self-interest; it arises within the monad by its own law and is directed toward the future good of the monad itself. Leibniz thus relates values to the fundamental human drives as well as to the feelings, and it is in his analysis of these motives that his exploration of the good begins. All broader and higher motives must be compatible with this basic egoism. Several higher interests serve to socialize our egoistic impulses and are therefore particularly important for law. One is the desire for praise. This is an unclear feeling or mirroring of the opinions of others, which moves men, even below the level of true honnetete, to consider others. It reflects an imperfect kind of social harmony but involves no distinct perception of it (No.6, II). A much more distinct expression of this harmony, and therefore far more important in Leibniz's social thought, is love. "To love is to find pleasure in the happiness of the beloved and his perfection." Love is thus three-dimensioned - it is always egoistic, since its motive is self-pleasure, but it is always directed toward the happiness of others (which, in turn, consists of their feeling for their own growth in perfection) and therefore is also directed toward perfection or God. Hence charity and piety are but aspects of the same fundamental social virtue. Upon this analysis of human motives Leibniz builds his conception of the three levels of justice in law. Strict law rests, as Hobbes saw, upon egoistic impulses and demands external power to prevent men from harming each other when their selfinterests conflict. Its maxim is neminem laedere. On the level of equity, however, or of charity in a narrow sense, no coercion from without is needed, for there is greater clarity as to the social conditions of happiness. Its maxim is suum cuique tribuere. The highest level,piety, is the basis of justice in honorable men themselves, for whom both wisdom and charity flow from considerations of the universal harmony. It presupposes the existence of God and a community of immortal minds over which he rules. Its maxim is the golden rule, which is summed up in honeste vivere (Nos. 44 and 59).59 This is not an unqualified Platonism. For Leibniz my duty involves a plurality both of people and of values. The harmonies which evoke my uneasiness and my impulsions are the incomplete and imperfect ones implied in my law of individuality. Egoism is the fundamental limit imposed upon me by my finiteness, in which I am not wholly like any of my fellows. All value involves personal effort and personal satisfaction, even the supreme good, the beatific vision. Leibniz repudiates the false mysticism of 'Averroists' like Valentine Weigel and Angelus Silesius, who describe this highest value as personal cessation or a kind of death. To be is to strive. Every value is relative to the point of view of an individual, yet values may increase in distinctness and adequacy as the objective harmony they involve is conceived more adequately. Without For references see p. 58
48 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS this harmony there would be no striving, and hence nd feeling of pleasure and pain. This pluralism is also implicit in Leibniz's analysis of social forms. His social thought is fundamentally medieval in important respects, since he seeks a universal society of good men, a universal church, and a legal basis for universal justice. Following Aristotle and Felden (No. 44, IV), he recognizes various types of societies built about natural needs and values and upon varied principles of human relationship. But all societies are to be measured by human happiness, and there is no indication that Leibniz favors an 'unlimited' society on the political level - "a society which concerns the whole life and the common good". Such totalitarianism he recognizes as desirable only within the family and among understanding friends. His theory of history too, insofar as he had one, supports this individualism; history is concerned with the social movement toward perfection (No. 69), but the universal harmony toward which it strives is to be expressed in the perfection, and therefore the happiness, of the individuals of whose relations history consists. Three particular fields of human value playa conspicuous role in Leibniz's thought. (1) Moral values. The moral end Leibniz usually sums up in the 'public good', that is, in the happiness or enduring pleasure of spirits in as wide a social extent as possible. In this he is a genuine humanist, even to identifying the love of others with the love of God himself. The place of the other (autrui) is the true perspective point in politics as well as morals, and the precept of Jesus Christ, to put oneself in the place of the other, serves not only the end of which our master spoke, namely morality, but that of politics as well [Bod. LH., XXXIV, 8, fol. 28]. Duty is the compulsion of the individual by acknowledged harmonies, social and ideal; hence it implies both pleasure and wisdom. Honestas is thus the basic personal virtue, love the basic social, and piety the ultimate metaphysical virtue. The unity of these Leibniz frequently affirmed. To Thomas Burnet he wrote, in an indirect appeal to Newton to publish his theory of colors: You know my principles, Sir, which are to prefer the public good to all other considerations, even to glory and gold. I have no doubt that a person of the force of Mr. Newton shares my belief. The sounder one is, the more one has this disposition, which is the great principle of the man of honor, and even of justice and true piety, for to contribute to the public good and to the glory of God is the same thing [1699; G., III, 261]. (2) Aesthetic value. Leibniz, as we have seen, found a clue to creation in the work of the architect who plans the most elegant structure which his medium and site allow (No. 51). Beauty is delight in felt or understood harmony and in the strivings which these feelings accompany. Though his remarks on aesthetics are casual and incomplete, Leibniz stimulated both classicists (Baumgarten) and romanticists, the former stressing the harmonies in beauty, the latter the unclear perceptions. 60 His own tastes were of course classical, though he seems also to have collected folklore and peasant verse and other expressions of simple feelings and intuitions (Bod. LH., chaps. V and XXXIX). His analysis of music reveals both interests. In music a mathematical order of physical vibrations, perceived indistinctly, "is transmitted by our hearing and creates a sym· pathetic echo in us, to which our animal spirits respond. This is why music is so well adapted to move our minds, even though this main purpose is not usually noticed nor sufficiently sought for "(No. 44, Ilr). Beauty is thus not merely feeling but impulsion
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 49 to higher harmonies, not necessarily themselves restricted to the experience of beauty. (3) The vision o/God. Mysticism is a significant motive in Leibniz's thought (Nos. 23 and 40). Yet upon examination his attitude toward it seems one of intellectual interest and appreciation rather than deep personal experience, for there is about him a kind of surface flatness to which depth and intensity of feeling are foreign. Leibniz was a lifelong student not only of various forms of religious excitement, on which he made notes and comments and for some of which he found naturalistic explanations, but also of the varied forms of the religious consciousness. In his later years he was suspected of disregarding the public practices of religion; Hanover burghers called him 'Love-nix' (Glaube nichts). Yet the experience of God is ingredient in his metaphysics, for the monads are closed to external influence save from God, of whom every moment of their being is a fulguration. There are passages in his writings expressive of an exalted piety, not merely in their content, but in the very handwriting and the periods of his rhetoric. The true vision of God is for him a morally compelling experience whose validity is to be tested by its social fruits. But the nature of the vision is intuitive; it may be on the level of unclear and confused perception, or on a higher plane, it may rise to an adequate grasp of the perfection upon which well-being, our own and others', depends. But what of disvalue? Leibniz is not insensitive to the evils of the world, but he cannot consistently recognize any evil except that of unclear and confused perception, that is, of narrowly egoistic impulsions based on very imperfect harmonies. His frequent quotation of Ovid's well-known confession is an acceptance of human imperfection. Video meliora proboque, deteriora sequor.61 But though he is not inclined to underestimate the strength of moral evil (No. 23, II), his philosophy gives it only an ambiguous place. One is never clear whether the realm of grace really exists already or whether it is still to be built. Evil is feeling and being impelled by an imperfection less than the best possible and is therefore to be overcome within the self-consciousness of man. But whence imperfection and disharmony, why less than the best possible or, indeed, than the perfect - these questions Leibniz, bound to the chain of logical order, cannot answer. XIII. THEOLOGY One of Leibniz's early projects, the Catholic Demonstrations, was a proposal to apply his general science and his metaphysics to a rational apology for orthodox Christianity so distinct and adequate that it should compel assent. It came to nothing, and the Theodicy, his published defense of God written many decades later, proved to be neither so rigorous nor so universally convincing, though it became the basis of his wider European influence. Both works show the centrality of theology in Leibniz's thought. His thought was to be a rational theology, and though he used the distinction between natural and revealed religion, he regarded both as on the same level of adequate perception; God, the 'region of ideas', the great calculator, must be shown to be the greatest of princes who reigns with perfect justice and love in the commonwealth of grace. But, in pressing the adequacy of reason, he left for faith only the role of personal assent and conviction, the established body of truth being beyond all possibility of For references see p. 58
50 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS doubt. Faith needed only to follow where reason led. Thus the paradox of his theological goal; wanting to establish Christian faith, he actually helped support the extreme rational optimism of the age which followed. Leibniz spent much care upon theological issues which were not central to his moral concern; conspicuous among these was the problem of Christ's presence in the Eucharist. But central to his thought was the problem of God, his providence, and man's relation to him. Christianity could be established as the religion of reason by showing that it provides that inclusive structure of meaning which modern science and moral order require for their unity. The hope of European order seemed to rest upon this issue, and Leibniz's strongest fears were directed at tendencies which seemed to deny either the existence of God or the substantial nature and order of creation. Atheism and libertinism, on the one hand, and 'Averroism' and Quietism, on the other - these were the two modern 'sects of naturalism' (G., VII, 333-34) which his system was to overcome. Thus the problems of his theology are, in the first place, the nature of God and his providence, the freedom of man, and, as its culmination, the realm of grace, that ideal social order in which man exercises his freedom as subject and son of God. Leibniz's first task was to prove the existence of God. According to the plan of 1668-69, the first part of his Catholic Demonstrations was entirely concerned with this problem. His arguments were at once both a priori and a posteriori, though he was compelled to cling to the former with unusual persistence because the entire structure of his system rests on the reality of perfection. Unless the perfect being can be established by the method of analysis, the entire conception of an analytic logic and a metaphysics of harmony is unfounded. (1) The first formulation of the argument for God, however, was a posteriori. This was the argument in the Confession of Nature against Atheists and the Catholic Demonstrations (No.5, I), a special case of the cosmological proof resting on Descartes's theory of matter. Assuming that bodies are real, there is no explanation within themselves of motion, figure, and cohesion. Since these depend upon active principles, their origin must, according to the principle of sufficient reason, be mental, and the harmony of the corporeal system demands that this mind be one. The cosmological argument remained Leibniz's most enduring one, though it was altered as his conception of the physical world changed. In its mature form it depends upon the distinction between existence and possibility and upon the application of the principle of sufficient reason to the existing order as a whole (No. 51). Granting that the existing world is a contingent system of causes, in both the immanent sense within each monad and the external functional sense between monads, it is still particular world, and we must grant that there might have been worlds organized on different systems of laws. Causal explanations within nature never escape contingency and therefore sti11leave unanswered the question, 'Why this world rather than another?' or, in the special case of man, 'Die! Cur hie?' To answer this question is to be driven beyond 'thisness' to the will of God as an explanation, since this question necessarily involves a principle of selection. Leibniz's contemporaries were not inclined to deny. the validity of this question and its answer. Newton had set up virtually the same argument, though based upon a different view of physical things, in the famous Scholium at the close of his Principia. It remained for a later, more positivistic era, to challenge the entire principle of reason
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 51 on which it rested, and to deny the metaphysical relevance of the fact that the universe is as it is and might have been otherwise. (2) With the introduction of a principle of selection, however, the cosmological argument becomes teleological. The anagogical principle to which Leibniz appeals (No. 50) is an effort to reason to the reality of perfect harmony from the limited perfection and interdependence of finite things. The argument has a cosmological and a humanistic part. The principle of the extremum, which Leibniz demonstrated in the case of the laws of dioptrics, is, as we have seen, of continuing importance and use in physics. Yet as a mathematical principle it implies at most that the natural order is a unique determination of possibility, as every integral equation is a uniquely determined case of a family of infinite members, with an arbitrary parameter, based on the same differential equation. 62 Only Leibniz's Platonism permitted that identification of goodness with logical determinateness which transformed his discovery into an argument for God. Applied to man and his purposes, however, the same reasoning becomes a value argument. Leibniz thought of it as one from the beginning. Chapter V of the Catholic Demonstrations, Part I, was to contain "a demonstration of infinite probability, or of moral certainty, that the beauty of the world arises from mind". In brief, man's value experience, aesthetic, moral, social, and religious, involves harmonies greater than himself, though the power of achieving them is in part his own. Against Malebranche he maintained that a finite spirit could perceive infinity, however imperfectly. This, he felt, was a particularly compelling argument in the realm of truth, the binder of the values. But the human quest for greater perfection in law, morality, art, science, and religion implies an order of perfection from which come both norms and fulfilment. Insofar as this argument regards God as sufficient reason for the absolute in our value experience, it is as valid as the cosmological, and no more so, since both involve the extension of the principle of sufficient reason from the descriptive and contingent to the possible and absolute. Yet the value argument possesses an empirical plausibility which the more general form of the teleological argument lacks. This is but one instance of many in which the psychological analogy, from the nature of man's consciousness to metaphysical principles, has a force which the mathematical analogy in Leibniz lacks, since the psychological evidence already, following Descartes's famous maxim, implies existence, and the leap from possibility to existence, the pitfall of all rationalism, is thus unnecessary. But the argument, of course, has its own empirical difficulty, the problem of evil. Sin is, as Russell points out, merely materia prima and the limited actions arising out of this source of confusion (No. 29). Within this inadequate a priori conception of evil, Leibniz offers the various explanations of badness that have been used in every theodicy which has appeared since - the appeal to ignorance, to the intrinsic goods involved in many apparent evils, to the possibility of higher spirits than man, to the necessity for restricting the good of the individual in the best society, to immortality and its assurance of continued growth toward perfection. Evil, being merely the religious term for the finiteness implied in existence, time, and plurality, thus becomes virtually a datum in the teleological argument. (3) Intimately involved in the preceding arguments for God's existence is that from the nature of eternal truths. Leibniz is, as we have seen, a conceptualist; truth involves intellect and therefore mind. Many contemporary thinkers wiII accept Leibniz's opinion that human thought implies the objective subsistence of logical relations but will deny For references see p. 58
52 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS their mental nature. Bertrand Russell, in particular, to whom the reader may be referred for a critical account of Leibniz's arguments, calls this one 'scandalous' because it confuses God's knowledge with the truths which he knows and implies ultimately that God's existence rests upon his own understanding. 63 But Russell's criticism is not itself without a trace of scandal, for nowhere else is he so substantialistic in his own thought, and nowhere else does he thus misinterpret Leibniz's theory of mind and ideas. Leibniz's view of mind, whether God's or man's, is not substantive in the Cartesian sense. Mind is ideas operating; it is itself a law which abides through a series of 'values' or events. God is not a knower who transcends his ideas and works according to them; here Leibniz's criticism of Descartes's voluntarism is decisive. But God, being perfect, must have self-awareness, and in this sense it may actually be said that God's existence does depend on his knowledge of the ideas. The significant question is not whether the eternal truths involve God in this sense but whether they involve a doctrine of creation and providence and the God which these imply. (4) But all these arguments are a posteriori and do not achieve the certainty which Leibniz demanded for this foundation of his system. They become conclusive only with the ontological argument, since they all involve the existence of harmonious ideas or perfection. Even before his stay in Paris, Leibniz was influenced by his study of Descartes, and a little later, of Spinoza, to wrestle with this proof (Nos. 7, I; 13; 14; and 16) Descartes proved that if the idea of a most perfect being is possible, it exists. But he did not prove that 'the most perfect being' is a possible idea; his definition may be purely verbal, as are those of such inconsistent pseudo-notions as the greatest number and the largest circle. How establish the possibility of a most perfect being? The closest Leibniz comes to an answer is his demonstration, to Spinoza in 1676, that perfect attributes must be compatible, a demonstration which he achieves only by defining perfections from the start as simple notions. But this begs the entire argument, since logical simplicity is relative; and the divine perfections cannot so easily be identified with the primary concepts and principles of my thought. 64 A more successful proof is never reached, and though Leibniz later repeats his criticism of Descartes and restates the argument, it is always equivalent to the assertion that perfection exists and that the rest of his principles follow from it. With Leibniz's failure at this point, his logic and his metaphysics fall apart, and the latter remains, as he frequently admits, a hypothetical structure. Thus his last philosophical summaries, the Principles 0/ Nature and 0/ Grace and the Monadology, reason from the nature of individuals and their interdependence to the universal harmony, and thus by the psychological analogy to God. The ultimate pattern of Leibniz's argument must therefore be considered as a posteriori. But when atheists are refuted, the problem of grace yet remains, and this involves the question of human freedom. Leibniz is deeply concerned with preserving the sovereignty of God without destroying a moral distinction between good men, whom he conceives as men of honor, and bad men or moral libertines. Man's will must enter into the efficacy of grace, and it must be his will and not God's. Yet to deny the divine source of all perfections, and the divine foreknowledge of all temporal events, is itself atheism. Moreover, Leibniz was always more concerned for orderly than for free living. "The highest perfection of man consists not merely in that he acts freely but still more in that he acts with reason; or rather, the two are the same thing" (No. 42, I, Sec. 37). Leibniz therefore sees little difficulty in his theory of the law of the individual
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 53 series, which is the true individual substance from which man's will flows-determined, indeed, but self-determined. There is no freedom of indifference or indeterminacy; all essence is logically determined, all existence, through the created individual laws. The element of probability which enters into human actions is of the same kind as that which enters into mechanical processes elsewhere in nature; ultimately both could be reduced, by an omniscient being, to the necessity by which different series of events follow from their individual laws and represent each other. Yet Leibniz is impressed, on the other hand, by the urgency of human choice and believes that the notion of the individual law does preserve for man a real freedom. The entire force of a monad's being, both its acts and the passive content of its experience, arise from its own nature; its dependence on the rest of creation is secondary and phenomenal, the realm of scientific description and generalization. Appetite and perception, becoming will and intellect in man and grasping the nature of God himself, are man's own. Practically, he must act as ifhis past is determined but his future not. The power is within himself in the law of his nature, though his attainments are as broad as the universe itself. It is in this sense, Leibniz holds, that God may be said to incline rather than to necessitate, though inclination is never blocked save by a stronger inclination. This is quibbling, and we must choose between the empirical Leibniz, interested in human experiences of truth and value, and the theological Leibniz interested in an a priori glorification of God. Yet it is quibbling that has been peculiarly convincing in the philosophical tradition, for the alternative is for many thinkers the abandonment of metaphysical order. The crown of Leibniz's theological thinking is found, however, in his account of the commonwealth of spirits, whose monarch is God, related to his subjects not merely as a king but as a father to his children. Here Leibniz's beliefs reach their emotional and moral climax. The kingdom of grace is the unfailing conclusion to every finished exposition of his thought; it is the bond of reference between his system and the ills of Europe. It gives an overreaching purpose to the realm of nature 6S, for man is the complex individual in whom the two realms are consciously united. It implies moral freedom on the part of its subjects, through deliberate and voluntary obedience to the order of law. It is at once the highest goal of man's efforts and the highest achievement of God's creation. Leibniz believes that it can be both, since man's moral growth follows God's creative plan, and man is so constituted by nature as to be fulfilled in the law of the kingdom, which is love. Both the value of human life and the glory of God's kingdom are infinitely enhanced by immortality. Leibniz has two arguments for it: granting the existence of perfection, it solves the problem of evil; and the nature of individual substance demands it. Every monad exists by virtue of its own law and its own power; since this cannot be interfered with from without, it cannot be destroyed - save by the intervention of God. That this means a repetition or continuation, in the case of man, of reflection, conscious memory, and purpose is Leibniz's faith, rooted in the moral requirements of a divine justice. Monads may continue in a greatly restricted state; this happens in the case of death. But soul and spirit monads always involve a materia prima and therefore a body, however reduced in complexity, of which this is the reflection. The laws of this body may involve the grounds of renewed awareness and memory. Immortality, not merely of the spirit but of the organism, is therefore the highest perfection of the unified kingdoms of nature and of grace. For references see p. 58
54 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS XIV. LEIBNIZ'S CONSISTENCY AND INFLUENCE The outstanding insecurities and strains in Leibniz's philosophical structure have been pointed out in the course of our exposition. But like other parts of the human adventure, philosophy advances by its inconsistencies; reculer pour mieux sauter - to step back in order the better to leap forward - was for Leibniz himself the rule of historical progress. We may stop briefly to consider some of the permanent values in the imposing and intricate pattern of his ideas. It was characteristic of his mode of philosophizing, and of his conception of error as well, that he rarely found falsehood in his own ideas and not much oftener in those of his adversaries. Usually he saw only incompleteness which was to be remedied by further, more adequate analysis. And in spite of shifts of emphasis from logic to physics and from universal to individual, it must be admitted that in the main his thought is a progressive unfolding of the notions involved in his particular perspective on the world, the law of his own intellectual nature, from the beginning. Yet the ambiguities, the gaps, and the contradictions are there, as we have seen. No philosopher was more eager to subject his views to criticism (though he rarely changed them as a result); yet debate never fully cleared up the ambiguities in his conception of simple ideas, primary matter, the nature of corporeal beings, the relation between mind and body, man's freedom. The most conspicuous gap is the missing cornerstone - his failure to prove the existence of perfection. The result of this is that as an a priori structure, his rationalism falls short of rigorous demonstration. And this is just where he left it himself, though he never explicitly gave up the hope of establishing his principles adequately through the ontological argument. But perhaps this failure in some ways merely makes clearer the value of the rationalistic mode of thought for our own time. For the result is a shift of emphasis from the eternal as a starting-point for philosophy to the use of reason in discovering and interpreting the temporal order of existence itself. The close relation between reason and perception is the clue to the power of Leibniz's method. It is true that his arguments rest on postulates that are unproved, except insofar as they are tested by their coherence and their empirical adequacy. All the more then do they demonstrate the structure of human understanding. Leibniz's successful application of rational principles to contingent and natural events is one of the great achievements of modern philosophy, and his rationalism remains valid as an exploration of the principles involved in the possibility of science and morality itself, as an exposition of the method by which experience is organized, verified, and corrected through analysis and synthesis. In this sense the rationalism of Leibniz remains a permanent supplement and corrective to Locke's empiricism. The other failures in Leibniz's thought are closely related to this underlying one. Thus his theory that logic and reality are completely commensurate must be surrendered, not merely because his own conception of the proposition was too restricted to serve as a logical net within which to capture existence, change, plurality, and freedom, but because reality is prior to and deeper than logic. It imposes itself on logic rather than the reverse. And this, again, leads to a shift from the effort to supply rigid logical limits to being, to the logical challenge inherent in the complexities and infinitely varying qualities of existence. There is no part of being to which the selective stripping
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 55 and labeling of logic cannot be made to apply, and its skeleton may ever thus be laid bare. But the logic that does so must follow rather than lead and copy rather than create. In his logical calculus and universal characteristic, Leibniz began to explore the traits of a logic which can do this. Though Leibniz achieved a genuine pluralism in existence through his conception of individual laws, it is not of a kind that supports the individualism even of the honorable man, the man of good will. For here too he never loosens the reins with which an intellectualistic God holds all existence in his grasp. Time and finitude are only necessary consequences of the greatest possible perfection. Here, again, the strong pluralistic and temporalistic interests of Leibniz which gradually come to the fore against this deterministic background may be emphasized. He was too good a historian and scientist not to give full attention to the principles of differentiation and change or to neglect the tools which his mathematics offered for measuring it. Much of his thinking is done from the individual outward, and he was a pioneer in exploring the secret parts and unplumbed depths of man's soul. Again, Leibniz had no explanation, except the enduring Augustinian one, of the source of limitation, opposition, and resistance within the universal harmony. There is logical profundity, but great obscurity as well, in the sorites involved in creation perfection implies plurality, plurality implies simultaneity and succession, time and space are the forms of activity and passivity and therefore involve opposition. But ultimately he can only point to the empirical fact; bodies do collide, impulses are opposed to each other, psychological and social forces do clash. Harmony is only partly a fact, and in part an ideal, a norm, in human experience. The realm of the possible and potential may indeed be a real realm, but the two worlds of essence and existence, and the two levels of truth built upon them, cannot be bridged from the top down but only imperfectly from the experience of the existent outward. Leibniz's own symbolic logic, finally, and his ideal of science require a conception of freedom which he does not accept. It lies within the power of the thinker to choose his own characters and signs; the man in error combines signs for which there are no corresponding ideas. And what is true of error is by that very fact true of evil as well. Man's free choice implies that possibility is broader than existence, as Leibniz insisted. But it follows directly that possibility cannot itself contain the principles which determine existence. Thus there appears a basic alternative, a shift in viewpoint, which the student who wishes to learn from Leibniz must face. His age and his own genius confirmed the logician and mathematician in him, while his devotion to fact pushed him to acknowledge the unclear, the indistinct, and the relative, to a point far beyond the superficial clarities and rationalizations of the age which followed him. One must choose between the Leibniz who recognizes the symbolic and analogical nature of human thought but seeks the universal logical and moral norms which make it possible and the Leibniz who would analyze possibility and find existence hidden within it. The choice is between his two great analogies - mathematical relationships or psychological continuity within a phenomenally presented environment. It is the choice of beginning either from the pure logic of analysis and failing to build a metaphysics or from the awareness of the human situation but with a willingness to proceed beyond phenomena to the principles on which they may be 'well founded'. To one student at least, it is the latter Leibniz, who begins with human problems and human symbols but retains the For references see p. 58
56 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS powerful tools of reason not only in mathematics and logic but in life, without sacriiicing the adventure of human creativeness, who seems to offer the more fruitful philosophical answers. The fertility of Leibniz's ideas is revealed in later thought. His influence, though not the acuteness of his analyses, now seems to have outlived and outreached Kant's. A school of followers established the principles of his mathematics and opened the way to the triumphs of modern theoretical mechanics. Even before his death another group of younger men professed discipleship in philosophy. Himself opposed to the sectarian attitude, he aroused strong partisanship in both fields. Unfortunately it was his speculative writings that immediately survived him, many of his scientific and logical works remaining buried in the library at Hanover. Along with Bayle's Dictionary and Locke's Essay, the Theodicy was a standard item in the libraries of 18th-century philosophical dilettantes. The mood of the Theodicy survived Voltaire's ridicule and, sacrificing depth as it achieved popularity, lived until the pessimism movement of the 19th century; even Darwin could not help reflecting it. The deeper influence of Leibniz's thought reached in other directions, however. Hume accepted his emphasis upon analysis in the spirit of a skeptic, tearing apart matters of fact from ideas of relations, and also moral purpose from logical possibility. Under the influence of Christian Wolff, on the other hand, a rationalized and materialized Leibnizianism reached the academic halls which he himself had repudiated systematized into a school philosophy by the sacrifice of many of its profundities such as the relativity of time and space, the organic and purely logico-dynamic nature of the monads, and all elements of inadequacy in perception. Wolff thus attempted the reconciliation of Leibniz and Newton on the latter's terms - a blunder which history has corrected. But Wolff also preserved the Leibnizian interest in possibility and aided Kant in finding his essential answers to the question of the possibility of judgments of existence. Accepting the synthetic nature of such judgments as ultimate, not merely for us but in principle, Kant explains them through the creative role of the ultimate principles of meaning, now categories with the power of constituting experience, not merely analyzing and understanding it. For Kant, as for Leibniz, space and time are the conditions in terms of which the categories of possible experience are schematized into the principles of empirical science. For him, as for Leibniz, will is practical reason, and freedom is determination by the rational nature. His Critique 0/ Judgment is, as Cassirer has pointed out, an exploration of the implications of harmony in nature; and God, freedom, and immortality remain for him fundamentalideas in the realm of possibility and of practical value. Kant's paralogisms and antinomies are Leibniz's attempted demonstrations (in the case of God) and infinite analyses (in the case of cosmology), seen through the analytic eyes of Hume. Thus Hegel, though aware of a theory of concreteness different from Leibniz's, is able to return from Kant to his great predecessor's theory that existence is the maximum determination of the possible, and his principle that predicates are included in their subjects - provided that the subjects are concrete in Kant's organic sense. Leibniz's theory that feelings and instincts too reflect universal harmonies exerted an influence beyond the Enlightenment and his own distrust of enthusiasm. The appearance of the New Essays in 1765 gave encouragement to the Romantic reaction against mere intellect and to a deepened classicism as well, with the result that Goethe's deep poetic faith in man's intuition, and his cosmic dynamism and monadism, but also
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 57 Hegel's rational synthesis of the various cultural values of romanticism and mysticism, appear as variants of the earlier thinker's views. In a more naturalistic period Herbart and Wundt (not to mention James) adopt his dynamic psychology, while Schopenhauer revives his theory of unconscious perceptions with biological emphasis. Toward the end of the century vitalism reappears in biology, and the revolution in physics offers both empirical and theoretical evidence for Leibniz's dynamism and relatiVIsm. Today most of these issues and convictions are still alive. Differences in viewpoint are still sharp. Schools are still flourishing. But there is again a strong impatience with philosophical sectarianism, and the spirit of Leibniz's quest for a philosophia perennis is more significant, perhaps, than his particular theories. In the combined attack upon common intellectual problems, there are aspects of his thought which once more may serve as rallying points for new and more advanced work. A few may be noted. (1) Leibniz's conviction that there are great human values in scientific discovery (if moral and social safeguards are maintained) and that the power of science lies in organized, co-operative research has seen triumphs in our days which are enormous beyond anything he imagined. But the problem, not merely of a philosophy of science, but of a philosophy, theoretical and practical, methodological and metaphysical, adequate to organize the scientific enterprise within an acceptable social and cultural order, still remains. (2) His vision of a general science of characters and operations is still alive, as are his own projects in the field - the construction of a universal calculus, a universal language, and a universal encyclopedia. His thought may well suggest that such a science may be compatible, not with a linguistic positivism alone, but with a metaphysics of universals and persons. The belief that analogy will serve as a method to reveal isomorphisms underlying a hierarchy of sciences is a related ideal that still defines directions for scientific advance. And the algorithms and models whose value he predicted in the various fields of human creativity are now finding application, as he foresaw, in education as well as in prediction and creation, and in the arts as well as the sciences and technology. (3) In metaphysics Leibniz's most fruitful contribution has been his ordered dynamism, for it stimulated the great modern revolutions in physics, biology, and psychology as well as in philosophy. Time once more succeeded space as the frame for existence, and substance was redefined in terms of structure and function, so that process remained amenable to mathematical analysis. Directly implied in this shift, too, was the new concept of organism, involving a plurality of processes reflecting a basic harmony of dependent parts. His analysis of possibilities in existence is in the spirit of neorealism, yet his epistemology is a mode of critical realism. It is not to be wondered at that the metaphysical syntheses which best respond to the scientific and moral interests of our own times, whose problems parallel in such complex forms those of the 17th century, should return to this pattern. Thus Peirce, who knew Leibniz better than any other American of his time, returns to his logic and reinterprets his basic categories existence, possibility, and harmony - as chance, logic, and love, breaking the great chain of being and releasing the free forces of existence. Whitehead too has given expression to the basic Platonism and dynamism which moved Leibniz, with results offering striking analogies as well as instructive differences from the earlier thinker's conclusions. An empiricism more concerned with the objective implications of reason, an existentialism with greater faith in logic (if this is not a contradiction in terms), For references see p. 58
58 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS a personalism more intent upon scientific analysis - these and others we may still learn from Leibniz. In spite of deep differences, a pattern of thought may thus be affirmed which stresses the organic unity and common relations of all being on the one hand, yet tries to do justice to freedom and purpose, fact and value. This would be the form of modern Leibnizianism. Finally, Leibniz's fundamental humanism, his concern for moral and cultural ends to be attained in a social environment of language, law, technology, and religion, supports the needed moral solutions for the problems of our warlike century. An organization of United Nations (at least in the European sphere) and an age of justice to be made effective through the common purposes of men of good will were not beyond the vision of Leibniz's age. But its choices were wrong, and the increase of evils which resulted defines the crisis of our own years. Good will still requires, not merely warm feelings, but both individual self-determination to the good and the perception of possible harmonies that are universal. And to correct our inadequate perceptions and build these harmonies in actu demands the perfection of common language, common law, and a common faith. REFERENCES According to the Gregorian calendar, which was not yet in effect in Leipzig when he was born but which had long been used in Roman Catholic countries. His birthdate is therefore often given as 10 days earlier, June 21. 2 The Latin motto is: "With every lost hour, a part of life perishes"; the German, "Deeds make men." 3 Leibniz's papers contain suggestions for improving the speed and comfort of travel; the notorious alchemist Johann Joachim Becher, inventor of the phlogiston theory, sought to discredit him by the charge that he proposed a coach which should travel from Hanover to Amsterdam in 6 hours. Leibniz also projected plans for improving the mails, bookkeeping, currency and exchange, statistics, and other tools of economic life. 4 This failure Leibniz traces back to the Council of Constance in 1414-18. For the Council of Trent he had so much respect that he used its decisions as definitive (with some private interpretations; cf. No. 28) for his own theological writing. 5 This term, so common in the literature of the 17th century, is based on the Stoic virtue of honestas, which we translate 'honor' for want of a better word. The reader should be warned, however, that the translation, though appropriate for 17th-century usage, does not fit the Stoic sense itself and that 'honor' here is used to designate inward virtue and quality of character, not a reputation. To the feared revolution Leibniz alludes in his earliest writings, especially those against atheism, as well as in his later ones. See the New Essays, IV, 16,4 (G., V, 444). 6 La crise de la conscience europeenne, 1680-1715, Boivin, Paris, 1935. 7 Bedenken welcher Gestalt Securitas publica interna et externa und Status praesens jetzigen Umstiinden nach auffesten Fuss zu stellen (Klopp, I, 193-315). 8 As a basis for this reform Althus had proposed the logic of Peter Ramus. 9 In his Observations sur Ie projet d'une paix perpetuelle (of the Abbe de Saint Pierre) Leibniz, repeating the introduction to his Tractatus de jure suprematus (1677), outlines his plan for a confederation of Christian nations in Europe, united under a church and an international council or senate. 10 The proposed Elements of Natural Law were to open with a criticism of Hugo Grotius, to whom Leibniz owed his emphasis upon the law of nature but with whose efforts to find a basis for this law independent of religion he disagreed from the first. 1
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 59 11 The reader interested in the details and issues of the bitter dispute about priority and plagiarism in the discovery of the calculus should consult C. B. Boyer, The Concepts o/the Calculus, Columbia University Press, New York, 1939, pp. 187ff.; M. Cantor, Vorlesungen iiber Geschichte der Mathematik, 2d ed., Vol. III, chap. LXXXIX; J. M. Child, The Early Mathematical Manuscripts 0/ Leibniz, Chicago 1920; A. de Morgan, Essays on the Life and Work 0/ Newton, Chicago 1914; and J. E. Hofmann, Leibniz' mathematische Studien in Paris, De Gruyter, Berlin, 1948. It is now well established that Newton and Leibniz made their studies independently, beyond suggestions and efforts to solve the problem which both might have found in Barrow, Pascal, and a host of others. Hofmann in particular points out the responsibility which Leibniz had in making the charges possible, while De Morgan criticizes Newton and the Royal Society. The symbols and terms still used are Leibniz's. 12 Bertrand Russell has once more repeated his charge (A History 0/ Western Philosophy, chap. XI), easily refuted by the facts, that Leibniz himself suppressed publication of his logical and metaphysical analyses out of a concern for personal advancement. Such an interpretation disregards the wide range of Leibniz's interests, his actual publication, and his efforts to prepare for and to secure publication. His problem was rather the lack of readers who grasped the more technical parts of his thought. A recent application of a mathematical discovery of Leibniz is the use of the binary number system in the construction of the large electronic computer at the Institute of Advanced Study, Princeton, under the direction of John von Neumann. It deserves comment that this numerical system, using only the numbers 1 and 0, was developed by Leibniz not only for its practical usefulness in computation but for its symbolic theological significance as 'the image of creation', but it serves this modem project in a most utilitarian sense, saving about twothirds of the tubes and components needed for the decimal system. 13 Louis Daville, Leibniz historien, Paris 1909. See also W. Conze, Leibniz als Historiker, Berlin 1951. 14 In a plan for his encyclopedia, drawn up in 1679, Leibniz includes in his classification of the sciences "Geopolitics, or concerning the state of our earth in relation to mankind, which includes all history and political geography" (Cout. OF., p. 40). 15 Couto OF., pp. 5, 3-4. Pacidius was a pen name of Leibniz; Theophilus was frequently the exponent of his views in his dialogues. Cf. No. 23 and the New Essays. 16 A note on passive obedience is significant enough in relation to the political strains of the time to be reproduced. To the younger Baron von Boineburg he wrote in 1695: "As for the matter you further touch upon, Sir, the great question of the power of sovereigns and the obedience which their peoples owe them, I usually say that it would be good for the princes to be persuaded that their people have the right to resist them, and for the people, on the other hand, to be persuaded of passive obedience. However I am quite of the opinion of Grotius, that one ought regularly to obey, the evil of revolution being greater beyond comparison than the evils which cause it. Yet I recognize that a prince can go to such excess, and place the wellbeing of the state in such danger, that the obligation to endure ceases. This is most rare, however, and the theologian who authorizes violence under this pretext should take care against excess; excess being infinitely more dangerous than deficiency" (Guh. L., II, Anmerkungen, p. 30). 17 "It is in his limitation that the master reveals himself." 18 Leibniz describes his reading habits to Foucher in 1675 (No. 11). 19 In sending the Principles o/Nature and o/Grace to Remond (No. 66) -he had already given a copy to Prince Eugene of Savoy, the great personification of honnetete - he wrote: "I have hoped that taken together with what I have published in the journals of Leipzig, Paris, and Holland, this little paper will contribute to the better understanding of my thoughts. In the Leipzig journal I have rather adapted myself to the language of the Schools, in the others more to the style of the Cartesians. In this last piece I try to express myself in a way that can be understood by those who are not accustomed to either of these styles." 20 A critical task should be done on the papers of Leibniz, which must be postponed until
60 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS they have appeared in a critical edition. This might be called a form-critical analysis of his writings. For the purpose of understanding the present selection, the following classifications are important. (1) Classification according to language. For instance, Leibniz thought of the Latin translation of the Theodicy as one which should contain more scholarly and exact distinctions than the French original. (2) Classification according to style, which is affected both by periods in time and by the purpose of the work. Leibniz's early works are often flowery, suffuse, and overweighted with ornament; the progress toward the clarity of phrase and cadence in the Monadology (1714) is by no means continuous. To the courtly, scholarly, and popular styles should be added the exalted language of many religious writings, reflected not merely in the length and rhythm of the periods but in the handwriting itself. (3) Classification according to stage of completion. Though completion is largely an unachieved ideal for Leibniz, there are definite stages in the progress. First come scraps of notations and reading notes. The first drafts are usually written on the left half of each page, with the right half reserved for later revisions and additions, which are sometimes more extensive than the first draft itself. Several revisions may then be recopied, often by secretaries, before a copy is ready for circulation or publication. 21 Disregarding omissions in Bodemann's catalogues, the Hanover library contains over 15000 letters, written in correspondence with 1063 different persons. 22 It is true that Herrenhausen may never have had a labyrinth until the reconstruction of recent years, but a plan from the period of John Frederick shows one. Leibniz owes the use of the figure in philosophy to Libertus Fromond, Labyrinthus de compositione continui (1631). Fromond (1587-1653) was friend and editor of Jansen. 23 Leibniz was, however, inclined to interpret this principle in a nominalistic rather than a Scotist sense, his early dissertation De principio individui rejecting the Scotist principle of haecceitas in favor of the view that "every individual is individuated in its entire being" (G., IV, 18-19,23-24). But in his later thought individuation occurs in the individual concept or law, and his position may therefore be considered a modern version of the Scotist one. See also p. 120, n. 17. 24 "When God calculates and carries out his thoughts, the world is made" (No. 17). 25 The sources of this principle are in Aristotle's Analyticapost., A, iv; De inter., 17, a; Cat., 1, a; etc. It was current in Leibniz's day, and Arnauld and Nicole used it as the test of axioms in the Port Royal Logic (The Art o/Thinking, Part IV, chap. VI). A criticism of Leibniz's faulty extension of Aristotle's principle to substance is to be found in H. W. B. Joseph, Lectures on the Philosophy 0/ Leibniz, pp. 85-87. 26 For Leibniz's use of this term see his correspondence with Des Bosses (No. 63). 27 "Whenever anything exercises its virtue or power, that is to say, when it acts, it improves and enlarges itself in proportion to its action" (No. 35, Sec. 15). 28 Leibniz seems not to have known the part played by Nicole in the authorship of the Art de penser until 1697, when Des BiIIettes told him of the collaboration of Arnauld and Nicole (G., VII, 457-58). 29 Leibniz frequently insists that we may use principles, like some of the geometric axioms of Euclid, with moral and practical certainty, without being able to demonstrate them from more general principles. 30 But Leibniz also recognized that, in particular truths of fact, this is true only 'virtually' or implicitly, in the sense that subject and predicate can always be found to contain some simpler concept along with differentia which distinguish them. This is true of particular affirmative propositions. See, for example, No. 26. 31 On the general science see Cout. L., chap. VI, and H. Scholz, 'Leibniz und die mathematische Grundlagenforschung', Jahresbericht der deutschen Mathematiker Vereinigung 52 (1942) 217-44. 32 See the works by Kabitz and Mahnke in the Bibliography. 33 See n. 25 above. 34 On the Scholastic doctrine of suppositum see p. 1 19, n. I I.
INTRODUCTION: LEIBNIZ AS PHILOSOPHER 61 35 The doctrine of the 'middle knowledge' of God, devised by the Jesuit Luis Molina (De liberi arbitrii concordia cum gratiae donis divina praescientia, praedestinatione, et reprobatione [1588] to solve the problem of human freedom and divine omniscience, was criticized by Leibniz in the Theodicy, Part I, Secs. 39-49. But he sometimes appropriated the term for his own theory of God's will as determining the optimum or the best possible (cf. No. 29; Cout. OF., pp. 22, 25-27, etc.). 36 The principle of the extremum or the optimum has had a long history since the classic debate between Maupertuis and Konig in the Prussian Academy in 1747. Mach ruled it out of physical considerations in his Science of Mechanics, 5th ed., Chicago 1942, pp.451-52, but in recent years it has reappeared as a principle of interpretation. W. R. Hamilton formulated it for classical mechanics in 1834; Helmholtz for electrodynamics in 1892; Hilbert related it to relativity theory in 1915 and 1917; and it has since appeared in most discussions of modem physical theory. Cf. Max Planck, Physikalische Rundblicke, Leipzig 1922, pp. 103ff.; Scholz, op. cit., pp. 227ff.; W. Dampier, A History of Science and Its Relations with Philosophy and Religion, New York 1932, pp. 487-88. 37 Leibniz's example here is a striking anticipation of the illustration used by G. E. Moore in the modem debate on the internality of relations (Philosophical Studies, pp. 277, 290). 38 These two problems involved the essentials for the differential and the integral calculus, respectively. The integral sign first appeared in Leibniz's papers on October 29, 1675; the differential 13 days later. 39 The historical beginnings of the mathematical study of probability are discussed in the correspondence with Bourguet and elsewhere (No. 69, letter of March 22, 1714). Leibniz was particularly interested in games as an expression of the free inventive spirit under regulated conditions and contributed an article to the first volume of papers of the Prussian Academy on the scientific study of games (Miscellanea Berolinensia, Part I, No.3). For a modem development and application of the theory of games in the spirit of Leibniz see Von Neumann and Morgenstern, Theory of Games and Economic Behavior, Princeton, N.J., 1944. The authors apply two Leibnizian principles: the combinatorial principle, with its functional assumptions, and the principle of the optimum. 40 See D. Mahnke, 'Die Entstehung des Funktionsbegriffes', Kantstudien 31 (1926) 426-28. For a metaphysical use of the analogy from mathematics see the last note on Foucher's criticism of Des Gabets (No. 11, IO; the second reply to Bayle, 1702 (No. 60); to Remond, February 11, 1715 (No. 68); etc. 41 Leibniz seems to have regarded Berkeley's SUbjectivism as paradoxical and a bid for attention, in his one mention of him in his correspondence (to Des Bosses; No. 61, letter of March 15, 1715). Malebranche's phenomenalism he criticized because of its denial of action to the physical world (No. 64). 42 Leibniz's physical analyses were completed at a time (1690-99) when he was particularly concerned to refute the error of occasionalists and pantheists in ascribing all power and action in nature to God alone (No. 53). 43 In No. 46, II, Leibniz uses the figure of a moving ship with its passengers completely inclosed, to illustrate his theory of the relativity of motion - the prototype of many more recent popular expositions of the special theory of relativity. 44 E. Rosier, 'Leibniz und das Vinculum Substantiale', Archiv fur die Geschichte der Phil. 24 (1913-14) 449-56. 45 See the monographs on the subject by M. Blondel and A. Boehm listed in the Bibliography. 46 Note the similarity to Kant's schematism of the pure concepts of the understanding, but with a realistic metaphysical reference instead of Kant's methodological one. 47 The term itself was used as early as Otto Casmann, Psychologia anthropologica, Hanau 1594, but Leibniz used pneumatica or elementa de mente until around 1695. Like others, he had difficulty at first in spelling the new term (Cout. OF., p. 526; PA, IV, i, 288). 48 PA., VI, i, 53-57. This note, from 1663-64, is already important for the mind-body problem;
62 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Leibniz recognized a matter and form within the soul itself, in addition to a matter and form in the body. 49 This theory of Leibniz does not appear until the New Essays. The term was Coste's translation of Locke's 'uneasiness', which Leibniz appropriated. Compare Locke's Essay concerning Human Understanding, Part II, chap. XX, with the corresponding passage in the New Essays. 50 Leibniz's distinctive use of the term 'apperception' seems also to have been suggested to him by the French reflexive form s'appercevoir used by Coste to translate 'to perceive'. The new use of the term first appears in the New Essays, Part II, chap. IX. The preface, in which it also occurs, was written later. 51 The belief encouraged by some histories of psychology, that the principles of association were first formulated in the well-known chapter in Locke's Essay (II, chap. XXXIII) is an error. See Leibniz's discussion in 1667 (No.2), which was itself hardly original. 52 See the New Method of Teaching and Learning Jurisprudence, Part II, Sec. 15 (PA., VI, i, 301). 58 cr. Otto Klemm, Geschichte der Psychologie (1911), pp. 177-78; F. Seifert, 'PsychologieMetaphysik der Seele', in Baeumler and Schroter, Handbuch der Philosophie, Vol. III. 54 lise Dohl, Bewusstseinsschichtung, Berlin 1935. 55 Until around 1684 Leibniz remains uncertain in his terminology in this matter. He uses 'perception' and 'cognition' interchangeably for the fundamental act of knowing, until about 1682, he shows a preference for the former term. Arnauld's use ofthe term in his controversy with Malebranche, which began with the True and False Ideas of 1683, must have strengthened Leibniz's decision to use it in the Discourse, intended for Arnauld. Likewise, he had been using 'represent' and 'representative' in the mathematical and symbolic sense for some time but did not apply it to the knowledge relationship itself, as did both Malebranche and Arnauld in their controversy, until the correspondence with Arnauld in 1686 (No. 36, I). 56 To Rudolf Christian Wagner, Leibniz admits that he uses the term 'soul' in a broad and a narrow sense: broadly as the principle of action or form in all monads, narrowly for living forms only (June 4, 1710; G., VII, 529). 57 To Bieriing, August, 12, 1711 (G., VII, 501-2). Leibniz seems not to have called God the monas monadorum, however, though he frequently called him a person. 58 The New Essays concerning Human Understanding (cf. Book I, chap. II) was probably completed as Leibniz left it by 1708, but it remained unpublished until 1765, when Raspe, the creator of the wonderful stories of Baron Miinchhausen, published it in his edition of Leibniz's works. Leibniz's notes on Shaftesbury's Characteristics (No. 65), another Platonist who influenced the Romanticists, are illuminating in this connection. 59 The three principles, from Ulpian Institutes i. i. 3, are "To injure no one; to give to each his due; to live honorably." 60 See E. Cassirer, Leibniz's System, pp. 458-72, esp. pp. 469-70. 61 Metamorphoses 7. 21: "I see the better and approve it; I follow after the lower." 62 See Petzold's explanation, quoted by Mach, op. cit., pp. 471ff. 68 A Critical Exposition of the Philosophy of Leibniz, chap XV, pp. 172-90. Russell, in 1900, may have been influenced, like G. E. Moore, to accept Brentano's and Meinong's distinction between mental act and object. 64 An examination of Leibniz's examples of simple ideas shows that he means by them, sometimes, the irreducible elements in logical analysis, and sometimes the ultimate perfections of God or his attributes. 66 There is some ambiguity in Leibniz's use of the terms 'nature' and 'natural', as of their equivalent ·physical'. Most generally the natural is equivalent to the whole realm of creation or existence, which is subject to subordinate regulations, and therefore includes man and history. Sometimes, on the other hand, it applies only to corporeal nature or the realm of phenomena, exclusive of the internal life of monads and their striving for perfection.
BIBLIOGRAPHY This list does not claim to be comprehensive, but aims to give the essential materials and tools for a more thorough study of Leibniz's philosophy and to indicate something of the range of interpretation which the various phases of his thought have received. The following bibliographical works are indispensable for Leibniz scholarship: Bod. B. Bodemann, Eduard, Der Briefwechsel des Gottfried Wilhelm Leibniz in der Koniglichen Offentlichen Bibliothek zu Hannover, Hanover 1889. Bod. LH. Bodemann, Eduard, Die Leibniz-Handschri/ten der Koniglichen {jffentlichen Bibliothek zu Hannover, Hanover 1895. Rav. Ravier, Emile, Bibliographie des oeuvres de Leibniz, Paris 1937. MUller, Kurt, Leibniz-Bibliographie: Verzeichnis der Literatur uber Leibniz, Klostermann, Frankfurt, 1967. The first two works provide a key to the Hanover manuscripts only but contain much material not elsewhere available. Ravier's book lists only publications of Leibniz's own writings, from 1663 to 1935 (882 items). Professor Paul Schrecker's corrections and additions in Revue philosophique de la France et de l'etranger 63 (1938) 324ff., should be consulted with this work, which is valuable for its many historical notes. Kurt MUller's bibliography covers the secondary literature on Leibniz from his death to 1967, and is thus an indispensable supplement to Ravier. II The most useful editions of Leibniz's own works including all those used for the translations given here, are the following: PA. Leibniz, G. W., Siimtliche Schri/ten und Briefe (ed. by the Preussische Akademie del" Wissenschaften, after 1945 the Deutsche Akademie der Wissenschaften), Darmstadt and Leipzig 1923-69. Only the following volumes have appeared in this monumental effort to publish a complete and critical edition: Reihe I: Politischer und historischer Briefwechsel, Vols J-VII. Reihe II: Philosophischer Briefwechsel, Vol I (1663-84). Reihe III: Politische Schriften, Vol. I, II. Reihe VI: Philosophische Schriften, Vol. I, II (1663-72), Vol. VII. Until this edition is completed, the student must rely on the following sources, none of which is adequate by itself. Dut. God. Guil. Leibnitii ... Opera omnia (ed. by Louis Dutens), Geneva 1768-. An outstanding example of 18th-cenlury editing and still the most comprehensive edition of Leibniz's work as a whole. G. Leibniz, G. W., Philosophische Schri/ten (ed. by C. I. Gerhardt), 7 vols., Berlin 1875-90. GM. Leibniz, G. W., Mathematische Schri/ten (ed. by C. I. Gerhardt), 7 vols., Berlin and Halle 1849-55. These two editions are still the most extensive collections of the philosophical and mathematical work with texts based primarily on the Hanover manuscripts.
64 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Erd. God. Guil. Leibnitii opera philosophiae quae extant (ed. by Joh. Ed. Erdmann), 2 vols., Berlin 1840. Erdmann's collection was also based on the Hanover materials. F. de C. Foucher de Careil, Nouvelles lettres et opuscules inedits de Leibniz, Paris 1857. Foucher de Careil had already published a less important collection of Lettres et opuscules inedits in 1854. In 1859 he began the publication of the collected Oeuvres, of which seven volumes of historical, political, and theological writings appeared. The texts are inferior to those of G., Erd., and Klopp. Klopp Die Werke von Leiblliz, Erste Reihe: Historisch-politische und staatswissenschaftliche Schriften (ed. by O. Klopp), 11 vols., Hanover 1864-84. Still the most inclusive source for Leibniz's political and historical works. Guh. DS. Leibniz' Deutsche Schriften (ed. by G. E. Guhrauer), 2 vols., Berlin 1838-40. Contains materials primarily of biographical interest. Mollat Mollat, G., Mitteilullgen aus Leibllizens ullgedrucktell Schriften, Leipzig 1893. A useful selection from the writings on ethics and the philosophy of law. Couto OF. Couturat, Louis, Opuscules etfragments ineditsde Leibniz, Paris 1903. The most complete edition of Leibniz's papers on logic and related fields, supplementary to Cout. L., which led to a new understanding of his importance in logic and methodology. Ger. Leibnizens nachgelassene Schriften physikalischen, mechanischen, und technischen lnhalts (ed. by E. GerIand), Leipzig 1906. Reveals the range of Leibniz's technological interests. Grua Grua, G., G. W. Leibniz: Textes inedits d'apres les manuscrits de la Bibliotheque provinciale de Hanovre, 2 vols., Paris 1948. A gleaning of unpublished materials in ethics, theology, religion, and political philosophy, with excellent notes. Jag. Jagodinski, I., Leibnitiana e1ementa philosophiae arcanae de summa rerum, Kasan 1913. An edition, with Russian translation, of notes from the Paris period. Sch. Leibniz, G. W., Ausgewiihlte philosophische Schriften im Origillaltext (ed. by H. Schmalenbach), 2 vols., Leipzig 1915-. A comparative text of an important selection of the philosophical works, collating the best published versions. Schrecker, Paul., G. W. Leibniz: Lettres etfragments inedits, Paris 1934. An excellent edition of papers and letters found in the National Library at Warsaw. BC. Leibniz, G. W., Hauptschriften zur Grundung der Philosophie (ed. by E. Cassirer; translated by A. Buchenau), 2d ed., 2 vols., Leipzig 1924. Along with German translations of the Theodicy and the New Essays, this makes up the most useful German version of Leibniz. Cassirer's notes are a valuable extension of his earlier interpretation (Cas.). Belaval, Yvon, (ed.), G. W. Leibniz: Confessio philosophi. La profession de foi du philosophe, Paris 1961. Other editions, including those of individual works, may be found listed in Ueberweg and Ravier. III The most important previously available English translations of Leibniz's philosophical works are the following: Duncan, G. M. (trans.), The Philosophical Works of Leibniz, 2d ed., New Haven 1908. Langley, A. G. (trans.), New Essays concerning Human Understanding, by Gottfried Wilhelm Leibniz; Together with all Appendix of some of His Shorter Pieces, 2d ed., Chicago 1916. Latta, R. (ed.)., Leibniz: The MOlladology and Other Philosophical Writillgs, Oxford 1898.
BIBLIOGRAPHY 65 Morris, Mary, The Philosophical Writings of Leibniz, Selected and Translated, Everyman's Library, New York, 1934. Montgomery, G. R. W., Leibniz: Discourse on Metaphysics, Correspondence with Arnauld, and Monadology, Chicago 1902. Schrecker, Paul and Anne Martin (tr.), Leibniz: Monadology and Other Philosophical Essays, New York 1965. Wiener, Philip P. (ed.), Leibniz Selections (Modern Students Library), New York 1951. All these collections contain materials not included in the present volumes. Among other translations may be mentioned H. W. Carr's edition of the Monadology, with introduction, commentary, and supplementary essays, London 1930; J. M. Child's Leibniz's Early Mathematical Manuscripts, Chicago 1921, with a critical discussion of the origin of the calculus; and the early translations in the Journal of Speculative Philosophy, 1867-71, by F. H. Hedge (No. 67), Thomas Davidson (No. 62), and A. E. Kroeger (Nos. 47 and 58). IV The best available biographical materials are still to be found in the following works: Guh. L. Guhrauer, G. E., Gottfried Wilhelm Freiherr von Leibniz: Eine Biographie, 2 vols., Breslau 1842. Though corrected and supplemented at many points, this is still the most complete biography. A condensation, in English, but without Guhrauer's rich collection of materials, appeared three years later: J. N. Mackie's Life of G. W. von Leibnitz Boston 1845. Fischer, Kuno, G. W. Leibniz: Leben, Werke, und Lehre, 5th ed., Heidelberg 1920. The appendix to this edition, by W. Kabitz, corrects both Fischer and Guhrauer on many details and reports on the biographical research until 1920. An account of Leibniz's life by the discoverer of many new details, Professor Paul Ritter, is found in Ueberweg, III (l2thed.), 307-14. Huber, Kurt, Leibniz, Munich 1951. This small book, written in part in prison and left incomplete when the Munich professor was sentenced to death by Hitler's Volksgericht in 1943, contains new information about the influences upon Leibniz and a contribution to critical appa· ratus as well. Much new material for a biography can be found in the monograph by Erich Hochstetter, Zu Leibniz' Gediichtnis, 1948. The definitive biography can be written only after the work of the German Academy edition is much nearer completion. On the 17th-century background, Voltaire's classic Siecle de Louis XIV may be supplemented by the following valuable studies: Clarke, G. N., The Seventeenth Century, Oxford 1929. Dilthey, W., 'Leibniz und sein Zeitalter', in Gesammelte Schriften, Vol. III, Leipzig 1927. Hazard, Paul, La crise de la conscience europeenne, 1680-1715,3 vols., Paris 1935. Meyer, R. W., Leibniz und die europiiische Ordnungskrise, Hamburg 1948. English translation by J. P. Stern, Leibnitz and the Seventeenth-Century Revolution, Cambridge 1952. V Out of the vast literature of interpretation which has been built upon Leibniz's thought, only those works which contribute to contemporary reappraisal and understanding have been selected. Of 19th-century interpretations, the most influential was that of J. E. Erdmann, Versuch einer wissenschaftlichen Darstellung der Geschichte der neueren Philosophie, Vol. IV, which centered attention upon Leibniz's metaphysics and theory of knowledge, and their relation to his scientific work, to the neglect of logic and methodology. In various measures
66 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS this work influenced the interpretations even of such men as Eduard Zeller, Geschichte der deutschen Philosophie seit Leibniz (1873), and Kuno Fischer, in the work mentioned in Section III. Fischer's analysis of the monad differs distinctly from that of Erdmann, however. J. T. Merz's Leibniz, Edinburgh 1884, also reflects Erdmann's point of view and limitations. Three great works, however, all appearing within a few years at the beginning of the 20th century, may be considered the beginnings of more recent criticism. All of them are profound but one-sided, and all three stress Leibniz's logic as the key to his thought. Cas. Cassirer, Ernst, Leibniz's System in seinen wissenschaftlichen Grundlagen, Marburg 1902. Cassirer's interpretation is Neo-Kantian and identifies Leibniz's logic with the formal principles of possible experience. In a supplement he criticizes the two following works. Cassirer makes it clear in a later note, however (BC., II, 95-96), that he considered this thorough study as merely preliminary, and not a complete account. Cout. L. Couturat, Louis, La /ogique de Leibniz d'apres documents inedits, Paris 1901. This careful and critical study is restricted to logic and the projects related to it. Couturat later described Leibniz's approach to metaphysics from logic in 'Sur la metaphysique de Leibniz', Revue de metaphysique et de morale 10 (1902) 1-25. Couturat's conception of logic was mathematical, and his interpretation is distinctly different from Cassirer's. Russell, Bertrand, A Critical Exposition of the Philosophy of Leibniz, Cambridge 1900. Russell reduces Leibniz's thought to basic premises and criticizes it as a deductive system. His admirable analysis involves a relative neglect, however, of the complex structure of the thought. Russell reviewed the positions of Cassirer and Couturat in 'Recent Work in the Philosophy of Leibniz', Mind 12 (1903) 177-201. Corrective in one way or another of these one-sided interpretations are the following important works: Boutroux, Emile, La philosophie allemande au XVII" siecle, Paris 1929. These lectures from 1887 to 1888, together with Boutroux's introductions to his editions of the Monadology and the New Essays, Book I, combine a concern for scientific methodology with an idealistic metaphysics. Joseph, H. W. B., Lectures on the Philosophy of Leibniz, Oxford 1949. Lectures for undergraduates; a clear and sharp analysis of some breaking points in the system. K. Kabitz, W., Die Philosophie des jungen Leibniz, Heidelberg 1909. Primarily a historical study, this work affirms the essentially metaphysical nature of Leibniz's thought. Lovejoy, A. 0., The Great Chain ofBeing, Cambridge, Mass., 1936, esp. chap. V. This study of the Platonic tradition in Western thought puts Leibniz into the proper historical stream and shows the ambiguity between his temporalism and eternal ism. Mahnke, D., Leibnizens Synthese von Individualmetaphysik und Universalmathematik, Halle 1925. Extremely valuable for its criticism of the important Leibniz interpretations since 1900. Mahnke himself seeks the unity of Leibniz's individualism and universalism in phenomenology. Pichler, H., Leibniz: Ein harmonisches Gespriich, Graz 1919. A sensitively conceived Leibnizian dialogue showing the unity of the logic, ethics, and aesthetics. Schmalenbach, H., Leibniz, Munich 1921. Seeks to interpret Leibniz's thought as the confluence of the streams of Protestant individualism and modem scientific universalism, combining a culture-historical with a metaphysical study.
BIBLIOGRAPHY 67 Wundt, W., Leibniz: Zu seinem zweihundertjahrigen Geburtstag, Leipzig 1917. A short but brilliant interpretation based on the physical theories. Among the more general introductions into Leibniz's thought, the student may find the following helpful: Belaval, Yvon, Leibniz: Initiation asaphilosophie, Paris 1962. Carr, H. W., Leibniz, London 1929. Honigswald, R., G. W. Leibniz, TUbingen 1929. Rescher, Nicholas, The Philosophy of Leibniz, Englewood Cliffs, N.J., 1967. Stammler, G., Leibniz (Fromann's Klassiker), Munich 1930. VI Of the special studies on separate fields of Leibniz's thought, the following selections are most useful. (l) For discussions of special metaphysical problems: Biema, Emile van, L 'espace et Ie temps chez Leibniz et chez Kant, Paris 1908. Blondel, M., Une enigme historique: Le "Vinculum substantiale" d'apres Leibniz et l'ebauche d'un realisme superieur, Paris 1930. Boehm, A., Le "Vinculum substantiale" chez Leibniz: Ses origines historiques, Paris 1938. Both studies emphasize the Scholastic origins of the concept. Grua, Gaston, Jurisprudence universeile et theodicee selon Leibniz, Paris 1953. Hicks, G. Dawes, 'The "Modes of Spinoza" and the "Monads" of Leibniz', in Critical Realism, London 1938. Hicks investigates the problem of Leibniz's success in establishing individualism within the bounds of an absolute. Jalabert, Jacques, La tMorie leibnizienne de substance, Paris 1947. Kanthack-Heufelder, K., Die psychische Kausalitiit und ihre Bedeuting fiir das Leibnizische System, I. Teil, Leipzig 1939. Ropohl, H., Das Eine und die Welt, Leipzig 1936. An examination of the problem of the one and the many. A list of Leibniz bibliographies is included. (2) On logic, epistemology, and methodology. DUrr, K., Neue Beleuchtung einer Theorie von Leibniz, Darmstadt 1930. Matzat, H., Untersuchungen iiber die metaphysischen Grundlagen der Leibnizschen Zeichenkunst, Berlin 1938. These works examine the foundations of the universal characteristic and logical calculus particularly their relations to metaphysics. Heimsoeth, H., Die Methode der Erkenntnis bei Descartes und Leibniz, Giessen 1914. A detailed and critical analysis of methodology in Leibniz, distinguishing it sharply from epistemology. Martin, Gottfried, Leibniz: Logic and Metaphysics. (tr. by P.S. Lucas), 1963. Parkinson, G. H. R., Logic and Reality in Leibniz's Metaphysics, Oxford 1965. Pape, Ingetrud, Leibniz, Zugang und Deutung aus dem Wahrheitsproblem, Stuttgart 1949. Wiener, Philip P., 'Notes on Leibniz's Conception of Logic and Its Historical Context', Philosophical Review 48 (1939) 567-86. (3) Mathematics and physics. Cantor's Vorlesungen ilber Geschichte der Mathematik remains the most careful study of Leibniz's contributions to the former field, and E. Mach's The Science of Mechanics is still useful, though far from adequate, in the latter. Hofmann, J. E., Die Entwicklungsgeschichte der Leibnizschen Mathematik wiihrend des Aufenthaltes in Paris, 1672-1676, Munich 1949.
68 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS See also the work by Hofmann listed in the Introduction, note 11. Scholz, H., 'Leibniz und die mathematische Grundlagungsforschung', Jahresber. der deutschen Mathematikervereinigung 52 (1942) 217-44. A clear account of Leibniz's general science as metaphysics, stressing the role of the principles of possibility, existence, and the extremum or best possible. Gueroult, M., Dynamique et metaphysique leibniziennes, Paris 1934. The most thorough study of the relation of physical to metaphysical views; traces the development of the physical concepts, with particular emphasis upon Leibniz's debt to Huygens. (4) Psychology and related fields. The most adequate general discussion is in Max Dessoir's Geschichte der neueren deutschen Psychologie (Berlin, 1902). Of the large body of monographs and studies, the following are perhaps most helpful. Dahl, I., Bewusstseinsschichtung: Ein Beitrag zur Entstehungsgeschichte ihrer Theorie, insbesondere durch Nachweis von Ursprungen bei Leibniz, Berlin 1935. Leibniz as forerunner of psychoanalytic concepts. Ganz, R., Das Unbewusste bei Leibniz, Zurich 1917. Grau, K. J., Die Entwicklung des Bewusstseinbegriffes im XVII. u. XVIII. Jahrhunderts, Halle 1916. Strahm, H., Die "petites perceptions" im System von Leibniz, Bern 1930. (5) Ethics and theology. Leibniz's ethics and value theory have been neglected. His position is described in L.le Chevallier's La Morale de Leibniz, Paris 1933. The work of two men, Baruzi and Kieft, is of basic importance in understanding his religious motives and ideas. Their works are as follows: Baruzi, J., Leibniz et ['organisation religieuse de la terre, Paris 1907. Baruzi, J., Leibniz, avec de nombreux textes inedits, Paris 1909. Both books contain much source material. Kieft, F. X., Der Friedensplan des Leibniz zur Wiedervereinigung der getrennten christlichen Kirchen, Paderborn 1903. Kieft, F. X., Leibniz; Der europiiische Freiheitskampfgegen die Hegemonie Frankreichs, Mainz 1913. A good English account of the unification efforts is G. T. Jordan's The Reunion of the Churches: A Study ofG. W. Leibnitz and His Great Attempt, London 1927. For the concept of God, the following may be consulted: Garland, A., Der Gottesbegriffbei Leibniz, Giessen 1907. Jalabert, Jacques, Le dieu de Leibniz, Paris 1960. Rolland, E., Le determinisme monadique et Ie probleme de Dieu dans la philosophie de Leibniz, Paris 1935. The interesting and unexplored field of Leibniz's relation to Malebranche is opened in G. Stieler's Leibniz und Malebranche und das Theodizeeproblem, Darmstadt 1930. Andre Robinet has published all of the texts involved in the relationship in Malebranche et Leibniz: Relations Personnelles, Paris 1955. Georges Friedmann's Leibniz et Spinoza, Paris 1946, is a thorough study of the historical and philosophical relations between these two thinkers. (6), Politics, law, and history. An enumeration of Leibniz's achievements in legal theory is found in the following works: MacDonell, John, 'Gottfried Wilhelm von Leibniz', in Great Jurists of the World, Boston 1914. Cairns, Huntington, Legal Philosophy from Plato to Hegel, Baltimore 1949, chap. IX. Grua, Gaston, Lajustice humaine selon Leibniz, Paris 1956.
BIBLIOGRAPHY 69 Schneider, Hans-Peter, Justitia Universalis: Quellenstudien zur Geschichte des christlichen Naturrechts bei Gottfried Wilhelm Leibniz, Frankfurt 1967. For the sources and historical importance of Leibniz's political concepts see the following: Basch, Victor, Les doctrines politiques des philosophes classiques de I'Allemagne, Paris 1927. Ruck, E., Die Leibnizische Staatsidee aus den Quellen dargestellt, Tiibingen 1909. On Leibniz's significance as a historian, consult: Conze, 'Leibniz als Historiker', in E. Hochstetter (ed.), Leibniz zu seinem 300. Geburtstag, De Gruyter, Berlin, 1951. Daville, Louis, Leibniz historien, Paris 1909. Two recent studies on Leibniz's relations to Russia are of contemporary interest. In some ways they supplement the older work by W. Guerrier, Leibniz in seinen Beziehungen zu Russland und Peter dem Grossen, Leipzig 1873, which contains most of the important sources. Benz, Ernst, 'Leibniz und Peter der Grosse' (1947), in Hochstetter, op. cit. Richter, L., Leibniz und sein Russlandbild, Berlin 1946. (7) An indication of the continued importance of Leibniz's thought may be found in the numerous publications which the tercentennial of his birth in 1946 called forth. The volume of essays prepared under the editorial leadership of E. Hochstetter, several times mentioned above, is of importance in summarizing recent research on the several aspects of Leibniz's work. Another collection of essays and three special editions of philosophical journals are also noteworthy: Gottfried Wilhelm Leibniz: Vortrage der aus Anlass seines 300. Geburtstages in Hamburg abgehaltenen wissenschaftlichen Tagung, Hamburg 1946. Journal of the History of Ideas, September 1946. Revue philosophique de la France et de l'hranger, October-December 1946. Zeitschrift fur philosophische Forschung, Erganzungsheft, 1947, and Band 20 (1966) 375-658. Revue internationale de philosophie 20 (1966) 163-345. A review of the literature after 1650 and a discussion of the critical issues involved is found in Loemker, 'Leibniz in our Time', Philosophische Rundschau 13 (1965) 83-111. The papers read at the Leibniz Philosophical Congress in observance of the 250th anniversary of his death at Hanover in November, 1966 are being published as Studia Leibniziana in five volumes.
PART I MAINZ AND PARIS, 1666-76
DISSERTATION ON THE ART OF COMBINATIONS 1666 (Selections) The Dissertatio de arte combinatoria, which Leibniz published in 1666, was an expansion of the dissertation and theses submitted for disputation the same year to qualify for a position in the philosophical faculty at Leipzig. The work contains the germ of the plan for a universal characteristic and logical calculus, which was to occupy his thinking for the rest of his life. That project is here conceived as a problem in the arithmetical combination of simple into complex concepts, Leibniz deriving basic theorems on permutation and combination and applying them to the classification of cases in logic, law, theology, and other fields of thought. His later judgment on the work was that in spite of its immaturity and its defects, especially in mathematics, its basic purpose was sound. Three introductory sections which supply the metaphysical and logical foundations of work are given here. They are (I) a demonstration of the existence of God with which he prefaced the work; (II) the 'corollaries' prepared for the disputation; and (Ill) the definitions introducing the work itself. The solution of the first two problems and several applications are also included. I. DEMONSTRATION OF THE EXISTENCE OF GOD [G, IV, 32-33] Hypotheses [Praecognita]i: 1. Definition 1. Godis an incorporeal substance of infinite power [virtus]. 2. Definition 2. I call substance whatever moves or is moved. 3. Definition 3. Infinite power is an original capacity [potentia] to move the infinite. For power is the same as original capacity; hence we say that secondary causes operate by virtue [virtus] of the primary. 4. Postulate. Any number of things whatever may be taken simultaneously and yet be treated as one whole. If anyone makes bold to deny this, I will prove it. The concept of parts is this: given a plurality of beings all of which are understood to have something in common; then, since it is inconvenient or impossible to enumerate all of them every time, one name is thought of which takes the place of all the parts in our reasoning, to make the expression shorter. This is called the whole. But in any number of given things whatever, even infinite, we can understand what is true of all, since we can enumerate them all individually, at least in an infinite time. It is therefore permissible to use one name in our reasoning in place of all, and this will itself be a whole. 2 5. Axiom 1. If anything is moved, there is a mover. 6. Axiom 2. Every moving body is being moved. 7. Axiom 3. If all its parts are moved, the whole is moved. For references see p. 83
74 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 8. Axiom 4. Every body whatsoever has an infinite number of parts; or, as is commonly said, the continuum is infinitely divisible. 9. Observation. There is a moving body. Proof [EKOeui~]: 1. Body A is in motion, by hypothesis No.9. 2. Therefore there is something which moves it, by No.5, 3. and this is either incorporeal 4. because it is of infinite power, by No.3; 5. since A, which it moves, has infinite parts, by No.8; 6. and is a substance, by No.2. 7. It is therefore God, by No.1 Q.E.D. 8. Or it is a body, 9. which we may call B. 10. This is also moved, by No.6, 11. and what we have demonstrated about body A again applies, so that 12. either we must sometime arrive at an incorporeal power, as we showed in the case of A, in steps 1-7 ofthe proof, and therefore at God; 13. or in the infinite whole there exist bodies which move each other continuously. 14. All these taken together as one whole can be called C, by No.4. 15. And since all the parts of C are moved, by step 13, 16. Citselfismoved, by No. 7, 17. and by some other being, by No.5, 18. namely, by an incorporeal being, since we have already included all bodies, back to infinity, in C, by step 14. But we need something other than C, by 17 and 19, 19. which must have infinite power, by step No.3, since C, which is moved by it, is infinite, by steps 13 and 14; 20. and which is a substance, by No.2, 21. and therefore God, by No. 1. Therefore, God exists. Q. E.D. 3 II. COROLLARIES FOR DISPUTATION 4 [G., IV, 41-43] An Arithmetical Disputation on Complexions, which Mr. Gottfried Wilhelm Leibniz of Leipzig will hold in the famous university of Leipzig, by permission of its distinguished philosophical faculty, on March 7,1666. I. Logic 1. There are two primary propositions. The first is the principle of all theorems or necessary propositions: what is (so) either is or is not (so), or conversely. The other is the basis of all observations or contingent propositions: something exists. 2. Perfect demonstrations are possible in all disciplines. 3. If we regard the disciplines in themselves, they are all theoretical; if their application, they are all practical. Those, however, from which the application follows more immediately are rightly called practical par excellence. 4. Although every method can be employed in every discipline, as we follow the traces either of our own investigation or of the producing nature in our treatment, it yet
MAINZ AND PARIS, 1666-76 75 happens in the practical disciplines that the order of nature and that of knowledge coincides, because here the nature of the thing itself originates in our thought and production. For the end in view both moves us to produce the means and leads us to know them, which is not true in the matters which we can merely know but cannot also produce. Moreover, although every method is allowed, not every one is expedient. 5. The end of logic is not the syllogism but Simple contemplation. The proposition is, in fact, the means to this end, and the syllogism is the means to the proposition. II. Metaphysics 1. One infinite is greater than another. (Cardan, Pract. Arith., chap. 66, nn. 165 and 260. Seth Ward is said to dissent in his Arithmetic ofInfinites. 5) 2. God is substance; creature is accident. 3. A discipline concerning created beings in general is needed, but this is nowadays usually included in metaphysics. 4. It is very improbable that the term cause expresses an unequivocal concept to cover efficient, material, formal, and final causes. For what is the word influx, more than a mere word? 6 III. Physics 1. Since we may observe that other cosmic bodies move about their own axes, it is not absurd that the same should be true of the earth; but neither is the contrary. 2. Since the most general difference between bodies is that of density and rarity 7, the four primary qualities may obviously be explained as follows: the humid is the rare, the dry is the dense, the warm is the rarefying, and the cold is the condensing. Everything rare is easily confined within external boundaries, but with difficulty within its own boundaries; everything dense, the contrary. In the rare, everything that rarefies facilitates the quickening of the homogeneous with respect to itself and the separation of the heterogenous; in the dense the way to this is blocked. A reason is thus supplied for the Aristotelian definitions. Nor does fire, which seems to be rare but must actually be dry, provide an exception to this, for I reply that one thing is to be said about fire per se and another of fire which inheres in other bodies, for in this case it follows the nature of these bodies. Thus it is clear that a flame, which is nothing but burning air, must be fluid just as is air itself. On the other hand, the fire which consists of burning iron is like iron itself. 3. It is a fiction that the force of the magnet is checked by steel. IV. Practical 1. Justice (particular) is a virtue serving the mean in the affections of one man toward another, the affections of enjoying and of harming, or those of good will and hate. The rule of the mean is to gratify another (or myself) as long as this does not harm a third person (or another). This must be noted in order to defend Aristotle against the cavil of Grotius, who speaks as follows in the Prolegomena of his de Jure belli et pacis (Sec. 4): That this principle (that virtue consists in the mean) cannot correctly be assumed as universal is clear even in the case of justice. For since he (Aristotle) was unable to find the opposites of excess and defect in the affections and the actions which follow from them, he sought them both in the things themselves with which justice is concerned. But this is obviously to leap from one genus of things to another, a fault which he rightly criticizes in others. 8 For references see p. 83
76 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Grotius, namely, maintains that it is inconsistent to introduce into the species of a classification something which is derived by another principle of classification; he calls this, not too philosophically, "leaping over into another genus". Certainly the mean in affections is one thing, the mean in things another, and virtues are habits, not of things but of minds. Therefore I show that justice is also found in a moderation of the affections. 2. Thrasymachus well says, in Plato's Republic, Book I, that justice is what is useful to the more powerful. For in a proper and simple sense, God is more powerful than others. In an absolute sense one man is not more powerful than another, since it is possible for a strong man to be kiIIed by a weak one. Besides, usefulness to God is not a matter of profit but of honor. Therefore the glory of God is obviously the measure of all law. Anyone who consults the theologians, moralists, and writers on cases of conscience will find that most of them base their arguments on this. Once this principle is established as certain, therefore, the doctrine of justice can be worked out scientifically. Until now this has not been done. 9 III. CUM DEO! [G., IV, 35-75] 1. Metaphysics, to begin at the top, deals with being and with the affections of being as well. Just as the affections of a natural body are not themselves bodies, however, so the affections of a being are not themselves beings. 2. An affection (or mode) of a being, moreover, is either something absolute, which is called quality, or something relative, and this latter is either the affection of a thing relative to its parts if it has any, that is, quantity, or that of one thing relative to another, relation. But if we speak more accurately and assume a part to be different from the whole, the quantity of a thing is also a relation to its part. 3. Therefore, it is obvious that neither quality nor quantity nor relation is a being; it is their treatment in a signate actuality that belongs to metaphysics. 4. Furthermore, every relation is either one of union or one of harmony [convenientia]. In union the things between which there is this relation are called parts, and taken together with their union, a whole. This happens whenever we take many things simultaneously as one. By one we mean whatever we think of in one intellectual act, or at once. For example, we often grasp a number, however large, all at once in a kind of blind thought, namely, when we read figures on paper which not even the age of Methuselah would suffice to count explicitly. 5. The concept of unity is abstracted from the concept of one being, and the whole itself, abstracted from unities, or the totality, is called number. 1 0 Quantity is therefore the number of parts. Hence quantity and number obviously coincide in the thing itself, but quantity is sometimes interpreted extrinsically, as it were, in a relation or ratio to another quantity, to aid us, namely, when the number of parts is unknown. 6. This is the origin of the ingenious specious analysis l l which Descartes was the first to work out, and which Francis Schotten and Erasmus Bartholin later organized into principles, the latter in what he calls the Elements of Universal Mathematics. Analysis is thus the science of ratios and proportions, or of unknown quantity, while arithmetic is the science of known quantity, or numbers. But the Scholastics falsely believed that number arises only from the division of the continuum and cannot be
MAINZ AND PARIS, 1666-76 77 applied to incorporeal beings. For number is a kind of incorporeal figure, as it were, which arises from the union of any beings whatever; for example, God, an angel, a man, and motion taken together are four. 7. Since number is therefore something of greatest universality, it rightly belongs to metaphysics, if you take metaphysics to be the science of those properties which are common to all classes of beings. For to speak accurately, mathematics (adopting this term now) is not one discipline but small parts taken out of different disciplines and dealing with the quantity of the objects belonging to each of them. These parts have rightly grown together because of their cognate nature. For as arithmetic and analysis deal with the quantity of beings, so geometry deals with the quantity of bodies, or of the space which is coextensive with bodies. Far be it from us, certainly, to destroy the social distribution of disciplines among the professions, which has followed convenience in teaching rather than the order of nature. 8. Furthermore, the whole itself (and thus number or totality) can be broken up into parts, smaller wholes as it were. This is the basis of complexions, provided you understand that there are common parts in the different smaller wholes themselves. For example, let the whole be ABC; then AB, Be, and AC will be smaller wholes, its parts. And the disposition of the smallest parts, or of the parts assumed to be smallest (that is, the unities) in relation to each other and to the whole can itself also be varied. Such a disposition is called situs. 12 9. So there arise two kinds of variation: complexion and situs. And viewed in themselves, both complexion and situs belong to metaphysics, or to the science of whole and parts. If we look at their variability, however, that is, at the quantity of variation, we must turn to numbers and to arithmetic. I am inclined to think that the science of complexions pertains more to pure arithmetic, and that of situs to an arithmetic of figure. For so we understand unities to produce a line. I want to note here in passing, however, that unities can be arranged either in a straight line or in a circle or some other closed line or lines which outline a figure. In the former case they are in absolute situs or that of parts to the whole, or order; in the latter they are in relative situs or that of parts to parts, or vicinity. In definitions 4 and 5, below, we shall tell how these differ. Here these preliminary remarks will suffice to bring to light the discipline upon which our subject matter is based. 13 DEFINITIONS 1. Variation here means change of relation. For change may be one of substance, or of quantity, or of quality; still another kind changes nothing in the thing but only its relation, its situs, its conjunction with some other thing. 2. Variability is the quantity of all variations. For the limits of powers taken in abstraction denote their quantity; so it is frequently said in mechanics that the power of one machine is double that of another. 3. Situs is the location of parts. 4. Situs is either absolute or relative; the former is that of the parts with respect to the whole, the latter that of parts to parts. In the former the number of places is considered, and the distance from the beginning and the end; in the latter neither the beginning nor the end is considered, but only the distance of one part from another part is viewed. Hence the former is expressed by a line or by lines which do not inclose For references see p. 83
78 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS a figure or close upon themselves, and best by a straight line; the latter is expressed by a line or lines inclosing a figure, and best by a circle. In the former much consideration is given to priority and posteriority; in the latter, none. We wiIl therefore do weIl to caIl the former order, S. And the latter vicinity. The former is disposition; the latter, composition. Thus by reason of order the following situses are different: abcd, bccla, cdab, dabc. But in b vicinity there can be no variation but only situs, namely, this: a c. Thus when the d very witty Taubman was dean of the philosophical faculty at Wittenberg, he is said to have placed the names of Master's candidates on the public program in a circular arrangement, so that eager readers should not learn who held the position of 'swine' .14 6. We will usually mean the variability of order when we take variations par exceIlence; for example, 4 things can be arranged in 24 ways.lS 7. The variability of a complex we call complexions; for example, 4 things can be put together in 15 different ways.16 8. The number of varying things we shall caIl simply number; for example, 4 in the case proposed. 9. A complexion is the union of a smaIler whole within the greater, as we have said in the introduction. 10. In order to determine a certain complexion, however, the greater whole is to be divided into equal parts assumed as minima (that is, parts now not to be considered as further divisible). Of these parts it is composed, and by the variation of them the complexion or lesser whole may be varied. Because the lesser whole itself is greater or less according as more parts are included at any time, we call the number of parts or unities to be connected together at one time the exponent, after the example of a geometric progression. For example, let the whole be ABCD. If the lesser whole is to consist of two parts, for example, AB, AC, AD, BC, BD, CD, the exponent will be 2; if of three parts, for example, ABC, ABD, ACD, BCD, the exponent will be 3. 11. We shaIl write the complexions with a given exponent as foIlows: if the exponent is 2, com2nation (combination); if 3, con3nation (conternation); if 4, con4nation; etc. 12. Complexions taken simply are all the complexions computed for all exponents; for example, 15 of the number 4. These consist of 4 units, 6 com2nations, 4 con3nations, 1 con4nation. 13. A useful (useless) variation is one which can (cannot) occur because ofthe nature of the subject matter; for example, the four (physical] elements can be com2ned six times, but two com2nations are useless, namely, those in which the contraries fire and water and the contraries air and earth are com2ned .... PROBLEMS Three things should be considered: problems, theorems, and applications. We have added the application to individual problems wherever it seemed worth while, and the theorems also. To some of the problems, however, we have added a demonstration. Of these, we owe the latter part of the first problem, and the second and fourth, to others; the rest we ourselves have discovered. We do not know who was the first to discover them. Schwenter (Delic., Book i, Sec. 1, prop. 32) says they exist in Jerome Cardan,
MAINZ AND PARIS, 79 1666-76 John Buteonis, and Nicolas Tartalea. But we have not found them in Cardan's Arithmetica practica, published in Milan in 1539. Christopher Clavius set forth especially clearly what has been found recently, in his Commentarium in Sphaeram Joannis de Sacro Bosco, published in Rome in 1585, pages 33 if}? Problem I To Discover the Complexions for a Given Number and Exponent 1. There are two ways of solving this problem, one for all complexions, the other for com2nations only. The former is more general, but the latter requires fewer data, namely, only the number and the exponent, while the former also presupposes the discovery of antecedent complexions. 1s 2. We have developed the more general method; the special one is popularly known. The more general solution is this: Add the complexions of the number preceding the given number, by the given exponent and by the exponent preceding it; the sum will be the desired complexions. For example, let the given number be 4 and the exponent 3; add the 3 com2nations and the 1 con3nation of the preceding number 3; (3 + 1 = 4). The sum 4 will be the answer. 3. But since the complexions of the preceding number are required for this solution, Table ~ must be constructed. In it the top line contains the numbers from 0 to 12 inclusive from left to right (we believe this is far enough, since it is easily extended); the vertical line at the left contains the exponents from 0 to 12, reading from top to bottom; and the bottom line, from left to right, contains the total complexions [complexiones simpliciter]. The lines between contain the complexions for the number given at the head of the corresponding column and for the exponent given at the left.19 4. The reason for this solution, and the basis of the table, will be clear if we demonTABLE I't o 1 2 3 4 ~ ~ ! 5 6 ~ 9 10 11 o 1 o 0 o o o o 0 0 0 0 o 0 o 0 o 0 o 0 0 0 2 1 o o o o 3 3 1 0 0 0 o 0 o 0 o o o 0 0 0 0 4 6 4 1 o o o o o o 5 10 lO 5 1 o o o o o 6 15 20 15 6 7n 21 35 35 21 1 7 o o o o o 1 o o o 8u 28 9m 36 84 lOb 45 120 56 70 56 28 8 1 126 126 84 36 9 252 210 120 45 o 1 0 1 o 210 10 o o 0 0 o o - - .T-O--I.--3~-7~--15~--3~--6-3~-127~-255. 51!. 12 t o o I !. o o o o o o o o ---- 2. 4. 8. 16. 32. 64. 128. 256. 512. lle 55 165 330 462 462 330 165 55 11 12r 66 220 495 792 mi 220 66 1 12 1023. 2047. 4095. 1024. 2048. 4096. o Q 1 ---------------------------- • The complexions taken simply (or the sum of the complexions of all given exponents), added to 1, equal the total of a geometric progression with base 2t. 20 ..• For references see p. 83
80 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS strate that the complexions for a given number and exponent arise from the sum of the complexions of the preceding number, for both the given and the preceding exponents. Taking the given number as 5 and the given exponent as 3, the antecedent number wiII be 4; it will have 4 con3nations and 6 com2nations, by Table ~. Now the number 5 has all the con3nations of the preceding number (since the part is contained in the whole), namely, 4, and it has besides as many con3nations as the preceding number has com2nations, since the unit by which the number 5 exceeds 4, added to each of the individual com2nations of 4, will make the same number of con3nations. Thus 6 + 4 = 10. Therefore the complexions for a given number, etc. Q.E.D. Problem II To Discover the Complexions Taken Simply for a Given Number Seek the given number among the exponents of a geometric progression with base 2; then the total of complexions sought will be the number or term of the progression whose exponent is the given number, minus 1. It is difficult to understand the reason or demonstration for this, or to explain if it is understood. The fact, however, is apparent from Table ~. For when added together, and the sum added to unity, the particular complexions of a given number always constitute, when one is added, the term of that geometric progression with base 2, whose exponent is the given number. But if anyone is interested in seeking the reason for this, it wiII have to be found in the process of resolving used in the Practica italica, vom Zerfallen. This must be such that a given term of the geometrical progression is separated into more parts by one than there are units (i.e., numbers) in its exponent. The first of these must always be equal to the last, the second to the next to the last, the third to the third from the last, etc., until, if it is broken up into an equal number of parts, the exponent or number of things being odd, the two parts in the middle will be equal (for example, 128 or 27 may be broken up into eight parts according to Table ~: 1,7,21,35,35,21,7,1); or, if the exponent is even and it must be broken into an odd number, the number left in the middle will have none corresponding to it (for example, 256 or 2 8 may be broken up into nine parts according to Table ~: 1, 8, 28, 56, 70, 56, 28, 8, 1). Someone may therefore think that this brings to light a new method which is absolute for solving problem 1; namely, by breaking up the complexions taken simply, or the terms of a geometric progression with base 2, by a method discovered with the aid of algebra. In fact, however, there are not sufficient data, and the same number can be broken up in several ways yet according to the same form. Application of Problems I and II Since everything which exists or which can be thought must be compounded of parts, either real or at least conceptual, whatever differs in kind must necessarily either differ in that it has other parts, hence the use of complexions; or by another situs, hence the use of dispositions. The former are judged by the diversity of matter; the latter, by the diversity of form. With the aid of complexions, indeed, we may discover not only the species of things but also their attributes. Thus almost the whole of the inventive part of logic is grounded in complexions - both that which concerns simple terms and that which concerns complex terms; in a word, both the doctrine of divisions and the doctrine of propositions; not to mention how much we hope to illumine the analytic part of
MAINZ AND PARIS, 1666-76 81 logic, or the logic of judgment, by a diligent examination of the modes of the syllogism in Example VI. The use of complexions in divisions is threefold: (1) given the principle of one division, to discover its species; (2) given many divisions of the same genus, to discover the species mixed from different divisions (this we will treat in Problem III, however); (3) given the species, to discover the subaltern genera. Examples are scattered throughout all of philosophy, and we will show that they are not lacking in jurisprudence. And in medicine every variety of compounded medicaments and pharmaceuticals is made by mixing various ingredients, though the greatest care is necessary in choosing useful mixtures. First, therefore, we will give examples of species to be discovered by this principle. 21 I. Among jurisconsults the following division is proposed (Digests, Gaius, XVII, 1, 2). A mandate is contracted in five ways: in favor of the mandator, of the mandator and mandatory, of a third person, of the mandator and a third person, of the mandatory and a third person. We shall seek out the adequacy of the division in this way: its basis is the question,/or whom, or the person in whose favor the contract is made; there are three of these, the mandator, the mandatory, and a third person. But there are seven complexions of three things: Three Inions: since contract may be in favor of only (1) the mandator; (2) the mandatory; or (3) a third person. The same number of com2nations: (4) in favor of the mandator and mandatory; (5) of the mandator and a third person; or (6) of the mandatory and a third person. One con3nation: (7) in favor of the mandator, the mandatory, and a third person all together. Here the jurisconsults reject as useless that 1nion in which the contract is in favor of the mandatory alone, because this would be advice rather than a mandate. There remain thus six classes. Why they kept only five, omitting the con3nation, I do not know. II. Aristotle (On Generation and Corruption, Book ii), with Ocellus Lucanus the Pythagorean, deduces the number of elements, or of the mutable species of a simple body, from the number of primary qualities, of which he assumes there are four, but according to these laws: (I) that every element is to be a compound of two qualities and neither more nor less, and it is thus obvious that Inions, con3nations, and the con4nation are to be discarded and only com2nations retained, of which there are six; and (2) that contrary qualities can never enter into one com2nation and that therefore two of the com2nations are useless because there are two contraries among these primary qualities. Hence there remain four com2nations, the same as the number of elements .... Moreover, as Aristotle derived the elements from these qualities, so Galen derived from them the four temperaments, the various mixtures of which later medics have studied; all of whom Claudius Campensis opposed in the past century, in his Animadversiones naturales in Aristotelem et Galenum (Leyden 1576) .... IV. In wind organs we call a register, in German ein Zug, a little shaft by whose opening the sound may be varied, not with respect to the perceived melody or pitch itself, but in its basis in the pipe, so that sometimes a shaking, sometimes a whisper, is achieved. More than thirty of such qualities have been discovered by the industry of our contemporaries. Assume that there are in some organs only twelve such simple effects; then there will be in all about 4095, as many as there are complexions taken simply of twelve things. So a great organist can vary his playing as he opens them For references see p. 83
82 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS together, sometimes many, sometimes a few, sometimes these, sometimes those. V. Thomas Hobbes, Elementa de corpore, Part I, chapter 5, classifies the things for which there are terms built into a proposition, or in his own terminology, the named things [nominata] for which there are names [nomina], into bodies (that is substances, since for him every substance is a body), accidents. phantasms, and names. Thus a name is a name either of bodies, for example man; or of accidents, for example, all abstractions, rationality, motion; or of phantasms, in which he includes space, time, all sensible qualities, etc.; or of names, in which he includes second intentions. Since these are com2ned with each other in six ways, there arise the same number of kinds of propositions, and adding to these the cases in which homogeneous terms may be com2ned (a body ascribed to body, accident to accident, phantasm to phantasm, secondary concept to secondary concept), namely, four, the total is ten. Out of these Hobbes thinks that only homogeneous terms can be usefully com2ned. If this is so, as the common philosophy certainly also acknowledges, and abstract and concrete, accident and substance, primary and secondary concepts, are wrongly predicated of each other, this will be useful for the art of discovering propositions or for observing the selection of useful com2nations out of the uncountable mixture of things.... VIII. The eighth application is in the formation of cases by the jurisconsults. For one cannot always wait for the lawmaker when a case arises, and it is more prudent to set up the best possible laws without defects, from the first, than to intrust their restriction and correction to fortune; not to mention the fact that in any state whatsoever, a judicial matter is the better treated, the less is left to the decision of the judge (Plato, Laws, Book ix; Aristotle, Rhetoric, Book i; Jacob Menochius, De arbitrariisjudicum questionibus et causis, Book i, proem. 1). Moreover, the art of forming cases is founded on our doctrine of complexions. For as jurisprudence is similar to geometry in other things, it is also similar in that both have elements and both have cases. The elements are simples; in geometry figures, a triangle, circle, etc; in jurisprudence an action, a promise, a sale, etc. Cases are complexions of these, which are infinitely variable in either field. Euclid composed the Elements 0/ Geometry, the elements of law are contained in the Corpus Juris, but in both works more complicated cases are added. The simple terms in the law, however, out of the combinations of which the rest arise, and as it were, the loci communes and highest genera, have been collected by Bernhard Lavintheta, a Francisan monk, in his commentary on the Ars magna of Lully (which see). To us it seems thus: the terms from whose complexions there arises the diversity of cases in the law are persons, things, acts, and rights .... The basis of terms is the same in theology, which is, as it were, a kind of special jurisprudence, but fundamental for the same reason as the others. For theology is a sort of public law which applies in the Kingdom of God among men. Here the unfaithful are like rebels; the church is like good subjects; ecclesiastical persons, and indeed also the political magistrate, are like the subordinate magistrates; excommunication is like banishment; the teaching of Sacred Scripture and the Word of God is like that of the laws and their interpretation; that of the canon like the question of which of the laws are authentic; that of fundamental errors like that of capital crimes; that of the Final Judgment and the Last Day like that of the judiciary process and the rendered judgment; that of the remission of sins like that of the pardoning power; that of eternal punishment like that of capital punishment, etc....
MAINZ AND PARIS, 1666-76 83 REFERENCES The term 'hypothesis' is used here in its Platonic and mathematical sense, applying to the given principles upon which the demonstration is based. The term praecognitum appears in late Scholastic works in the context of ontology. 2 Leibniz's facile identification of the whole with a collective name, and the part with a particular subsumed under this name, is supplemented below (No.1, III, 4) with a definition of the whole as a numerical relation between parts. Kabitz has shown that Leibniz's epistemology in this early period was nominalistic, sensationalistic, and naively realistic. His attitude toward nominalism is corrected in the introduction to the work of Nizolius (No.6), but the distinction between names or symbols and the real order represented is developed later, as the theory of expression or representation becomes explicit. 3 For the next stage in Leibniz's cosmological argument for God's existence see No.5, I; the mature formulation is in No. 51. 4 These theses were prepared for public disputation and first printed together with the definitions and first two problems. They are found in the footnote in G., IV, 41-43. 5 Leibniz has in mind the Arithmetic of Infinites of John Wallis rather than Seth Ward. 6 The theory that causality consists of an in/fuxus physicus had been proposed by Francis Suarez (1548-1617) as a solution to the problem of efficient causality and had established itself through the wide use of his Disputationes metaphysicae (cf. Disp., XII, ii, 4). 7 Leibniz much later reports that as a boy of 15 or younger he had walked in the Rosental near Leipzig, debating whether to accept the old philosophy of forms or the new atomism and 1
84 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS mechanism and that he had decided in favor of the latter (G., III, 205, 606). Kabitz has shown that his memory was in error here and that this decision could not have been made earlier than 1664 (K. Fischer, Gottfried Wilhelm Leibniz [5th ed.], p. 715). He is thus a mechanist at this point, convinced that a quantitative determination is possible of all qualities. But how much his thinking is still in the framework of Aristotelianism this and the following selections show. 8 Hugo Grotius, On the Law of War and Peace, Oxford 1925, p. 25. The influence of Grotius was of decisive importance in the formation of Leibniz's legal thinking. Cf. p. 58, note 10. g The letter to Thomas Hobbes (No.4) contains another statement of this argument. 10 In providing a metaphysical basis for the category of number, Leibniz is already searching, following the tradition of Nicolas of Cusa, Galileo, and Descartes, for a mathematical science more general than arithmetic and geometry but including both and thinks of it in terms of the numbering of parts and their possible relationships. It was in the Paris period that he found that numbers are incapable of maximal determination and separated mathematics from metaphysics. 11 That is, algebra. Leibniz here overlooks the algebraic discoveries of Vieta, Cardan, and others. At this time he knew Descartes only by hearsay (cf. No.3) and little mathematics beyond Euclid. Francis Schooten, professor at Leyden, edited the Opera mathematica of Francis Vieta in 1646 and also prepared an arrangement of Descartes's geometry which Erasmus Bartholinus published as the Principia matheseos universalis seu introductio in geometriam Cartesii. 12 "Disposition is the arrangement of that which has parts" (Aristotle, Metaphysics 1027b). 13 Mathematics is thus in this period of Leibniz's thought an abstract consideration of metaphysical relations, particularly of those relational properties of substance upon which quantity rests. Leibniz's general mathematics and logic were always grounded in metaphysical principles. 14 Variations thus include, in modem terminology, both combinations and permutations, while situs is a permutation. When this permutation is in circular order (as in the case of the rearrangement in relation to each other of men seated about a table), it is vicinity; when relative position to the whole is involved, it is order. 15 That is, the number of permutations of four things taken four at a time is 24. 16 Complexions are in modem terminology combinations; the latter term Leibniz reserves for the special case of complexions of the second order. His example involves the total combinations of four things, with exponents from 1 to 4. Later he calls this "complexions taken simply" (Sec. 12). 17 Leibniz's source was Daniel Schwenter, Deliciae physico-mathematicae, Nlimberg 1651-53. 18 Leibniz seems to have known a formula only for the combination of n things taken two at a time, namely, C2 n =n(n-l), and to have been ignorant of the more general form. He therefore chooses a tabular method suggestive of Pascal's triangle. 19 Note that the table involves a derivation of complexions by the additive use of 0 and 1 only and thus anticipates Leibniz's later interest in the binary number system. 20 Thus the total combinations of n terms=2n-1. We omit several sections dealing with special aspects of the rule for complexions. 21 Leibniz now offers twelve applications, most of which must be omitted because of length. For his thought about traditional logic the sixth, here omitted, is perhaps most significant. It contains his deduction of the valid modes and figures of the Aristotelian syllogism.
2 A NEW METHOD FOR LEARNING AND TEACHING JURISPRUDENCE 1667. Revision Notes, 1697-1700 (Selections from Part I) Written on his journey from Niirnberg to Frankfort in 1667. this study of the psychology of learning. the organization of knowledge. and the logical bases of law was designed to attract the attention of John Philip of SchOnborn. the elector ofMainz and political leader of the relatively independent Rhenish confederation. and to secure for Leibniz a position at his court. This it eventually succeeded in doing, and Leibniz was appointed in 1668 to work with Herman Andrew Lasser in revising the legal code (No.7). Part I. from which these selections are taken. develops a psychology and philosophy of education which is Aristotelian and therefore functional in conception. It includes also a logical analysis of the fields of learning. Part II. here omitted. is devoted to an analysis of the law. its philosophical foundations. and a program for teaching it. Its discussion of the three levels of natural right and justice is essentially the same as the later form in Nos. 43 and 58. In the last years of the century. Leibniz undertook a revision of this early work. His more important revision notes are given infootnotes. to show the similarity of many ofhis early with his more mature views. PART I. GENERAL AND COMMON TO ALL FACULTIES: ON A BASIS FOR STUDIES IN GENERAL [PA., VI, i, 266-72] 1. By a basis for studies we mean a certain kind of reasonable order; that is, a method for arriving at a state of perfected actions. 2. This state is called habit, which I define as a permanent but acquired readiness to act. 3. A subject of habit is whatever is capable of action. For it is a fact that even inanimate things can be habituated to certain actions. Thus chemists restore the most volatile spirit of wine [alcohol] by many circulations and agree in teaching that metals themselves will pass over the alembic by many distillations and cohobations with a menstruum. 1 In the Elementa de corpore Thomas Hobbes teaches that by frequent bending metal leaf acquires the habit of a kind of resilience. 4. No one who has read the booklet of Rorarius: That beasts use reason better than man, or Pliny's wonderful study of the elephant rope-dancer, or the praise of elephants and dogs in Lipsius' Letters can doubt that beasts are teachable. 2 A recent exhibit in Vienna of horses dancing in a ring makes these things all the more credible. 5. Since infants differ but little from beasts in their early years as to their external For references see p. 90
86 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS use of reason, their teachers may conveniently borrow some things from the trainers of animals. For the masters of horses, dogs, and birds have their own peculiar devices for teaching them to speak, hunt, or sing. 6. In general, however, the instrument they use is food - plenty when the animals obey, none when they refuse.... So it is said that the people of the Balearics offered no food to boys until they had completed their assigned tasks. And "teachers give boys sweet cakes, so that they will want to learn first principles". From this custom there remains in some boarding schools a punishment by hunger - das Cariren. 7. This device may be used with children but not with freer minds who are already making more use of reason. In place of bodily food, these must be offered the food of the mind, namely, honor. Hence there has arisen a system of classes and places in the lower schools and of promotions in the universities. In ancient times those boys who were unusually outstanding were led home by the rest with acclamations, as we know from the example of Cicero. 8. So much for the subject of habits. The cause or method by which a habit is acquired is either supernatural infusion or natural practice. In sentient beings, insofar as they are sentient, the latter is called teaching. 9. Infusion is either divine or diabolical. We have an example of divine infusion in the apostles' gift of tongues, although this is in fact not thought to have lasted beyond the ecstasy itself and was therefore not a habit, since it was not permanent. In church history we have a similar example in St. Ephraim the Syrian, who suddenly received a knowledge of the Greek language through the prayers of Basil the Great. Examples of diabolic infusions are not lacking in his slaves. 3 Nor need we think that divine infusion is entirely lacking in our own times; we implore the divine blessing on our own studies to this end. 10. From infusion let us proceed to practice. This is done by means of the quantity of impressive action. But quantity is either extensive or intensive; extensive quantity consists in the number of actions, intensive in the magnitude or the strength required to impress the habit. The earlier requirement is popularly recognized when people say that habit is built by frequent actions; on the latter people are usually silent. 11. The effectiveness of number or frequency is popularly confirmed in the proverb: Add little to little, and you gather a great pile. And Ovid says: Gutta cavat lapidem, consumitur annulus usu, Et teritur pressa vomer aduncus humo. Aesop's tortoise, who is quicker than the eagle, applies here, as does the German proverb: "Wer langsam geht kommt auch nach."4 From this principle arises the human device of attacking in parts a matter which cannot be mastered if attacked as a whole. We break marble by filing, carry off mountains in baskets, and empty cisterns with buckets. So we compute vast sums by parts in arithmetic, and in geometry we divide areas into triangles. 12. From this principle arises the necessity of repetition, upon which permanence, the ultimate essential of habit, largely depends. For we learn by practice to accept and dismiss some figures quickly, like a wax tablet, and others slowly, like a bronze one. Likewise, some people accept and reject the flames of rage quickly like straw, and others slowly like burning iron. Hence the Pythagoreans held that no one should fall asleep before "he had reviewed all of his deeds for the whole day". For it is harmful to
MAINZ AND PARIS, 1666-76 87 spread out repetition too far through the year, as is commonly done in schools. But daily studies may advantageously be summarized just before night, and then at the end of seven days, and again at the end of a month. Then all the months can be summarized at the end of the year, and so what is most important may be reviewed on separate levels. I am not aware that anyone has made this observation before .... 14. So much for frequency of action; we proceed to intensity or magnitude. One act carried out with a distinctive force of impression often accomplishes more than many repetitions. For example, we easily remember unusual facts, unexpected jokes, and acts that are uniquely related to our own interest, such as those which bring us praise or blame.... 15. It is best, however, to mix frequency with magnitude. This happens especially when action begins with the smallest and is increased continuously and by degrees until it reaches a maximum. Chemists prescribe this in applying fire to the alteration of inanimate things. Milo of Croton is said to have hardened himself through an artifice of this kind. Every day he carried a calf a certain distance, so that, as the calf's weight increased, his strength also insensibly increased, until at last he carried a bull in the Olympic games. The art of drinking can be taught on the same basis, if one increases his capacity by a glass as often as each week. So the Frenchman who saw some Germans at the mineral springs of Swalbach, getting used to drinking more and more water by betting with each other, thought that this was a drinking game, a Sauffschule, in which the Germans learned with water the art in which they were to excel with wine .... The same principle is most useful in memorizing a speech verbatim; the first phrase is read off first, then the first and second together, then the first, second, and third, etc. This device is also used in some girls' games. It is remarkable how easily the whole is memorized on this basis. The stern reader will forgive me for using these trifling examples, if trifles help us to be more skilful in serious instruction. 16. So much for habituation or the cause of habits, even when the common sense is lacking. 5 We must now come to teaching. To teach is to form a habit in a sentient being as such, or through his sense. Hence this art as a whole is called didactic. For even those who learn by themselves teach themselves; hence the name autodidact. 17. Teaching is to the soul as medicine is to the body of an animal. Just as the physician aims to heal (1) carefully, (2) swiftly, and (3) pleasantly, so the same things are required in the care of the soul; teaching should be (1) sound, (2) swift, and (3) pleasant ... . 18 .... Frequency of action makes teaching firmly implanted; magnitude makes it quickly implanted. These causes are common to animate and inanimate habits, and enough has been said about them. 19. But the last aim, to teach pleasantly, applies only to animate beings and must be discussed here. For there is a unique basis for habituation in animals, which makes them more capable of receiving instruction because they experience pleasure when they excel and grief when they stop up their ears. In beasts this is accomplished by food and petting, in man by utility (his food, as it were) and honor (his petting). But we have already discussed these in Sections 6 and 7. 6 20. Learning is pleasant, moreover, not only if the ends proposed are pleasant, but also if the met hods oflearning are pleasant. ... 21. We have spoken, first, of the cause of habit common to inanimate things, beasts, and men, namely habituation (from Sees. 10 to 15); then of the cause of habit For references see p. 90
88 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS common only to beasts and men, namely teaching. It remains to discuss the cause of habit distinctive of men, education by principles. 22. Habits proper to men are either of memory, of invention, or of judgment. Hence there is a threefold doctrine of these habits - mnemonics, topics, and analytics. For propositions, which are of course distinctive of men only, can be memorized, made, or judged. Topics and analytics, moreover, are to be combined in the single term logic, so that the parts of didactics are mnemonics and logic. Methodology may well be added to these. Mnemonics establishes the matter, methodology the form, and logic the application of form to matter. 23. The basis of mnemonics is some perceptible thing called a sign, which is joined by a definite relation to the thing to be remembered. This relation is either one of comparison - namely, similarity or dissimilarity - or one of connection - such as that of whole and part, part and part, cause to effect, and sign to thing signified. Thus words are invented because it would otherwise be most difficult for men to remember things. Words are not merely signs of my present thoughts to others but are also signs of my past thoughts to myself, as Thomas Hobbes has shown at the beginning of his Elementa de corpore. 7 Those signs are most mnemonic, moreover, which are most perceptible, so to speak, such as words which are not merely heard but are heard with joy - for example, songs and the termini clappantes, as they are commonly called, which boys put together with great fitness in learning their vocabularies .... 24. The basis of the topics, or the art of invention, is the loci, that is, transcendent relations such as whole, cause, matter, similarity, etc. As we have shown in our Dissertation on the Art of Combinations, propositions are made from things connected by any such relation through the combinatorial art. The contributions made to this subject by Raymund Lully in various works and by Henry Bisterfeld in his Epitome of the Art of Thinking are also not to be despised. 8 25. Analytics, or the art of judging, seems to me to be almost completely reducible to two rules: (1) no word is to be accepted without being explained, and (2) no proposition is to be accepted without being proved. These I believe to be far more absolute than the four Cartesian rules in the First Philosophy9, the first of which is that whatever I perceive clearly and distinctly is true. This is deceptive in endless ways. 26. Methodology, or the art of arranging, turns about method. A method is either natural, in which case the rule is that if one thing can be known without a second, but the second cannot be known without the first, the first should be put before the second; or it is occasional, in which case no rule can be given, since such cases vary in endless ways ....10 31. Now follow the habits of the mind. Every action of the mind is thought, for to will is nothing but to think of the goodness of a thing. I I Furthermore, all thinking is of some proposition. For mere simple terms are found only among beasts; the sense perception [imaginatio] 12 of man is never without some reflection. 32. Every proposition is either singular (hence history; for example, a magnet holds up the iron casket of Mohammed in Mecca - assuming for the sake of example that this is true); or it is contingent and universal, depending on induction from singular propositions (hence observation; for example, a magnet lifts iron); or it is necessary and universal, demonstrable from the terms themselves (hence science; for example, whatever moves is moved by some other thing, or, if a magnet lifts iron, there must be corporeal effluvia passing from the magnet to the iron).13
MAINZ AND PARIS, 1666-76 89 32a. Hence history is the mother of observation. On its nature, constitution, and classification Francis Bacon of Verulam is excellent in his incomparable treatise De augmentis scientiarum and no less so in the brilliant Novum organum scientiarum. The same materials involve history, observation, and theorems, science being the combination of these. For example: History: The wife of Fabius Maximus, who lived under Augustus Caesar, was garrulous. Observation, topical: Women are garrulous. Theorem or maxim: Do not trust a garrulous person with a secret. So we classify propositions in general, not on the basis of the copula and signs, as in section 31, but on the basis of their terms. 33. Terms are either simple or composite. Simple terms are those which cannot be made clear by more familiar terms, because they are given immediately to sense, that is, they are themselves sensible qualities. That which has sensible qualities, or is perceptible, is called a being. This is the most perfect definition of being, for whenever we wish to prove that something is, we do so by the fact that we or others sense it either in itself, by immediate sensation, or mediated by the sensation of something else which cannot be without it. Qualities taken together at the same time (or imaginability) constitute essence; sensibility constitutes existence. From the thought of many beings taken together there arise relations or the affections of being. 14 For the following kinds of comparison arise from co-imaginability or co-essence: the same, different, similar, dissimilar, contrary, genus, species, universal, singular. But from consensibility or coexistence there arise the following forms of connection: whole, part, order, one, many, necessary, contingent, togetherness, cause, etc. Universal metaphysics grows from this.ls 34. Sensible qualities are of two kinds: some perceived in the mind alone, others in fantasy or by means of mediating bodily organs. In the mind are perceived only two sensible qualities: thought and causality.16 Thought is a sensible quality either of the human intellect or of something 'I know not what' within us which we observe to be thinking. But we cannot explain what it is to think any more than what white is or what extension is. We conclude by demonstration that this quality is also in God and the angels. Upon the sensible quality called thought is built logic, which is after metaphysics the most noble science and one which Aristotle carried over by demonstration into mathematical form. 35. The other sensible quality found in mind alone is causality - when it can be proved demonstratively from an effect that it has some cause, even though latent. 17 This quality, abstracted from others such as motion and figure, is in the world cause or God, as well as in the causes of certain miracles in the world, or angels, and finally, in our own minds 18 as the cause of bodily motion. But we cannot explain the method of causality. This is the subject matter of pneumatics, which deals with the external actions of incorporeal being, as logic deals with their internal actions, or thought. Here belongs also practical philosophy, or the doctrine of the pleasant and the useful, and of justice or what is of common value in a community. To it belongs also the demonstration of the existence of God and of his attributes, of angels, and of an incorporeal mind or immortal soul within us. My own thinking has arrived at mathematical certainty in these matters through a remarkable principle which I hold to be far more important for tranquillity of mind and faith in eternal life than if I had discovered perpetual motion or the quadrature of the circle. 36. Qualities mediated by corporeal organs are either sensible or common to many For references see p. 90
90 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS organs. The latter are number, which is perceived by all the external senses and is the basis of arithmetic, and extension 19 with its various modes, which are perceived by sight and touch only and are the basis of geometry. Whatever has another sensible quality besides extension and number is called body. Whatever does not have this added quality is called a vacuum. Here physics arises. 20 The most simple sense is touch, however, through which we perceive motion. The general problem of physics is the explanation of motion, because, as we shall show next, there is nothing in the other qualities but a subtle motion, by which they can all be explained, if we assume extension. There are also special qualities of touch, such as solidity, fluidity, tenacity, smoothness, etc. Facts should be gathered most diligently about these, and also about light and colors, sounds, odors, and tastes, so that their causes in matter and motion may be better known. . 37. The abstract philosophy of qualities is followed by a concrete philosophy about the things into which these qualities coalesce. Here the qualities of things are surveyed empirically and recounted; nothing is proved anew but merely subsumed from what was previously demonstrated in the abstract philosophy. Here we are concerned with God, angels, and our mind; with fire, vapors, meteors, water, and various kinds of liquids; with earth and minerals, plants, and animals. Here then we survey, not the connection of qualities to each other and to their subjects, but the connection of subjects with qualities. This part of philosophy can be called eidographic; the preceding part, poiographic. 38. Finally, we conclude with cosmography, in which the connection of subjects to each other is expounded, and how they are distributed in the world.... Now I am sure that I have exhausted everything in my classification of the disciplines and have outlined the elements of the sciences briefly but soundly. 21 ••• REFERENCES Leibniz had mastered the terms and much of the literature of alchemy as a member of the Rosicrucian society in NUmberg. 2 Jerome Rorarius (1485-1556) was best known for his Quod animalia bruta saepe ratione utantur melius homine. It was to the article on Rorarius in his Dictionary that Bayle later attached his criticism of Leibniz's philosophy (Nos. 52 and 60). Justus Lipsius (1547-1606) was a Flemish philologist and humanist; his Epistolarum centuriae duae was published in Leyden in 1591 and frequently republished. 3 Leibniz seems thus to accept witchcraft in 1667; later he commends the work of the Jesuit Friedrich Spee (Cautio criminalis, 1631) and of the Protestant pietist Philip Jacob Spener, with whom he began a correspondence while at Mainz, in opposing the widespread injustice of the witch processes (cf. Theodicy, I, Sec. 97). 4 "Drops hollow out a stone, the ring is worn by use, And by its pressure the ground wears away the crooked plough share." The German proverb: 'The slow traveler gets there too.' 5 Aristotle's doctrine of the common sense (De anima iii. i. 425) appears in Leibniz and other 17th-century thinkers as active perception. See p. 294, note 2. 6 Leibniz mentions Comenius only once in the New Method but more frequently in his later revision notes. The similarity of Sections 17-20 to the Analytic Didactic, Sections 128-60, is striking. It will be observed that Leibniz discusses frequency, intensity, recency, and emotional effect as factors in habituation many years before Locke's famous chapter on association. His interpretation of these factors is functional rather than conceptual, and he is careful to dis tin1
MAINZ AND PARIS, 1666-76 91 guish such learning through habituation from the use of intelligence. This corresponds to his later distinction between the empirical consecutions which men and animals have in common and reasoning of the kind which is restricted to man. 7 De corpore, Book i, chap. ii. 8 Leibniz frequently criticized the effort of Raymond Lully (1235-1315) to found an Ars magna in which all possible combinations of primitive concepts were to be explored. John Henry Bisterfeld, professor at Leyden and follower of Comenius, was the source of many of Leibniz's early opinions on methodology, particularly of his conception of harmony and a method of discovery and judgment. Leibniz's notes on his works are printed in PA., II, i, 151-61. 9 Leibniz's reference to the Meditationes de prima philosophia is incorrect; the four rules appear in the Discours de la methode, Part II. Revision note of 1697-1700: " ... Two rules: (1) that no derivative notion is to be accepted unless it is explained, and (2) no derivative proposition unless it is proved. Explanation takes place through definition, proof through the syllogism, which provides a conclusion by force of its form, even if it does not always make use of the Scholastic arrangement, and not everything necessary to the conclusion is expressed, in order to avoid tedium. But it is no small matter to have a way of reasoning infallibly on this basis if we do not avoid the effort involved. The rules of Descartes are less adequate, however. Certainly the first one - that what is perceived clearly and distinctly is true - is itself untrue (unless it be restricted on some ground), and proves, not existence, but only possibility. Nor is it very useful, unless we already have the criteria of clearness and distinctness which I once stated in a study on truth and ideas [No. 33]. This is not the place to explain which notions and truths are derivative, which primitive, and which it is sometimes useful to treat as primitive." 10 Sections 27-30 discuss bodily habits. 11 Revision note: "To will is nothing but the striving [conatus] arising from thought, or to strive for something which our thinking recognizes as good. Every thought is put in an enunciation or proposition or an affirmation or negation. For the use of even simple terms involves an affirmation of their possibility, and the act of reflection recognizes something active in ourselves." 12 The reader should be warned against the many meanings of imaginatio, which range from imagination through sense perception to intuition. In general, the term implies the activity of mind as opposed to sensation and is therefore more closely related to intellect than now. p. 138, note 5; and p. 553, note 3. 13 Leibniz's distinction between truths offact and truths of reason, or contingent and necessary propositions, is not clearly developed until about 1679, when his logic has supplemented the strongly empirical emphasis in the present work. 14 Revision note: "So it can be said that the essence of a thing is its distinct conceivability (or imaginability) by us; its existence is its distinct perceptibility (or sensibility). For the composite of its qualities taken together constitutes the essence of a thing; its perceptibility proves its existence; that is, if a thing is not actually sensed, there is no thing." 15 Revision note: "From this grows metaphysics as a whole, to which the doctrine of quantity and quality in their widest sense can be referred, in logistics and the art 0/ combinations, respectively. The former deals with propositions and their calculus (and hence with the one and the many, the whole and its parts), the latter with forms (or similarity and orders of determination). Logistics or the science of quantity makes use of infinite as well as finite magnitude. Determinate number belongs to arithmetic, indeterminate to algebra. I have begun to build a science of the infini te through the invention of a new calculus; until now we have had only scattered bits of this." 16 Revision note: "Only two qualities are perceived in mind: perceptivity (or the power of perceiving) and activity (or the power of acting). Perception is the expression of many things in one, or in simple substance; if it is combined with the reflection of the percipient, it is called thought. We judge perception to apply not only to us but also to other living or organic beings, cr.
92 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS and thought to be not only in us but also (and, indeed, most perfectly) in God. This quality of the percipient is treated in logic, which, it happens, is at once a noble science in itself and serves other sciences as instrument by carrying the theorems of metaphysics into practice in investigating other truths." 17 Revision note: "Activity or force is perceivable in the mind alone; that is, the state of a thing from which change follows. We experience this intimately in ourselves, but also infer it in others from its effects. There is a double force - that of acting and that of resisting. The former is immaterial, the latter material, which resists action through it does not act unless impelled from without. Immaterial forces are the separate intelligences, as well as primary souls or entelechies in bodies. The simple, maximum exercise of force is conatus toward action." Notes 5 and 6 on p. 90 show how early Leibniz had formulated the psychological basis of his monadology. The shift from thought and causality to perception and force reflects the changes in his thinking in 1679 and the years immediately following. 18 Revision note: " ... as the cause of change in us, which we can also say is in a certain sense the cause of the motion of the body, though it is difficult to explain how it acts. Perhaps, like others, we should attribute this power of acting externally, not to the influx of the mind into the body or to the reaction of the body, but to God, who affects the body at the bidding of the mind or rather, who has, according to this opinion, so formed all things from the beginning that they respond to each other in time. Yet there remains the force of the action itself, insofar as the external changes follow the will of the soul in accordance with this divine institution. Conatus is itself of two kinds - that of a simple or of a composite thing. A simple thing is a percipient, and the conatus of the percipient as such is also called appetite, in a thinking being will. ... In a composite being or a body, conatus is motive force; mechanics deals with this." 19 Revision note: " ... extension and resistance. Number is perceived by all of the external senses, but because it is also perceived by the internal sense, and even more so, arithmetic is more rightly subordinated to metaphysics. Extension, which is perceived by sight and touch only, involves number, but adds situation to it, or the order of coexistence, and hence adds quality to quantity. Thus figures arise as modifications of extension; hence geometry." 20 It may be pointed out that in this empirical account of the structure of these categories Leibniz is not developing a theory of their ontological status. On the question of a vacuum, for instance, he is uncertain for a long time. See No.3. 21 Sections 39-42 contain a chronological account of the educational process which begins with infancy and ends at the age of 20. Leibniz prepared many more classifications of the sciences, particularly in his studies for the universal encyclopedia. The best-known discussion is in the New Essays, Book IV, chap. XXI.
3 LETTER TO JACOB THOMASIUS April 20/30, 1669* Jacob Thomasius had been one 0/ the more influential 0/ Leibniz's teachers at Leipzig. Though he seems to have lectured only on rhetoric while Leibniz was in the university, he supervised his first dissertation, De principio individui; and the letters which Leibniz wrote to him after leaving Leipzig show the high respect which the pupil had/or his master. Leibniz's intention 0/ reconciling the ancient and the new philosophy appeared early in his thought. This letter contains an effort to show Aristotle consistent with the modern philosophers rather than with the Scholastics. It was evoked by his comment on Thomasius' Origines historicae philosophiae et ecclesiasticae. the second edition 0/ which appeared in 1669 and was for long one 0/ the most accurate histories 0/ancient philosophy. Leibniz thought well enough 0/ this letter to have it printed at the end 0/ his pre/ace to the Nizolius edition in 1670 (No.8). in which related matters were discussed. The letter is here translated in the/orm in which Thomasius received it, with the exception 0/ certain obscure passages which even he apparently could not understand. 1 At these points substitutions have been made from the version 0/1670. [G., I, 15-27; IV, 162-74] The 'foretaste' of a history of philosophy which you have written has set all our mouths to watering more than I can tell you, for it shows clearly how great a difference there is between a mere enumeration of names and such profound reasons as you give for the interconnections between doctrines. You know that I am no flatterer. But wherever I hear people who understand these matters speak of your essay, they are unanimous in saying that there is no one from whom we can better hope for the entire history of philosophy than from you. Most of the others are skilled rather in antiquity than in science and have given us lives rather than doctrines. You will give us the history of philosophy, not of philosophers. Joseph GJanvill's history of the growth of the sciences since Aristotle is said to be in press in England. 2 But I believe that in general he will trace only the mathematics, mechanics, and physics of the more noteworthy periods and so detract nothing from you. I wish, indeed, that you would produce both a style and a method [stilum filumque] for this new age and warn our unseasoned youth that it is wrong to give our moderns credit either for everything or for nothing. Baghemin is not the only one whom you ought to criticize 3; there are Patricius, Telesius, Campanella, Bodin, Nizolius, Fracastori, Cardan, Galileo, Bacon, Gassendi, Hobbes, Descartes, Basso, Digby, Sennert, Sperling, Derodon, Deusing. and many other names among whom the mantle of philosophy is torn apart. It will be play for you, but fruitful for the public, to remind the world of them. Who would disagree with your estimate of Baghemin?4 There is no elegance in his hypotheses, no consistency in his reasoning, but only utterly monstrous opinions. For references see p. 103
94 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Unless he has something useful to say in specific physical observations, certainly he had better remain silent. It seems to me that the parents of his opinion that God is primary matter are Scaliger, Sennert, and Sperling - for he professes also to be a disciple of the latter - who affirm that forms are produced, not from the passive power of matter, but from the active power of an efficient cause. From this they conclude that God produces creatures rather from his own active power than from the objective and, so to speak, passive power of nothing. In their opinion, therefore, God produces things out of himself and is thus the primary matter of things. But you will judge more correctly on this subject. I agree with you completely in regard to Descartes and Clauberg, that the disciple is clearer than the master. But on the other hand, I should venture to say that hardly any of the Cartesians have added anything to the discoveries of their master. Certainly Clauberg, Raey, Spinoza, Clerselier, Heerbord, Tobias Andreae, and Henry Regius have published only paraphrases of their leader. However, I am calling Cartesians only those who follow the principles of Descartes; such great men as Bacon, Gassendi, Hobbes, Digby, and Cornelius van HoghelandeS, who are commonly confused with the Cartesians, are definitely to be excluded from their number, since they were either equals or even superiors of Descartes in age and in ability. As to myself I confess that I am anything but a Cartesian. I maintain the rule which is common to all these renovators of philosophy, that only magnitude, figure, and motion are to be used in explaining corporeal properties. Descartes himself, I hold, merely proposed this rule of method, for when it came to actual issues, he completely abandoned his strict method and jumped abruptly into certain amazing hypotheses. Vossius rightly criticizes him for this in his book on light. Hence I do not hesitate to say that I approve of more things in Aristotle's books on physics 6 than in the meditations of Descartes; so far am I from being a Cartesian! In fact, I venture to add that the whole of Aristotle's eight books can be accepted without injury to the reformed philosophy. This by itself meets your arguments about the irreconcilability of Aristotle and the modems. For the most part Aristotle's reasoning about matter, form, privation, nature, place, infinity, time, and motion is certain and demonstrated, almost the only exception being what he said about the impossibility of a vacuum and of motion in a vacuum. For to me it seems that neither a vacuum nor a plenum is necessary; the nature of things can be explained in either way. Gilbert, Gassendi, and Guericke argue for a vacuum; Descartes, Digby, Thomas White, and Clerke in his book on the plenitude of the world, for a plenum; Thomas Hobbes and Robert Boyle for the possibility of either. I admit that the rarefaction of things is difficult to explain without a vacuum, though it is possible. 7 I have recently seen a book by Jean Baptiste du Hamel, a learned Frenchman, on the agreement of the old philosophy and the new, which was published lately in Paris. In it he brilliantly explains the hypotheses of some of the best-known ancient and recent thinkers and often criticizes them with discernment. He also says a good bit about the divisions of opinion concerning the vacuum. For the rest, scarcely any sane man will question the many other arguments of Aristotle in his eight books on physics and in the whole of his metaphysics, logic, and ethics. Who would disagree, for instance, with his theory of substantial form as that by which the substance of one body differs from that of another? Nothing is more true than his view of primary matter. The one question is whether A ristotle's abstract
MAINZ AND PARIS, 1666-76 95 theories of matter, form, and change can be explained by magnitude, figure, and motion. This the Scholastics deny and the philosophical reformers affirm. The latter opinion seems to me to be not only the more true but also the more consistent with Aristotle. Let me discuss each briefly. First, about Aristotle. The Scholastics have strangely perverted his meaning; no one knows this better than you, distinguished Sir, who were the first to bring many errors of this kind to light. Since not only you acknowledge this, but also Soner and Dreier in metaphysics, Viotti, Zabarella, and Jung in logic, and Jason Denores, Piccart, Conring, Felden, Durr, and many others in civil law; why, I ask, shall we not expect the same or even worse in physics, where aid must be sought from the senses, from experience, and from mathematics - instruments which the Scholastics, shut up in their monasteries, lacked almost entirely? It is therefore probable enough that they were wrong in physical matters; what if I show that it is even more, namely, certain? This can be done in two ways. It can be shown either that the reformed philosophy can be reconciled with Aristotle's and does not conflict with it or in addition, that the one not only can but must be explained through the other, nay, that the very views which the modems are putting forth so pompously are derived from Aristotelian principles. The former way establishes the possibility of their being reconciled; the latter, the necessity. But if the reconciliation is shown to be possible, it is by that fact also accomplished. Even if the interpretations of both Scholastics and modems were possible, the clearer and more intelligible of two possible hypotheses must always be chosen, and without any doubt this is the hypothesis of the modems, which conceives no incorporeal entities within bodies but assumes nothing beyond magnitude, figure, and motion. I cannot better show this possibility of reconciling the two than by asking for any principle of Aristotle which cannot be explained by magnitude, figure, and motion. Primary matter is mass itself, in which there is nothing but extension and antitypy or impenetrability.8 It has extension from the space which it fills. The very nature of matter consists in its being something solid and impenetrable and therefore mobile when something else strikes it, and it must give way to the other. Now this continuous mass, which fills the world while all its parts are at rest, is primary matter, from which all things are produced by motion and into which they are reduced through rest. There is no diversity in it but only homogeneity, except through motion. Hence all the knots of the Scho lastics are already untied. First, they ask about its entitative actuality prior to all form. The reply must be that it is a being prior to all form, since it has its own existence. For whatever is in some space exists, and this cannot be denied of mass itself, even if it entirely lacks motion and discontinuity. But the essence of matter or the very form of corporeity consists in antitypy or impenetrability. Matter has quantity too, though this is indefinite, or interminate as the Averroists call it. For being continuous, it is not cut into parts and therefore does not actually have boundaries. But it does have extension or quantity. Everything fits together wonderfully, not as concerns the extrinsic limits of the world or the mass as a whole, but as concerns the intrinsic limits of its parts. Let us pass from matter to form in good order [per dispositiones]. Here too everything agrees remarkably if we assume that form is nothing but figure. For since figure is the boundary of a body, a boundary is needed to introduce figure into bodies. But a discontinuity of parts is necessary in order to have a variety of boundaries arising in matter. For by the very fact that parts are discontinuous, each one will have separate For references see p. 103
96 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS boundaries, since Aristotle defines the continuum as things whose limits are one [WV't"tIeUxa-ra 8V].9 But discontinuity can be introduced into the formerly continuous mass in two ways - first, in such a way that contiguity is at the same time destroyed, when the parts are so pulled apart from each other that a vacuum is left; or in such a way that contiguity remains. This happens when the parts are left together but moved in different directions. For example, two spheres, one included in the other, can be moved in different directions and yet remain contiguous, though they cease to be continuous. This makes it clear that, if mass were created discontinuous or separated by emptiness in the beginning, there would at once be certain concrete forms of matter. But, if it is continuous in the beginning, forms must necessarily arise through motion. (I am not now speaking of the annihilation of certain parts to secure a vacuum in matter, since this is supernatural.) For division comes from motion, the bounding of parts comes from division, their figures come from this bounding, and forms from figures; therefore, forms come from motion. From this it is clear that every arrangement into a form is motion, and the vexatious problem of the origin of forms is answered. The distinguished Herman Conring could only answer to this problem, in a special dissertation, that forms arise from nothing. 10 We shall say that they arise from the power of matter, not by producing something new, but merely by taking away something old and causing boundaries through a division of parts, just as anyone who makes a column does nothing but remove the superfluous parts. What is left after the rest has been removed takes on, by this very fact, the figure which we call a column. For all the figures or forms which are contained in the mass lack only determination and actual separation from the others which adhere to them, If this explanation is adopted, all the arguments advanced against the origin of forms from the power of matter itself become child's play and trifles. It now remains for us to come to change. Changes are commonly and rightly classed as generation, corruption, increase, decrease, alteration, and change of place or motion. l l Modern thinkers believe that these can all be explained by local motion alone. In the first place, the matter is obvious in the case of increase and decrease, for change of quantity occurs in a whole when a part changes its place and is either added or taken away, We need only to explain generation, corruption, and alteration through motion. I observe in advance that numerically the same change may be the generation of one being and the alteration of another; for example, since we know that putrefaction consists in little worms invisible to the naked eye, any putrid infection is an alteration of man, a generation of the worm. Hooke shows similarly in his Micrographia that iron rust is a minute forest which has sprung up; to rust is therefore an alteration of iron but a generation of little bushes. Moreover, generation and corruption, as well as alteration, can be explained by a subtle motion of parts. For example, since white is what reflects the most light and black is what reflects the least, those things whose surfaces contain many small mirrors will be white, This is why foaming water is white, for it consists of innumerable little bubbles, and each bubble is a mirror, while before, the water as a whole was but one mirror - just as there are as many mirrors as there are fragments when a glass mirror is broken. This is also why pounded glass is whiter than when it is intact. Similarly, water broken into distinct mirrors by bubbles therefore becomes white, and this is also the reason why snow is whiter than ice, and ice than water. For it is false that snow is condensed water; it is rather rarefied and therefore is lighter than water and occupies more space. The sophism of Anaxa-
MAINZ AND PARIS, 1666-76 97 goras about black snow is to be refuted in this way. Such considerations make it clear that colors arise solely from a change of figure and position in a surface. If we had space, it would be easy to explain light, heat, and all qualities in the same way. Now if qualities are changed by motion alone, substance will also be changed by that very fact, for a thing ceases to be if all, or even some, of the qualities requisite to it are changed. For example, if you remove either light or heat, you destroy fire. And you accomplish both by stopping motion. This is why a covered fire will die for lack of the air which feeds it, not to speak of the fact that an essence differs from its qualities only in relation to sense. Just so, the same city presents one aspect if you look down upon it from a tower placed in its midst; this is as if you intuit the essence itself. The city appears otherwise if you approach it from without, which is as if you perceive the qualities of a body. And just as the external aspect of a city varies as you approach it differently, from the west or from the east, the qualities of a body vary with the variety of our sense organs. 12 From this it is evident that all changes can be explained by motion. It is no objection that generation occurs in an instant while motion involves succession, for generation is not motion but the end of motion; the motion is already finished at that instant, for a certain figure is produced or generated at the very last instant of motion, as a circle is produced in the final moment of a revolving motion. This also makes clear why the substantial form consists in something indivisible and cannot be increased or decreased. For neither can a figure be increased or decreased. Even if one circle is greater than another, one circle is not more circle than another, for the essence of a circle consists in the equality of all lines drawn from its center to its circumference. But equality itself consists in an indivisible; nothing can be more or less equal. Nor should the objection be made that figure and magnitude are accidents, for they are not always accidents. Fluidity may, for example, be an accident of lead, for lead flows only in fire, but it belongs to the essence of mercury. Now the cause of fluidity is undoubtedly the free curved figure of parts, whether they be spherical, cylindrical, oval, or spheroid. Therefore the curved figure of its subtle parts is an accident of lead, but essential to mercury. The reason for this is that all metals arise from mercury fixed by saIts, while the nature of salts consists in rectilinear shapes adapted to rest. Thus if we dissolve salts in water and let them crystallize freely, some crystals appear as tetrahedrons, others as hexahedrons, octahedrons, etc., as chemists know, but none appears round or curvilinear. Hence the saIts are the cause of fixity, and the acid salts mixed with the smallest parts of mercury in the bowels of the earth impede the freedom of the curvilinear parts by inserting themselves between them and produce metal. But in fire the metal returns to the nature of mercury, for fire, inserting itself between the smallest parts, frees the curvilinear particles of mercury from the plane-sided salts; hence metal flows in the fire. So there is obviously almost nothing in Aristotle's physics which cannot be readily explained and made clear through the reformed philosophy. These examples, moreover, have occurred to me spontaneously while writing this; others are collecting many more throughout the whole of natural philosophy. I have no fear that you will ascribe what I have said to my following too closely the accounts and authority of Raey.13 I had thought this way long before I had even heard of Raey. I have read him, of course, but in such a way that I now scarcely recall what he said. Nor is he the first or the only one to reconcile Aristotle with modem philosophy. Scaliger seems to me to have paved the way, and in our own times Kenelm Digby and For references see p. 103
98 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS his follower Thomas White - the former in a book on the immortality of the soul, the latter in his peripatetic institutions - have dealt explicitly with the same thing, long before Raey. Abdias Trew and particularly Erhard Weigel are in harmony with them. 14 So far it has been shown only that the two positions can be reconciled; it still remains to show that they ought to be. For what does Aristotle discuss, in the eight books of the Physics, besides figure, magnitude, motion, place, and time? If the nature of body in general can be explained in terms of these, then the nature of a particular body must be explained in terms of a particular figure, a particular magnitude, etc. In fact, he himself says in the Physics, Book iii, Section 24, that all natural science concerns magnitude (with which figure is, of course, associated), motion, and time. He also says, repeatedly, that the subject of physics is movable bodies and that natural science deals with matter and motion. He does, it is true, make the heavens the cause of all that takes place in the sublunary realm. But the heavens, he says, act on the inferior realms only through motion. Moreover, motion produces only motion or the limits of motion, which are magnitude and figure, and from these result position, distance, number, etc. Everything in nature must therefore be explained through these. This same Aristotle says frequently, as for instance, in the Physics, Book i, Section 69, that the relation of bronze to the statue is the same as that of matter to form. For the rest, I have proved that figure is a substance, or rather that space is a substance and figure something substantive, because all science deals with substance, and it cannot be denied that geometry is a science. You have replied that you can produce a passage in which Aristotle denies that geometry is a science more quickly than I can produce one in which he affirms that it is. I have no doubt, distinguished Sir, that there are certain passages in Aristotle which can be stretched or twisted to this end. Yet I think that these are outweighed by countless other admissions of his. For what occurs more frequently in all the books of the Analytics than examples from geometry? He seems to have intended geometric demonstrations to serve as patterns for the rest, so to speak. Now it would be absurd to make the less noble a pattern for the more noble. The Scholastics, in fact, thought so meanly of mathematics at first that they made every effort to exclude it from the number of the perfect sciences, chiefly on the ground that it does not always demonstrate from causes. But, if we consider the matter more accurately, it will be seen that it does demonstrate from causes. For it demonstrates figures from motion; from the motion of a point a line arises, from the motion of a line a surface, from the motion of a surface a body. The rectangle is generated by the motion of one straight line along another, the circle by the motion of a straight line around an unmoved point, etc. Thus the constructions of figures are motions, and the properties of figures, being demonstrated from their constructions, therefore come from motion, and hence, a priori, from a cause. Geometry is thus a true science, and, Aristotle not to the contrary, its subject, which is space, is a substance. Nor is it so absurd that geometry should deal with the substantial form of bodies. For note the passage in Aristotle's Metaphysics, Book xiii, Section 3, in which he says expressly that geometry disregards material, final, and efficient cause; this being assumed, it follows that it deals either with substantial or with accidental form. But it does not deal with accidental form, since the real definition of an; accidental form involves a subject in which it inheres, or matter. But Aristotle says that geometry disregards matter. Therefore geometry deals with substantial form. So there occurs to me, as I write this, a beautiful harmony among the sciences; namely, that under careful
MAINZ AND PARIS, 1666-76 99 examination it appears that theology or metaphysics deals with the efficient cause of things, or mind; moral philosophy, whether ethics or law (for as I learned from you, these are one and the same science), deals with the final cause of things, or the good; mathematics (I mean pure mathematics, for the rest is a part of physics) deals with the form or idea of things, or figure; physics deals with the matter of things and the unique affection resulting from the combination of matter with the other causes, or motion. For mind supplies motion to matter in order to achieve a good and pleasing figure and state of things for itself. Matter in itself is devoid of motion. Mind is the principle of all motion, as Aristotle rightly saw. For to come to this problem, Aristotle seems nowhere to have imagined any substantial forms which would themselves be the cause of motion in bodies, as the Scholastics understood them. 15 He does indeed define nature as the principle of motion and of rest and calls form and matter nature, though form more so than matter. But from this it does not follow, as the Scholastics contended, that form is a kind of immaterial being, though insensible in bodies, which spontaneously imparts motion to a body, for example, downward motion to a stone, without the help of an external thing. For form is indeed the cause and principle of motion, but not the primary one. No body moves unless it is moved from without, as Aristotle not only rightly says but demonstrates. For example, assume a sphere to be on a plane. If it is once at rest, it wlll not move by itself in all eternity, unless an external impulsion is added, for example, another body. In that case the other body is the cause of the impressed motion, while the sphere's figure or sphericity is the cause of the received motion, for if this sphericity had been absent, perhaps for this occasion only, the body would not give way so easily to the other one. This shows that the Scholastic concept does not follow from the Aristotelian definition of form. I admit therefore that form is the principle of motion within its own body, and that body is itself the principle of motion in another body. But the first principle of motion is the primary form, which is really abstracted from matter, namely mind, which is at the same time the efficient cause. Hence freedom and spontaneity belong only to minds. Therefore it is not absurd that of the substantial forms only mind should be designated as the first principle of motion, all the others receiving their motion from mind. And as I said, Aristotle regards it as certain that no body has a principle of motion within itself alone l6 , and it is by this argument that he ascends to the prime mover. You make two answers to this objection. First, that this argument has no effect against Epicurus, who ascribes spontaneous downward motion to his atoms. I admit that the argument has no effect against him unless it be first proved to him that it is absurd and impossible for a body to receive motion from itself, a thing which Cicero has already done, if I am not mistaken, in his books on the nature of the gods, where he elegantly ridicules Epicurus for introducing something into his hypothesis in this way, without cause or reason. For there is 17 no 'downward' in the nature of things, but only in relation to us, nor is there any reason why any body should move in one direction rather than another. So we shall easily reply to Epicurus when he denies that whatever moves is moved by something external to itself and vindicate the certainty which we seek for the existence of God. Your second objection is that Aristotle seems to have reasoned not so much from the axiom that the principle of motion is outside the body which is moved but rather from another, that there is no infinite progression. But consider carefully, honored Sir, For references see p. 103
100 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS whether he does not in fact need the combination of both. For unless it be admitted that whatever moves is moved from without, we shall obviously arrive at no progression at all, to say nothing of one to infinity. For your adversary will attack your very beginning and respond that any given body suffices to produce its own motion through its substantial form and that hence no mover is necessary, certainly not a prime mover. So the ladder would collapse at the very bottom step, its foundation, as it were, removed. Furthermore, Epicurus too admitted an infinite progression; so we must consider not so much what Epicurus did or did not admit but what can be demonstrated with certainty.1s Now that we have reconciled the reformed philosophy with Aristotle, it remains to show its truth per se in the same way that the Christian religion can be proved by reason and experience as well as from sacred scripture. It must be proved that there are no entities in the world except mind, space, matter, and motion. A thinking being, I call mind. Space is a primary extended being or a mathematical body, which contains nothing but three dimensions and is the universal locus of all things. Matter is a secondary extended being, or that which has, in addition to extension or mathematical body, also a physical body, that is, resistance, antitypy, solidity, the property of filling space, and impenetrability, which consists in its being constrained either to give way to another being of this kind which strikes it or to stop it. Motion therefore comes from this quality of impenetrability. So matter is a being which is in space or coextensive with space. Motion is change of space. But figure, magnitude, situation, number, etc., are not entities really distinct from space, matter, and motion but are merely properties brought about within space, matter, motion, and their parts by a supervening mind. I define figure as the limit of the extended; magnitude, as the number of parts in the extended. I define number as one and one and one, etc., or as unities. Situation reduces to figure, for it is a configuration of a plurality. Time is nothing but magnitude of motion. Since all magnitude is a number of parts, why should it be surprising that Aristotle defined time as the number of motion? Heretofore these terms have merely been explained, however, and the sense in which we are using them interpreted; nothing has been proved. Let us now show that we need no other things to explain the phenomena of the world and to determine their possible causes - indeed, that there cannot be other things. However, if we show that no other things are necessary besides mind, matter, space, and motion, this will itself make it clear that the hypotheses of those recent thinkers, who use only these to explain phenomena, are the better ones. For it is a defect in hypotheses to assume what is unnecessary. A reading of recent philosophers does in fact show sufficiently that everything in the world can be explained in these terms alone, and my exposition, above, of the possibility of reconciling Aristotle with them is thereby confirmed. It must also be noted that those hypotheses are better which are clearer. The human mind can in fact imagine nothing other than mind (when it thinks of itself), space, matter, motion, and the things which result from the relations of these terms to each other. Whatever more you add to them is only words which can be spoken and variously combined but not explained or understood. Who can imagine a being which partakes neither of extension nor of thought? So what need is there to assume incorporeal souls in beasts and plants, substantial forms for the metallic elements, without extension and thought? 19 Campanella in his book De sensu rerum et magia and Marcus Marci on operative ideas were wrong but consistent with their own hypotheses, and
MAINZ AND PARIS, 1666-76 101 therefore more correct, in ascribing sense, knowledge, imagination, and will to the substantial forms of inanimate things. The occult philosophy of Agrippa is not unlike this; he assigns an angel to everything as its obstetrician, so to speak. Scaliger's discussion of the plastic power and its wisdom is also similar. Thus we return to as many little gods as there are substantial forms - to a heathen polytheism. In fact, all those who speak of these incorporeal substances of bodies cannot explain what they mean without a translation into terms of mind. 20 Hence they ascribe to them appetite, or21 a natural instinct from which natural knowledge arises. The result is such axioms as these: nature does nothing in vain; everything avoids its own destruction; nature strives for continuity; like enjoys like; matter desires a nobler form; and others of this kind, though there is in fact no wisdom in nature and no appetite; yet a beautiful order arises in it because it is the timepiece of God. From these considerations it is clear that the hypotheses of the reformed philosophy are superior to those of the Scholastics, in that they are not superfluous but on the contrary clear. It remains to prove by more subtle reasoning, that in explaining the nature of bodies we cannot assume any other entities than those which I have named. This is done as follows. Everyone calls that a body which is endowed with some sensible quality. Many of these sensible qualities can be removed from the body in such a way that it remains a body nevertheless. For even if a body lacks color, odor, taste, it is still called a body. You will admit that air, for example, is a body, although it is transparent and frequently lacks color, taste, and odor. Similarly the air is a body even when it lacks sound. Therefore those qualities that can be seen, heard, tasted, and smelled may be rejected as not at all constituting the nature of a body. The problem is thus reduced to the tactile qualities. In fact, such primary qualities as heat, humidity, dryness, and cold can be absent individually; heat can be absent from water, humidity from earth, dryness from air, and cold from fire, yet each of these may be a body. That the other tactual qualities, for example, smoothness, lightness, tensity, etc., do not constitute the nature of a body is generally admitted, and appears from the very fact that they are called secondary and therefore arise from others which are constitutive, and also because there is not one of them which cannot be absent from a body. It remains therefore to seek some sensible quality which occurs in all bodies and only in bodies and by which men may distinguish body from nonbody, as if by a criterion. Beyond any doubt this is mass or antitypy, together with extension. For whatever men sense as extended, they do not at once call it a body, for they sometimes consider it a mere appearance or phantasm - thought it is in fact always a body and has antitypy, even when this quality may appear to our intellect only, not to our senses. But they do call a body what they not only see but also touch, that is, what they discover has antitypy, and they deny this name to whatever lacks antitypy. Whether learned or ignorant, therefore, men find that the nature of body consists in two things - extension and antitypy together. The former we derive from sight, the latter from touch, and by the combination of both senses we usually ascertain that things are not phantasms. To be extended, however, is nothing else but to be in space, and antitypy is the impossibility of being in the same space with another thing, but one or the other having to move or be at rest. The nature of body therefore evidently is constituted by extension and antitypy, since there is nothing in things without a cause, and nothing ought to be supposed in bodies whose cause cannot be discovered in their first or constitutive principles. But this cause cannot appear unless these principles are well defined. ThereFor references ;'ee p. 103
102 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS fore we can assume nothing in bodies which does not follow from the definition of extension and antitypy. But from these concepts are derived only magnitude, figure, situation, number, mobility, etc. Motion itself is not derived from them. Hence there is no motion, strictly speaking, as a real entity in bodies. I have demonstrated, instead, that whatever moves is continuously created and that bodies are something at any instant in assignable motion, but that they are nothing at any time midway between the instants in motion - a view that has never been heard of until now but which is clearly necessary and will silence the atheists. Hence it is clear that the explanation of all qualities and changes must be found in magnitude, figure, motion, etc., and that heat, color, etc., are merely subtle motions and figures. As for the rest, I venture to assert that atheists, Socinians, naturalists, and skeptics can never be opposed successfully unless this philosophy is established. I believe this philosophy is a gift of God to this old world, to serve as the only plank, as it were, which pious and prudent men may use to escape the shipwreck of atheism which now threatens US. 22 Though my acquaintance with learned men has been very slight and recent, I shudder when I think how many I have met who are at once brilliant thinkers and atheists. An unpublished book by Bodin is being circulated from hand to hand (and like Naude, I wish that it would never be published); a most effective work, which he calls "the secret of sublime things" 23 and in which he is the professed enemy of the Christian religion. The dialogues ofVanini are child's play compared to it. I have read it carefully, and I thank God with all my heart for instructing me in these philosophical defenses, by which I was able easily to tum back his shafts. I should be ungrateful, however, if I denied my debt to you for many of them. The efforts which the enlightened Spizel is once more exerting to eradicate atheism must be praised. I believe you have seen his letter about this argument, which was published at this book fair. Listen to an experience which I had in connection with him. In a period of leisure, but working in the confusion of an inn, I once wrote about two sheets in which I tried to demonstrate, more accurately than usual, the immortality of the soul and the existence of God. I sent these sheets to a friend who passed them on to the reverend Mr. Spener, a pastor in Frankfurt, with their authorship properly concealed. Spener sent them to Spizel, and Spizel recently attached them to the end of his letter to Anton Reiser on the eradication of atheism, with the title Confession of Nature against A theists. 24 I do not disapprove, but I regret that the sketch was printed most incorrectly; the sorites particularly, in which I tried to prove the immortality of the soul, was thrown into great confusion by changing the beginnings of the lines. Spizel admitted that he did not know who the author was. I should appreciate a judgment about the reasoning in the demonstration. I do not seek praise but criticism, since it is in the interest of religion not to be defended perfunctorily. Meanwhile I have already penetrated much more deeply, I think, into both problems, for you wiIl not read there what I have found out since about the perpetual creation involved in motion, and about the innermost nature of a thinking being or a mind. 25 '" For the rest, distinguished Sir, I have discussed this whole matter with you at greater length, because I have no more learned and equitable judge of these things. Since you have thrown light into all the comers of ancient learning, and do not spurn the discoveries of the modems when they are worthy, you alone of all men can best explain them and examine this. For you are right in holding that although new opinions may be offered and their truth most convincingly shown, we ought almost never to depart from
MAINZ AND PARIS, 1666-76 103 the generally accepted terms. If the Scholastics had done this, we would not be in difficulty now. Farewell, ornament of our land, and may you not only complete your lucidly developed theories but publish them. For many ofthem are both conceived and carried through with rare felicity of mind. REFERENCES * The double date at the head of many of Leibniz's letters is to be explained by the calendar reform then being carried out (cf. Introduction, note 1). Following the report of his astronomers, Pope Gregory XIII had directed that 10 days be dropped from the calendar. This was done at once in all Catholic countries, in 1600 in Scotland, in 1700 in the Protestant states of Germany (Leibniz himself helping to bring about the change), but not until 1752 in England. The earlier date is therefore 'old style' (in use in Protestant countries in general, though not in Germany after 1700), the latter 'new style', in Catholic countries. Leibniz was in this case in Catholic Mainz, Thomasius in Protestant Leipzig. 1 See below, note 18. 2 Joseph Glanvill's Plus ultra. or the Progress and Advancement of Knowledge since the Days of Aristotle, appeared in 1668. Leibniz in 1679 adopted the title tentatively for his encyclopedia. 3 In his preceding letter Thomasius had mentioned a certain Baghemin of Stettin, who had asked the theological and philosophical faculties for a criticism of his new philosophy (G., I, 14). 4 The 1670 version reads: "Who would disagree with your judgment on the opinion that considers God as the primary matter of the world?" 5 In the 1670 version Spinoza is removed from the list of Cartesians, and Galileo added to and van Hoghelande removed from the non-Cartesians. 6 Leibniz uses the Greek title nepi </>vulTdi<; OxpOrxU8Wr;. 7 Guericke's demonstration of the vacuum had taken place in 1654 and was well known, though Leibniz, in corresponding with him in 1671, was still urging publication of his discovery. 8 Leibniz's term is massa; thus Mach (The Science of Mechanics, 5th ed., p. 366) is in error in saying that he used this term only in 1695 and "probably borrowed it from Newton". His use is not, of course, Newtonian, though both men vary in their use of the term, sometimes regarding it as synonymous with matter, sometimes using it as a specific measure of a physical property. Note, however, that Leibniz uses it to mean extension and antitypy or impenetrability; he has not yet adopted Kepler's and Galileo's definition of mass as essentially inertia (cf. E. Hoppe, Geschichte der Physik, Munich 1913, p. 61). The term tlV'rl'rvnia is a permanent favorite of Leibniz's. It was used for hardness by Plutarch and Sextus Empiricus. 9 Metaphysics 1068b;Physics 231a21f. 10 In a marginal note to the 1670 version Leibniz says, "Conring said the contrary." The letter to Conring, given in No. 18, alludes to this misunderstanding. 11 For Aristotle's analysis of motion see Physics viii and Metaphysics xii. 12 The figure of the city's perspectives is one of the most happy of Leibniz's figures; it is not usually recognized that the view from the tower represents an absolute essence. The distinction between the essence of a substance and its qualities, or between essence and modes, is basic in Leibniz's logic and metaphysics, supporting his use of an intentional logic and his doctrine of substance. 13 Jean de Raey (d. 1702) had tried to synthesize Aristotle and Descartes in his Clavis philosophiae naturalis seu introductio ad naturae contemplationem Aristotelico-Cartesianam (1654). Thomasius had implied (G., 1,12) that Leibniz was influenced by him. 14 The works referred to are Julius Caesar Scaliger, Exotericarum exercitationum liber (1537) (a criticism of Cardan); Kenelm Digby (1603-65), Demonstratio immortalitatis animae ratio-
104 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS na/is (1664); Thomas White (or Albus, Anglus, Candidus) (1582-1676), Institutiones peripateticarum ad mentem summi c1arissimique philosophi Kene/mi Equitis Digbaei (1646); Erhard Weigel (1625-99), Analysis Aristotelica Euclidea (1658) (Weigel had been Leibniz's teacher at Jena and influenced his mathematical ideas greatly); Abdias Trew (1597-1669), Directorium mathematicum (1657). On Scaliger see below, p. 130, note 3. 15 In Leibniz's mature thougllt substantial forms are active principles, but he frequently says that he returned to them after a mechanistic period in which he had abandoned them. And he does not, like the Scholastics, ascribe them to inorganic bodies. Insofar as he substantializes form (i.e., figure) in this letter, it amounts to an extension of the concept of substance to include geometric form; this is therefore a rejection of the Scholastic usage, but not like his later theory. See also No.5, III, and p.120, note 18. 16 The sentence thus far is omitted in G., I, 23, but restored in the 1670 version (G., IV, 170). 17 Reading esse for ese (G., I, 23). 18 The following 15 lines in G., I, 23-24, were received by Thomasius himself in a corrupted form, as his marginal notations, according to Erd., indicate. They were omitted in the 1670 edition and are omitted here. 19 Following the version of 1670. 20 This sentence is omitted entirely from G., I, 25. Leibniz's criticism of active principles in inorganic nature, here directed at the Scholastic theory of substantial forms, as well as against Thomas Campanella (1568-1639), De sensu rerum et magia Iibros quattuor (1620), and Marcus Marci of Kronland (1595-1667), Philosophia vetus restituta (1662), is continued throughout his later writings. Campanella, Marcus Marci, and Scaliger all advocated creative ideas or powers of some kind in nature. 21 Reading vel (1670) for et (1669). 22 In the 1670 version Leibniz completes the paragraph from this point as follows: "I have argued this matter in an extemporaneous sketch which I put in the hands of Theophilus Spizel. Thougll it did not deserve it, he sewed it, like a tattered patch on royal purple, to his recently published letter to Reiser on the eradication of atheism, with the title, A Confession of Nature against Atheists" (cf. No.5, I). 23 Jean Bodin's Colloquium heptaplomeres de abditis rerum sublimium arcanis, a dialogue on religious tolerance, was not published until 1857. Leibniz's wish was thus almost fulfilled. His later judgment on the work was more favorable (Guh. L., I, Notes, p. 14). 24 See No.5, I. Philipp Jacob Spener (1635-1705) was one of the founders of pietism, a pastor in Frankfurt after 1666, where he founded the Collegia Pietatis in 1670. He was later famous as pastor of the Nicolaikirche in Berlin. Theophilus Spizel (1639-91) was a Lutheran clergyman and scholar. 25 Leibniz's theory of 'continuous creation' here seems merely to mean the source of all motion in God and is therefore very similar to the Cartesian opinion which he later criticized (cf. to De VoIder, No. 55, I), A short paragraph alluding to obscure current events is omitted.
4 LETTER TO THOMAS HOBBES July, 1670 Hobbes's early influence on Leibniz is conspicuous, though Couturat has adequately refuted Tonnies' effort to trace his logical method back to the English thinker (Cout. L., pp. 457-73). Leibniz was much impressed by both the De corpore and the De cive but sought to supplement them, the former with an Elementa de mente, the latter with a theological arguments for justice as the will ofthe most powerful, namely God. Leibniz's youthful and flattering attempt to begin an exchange of letters failed, both at this time and later when he tried again in Paris. The letter presents his opinions about Hobbes in exaggerated form but is of interest also for his physical views at a period between that of the letter to Thomasius (No.3) and the Theory of Abstract Motion of 1671. [G., VII, 572-74]1 Mainz, July 13/22, 1670 Most esteemed Sir, To my great delight I recently learned from the letters of a friend visiting in England that you are still alive and in full health at so great an age. Hence I could not refrain from writing. If my doing so is inopportune, you can punish it by silence; for me it will still suffice to have given witness of my feeling. I believe I have read almost all your works, in part separately and in part in the collected edition, and I freely admit that I have profited from them as much as from few others in our century. I am not given to flattery, but everyone who has had the privilege of following your writings on the theory of the state will acknowledge, as I do, that nothing can be added in such brevity to its admirable clearness. There is nothing more polished and better adapted to the public good than your definitions. Among the theorems which you deduce from them there are many which will remain established. There are some who have abused them, but I believe that in most cases this occurred because the right principles of application were ignored. If one were to apply the general principles of motion - such, for example, as that nothing begins to move unless it is moved by another body, that a body at rest, however large, can be impelled by the slightest motion of a moving body, however small, and others - if one were to apply these by an ill-timed leap to sensible things, he would be derided by the common man unless he had demonstrated in advance, and to minds prepared for it, that for the most part bodies which seem to be at rest are insensibly in motion. Similarly, if one were to apply what you have demonstrated about the state and republic to all groups which are commonly called by that name, and what you attribute to the supreme power to all who claim for themselves the name of king, prince, monarch, or majesty, and your views about complete freedom in the state of nature to all cases in which citizens of different states transact certain affairs among themselves; then, ifl am not mistaken, he too would be very much in error about For references see p. 107
106 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS your opinion. For you acknowledge that there are many communities on earth which are not one state but a confederation of many and that there are many titular monarchs to whom others have never transferred their will. Nor will you deny that, assuming a ruler of the world, there can be no purely natural state of man which would place him beyond the pale of any community, since God is the common monarch of all; and that certain men are therefore wrong in ascribing license and impiety to your hypotheses. As I have said, I have always understood your works in this way, and I acknowledge that I have received great light from them in carrying out a work on rational jurisprudence on which I am collaborating with a friend. For I observed the unbelievable subtlety and soundness of expression with which the Roman jurisconsults gathered their answers which are preserved in the Pandects - qualities in which your own writings strongly resemble theirs. I realized that a large part of them were arrived at almost entirely by demonstration from the law of nature alone and that the rest were deduced with the same degree of certainty form a few principles which were arbitrary, it is true, but drawn from the practice of the Republic. When I first set my feet in the paths of jurisprudence, therefore, I began four years ago to work out a plan for compiling in the fewest words possible the elements of the law contained in the Roman Corpus (in the manner of the old Perpetual Edict), so that one could, so to speak, finally demonstrate from them its universal laws. There are many laws which will prove refractory to this method, especially in the Imperial Rescripts,because they do not belong to natural law. However, these are clearly discernible among the rest and will be counterbalanced by the multitude of the others - especially since I venture to assert that half of the Roman law is mere natural law. And it is well known that almost all of Europe uses this law wherever it has not been distinctly invalidated by local custom. But I must confess that I sometimes vary these long and tedious concerns with other more pleasant ones, for I also have the habit of sometimes meditating upon the nature of things, though this is like being carried into a foreign world. I have been thinking about the abstract principles of motion, where the foundations which you have laid seem to me remarkably justified. I agree absolutely with you that one body is not moved by another unless the latter touches it and is in motion and that, once begun, every motion continues unless impeded by something. Yet I confess that there are certain matters about which I have hesitated, especially about this: I have not found that you account clearly for the cause of consistency, or what is the same thing, of cohesion in things. For if, as you seem somewhere to suggest, reaction is the sole cause of cohesion, there will be a reaction even without an impact, since reaction is motion in opposition to a pushing body, but the impact does not produce the opposition to itself.2 But reaction is a motion of the parts of a body from its center outward to its circumference. This motion is either unimpeded or impeded. If unimpeded, the parts of the body will move outward and so depart from the body to which they belong, which is contrary to experience. If impeded, the motion of reaction will stop unless it is revived by external help of a kind which you do not generally find here. I do not mention that it can hardly be explained what cause it is that moves any single body to strive [eonor] from center to circumference in every sensible point, or how the reaction of the body struck can alone be the cause of the impetus of the rebound increasing with the impetus of the striking body - while it would be consistent with reason for a greater impetus of incidence to diminish the reaction. But perhaps these small doubts of
MAINZ AND PARIS, 1666-76 107 mind have arisen because I do not sufficiently understand your views. I should think that the conatus of the parts toward each other, or the motion through which they press upon each other, would itself suffice to explain the cohesion of bodies. For bodies which press upon each other are in a conatus to penetrate each other. The conatus is the beginning; the penetration is the union. 3 But when bodies begin to unite, their limits or surfaces are one. Bodies whose surfaces are one, or ra 8uxara 8V\ are according to Aristotle's definition not only contiguous but continuous, and truly one body, movable in one motion. You will recognize that, if there is any truth in these thoughts, they will change many things in the theory of motion. It remains for me to show that bodies which press upon each other are in a conatus to penetrate. To press is to strive into the place hitherto occupied by another body. Conatus is the beginning of motion, and therefore the beginning of existence in the place into which the body is striving. To exist in a place in which something else exists is to have penetrated it. Therefore pressure is the conatus of penetration. But there can hardly by anyone more accurate in examining demonstrations than are you, distinguished Sir, and you will judge these matters more exactly. 5 ••• For the rest, I wish that we might hope for a kind of collection of your thoughts from the publication of your works up to the present time, especially since I have no doubt that you have reasoned out the principles involved in so many of the new experiments which you and doubtless many other men of genius have produced in recent years - principles which it would be in the interest of mankind not to lose. I wish also that you had expressed yourself more distinctly about the nature of mind. For though you have rightly defined sensation as a permanent reaction, as I said a little earlier, there is no truly permanent reaction in the nature of mere corporeal things. It only appears so to the senses but is in truth discontinuous and is always stimulated by a new external cause. So I fear that when everything is considered, we must say that in beasts there is no true sensation, but only an apparent one, any more than there is pain in boiling water; and that true sensation such as we experience in ourselves cannot be explained by the motion of bodies alone - especially since you never demonstrate, so far as I know, the proposition which you use so often, to the effect that every mover is a body. 6 But I am burdening you too long with my trifles! I shall stop now, since my witness has been given. And I shall always profess, both among friends and, God willing, also publicly (since I am myself a writer), that I know no one who has philosophized more exactly, clearly, and elegantly than you, not even excepting that man of divine genius, Descartes himself. I wish that you, my friend, who of all mortals could best do it, had taken into consideration what Descartes attempted rather than accomplished - that you had ministered to the happiness of mankind by confirming the hope of immortality. May God preserve you still a very long time to achieve this task. REFERENCES This is the text copied by F. T6nnies from the original letter in the British Museum. The text in G., I, 82-85, is inaccurate. 2 Hobbes's discussion of the reaction of bodies in impact is in the De corpore, Book III, chap. XV, Sec. 2, thought he does not, as Leibniz implies, explain cohesion by means of it. a We have retained the original term conatus, though Hobbes himself rendered it 'endeavor'. 1
108 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Like Hobbes, Leibniz at first identifies it with minimal motion; only much later, after his own distinction between force and motion, does it become 'dead force'. 4 Seep. 103, note 9. 5 A short paragraph on the origin of springs is omitted. 6 The denial of sensation to the lower animals suggests a Cartesian influence; Leibniz soon drops it, however, for the view expressed in 1671 that there is a striving in all being but that its essential combination with memory or reflection becomes the distinguishing feature of mind as against matter (cf. No.7, I, Sec. 17, and No. 10).
5 THEOLOGICAL WRITINGS RELATED TO THE CATHOLIC DEMONSTRATIONS 1668-70 Leibniz's concern with theology was greatly stimulated by the Roman Catholic pietism of the court at Mainz. In this early period his chief theological interests were to prove the existence of God, to justify his ways with men, to establish the proofs of immortality, and to demonstrate the essential agreement of Catholic and Protestant doctrines of the Eucharist. Both law and physics were held to support theology, law deriving its ultimate base from the divine harmony, and the nature of bodies, their cohesion and motion, providing an infallible demonstration of the existence ofimmaterial order and power. The project of a definitive apology for Christianity, to be called the Demonstrationes Catholicae, arose out of discussions with Baron Boineburg in 1669 or 1670 and was later revived at Hanover in 1679. 1 As planned in 1669, this work was to consist of a series of philosophical prolegomena and four parts. The prolegomena were to include logic, metaphysics, physics, and practical philosophy. The parts were to deal in order, with the demonstrationfor the existence of God, the demonstration of immortality, the proof of the Christian mysteries, and a demonstration of the authority of the church and scripture. Leibniz's turn to Platonism at this time is reflected in his summary of the proposed chapter Ii of Part III, which also refutes the common charge that his concern with religion was purely political in motive: "The beatific vision or intuition of God face to face is the contemplation ofthe universal harmony of things, because God or universal mind is none other than the harmony of things or the principle ofbeauty within them." 2 The occasion for writing the first of the three following selections is given in the letter to Thomasius (No.3). The proof of the existence of God may be compared with that in No.1, l. The other two selections are probably preliminary studies intended for Parts II and III of the Catholic Demonstrations, respectively, included here for their bearing on Leibniz's psychology and his doctrine of ideas. I. THE CONFESSION OF NATURE AGAINST ATHEISTS 1669 [G., IV, 105-10] Part l. That Corporeal Phenomena Cannot Be Explained without an Incorporeal PrinCiple, That Is God Francis Bacon of Verulam, a man of divine genius, has rightly said that casually sampled philosophy leads away from God but that drunk more deeply, it leads back to him.3 This is confirmed in our own century, which is fruitful alike of science and of impiety. For through the admirable improvement of mathematics and the approaches which chemistry and anatomy have opened into the nature of things, it has become For references see p. 119
110 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS apparent that mechanical explanations - reasons from the figure and motion of bodies, as it were - can be given for most of the things which the ancients referred only to the Creator or to some kind (I know not what) of incorporeal forms. The result was that truly capable men for the first time began to try to save or to explain natural phenomena, or those which appear in bodies, without assuming God or taking him into their reasoning. Then, after their attempt had met with some little success, though before they arrived at foundations and principles, they proclaimed, as if rejoicing prematurely at their security, that they could find neither God nor the immortality of the soul by natural reason, but that in these matters faith must rest either on civil laws or on historical records. This was the judgment of the most acute Mr. Hobbes, whose great discoveries should earn for him our silence on this matter if his authority had not explicitly affected this view for the worse. Unfortunately there are others who have gone even further and who now doubt the authority of the sacred scriptures and the truth of history and the historical record, thus bringing an unconcealed atheism into the world. It seemed to me unworthy for our mind to be blinded in this matter by its own light, that is, by philosophy. 1 began therefore myself to undertake an investigation, and alI the more vigorously as 1 became more impatient at being dispossessed by the subtleties of these innovators of my life's greatest good, the certainty of an eternity after death and the hope that divine benevolence would sometime be made manifest toward the good and the innocent. Setting aside all prejudices, therefore, and suspending the credit of scripture and history, 1 set my mind to the anatomy of bodies, to see whether the sensory appearance of bodies can be explained without assuming an incorporeal cause. At the beginning 1 readily admitted that we must agree with those contemporary philosophers who have revived Democritus and Epicurus and whom Robert Boyle aptly calls corpuscular philosophers, such as Galileo, Bacon, Gassendi, Descartes, Hobbes, and Digby, that in explaining corporeal phenomena, we must not unnecessarily resort to God or to any other incorporeal thing, form, or quality (Nec Deus intersit, nisi dignus vindice nodus inciderit) 4 but that so far as can be done, everything should be derived from the nature of body and its primary qualities - magnitude, figure, and motion. But what if 1 should demonstrate that the origin of these very primary qualities themselves cannot be found in the essence of body? Then indeed, 1 hope, these naturalists will admit that body is not self-sufficient and cannot subsist without an incorporeal principle. 1 will prove this without obscurity or detours. For if these qualities cannot be derived from the definition of a body, they obviously cannot exist in bodies left to themselves. Every reason for an affection must be derived either from the thing itself or from something extrinsic to it. But a body is defined as that which exists in space. All men call what they find in some space a body, and conversely, they find what they call a body in space. s This definition consists of two terms, 'space' and 'to exist in'. On the term 'space' are based the magnitude and figure of a body, for a body has the same magnitude and figure as the space which it fills. But there remains a doubt as to why it fills this much space and this particular space rather than another; for example, why it should be three feet long rather than two, or why square rather than
MAINZ AND PARIS, 1666-76 111 round. This cannot be explained by the nature of bodies themselves, since the same matter is indeterminate as to any definite figure, whether square or round. Therefore only two replies are possible. Either the body in question must be assumed to have been square from all eternity, or it has been made square by the impact of another body - if, that is, you refuse to resort to an incorporeal cause. If you say it has been square from all eternity, you give no reason for it, for why should it not have been spherical from all eternity? Eternity cannot be considered the cause of anything. But, if you say that it was made square by the motion of another body, there remains the question of why it should have had any determinate figure before such motion acted upon it. And if you refer the reason for this, in turn, to the motion of another body as cause, and so to infinity, each of your replies wiII again be followed by a question through all infinity, and it wiII become apparent that this basis for asking about the reason for each reason will never be removed, so that no full reason for the figure wiII ever be given. Therefore it appears that the reason for a certain figure and magnitude in bodies can never be found in the nature of these bodies themselves. We said that the definition of a body has two terms - 'space' and 'existence-in' - and that though the term 'space' involves some magnitude and figure, it does not involve a determinate magnitude and figure. Motion pertains to existence-in-this-space, for when a body begins to exist in a different space than it did before, this very fact implies that it is moved. Considering the matter more accurately, however, it becomes clear that mobility arises from the nature of a body but that motion itself does not. Since the body is in this space, it can also be in another space equal and similar to the first, that is, it can be moved. For to be able to be in another space than at first is to be able to change space, and to be able to change space is to be movable. For motion is change of space. Actual motion, however, does not arise from existence-in-space; this involves rather the contrary when a body is left to itself, namely, permanence in the same space, or rest. Therefore no reason for motion can be found in bodies left to themselves. Hence it is futile to try to escape as do those who give the following reason for motion: that every body either moves from all eternity or is moved by another body which is contiguous to it and in motion. For if they say this body moves from eternity, there is no clear reason why it should not rather have rested from all eternity, since time, even if infinite, cannot be thought of as a cause of motion. But if they say that this body is being moved by another body contiguous to it and in motion, and this again by another, and so without end, they still have given no reason for the first, and second, and third, or anyone whatever being moved, as long as no reason is given for the consequents being moved, which does not also apply to all the antecedents being moved. For the reason for a conclusion is not fully given as long as no reason is given for the premise, especially since the same doubt remains in this case without end. Thus it has been sufficiently demonstrated, I think, that there can be no determinate figure and magnitude, or any motion whatever, in bodies left to themselves. Because it is a matter for further investigation, I shall remain silent here on the question of whether anyone has heretofore derived the firmness of bodies from their nature itself. By the firmness of bodies we mean (1) that a large body does not give way to a small one which pushes it; (2) that bodies or their parts cohere with each other, this being the basis for those tactile qualities commonly called secondary, namely solidity and fluidity, hardness and softness, smoothness and roughness, tenacity and fragility, For references see p. 119
112 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS friability, ductility, malleability, and fusibility; and (3) that a hard body is reflected when it strikes another which does not give way. In brief, three properties constitute firmness: resistance, cohesion, and reflection. I shall be glad to call anyone a great philosopher who can explain these by means of the figure, magnitude, and motion of bodies. There appears to be only one way - to assume that a body resists another which strikes it, and rebounds from the blow, because its surface parts are insensibly moved in the collision. But let us assume that the striking body approaches the other, not along the line in which the parts of the body are to meet the blow, but in another, perhaps oblique to it; then according to this view all reaction, resistance, and reflection will cease at once, which is contrary to experience. But cohesion clearly cannot be explained through reaction and motion. If I push part of a paper, the part which is pushed gives way; therefore no reaction or motion of resistance can be assumed. But not only does it give way; it also carries with it the remaining parts which adhere to it. It is indeed truly and with good reason that Democritus, Leucippus, Epicurus, and Lucretius of old, and their modem followers, Peter Gassendi and John Chrysostum Magnenus, asserted that the whole cause of cohesion in bodies may be explained naturally through the interweaving of certain shapes such as hooks, crooks, rings, projections, and in short, all the curves and twists of hard bodies inserted into each other. But these interlocking instruments themselves must be hard and tenacious in order to do their work of holding together the parts of bodies. Whence this tenacity? Must we assume hooks on hooks to infinity? Yet whatever reason there is for questioning this in the first case will exist also in the second and third, and so without end. There remains only one answer which these most subtle philosophers can make to such objections; they may assume certain indivisible corpuscles, which they call atoms, as the ultimate elements of bodies, which, by their varied shapes, variously combined, bring about the various qualities of sensible bodies. But no reason for cohesion and indivisibility appears within these ultimate corpuscles. The ancients offered one, but it was so inept that their recent followers are ashamed of it, namely, that the parts of atoms cohere because no vacuum comes between them. From this it would follow that all bodies, once they touch each other, ought to cohere inseparably in the manner of atoms, since there can be no intervening vacuum when any two bodies touch. Nothing is more absurd than such perpetual cohesion or more foreign to experience. In explaining the atoms, we may therefore rightly resort to God, who endows with firmness these ultimate elements of things. I marvel that neither Gassendi nor any other of these most acute philosophers of our century has noticed this excellent opportunity to demonstrate the divine existence. For through the ultimate analysis of bodies, it becomes clear that nature cannot dispense with the help of God. But since we have demonstrated that bodies cannot have a determinate figure, quantity, or motion, without assuming an incorporeal being, it readily becomes apparent that this incorporeal being is one for all because of the harmony of things among themselves, especially since bodies are moved not individually by this incorporeal being but by each other. But no reason can be given why this incorporeal being chooses one magnitude, figure, and motion rather than another, unless he is intelligent and wise with regard to the beauty of things and powerful with regard to their obedience to his command. Therefore such an incorporeal being will be a mind ruling the whole world, that is, God.
MAINZ AND PARIS, 1666-76 113 Part II. The Immortality of the Human Mind, Demonstrated in a Continuous Sorites The human mind is a being, one of whose actions is thinking. If one of the actions of a being is thinking, one of its actions is immediately perceptible, without supposing parts in it. For thought is (1) a thing that is immediately perceptible, mind being immediate to itself when it perceives itself thinking. (2) Thought is a perceptible thing without awareness of parts. This is clear from experience. For thought is that 'something, I know not what' which we perceive when we perceive what we think. But when, for example, we perceive that we have thought of Titius, we not only perceive that we have the image of Titius in our mind, for this has parts, of course; such an image is not enough for thinking. For we have images in the mind even when we do not think of them, but we perceive, besides, that we have been aware of this image of Titius, and in this awareness of our images itself we find no parts. 6 Assume a being performing a certain action which is immediately perceptible, without a perception of its parts. Then this certain action is a thing without parts; For a quality immediately perceived in a thing actually belongs to it, since: The cause of error is the medium, for if an object of perception were the cause of error, it would always be perceived falsely; if the subject were the cause, it would always perceive falsely. If something has for one of its constituents a thing without parts, then one of its actions must be other than motion; For all motion has parts, by Aristotle's demonstration and common agreement. A being whose action is not motion is not a body; For all bodily action is motion, since every action of a thing is a variation of its essence, and the essence of a body is being in space. But motion is a variation of existence in space. Therefore every action of a body is motion. Whatever is not a body is not in space; for to be in space is the definition of a body. Whatever is not in space is not movable, for motion is change of space. Whatever is immovable is indissoluble, for dissolution is the motion of a part. Everything indissoluble is incorruptible, for corruption is internal dissolution. Everything incorruptible is immortal, for death is corruption of the living, or dissolution of its fabric, through which self-moving things obviously move themselves. Therefore the human mind is immortal. Q.E.D. II. A FRAGMENT ON DREAMS 7 [PA., VI, ii, 276-78] The power of persuasion consists sometimes in giving reasons, sometimes in moving the affections, and sometimes, at the heart of both of these as it were in the art of attracting attention. This consists in certain distinct rules. For we do not carry out most of the things which we know, because we do not pay attention between our actions. But attention is nothing but reflection. For references see p. 119
114 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Sleep differs from waking in that when we are awake everything is directed, at least implicitly, toward an ultimate goal. But in dreaming there is no relation to the whole of things. Hence to wake up is nothing but to recollect [reeolligere] one's self, to think as follows: Die cur hie? Sich besinnen. 8 To begin to connect your present state with the rest of your life or with you yourself. Hence we have this criterion for distinguishing the experience of dreaming from that of being awake - we are certain of being awake only when we remember why we have come to our present position and condition and see the fitting connection of the things which are appearing to us, to each other, and to those that preceded. In dreams we do not grasp this connection when it is present, nor are we surprised when it is absent. It is to be noted, however, that now and then the dreamer himself observes that he is dreaming, yet the dream continues. Here he must be thought of as if he were awake for a brief interval of time, and then, once more oppressed by sleep, returned to his previous state. It is also to be noted that some men can wake themselves up, and it is a familiar experience of mine that, when some pleasing vision presents itself, I notice that I am dreaming and try my eyes and pull them open with my fingers to admit the light. We should also think about the cause of sensations of falling out of bed, which are popularly ascribed to lapses into sin, and which occur sometimes, and to some people, almost between the limits of sleep and waking, so that they are suddenly awakened at the very moment of falling asleep. Sometimes when this has happened to me, I can scarcely persuade myself to fall asleep all night. For in the first moment of falling asleep, I suddenly recollect myself and, sensing this fact, leap up. Nor ought we to overlook the spontaneous ejection of semen without any contact in sleep; in wakers it is expelled only when they are strongly agitated, but in sleep the spirits are moved internally by a strong imagination alone and without any rubbing of the members. I have also heard this confirmed by a physician. Hobbes says that everything appears as present in sleep and that therefore there is no judgment or wonder, but only the occurrence of appearances, as of things observed by the eyes when they are awake and not closed. But, you say, surely we often experience judgment or reflection in dreams, or at least a knowledge of the past which involves judgment, for we both deliberate and remember. But I reply that in dreams we do not do this anew, about the appearances as they are presented, but that a judgment presents itself in a dream only if it is a judgment about the presented appearance which comes from an earlier thought and now recurs as a whole, even though we do not know that it contains the earlier thought. For entire conversations occur to us which are certainly not without judgment, and even dialogues and arguments, not because we are now making judgments about them, but because judgments already made recur with the experiences themselves. There is one very remarkable thing in dreams, for which I believe no one can give a reason. It is the formation of visions by a spontaneous organization carried out in a moment - a formation more elegant than any which we can attain by much thought while awake. To the sleeper there often occur visions of great buildings which he has never seen, while it would be difficult for me, while awake, to form an idea of even the smallest house different from those I have seen, without a great amount of thought. I wish I could remember what marvelous discourses, what books and letters, what poems beautiful beyond all doubt, but never previously read, I have read in dreams without my shaping them at all, just as if they had just been composed and offered to
MAINZ AND PARIS, 1666-76 115 my sight. This is known: Hac sunt in fossa Bedae Venerabilis ossa. 9 The dream of a poetic monk substituted this word for the unfitting word presbyter. Noteworthy, too, is what Colomesius tells in his lesser works about a song which Gaulminus dreamed about the immortality of the soul. I do not believe that there is a mortal man who would not confess to me that there have often occurred to him while he dreamed, spontaneously and as if made in a moment, elegant visions and skilfully fashioned songs, verses, books, melodies, houses, gardens, depending upon his interests - visions which he could not have formed without effort while awake. Even such unnatural things as flying men and innumerable other monstrosities can be pictured more skilfully than a waking person can do, except with much thought. They are sought by the waker; they offer themselves to the sleeper. There must therefore necessarily be some architectural and harmonious principle, I know not what, in our mind, which, when freed from separating ideas by judgment, turns to compounding them. 10 A reason must be given why we do not remember waking experiences in a dream but do remember the dream when awake. III. ON TRANSUBSTANTIATION 1668(7) [PA., VI, i, 508-12] With the help of God, we have undertaken to show the possibility of the transubstantiation of bread and wine into the body of Christ who suffered for us, which the Catholic church teaches occurs at the time of consecration. It is to be demonstrated, accordingly, that: 1. Bread and wine, losing their own substance, acquire the substance of Christ's body; 2. and become everywhere numerically identical with it, 3. only their appearance or accidents remaining; 4. the substance of Christ's body being present in all places where the appearance of consecrated bread and wine exists. This proof depends on the interpretation of the terms 'substance', 'appearances' or 'accidents', and 'numerical identity', which we develop on the basis of their meanings as accepted by the Scholastics, but which we explain clearly. (I) 1. Substance is being which subsists in itself. 2. Being which subsists in itseljis that which has a principle of action within itself. Taken as an individual, being which subsists in itself, or substance (either one), is a suppositum. In fact, the Scholastics customarily define a suppositum as a substantial individual. Now actions pertain to suppositaY Thus a suppositum has within itself a principle of action, or it acts. Therefore a being which subsists in itself has a principle of action within it. Q.E.D. 3. If that which has a principle of action within itself is a body, it has a principle of motion within itself. Every action of a body is in fact motion, because every action For references see p. 119
116 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS is a variation of essence. So every action of a body is a variation of the essence of body. But the essence or definition of a body is being in space. Accordingly a variation in the essence of body is a variation of existence in space. But variation of existence in space is motion. Thus every action of a body is motion. Q.E.D .... 4. No body has a principle of motion within itself apart from a concurrent mind. This has been demonstrated in Part I of the Catholic Demonstrations, where the existence of God is proved. 5. Therefore no body is to be taken as substance, apart from a concurrent mind. 6. Whatever is not substance is accident or appearance. 7. Hence body is accident or appearance apart from a concurrent mind. 8. Something is substance when taken together with a concurrent mind; something taken apart from concurrent mind is accident. Substance is union with mind. Thus the substance of the human body is union with the human mind, and the substance of bodies which lack reason is union with the universal mind, or God. The idea is the union of God with creature. 12 9. Thus the substance of body is union with a sustaining mind. 10. That whose substance is in its union with a concurring mind is transsubstantiated when its union with the concurring mind is changed. 12.'3 Hence bread and wine as bodies, when the concurrent mind is changed, are substantiated into the body of Christ, or taken up by Christ (inasmuch as the special concourse of the mind of Christ which takes on the bread and wine, in addition to its body, is substituted for the general concourse of the universal or divine mind with all bodies). Q.E.D. (II) 13. If a body consecrated and appropriated by the mind of Christ has the same concurrent mind as the glorious body of Christ who suffered for us, 14. it has numerically the same substantial form or the same substance as the body of Christ who suffered for us, by No.9. 15. Accordingly the bread and wine in transubstantiation are the numericaIly identical substance as the body of Christ who suffered for us. Q.E.D. (III) 16. A body which is thus transubstantiated is changed in no way except in the substantial form or idea of the concurring mind, by No.9. 17. That in which nothing is changed except the concurrent mind can retain all its qualities or accidents or, if you prefer, species. For mind is compatible with all accidents which do not receive or lose essence through it, but only action. 18. Therefore all accidents or species are preserved in the transubstantiated bread and wine; extension, firmness, color, odor, etc., can remain. Q.E.D. (IV) 19. AIl mind lacks extension. See the Catholic Demonstrations, Part II. 20. Whatever lacks extension is not coextensive with space. '4 21. Whatever is not coextensive with space is not in a place by itself. 22. Mind is therefore not in a place by itself. 23. Mind acts upon a body which is in space.
MAINZ AND PARIS, 1666-76 117 24. To this degree, therefore,itcan be said to be in space by operation. St. Thomas. 1S 25. Every action of a mind is thought. 26. Mind can think many things together. 27. Therefore mind can by its action be in many places at once. 28. Therefore the mind of Christ can impart operation, action, or subsistence both to the glorious body of Christ and to the species of consecrated bread and wine, at the same time, and in varying cases in various p laces on the earth. 29. Hence the mind of Christ can be present everywhere in the species of consecrated bread and wine. 30. The mind of Christ, concurring in his glorious body which suffered for us, is his substance, by No.9. 31. Therefore the substance of the glorious body of Christ can be present everywhere in the species of bread and wine. Q.E.D. These theorems of ours differ very little from the accepted philosophy. In Aristotle, nature is the principle of motion and of rest. But substantial form is properly nature in the same philosopher. Hence Averroes, Angelus Mercenarius, and Jacob Zabarella also assert that substantial form is the principle of individuation. Those who locate the nature of subsistence in the union of matter and form, like Murcia, agree with this as well. 16 ••• Our Scholastics will be embarrassed, I believe, not by the contents of this but by the words. I seem to hear them speaking as follows: "What? You who presume to demonstrate the possibility of transsubstantiation, do you expect to satisfy the Church with terms chosen at your own pleasure? After all, you must use the terms 'substance', 'transubstantiation', 'accident', 'species', and 'identity' in that sense which the Council of Trent is believed to have favored, and there is no doubt that this council favors that which the chorus of Scholastics has observed. Unless you adhere to this, you deserve the sentence of the Church; you show the mind of a heretic." Right, 0 Scholastics! But your warning is too late, since I have already done what you require. For neither my conception of identity, nor that of transsubstantiation, nor of accident or species is an innovation. This from the preceding demonstration. For I demonstrate the numerical identity of substance from the numerical identity of substantial form, in conformity with the principles of the noblest Scholastic and Aristotelian philosophers, those for whom substantial form is the principle of individuation. 1 ? I define transubstantiation as change of substantial form. I call appearance whatever can be thought of in a real body deprived of substantial form, that is, matter taken with its accidents. I call substance an entity subsisting in itself. An entity which subsists in itself is the same as what the mass of Scholastics mean by suppositum. For a suppositum is a substantial individual - as, for instance, a person is a rational substantial individual - or a certain substance in particular. Moreover, the School has generally established it as a property of suppositum that it is itself denominated by action; hence the rule that actions belong to supposita. It is clear from this that the suppositum, substance, or entity which subsists in itself - which are all the same thingis defined correctly in the Scholastic sense also, as that which has a principle of action within itself, for otherwise it would not act but be an instrument of some agent. From this it follows further that substantial form is itself a principle of action 18; in bodies, of motion. To make the consistency appear even greater, the same interpretation of substantial form follows from another principle of Aristotle and the Scholastics. For For references see p. 119
118 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Aristotle himself, and the noblest of his followers, agreed that substantial form is nature. Nature is the principle of rest and motion. Therefore, even in Aristotle's sense, substantial form is the principle of rest and motion. A different objection will perhaps be made which is not to be despised, namely, that it follows from this hypothesis that there is one substantial form for all bodies, the concurrent divine mind. But this does not follow. For although the divine mind is the same, the concurrent divine mind is not. 19 For the divine mind consists of the ideas of all things. 20 Therefore, since the idea of thing A is one thing, the idea of B another, the result is that one idea of the divine mind concurs with A, another with B. That the composition of ideas does not constitute parts of the divine mind is elsewhere demonstrated with the example of a point. The idea of Plato is therefore the same as the substantial form of Aristotle. From this it is apparent that there is not one substantial form for all bodies but a different one for different bodies, for as the disposition of nature is varied, the form and idea are also varied; the motion and rest of a body derive from this fact. It must be shown from the hypothesis of those who hold matter to be mass [moles] that they do not require it to be a substance, since those who consider matter to be something insensible do require it to be a substance. It is to be demonstrated from the agreement of philosophers that the substance of a thing does not appear to sense. The word 'mind' must therefore necessarily mean something different from that today usurped by sense; otherwise it would appear to sense. 21 The substance of each thing is not so much mind as it is an idea of a concurrent mind. In God there are infinite, really diverse, substances, yet God is indivisible. The ideas of God are the substances, but not the essences, of things. The idea of God is not the substance of things which are moved by mind. In idea there is contained ideally both passive and active potentiality, both active and passive intellect. Insofar as the passive intellect concurs, there is matter in the idea; insofar as the active intellect, there is form. N.B. Bread and wine are not transessentiated but transubstantiated. Somewhere in the breviary it is said that the body of Christ is made bread and wine, but this is metonymy. The language of the Council of Trent must be adhered to rigorously; bread and wine are not substance but substantiated being. It is less than correct to say that man is a substance; this is foreign to the use and nature of the word and a modification of the abstract into the concrete. Therefore it cannot be allowed except by metonymy .... SUPPLEMENT: NOTES ON THE EUCHARIST 1668 [PA., VI, i, 513] This demonstration has a threefold use - to confirm those who think rightly, to attract the rest, and to prove philosophy a useful and necessary beginning for theology. The substance of things is an idea. Idea is the union of God and creatures, so that the action of agent and patient is one. A point is at once common to two lines or intersectors. Most apt of all, an angle is at once center and lines. N.B. There are no ideas in God except as there are things outside of him. Thus a point is not a center except of lines. Now if the substance of things is an idea, and it is asked whether this is everywhere, I reply that it is not everywhere, any more than a
MAINZ AND PARIS, 1666-76 119 creature is elsewhere than in the creator, and that the act of God is in the creature, though God is everywhere. Neither is an angle in all of its sides, although it may be a center of all its sides. It is in this way that the substance of things is in things or appearances. But how God can bring it about that his idea should be in still other places than the appearances, or that it should be a substance in other appearances (for idea or pattern is opposed to examples or instances - this is a question that deserves accurate thought. The ideas of God and the substances of things are the same in fact, different in relation; they are, moreover, as action and passion. However, since the substances of things are the act of God on species, we must think of how it can come about that his act upon one species is numerically the same as his act upon another. But the substance of the body of Christ is its union with Christ, for the substance of everything is its union with mind. Now it is asked how it is possible that the mind of Christ acts in another body than that upon which it ordinarily acts. I reply that God can bring it about that one mind shall be in two bodies when he thinks the same mind or when he thinks of acting immediately upon two bodies. For whatever God can think, that he can also do - at least if he wishes and holds it for the best. ... REFERENCES 1 For the story of the project see the letter to Duke John Frederick of Hanover in 1679 (No. 28). 2 3 4 PA., VI,i,499. Advancement ofLearning, Book I (Spedding and Heath, III, 267-68; cf. I, 436). Horace Ars poet. 191: "And let no god intervene, unless a knot come worthy of such a deliverer" (Fairclough). 5 Leibniz follows Aristotle and the Scholastics in distinguishing always between body (corpus, corps) and matter, and the reader should not confuse the two concepts. Matter is never substance but is known only in abstraction from it. Here it is logically prior to corporeal substance; body is a determinate and bounded quantity of matter. Later, with the distinction between primary and secondary matter, matter is regarded as the passive, resisting aspect of monads and bodies. 6 This is not to be interpreted as an anticipation of Leibniz's later theory of unconscious perceptions, since the inner awareness, internal sense, or reflection of which he speaks is not a condition of consciousness itself. Cf. the discussion of reflection in the next selection. The argument which follows is an adaptation of Plato's old argument for immortality from the indivisible unity of the soul. 7 Part II, chapter III, of the Catholic Demonstrations was to be a demonstration of immortality based on "the wonderful construction of dreams". This selection shows Leibniz's concern for "saving the phenomena" of mental life, as the preceding selection shows his concern also for physical phenomena. 8 "Speak! Why are you here?" "Tc call to one's mind." 9 "In this grave lie the bones of the venerable Bede." 10 The argument for immortality was obviously to rest upon this spontaneously active but unconscious principle in the mind. It points to the law of the individual, from which, in Leibniz's later thought, all the activities and properties of the mind flow. 11 For the late medieval doctrine of suppositum see E. A. Moody, Truth and Consequence in Medieval Logic, Amsterdam 1953. The conception of suppositum, as individual subsistent substance, was established in Suarez, Disputationes metaphysicae, Disp. 34. That actiones sunt
120 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS suppositorum is one of Leibniz's basic metaphysical principles, and the consistency of his pluralism and his logic depends upon his equation of this principle with the doctrine that in a true affirmative propositionpredicatum subjecto inest. Cf. Introduction, Sec. V. 12 The doctrine of ideas stated in the remainder of this selection and in No.6, II, is central in the development of Leibniz's metaphysics (cf. Loemker, 'Leibniz's Doctrine of Ideas', Phil. Rev. 55,1946,229-49). 13 Section 11 is missing in the manuscript. 14 Added note of Leibniz: "At this point it is to be proved, against Descartes, that space and extension really differ from body, because otherwise motion would not be a real thing, and a vacuum would be necessary." 15 Added note by Leibniz: "Ideas are unities of mind and body, as angles are unities of points and lines. Ideas are the same as the substantial forms of things. Thus ideas are in God as all action is in an agent, and as creation is in God. If it is asked whether an idea is created or not, I reply, is the created a creature or not?" 16 An imperfect section of the text, finding authority for the theory of ideas in Plato, Aristotle, Stoics, and Averroes, is omitted. It will be noted that in what follows Leibniz avoids the imputation of Averroeism by a distinction between mind and ideas. 17 Leibniz's departures from Thomism are significant; his view of individuality and of the soul is here Scotistic, though he had earlier rejected Scotus' principle of individuality. The unity of matter as an aggregate is never itself material but logical and mental. The soul itself, in tum, has its own matter, distinct from its body. Scotus seems also to have anticipated Leibniz's distinction between the bases of certainty in truths of reason and truths of fact, as well as his attempt to correct the ontological argument. 18 Cf. p.l04, note 15; this is already a different view of substantial form from that of the letter to Thomasius. 19 Added note by Leibniz: "Therefore it is not changed by the disposition of species to corruption. " 20 Leibniz's note: "St. Thomas also thinks that the sacrament could have been celebrated at the time when the soul of Christ was separate. I do not know whether this is true. Perhaps, however, it could be understood separated from it in the same way that it is now separated from the host, namely, with suspended action." 21 In the Paris notes Leibniz rejects Spinoza's definition of mind as the idea of the body (No. 12). His attempted safeguards here against a monistic trend are later developed in the refutation of Spinoza, Malebranche, and Sturm.
6 PREFACE TO AN EDITION OF NIZOLIUS 1670 (Selections) Leibniz was induced by Boineburg to prepare an edition 0/ a work published in 1553 by the Italian humanist, Marius Nizolius, and entitled On the True Principles of Philosophy, against Pseudo-Philosophers. 1 For this edition he wrote an introduction which he called 'A Preliminary Dissertation on Editing the Works o/Others, on the Scope o/the Work, on Philosophical Diction, and on Nizolius' Errors', but to which he also referred, on the title-page, as 'On the Philosophical Style 0/ Nizolius'. Written in Leibniz's most erudite style, this pre/ace is stuffed with historical and bibliographical allusions, most 0/ which are here omitted. Its permanent interest lies in his discussion 0/ language, particularly philosophical language, his theory 0/ the relation 0/ logic to rhetoric and metaphysics, his theory 0/ induction, and his evaluation 0/ Scholasticism and nominalism. [G., IV, 138-76] ... In general, there seem to me to be three praiseworthy marks of speech - clarity, truth, and elegance. Utility is a property rather of things themselves. That is clear which is well perceived; so speech is clear if the meanings of all its words are known, at least to the attentive. An utterance is true whose meaning is perceived through a right disposition of both the percipient and the medium; for clarity is measured by the understanding, truth by sense. This is the unique and truest definition of truth, from which all the canons of right judgment can be derived, whatever may have been said heretofore. But this must be explained elsewhere; here we will merely make it clear with an example. The sentence, 'Rome is situated on the Tiber', is true for the reason that nothing more is needed to understand what it says than that the sentient being and the medium be in a right relation. The sentient should certainly not be blind or deaf, and the medium or interval should not be too large. If this be granted, and I be in Rome or near it, it will follow that I shall at one glance see the city and the river and realize that this city is situated on this river, and I shall hear the city called Rome and the river called the Tiber. Something similar is true in abstract matters; the sentence, 'The number 2 is even', is true because if! see (or hear, touch, think of) the number 2, I see one and one (by the definition of the number 2 perceived through hearing or reading) and nothing more. Hence I see two parts in the pair, one and one, equal to each other and making up the whole, since one equals one. But a number whose two parts make up the whole and are equal is called even (by the definition of even, perceived through reading or hearing). Therefore, whoever perceives that a given number is 2 perceives that it is even and therefore that the given sentence is true. Speech is elegant if it is pleasant to hear or read. But, since our discussion concerns For references see p. 130
122 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS philosophical discourse and the style which befits it, we shall omit elegance for the present, although we may admit that it can be of great service in securing attention, in moving minds, and in impressing things more deeply on the memory. Only that degree of certainty is to be had which a given matter admits. 2 But even when defined most rigorously, certainty is nothing but the clearness of truth, so that it follows from the very notion of certainty that the qualities of philosophical discourse, that is, of speech seeking certainty, are clarity and truth. Indeed, the truth of a proposition obviously cannot be known unless the meaning of its words is known, that is, unless it is clear (by the definition of clear speech). Clearness in speech applies not merely to the words but also to constructions. For if a construction is not clear, one may indeed know what the words mean simply and taken singly but not what they mean in this particular place and related to the others. But in the matter of obscurity of construction, speakers and poets are more apt to sin than are our philosophers. Therefore we shall speak of the clarity of words taken by themselves .... The clarity of a word arises from two factors - either from the word in itself or from its context in speech. The clarity of a word in itself, again, has two sources - origin and usage. The origin of a word, finally, can be resolved into two factors - the use of the root and the analogy of the derivation made from the root. Usage is the meaning of a word known in common by all who use the same language. Analogy is a meaning reached by shifting, or by derivation, which is likewise known to all who use the same language. For example, the usage or meaning of the word fate is the necessity of events. In origin it is compounded from the usage of the root and from analogy. The root isfor orfari, the meaning of the root is 'to say' (dicere); the analogy of fate is fatum, the perfect passive participle of the designated verb in Latin, so that the origin of fate and dictum is the same. Mostly, too, usage has arisen from origin by a certain figure of speech. This appears in the given example, since fatum is originally the same as dictum but means in usage what will happen necessarily. Let us see, therefore, whose dictum will happen necessarily; it is manifest that God's commands alone fit this description. Thus by origin fate is dictum, then by antonomasia or par excellence, the dictum of God, then by synecdoche the dictum of God concerning the future, or the decree of God, and finally by the metonymy of cause, what will happen necessarily, which is the present usage of the word. Thus the good grammarian, and the philosopher as well, must deduce the usage of a word from its origin by a continuous sorites of figures of speech, so to speak. I consider Julius Caesar Scaliger the great master in this work. His books on origins are now lost, to the great detriment of philosophy, except as his son has perhaps used them in his notes on Yarro, but these differ for the most part from what his father had already published and scattered through his own writings. So, although we have greater eruditton in the thought of the son, we have lost the greater acumen and philosophy in the book of origins of the father. 3 This rule mus t be adhered to in applying words - if the origin disagrees with the usage, we should follow the usage in speech rather than the origin; but if the usage is either doubtful or does not forbid it, we should rather cling to the origin. If the word has multiple usages, one must either be careful to abstract some so-called formal meaning, that is, the meaning which includes all usages in it, ... or if this cannot be done, one must at least establish some one usage which may be called original, i.e., from which the others follow in the same way in which it itself follows from the origin, namely, through a series of figures of speech .... In either case, whether selecting the
MAINZ AND PARIS, 1666-76 123 more original usage or the formal meaning, one must make sure above all else to choose among the many usages offered that one which is nearest the origin of the word. Once chosen, however, the meaning must be reduced, jf there is place, to a definition and submitted to the reader or listener. For a definition is nothing but the expressed meaning of a word or more briefly, the meaning signified. In a definition care must be taken not only that the definition be reciprocally true but also that it be clear. Technical terms are therefore to be shunned as worse than dog or snake, and one must abstain particularly from those words for categories which are far removed from Latin usage. Once set up, the definition is to be adhered to consistently, so that wherever you substitute the definition for the term defined, there results no absurd statement. Even if no definition is given beforehand, the use of a word should be uniform so that the same definition could be substituted anywhere. Thus, for any given word, we should see what meaning is to be attached to it and conversely, what word should be attached to a given meaning. In this, both brevity and clarity must be respected. The greatest clarity is found in commonplace terms with their popular usage retained. There is always a certain obscurity in technical terms . ... An analogy should be both generally accepted and fitting, so that the definition of the new word which we intend can be molded from the meaning of the root and the analogy. For example, haecceitas does not have a usual analogy; hoccitas (or hoccimonia) would be better, like quidditas, not quaedeitas. The definition of hoccitas can be formed from its root and the analogy, for the root is hoc and the analogy itas. Moreover, this analogy or reason for the derivation refers to the reason for the root word or to that quality of the root due to which it is what it is said to be. Thus hoccitas will be the reason why something is called hoc (just as Aristotle defines quality as that by which we are said to be quales) or the quality of this insofar as it is this. Nor is it surprising that we define abstract matters in terms of concrete, since the concrete is more familiar .... ... Technical terms are to be avoided, as I have said; indeed, they are to be used with care whenever possible. But this is not always possible because of the prolixity which would result if popular terms were always used. For example, a square is quadrilateral, equilateral, and rectangular, but the words 'equilateral', 'quadrilateral', and 'rectangular' (not to mention 'plane') are technical in their turn. Hence they can be further resolved. That is quadrilateral which has only four sides. A side is a bounding line. That is rectangular all of whose angles are right. An angle is the intersection of lines; right is that which is equal on both sides. Thus if we are to avoid technical terms, we shall have to put all these words in place of the word square: that figure, all of whose bounding lines are equal and whose bounding lines are only four, and in which all intersections of terminating lines are equal on both sides. If even greater rigor is demanded, the words line, bounding, intersection, and equality must be further resolved, for their popular usage does not exactly fit the concepts of geometry .... I believe that even the blind can see how annoying it would be, and how awkward, to have always to use all these words in place of the word 'square' in our demonstrations. To this can be added what I have already said in many passages of the Art of Combinations. Our judgments are thus rendered more reliable by this process of analyzing technical terms into merely popular ones; hence a perfect demonstration merely carries out such analysis to the ultimate and best-known elements. But if this entire analysis were done in one place - the subject and predicate of each judgment into their definitions, and the For references see p. 130
124 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS ingredient terms of the definitions into further definitions - or if we had constantly to return to other definitions or demonstrations we had already given or to the works of some author who had done this, our memory would be overtaxed. Hence it has been necessary to devise technical terms for those things to which people have not assigned names, either because they have not thought of them (like the quadratic curve) or because they use them rarely (like hyperbolas and parabolas) and believe it sufficient to designate them by circumscription if this is sometimes desirable. There is certainly nothing which cannot be expressed in popular terms, at least by using many of them. Hence Nizolius rightly urges that anything be regarded as nonexistent, fictitious, and useless to which there cannot be assigned a word in the vernacular, however general; that is, as I interpret him, a word which joined together with other general words can express the matter. For philosophers are not always superior to common men in that they think of different things, but rather in that they think in another way, that is, with the eye of the mind, with reflection and attention, and comparing things with each other. But there is no better way to arouse the attention of men for a certain matter than to assign it a definite word to serve as a memory token for myself, and a sign for others to distinguish it by. So far are philosophers from thinking more hidden and noble thoughts than other men, moreover, that even before the incomparable Lord Bacon of Verulam and other enlightened men recalled philosophy from its airy digressions, or from an imaginary space, back to earth and to the guidance of life, there were certain barbering alchemists who had sounder and clearer insights into the nature of things than did any philosophaster sitting behind closed doors, bent exclusively over his haecceitates or his hoccitates. I do not deny, however, that there are also many men of sound and useful learning among the philosophers, especially among those who draw from the springs of Aristotle and the ancients rather than from the cisterns of the Scholastics. Therefore philosophers often think just what other men think but with attention to what others have neglected. Joachim Jung of Hamburg, for instance, a true philosopher, has observed, collected, compared, and classified many species of insects which many mortals have undoubtedly seen but overlooked and trampled under foot and has assigned new names to them on the basis of this comparison. We hope that these and other meditations of his wiII be edited very soon by the enlightened Vogel. 4 But sometimes, I admit, philosophers perceive bodies or bodily qualities which other people never have perceived. Thus the chemists frequently produce new and hitherto unknown bodies by a variety of mixtures and analyses. The same thing happens in the mixtures of medical men, many of which have given their creators, whose names were assigned to them, more lasting fame than if a statue of granite bearing a eulogy had baen erected to them. Beyond a doubt, whoever first used the microscope saw many new qualities such as hitherto unknown colors. In these cases either new names must be formed or old ones adapted by some figure of speech based on the relation of the new thing or quality to the old. We may thus regard it as established that whatever cannot be explained in popular terms is nothing and should be exorcised from philosophy as if by an incantation, unless it can be known by immediate sense experience (like many classes of colors, odors, and tastes). So it is customary for certain capable philosophers to urge the brilliant masters of dialectic and disputation either to explain their terms clearly or,
MAINZ AND PARIS, 1666-76 125 if they want to avoid this vexing task, to step down to some living and popular language and attempt to explain their meaning in it. When this happens, it is remarkable either how they become confused or, if they attempt the change, how they are ridiculed by all men of judgment and experience who are present and who are not interested exclusively in the Latin language. This, I am convinced, is the reason why the exaggerated Scholastic style of philosophizing has gradually become obsolete in England and France, for people there have long since begun to cultivate philosophy in their own tongue, so that in a measure the common people, and even women, have become able to judge about such matters. The same thing would undoubtedly happen in Italy and Spain if the Scholastic theologians had not come to the aid of their philosophical cousins there. In Germany the Scholastic philosophy is more firmly established because, among other reasons, a late start was made in philosophizing in German, and even now we have hardly made an adequate beginning. But I venture to say that no European language is better suited than German for this testing and examination of philosophical doctrines by a living tongue. For German is very rich and complete in real-terms, to the envy of all other languages. No people have for centuries more diligently cultivated the practical arts, among them especially the mechanical arts, so that even the Turks use German names for metals in the mines of Greece and Asia Minor. On the other hand, the German language is easily the poorest for expressing fictions, certainly far less fitted for this than French, Italian, and other languages derived from Latin. For in the daughter-languages of Latin, a term of barbarous Latinity can easily be converted into good French or Italian through a slight twist. Hence many terms of Scholastic philosophy have been retained in some way in French translation. But no one has attempted such a thing in German without being hissed by everybody. Whoever wishes to retain or to twist Latin terms into German will not be philosophizing in German but in Latin. 5 And to no avail; he would not be understood by anyone ignorant of Latin, for unlike Italian and French, German is worlds removed from the Latin. The reason why philosophy has only more recently been dealt with here in the vernacular is that the German language is incompatible, not with philosophy, but with a barbarous philosophy. And since this barbarous way of philosophizing has only lately been rejected it is not surprising that our language has been slow to come into philosophical use .... ... Since we have established the fact that there is nothing which cannot be explained in popular terms and that the more popular the terms, the clearer is the discourse, ... it is obvious that the norm and measure for selecting terms should be the most compendious popularity or the most popular compendiousness. Hence wherever equally compendious popular terms are available technical terms are to be avoided. This is indeed one of the fundamental rules of philosophical style, though violated frequently, especially by metaphysicians and dialecticians. For dialectical and metaphysical subjects occur commonly in the utterances, writings, and thoughts of uneducated people and are met with frequently in everyday life. Spurred on by this frequent demand, the people have as a result designated these subjects by special words that are familiar, very natural, and economical. When such words are available, it is a sin to obscure matters by inventing new and mostly more inconvenient terms (to say nothing of the awkwardness often shown in manufacturing such words), and to make one's self admired only by the ignorant but ridiculous to others. The same thing holds true in morals, politics, and law. Since these fields are all alike open to the understanding of all, we can rarely hope For references see p. 130
126 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS for anything but obscurity to result from inventing new terms in them. I say rarely, for I admit that there is no science in which technical terms are not needed, especially when the common people either do not understand the matter or dismiss it from their attention. It is in mathematics, physics, and mechanics that new terms or terms with new applications are most necessary, for the matters dealt with in these sciences are not directly obvious to the understanding or in frequent common use .... ... One further warning seems worth while here, since its opposite is commonly held; in philosophizing accurately, only concrete terms should be used. For the most part Aristotle himself seems to me to have done this; he uses noaov, nOlOV, 7:0. np6~ 7:l rather than noa67:1J~, n0l67:1J~, aXf;al~, or if it were proper to speak: this way, npoa-7:lv67:1J~. But his adherents generally change this, as if it were too awkward, and fancy themselves as more subtle, the gods willing, when they use abstract terms exclusively. Yet it appears certain that this passion for devising abstract words has almost obfuscated philosophy for us entirely; we can well enough dispense completely with this procedure in our philosophizing. For concretes are really things; abstractions are not things but modes of things. But modes are usually nothing but the relations of a thing to the understanding, or phenomenal capacities. Indeed, modes can be repeated to infinity, so that there are qualities of qualities and numbers of numbers. If all these were things, not only infinity but contradiction would result. For if being-ness [entitas] were a being [ens], if real-ness were real, if somethingness [aliquiditas] were something, the thing would be the form of itself, or a part of its own concept, which implies a contradiction. If therefore anyone wants to give a perfect exposition of the elements of philosophy, he must abstain from abstract terms almost entirely. I do recall that the astute Hobbes ascribes some usefulness to abstract terms, by the very convincing argument that it is one thing, for example, to double some warm water, another to double its warmth. But this duplication of heat can itself be expressed in concrete terms, for if I say that the same thing has been made twice as hot, or that the effect by which the heat is measured is doubled, everyone will understand that it was not the hot water but the heat that was doubled. So I must confess that I have never found any great use for abstract terms in rigorous philosophizing but rather many and great abuses and very dangerous ones .... . .. So far we have shown that technical terms are to be avoided as far as possible. Now we must note that whether terms are popular or technical, they ought to involve either no figures of speech or few and apt ones. Of this, the Scholastics have taken little notice, for strange though this sounds, their speech abounds with figures. What else are such terms as to depend, to inhere, to emanate, and to inflow? On the invention of this last word Suarez prides himself not a little. The Scholastics before him had been exerting themselves to find a general concept of cause, but fitting words had not occurred to them. Suarez was not cleverer than they, but bolder, and introducing ingeniously the word influx, he defined cause as what flows being into something else, a most barbarous and obscure expression. 6 Even the construction is inept, since influere is transformed from an intransitive into a transitive verb; and this influx is metaphorical and more obscure than what it defines. I should think it an easier task to define the term 'cause' than this term influx, used in such an unnatural sense . ... Only truth remains to be discussed, but it is the logician's proper task to teach the rules as to how truth is to be achieved and confirmed and all the devices for invention and judgment. For the logician, in tum, the otherwise necessary burden of
MAINZ AND PARIS, 1666-76 127 examining and painstakingly discussing all his terms is wonderfully lightened if they are accurately clear. For if no word is used unless its meaning is clearly and accurately defined, all equivocation is necessarily banished, and with this a vast throng offallacies will at once disappear. Hardly anything more will then be required for sound judgment than that the senses be protected against error by means of the right constitution of the sense organs and the medium, and the intellect by observing the rules for ratiocination. Under these circumstances, I almost believe that just as there are two parts of rhetoric, one concerned with combining words elegantly, ornately, and effectively, the other with stirring the emotions, so there are also two parts of logic, the one verbal, the other real; one dealing with the clear, distinct, and proper use of words or with philosophical style, the other with the guidance and control of thinking. ... Therefore Nizolius is not wrong in his frequent insistence that precise formulation be used in logical disquisition, nor, perhaps, are we in this preface, in which we have expanded beyond Nizolius this principle which is necessary in every part of an encyclopedia. For our special purpose in preparing this edition is to contribute something, even through the work of another author, to the establishment of that sounder philosophy which the concerted efforts of the greatest geniuses are now advancing so excellently everywhere. We therefore hope that the reading of Nizolius' treatise will result in rich fruitage in philosophical matters, by leading men more and more to use this sober, proper, natural, and truly philosophical way of speaking. . .. The errors of Nizolius are many and great. ... Certainly the masterpiece is his imputing the errors of the Scholastics to Aristotle and his heaping loud reproaches upon men more prudent than himself, John Pico, Leonicenus, Rudolph Agricola, and Vives, whom he accuses of adulation because they tried to defend Aristotle. But after so many efforts have been made by the most learned scholars in interpreting Aristotle and overcoming the misunderstandings of uncultured people, nothing is better known in our own century than that Aristotle is free and innocent of all this ineptness with which the Scholastics are so often polluted.... He who consults the interpreters whom I have just mentioned 7 will readily admit, I believe, that Aristotle is far different than he is commonly described and that we must not, as did Valla, Nizolius, Basso, and other Aristotelianizers, read back into the author of the text what we find to be due either to the inexperience of his interpreters or to their being put at disadvantage because of the times in which they lived .... I do not hesitate to say that the older Scholastics are far superior to certain of our contemporaries in acumen, soundness, prudence, and even in their more cautious avoidance of useless questions. For some of our contemporaries, who can hardly add anything worth printing to the ancients, do only one thing; they accumulate references, invent countless absurd questions, divide one argument into many, change methods, and contrive new terms again and again. This is how they produce so many and such bulky books. How greatly inferior the insights of the Scholastics of this and the preceding centuries are to the earlier ones can be shown by the nominalist sect, the most profound of all the Scholastics, and the most consistent with the spirit of our modern philosophy. This sect, once very prosperous, is now extinct, certainly among the Scholastics. This seems to indicate that there has been a decrease rather than an increase in penetration. But since Nizolius did not hesitate openly to call himself a nominalist, near the end of Book I, chapter vi, and since the nerve of his argument consists in his destruction of For references see p. 130
128 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS the reality of forms and universals, I consider it worth while to present certain facts about the sect. Nominalists are those who believe that all things except individual substances are mere names; they therefore deny the reality of abstract terms and universals forthright. The first nominalist, it is believed, was a certain Roscelin of Brittany, who aroused bloody conflicts in the academy of Paris .... The sect had long been eclipsed, however, when the Englishman William of Occam, a man of the greatest genius and learning for his age, first a disciple but soon the greatest opponent of Duns Scotus, unexpectedly revived it. Gregory of Rimini, Gabriel Biel, and many of the Augustinian order agreed with him, and Martin Luther's earlier writings also show clearly a love of nominalism, until in the course of time, the monks all began equally to be affected by it. The general rule which the nominalists frequently use is that entities must not be multiplied beyond necessity. This rule is frequently opposed by others as violating the divine opulence, which is generous rather than parsimonious and takes pleasure in the variety and abundance of things. But those who raise this objection have not, I think, grasped the meaning of the nominalists, which, though more obscurely stated, reduces to this: the simpler a hypothesis is, the better it is. And in accounting for the causes of phenomena, that hypothesis is the most successful which makes the fewest gratuitous assumptions. Whoever acts differently by this very fact accuses nature, or rather God, its author, of an unfitting superfluity. The hypothesis of any astronomer who can explain the celestial phenomena with few presuppositions, namely, with simple motions only, is certainly to be preferred to that of one who needs many orbs variously intertwined to explain the heavens. From this principle the nominalists have deduced the rule that everything in the world can be explained without any reference to universals and real forms. Nothing is truer than this opinion, and nothing is more worthy of a philosopher of our own time. So much so that, I believe, Occam himself was not more nominalistic than is Thomas Hobbes now, though I confess that Hobbes seems to me to be a super-nominalist. For not content like the nominalists, to reduce universals to names, he says that the truth of things itself consists in names and what is more, that it depends on the human will, because truth allegedly depends on the definitions of terms, and definitions depend on the human will. This is the opinion of a man recognized as among the most profound of our century, and as I said, nothing can be more nominalistic than it. Yet it cannot stand. In arithmetic, and in other disciplines as well, truths remain the same even if notations are changed, and it does not matter whether a decimal or a duodecimal number system is used. The same thing is true of all the reformers of philosophy today; ifthey are not supernominalists, they are almost all nominalists. Hence Nizolius is all the more appropriate for our times .... ... Finally, a serious error of Nizolius concerning the nature of universals must not go unnoticed, for if the reader is not careful enough, it willead him far astray from the course of true philosophy. He tries to convince us that a universal is nothing more than all singulars taken simultaneously and collectively and that when I say, 'Every man is an animal', the meaning is that all men are animals. This is indeed true, but it does not follow that universals are collective wholes. Nizolius proves it in this way: Every whole is either continuous or discrete. A universal is a whole that is not continuous and is therefore discrete. But a discrete whole is collective, and the concept of the genus man is not different from that of a herd. So the meaning of this proposition,
MAINZ AND PARIS, 1666-76 129 every man (or the whole genus man) is rational, is the same as this, all/he sheep which graze here are white, or the whole flock is white. But you are mistaken, Nizolius. The discrete whole contains another genus besides the collective, namely, the distributive. For when we say: every man is an animal, or all men are animals, the acceptation is distributive; if you take that man (Titius) or this man (Caius), you will discover him to be an animal, or a sentient being. If, as Nizolius holds, every man, or all men, is a collective whole, and the same as the whole genus man, an absurd expression will result. For if they are the same, we may substitute the whole genus man in the proposition that all men are animals or every man is an animal, and we have the following very inept proposition: the whole genus man is an animal. The same holds true for a flock, for if the universal abstracted from all the sheep which graze here were, as Nizolius holds, identical with the collective whole of them, this proposition would be true: the whole herd is a sheep. Let us examine still another example, which leaves less room for some desperate evasion. The old jurisconsults, who spoke Latin accurately, as Nizolius will not deny, affirm that if someone makes a bequest like this, the genus is legacy: I give and bequeath my horse to Titius. But in the sense of Nizolius, since the genus is the whole abstracted from the singulars, it would be the same if he had said, 'I give and bequeath all my horses to Titius'. A rare sample of jurisprudence, indeed! But by substituting the distributive whole for the collective, on the contrary, the case becomes clear, for the sense will be, I give and bequeath this or that horse to Titius. Let us add this point: if in the proposition, every man is an animal, the genus is affirmed of the species, and if the genus is a universal, and the universal is the whole genus abstracted from the individuals: then if we substitute all animals taken together for the word 'animal', this proposition will result: man is all animals taken together, while it suffices to say that man is some animal, or anyone of the universal genus of animals. This error of Nizolius is, in truth, no small one, for it conceals an important consequence. If universals were nothing but collections of individuals, it would follow that we could attain no knowledge through demonstration - a conclusion which Nizolius actually draws - but only through collecting individuals or by induction. But on this basis knowledge would straightway be made impossible, and the skeptics would be victorious. For perfectly universal propositions can never be established on this basis because you are never certain in induction that all individuals have been considered. You must always stop at the proposition that all the cases which I have experienced are so. But since, then, no true universality is possible, it will always remain possible that countless other cases which you have not examined are different. But, you may ask, do we not say universally that fire - that is, a certain luminous, fluid, subtle body, usually flares up and burns when wood is kindled, even if no one has examined all such fires, because we have found it to be so in those cases we have examined? That is, we infer from them, and believe with moral certainty, that all fires of this kind burn and will burn you if you put your hand to them. But this moral certainty is not based on induction alone and cannot be wrested from it by main force but only by the addition or support of the following universal propositions, which do not depend on induction but on a universal idea or definition of terms: (1) if the cause is the same or similar in all cases, the effect will be the same or similar in all; (2) the existence 0/ a thing which is not sensed is not assumed; and, finally, (3) whatever is not assumed, is to be disregarded in practice until it is proved. From these principles arises the practical or moral certainty of the proposition that all such fire burns .... Hence it is clear that induction in itself For references see p. 130
130 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS produces nothing, not even any moral certainty, without the help of propositions depending not on induction but on universal reason. For if these helping propositions, too, were derived from induction, they would need new helping propositions, and so on to infinity, and moral certainty would never be attained. Perfect certainty can clearly never be hoped for from induction, even with the addition of any aids whatever. By induction alone we should never perfectly know the proposition that the whole is greater than its part. For someone would soon appear and for some reason deny that it is true in cases not yet observed. We know this from the fact that Gregory of St. Vincent denied that the whole is greater than its part, at least of angles of contact, and that others have denied that it is true of infinity. Thomas Hobbes (or someone) began to doubt the geometric proposition which was proved by Pythagoras and regarded as worthy of the sacrifice of a hecatomb. I have read this with some amazement. 8 ••• REFERENCES 1 Anti-Barbarus, seu de veris principiis et vera ratione philosophandi contra pseudophilosophos, Parma 1553. Aristotle Eth. Nic. i. i. The most important work ofthe father, Julius Caesar Scaliger, Italian humanist (1484-1558), is his Exotericarum exercitationum fiber in criticism of Cardan's De subtilitate (1557). The son, Joseph Justus Scaliger (1540-1609), reputedly France's greatest philologist, is best known through the collections of anecdotes, the Scaligeriana (1666, 1669, etc.). 4 For many years Leibniz was concerned for the publication of the manuscripts of Joachim Jung (1587-1657), eminent scientist and atomist of Hamburg, whom he considered the equal of the most prominent scientists of other countries. His efforts failed, and the manuscripts were destroyed by fire in 1691. Leibniz purchased the library of Martin Vogel for the Duke of Hanover-Brunswick in 1678. 5 This brings to mind Schleiermacher's remark that Grotius and Leibniz could not have philosophized in German and Dutch, at least without being entirely different men. Cf. Guh. DS., II, 409-10. But Leibniz did succeed in using popular German effectively in explaining his opinions (cf. Nos. 40 and 48). 6 See p. 83, n. 6. 7 The omitted section contains an account, first of critics of Aristotle, and then of recent interpretations and defenses of him in Italy, Germany, and England. 8 Hobbes's attempts to correct Euclid are indeed such as to arouse amazement, though his bad reputation as a geometrician rested primarily upon his twelve attempts at circle-squaring in the De corpore (chaps. xviii-xx) and the bitter dispute which followed, particularly with John Wallis. But his criticism of Cartesian geometry, his examination of geometric axioms, and his operational interpretation of geometric reasoning must early have proved suggestive to Leibniz. Cf. J. Laird, Hobbes, Oxford 1934, pp. 37-38, 102 ff., 264-65. 2 3
7 ELEMENTS OF NATURAL LAW 1670-71 The project in legal reform in which Leibniz was engaged at Mainz with Herman Andrew Lasser took the form of a work on Rational Jurisprudence. Lasser took charge of the last two parts, concerned with the actual reform of the law; Leibniz undertook the first two - the Elements of Natural Law and the Elements of Contemporary Civil Law. The first principles of law and justice are for Leibniz essentially the same as those of his theology, since God is, after all, the supremely powerful lawgiver and the source of all harmony. But the ethical consequences of these metaphysical principles are made clear in law rather than in theology. This long discussion of the elements of naturallaw l , written not before 1670, relates the project of legal reform to the cultural state of Europe and explains Leibniz's principles as they apply to law, ethics, and aesthetics. It is the most complete of many studies in natural law from this period. [PA., VI, i, 459-65] It is obvious that the happiness of mankind consists in two things - to have the power, as far as is permitted, to do what it wills and to know what, from the nature of things, ought to be willed. Of these, mankind has almost achieved the former; as to the latter, it has failed in that it is particularly impotent with respect to itself. For the power of man has certainly increased immensely in the present age, and of the two elements of our earth, one is almost tamed and the other restored from the rapacity of the former. We have spanned the seas by a kind of mobile bridge and so united lands that were once divided by enormous gaps. The heavens themselves cannot defeat us, and when they hide their stars, we find help in deformed bit of glass. And having moved them nearer to us and multiplied our eyes to be admitted into the interior of things and to enlarge the face of the world a hundredfold, we then suddenly have disclosed to us new worlds and new species, both equally admirable - the one in magnitude, the other in smallness. Nor do we lack glasses [conspicilia] of another kind, by which to survey the scattered bits not merely of space but of time. The light of history has been brought to us, so that we seem to have lived always. A new kind of monument has been prepared - though of paper, yet more enduring even than bronze - by which great geniuses may survive all the injuries of barbarous and tyrannical times and always anticipate the assured immortality of heaven by an imaginary eternity of fame. We have thus embraced time in our writings, the heavens in our telescopes, the earth in travel, and the sea in ships. The other elements follow this example. The air too now reveals its secrets which have been hidden from all eternity. Fire has already conspired, by the inexplicable goodness of God, to serve as a kind of commendable torture wherever other things persist in For references see p. 138
132 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS denying his powers and has given us those thunderbolts which no force can equal except when human madness opposes them to each other. 2 Now that we are conquerors of the world, there assuredly remains an enemy within us; everything is clear to man but man, the body to the mind, and the mind to itself. To drop the tragic style and speak more naturally, we are ignorant of the medicine of bodies and of minds. We treat the former as does an agent something for the sake of gain; we treat the latter as a boy does his lesson - as nothing, for he learns it in the hope of forgetting it. It is not surprising, therefore, that until now we have established no science of the pleasant, or the useful, or the just. The science of the pleasant is medicine, that of the useful is politics, and that of the just is ethics. The physician should explore our structure, the position and motion of our parts, the causes of pleasures, so that he may conserve and produce them, and of our pains, on the other hand, so that he may remove and prevent them. To this end he should make use of such aids as characteristics, optics, music, perfumes, cooking, as well as chemistry and botany. We possess an unbelievable mass of unusual 0 bservations, but they are crude, undigested, and without use except almost by chance. To what end has this material been gathered and made ready with so much study, jf we are to postpone until another century the construction of our happiness? Why not strike a blow with combined forces against this persistence of nature in concealing herself? Why, I ask, unless it is because the blame for the imperfection of natural science must fall back upon the public, since they could improve it if everyone wished it, and if individuals wished that all should wish it in general? All will not do together, however, what individuals will and can do, unless the matter is attacked in the right way and on the basis of the secrets of true politics, by those to whom it is given to make a great part of mankind happy as an example to the rest and to make themselves happy through this part. For those who appraise this matter truly understand that the sciences of the just and the useful, that is, of the public good and of their own private good, are mutually tied up in each other and that no one can easily be happy in the midst of miserable people. Until now we have therefore been ignorant of, that is we have not imbibed, we have not drunk from the true springs of equity and of good. We can indeed be ignorant of what we have read, heard, and even thought a thousand times, if reflection, so to speak, and the attention of the mind have been absent. For what we know that we know, we also will to use. But what we do not know that we know, we do not know at all. There are two things which make us take notice - eloquence and demonstration. The former moves the affections and brings the blood to boil, so to speak. The latter creates a clear comprehension in the mind. Hence the former vanishes unless it takes on demonstrative form and is only the senseless ecstasy of a mob agitated by frantic emotions. The latter affects but few indeed, and only great men, but those great men in whom alone there is hope for improvement in this greatest of centuries, in which a kind of consuming hunger brings all great talents to the solid nourishment of truth. If we were to satisfy these, if we were to urge them to do their own thinking, if we were to establish truth on a firm ground, then we might be able to lessen the flow of eloquence. Of the entire utility of this I have written elsewhere, I hope not too popularly. Now it will suffice to sow the seeds of that science which shows how individuals should give way to the good of all if they wish happiness to revert to themselves, increased as by
MAINZ AND PARIS, 1666-76 133 a rebound. The answer to this problem has been intrusted to the Elements of Law and Equity 3, which we shall now undertake to develop with the good will of Heaven. 1. The doctrine of Right belongs to those sciences which depend on definitions and not on experience and on demonstrations of reason and not of sense; they are problems oflaw, so to speak, and not of fact. For since justice consists in a kind of congruity and proportionality, we can understand that something is just even if there is no one who practices it or upon whom it is practiced. Just so the relations of numbers are true even if there were no one to count and nothing to be counted, and we can predict that a house will be beautiful, a machine efficient, or a commonwealth happy, if it comes into being, even if it should never do so. We need not wonder, therefore, that the principles of these sciences possess eternal truth. For they are all conditionalia, conditional truths, and treat not of what does exist but of what follows if existence be assumed. They are not derived from sense but from a clear and distinct intuition [imaginatio], which Plato called an idea, and which, when expressed in words, is the same as a definition.4 That which can be understood clearly, however, is not always true, though it is always possible; and it is also true, in addition, whenever the only question is that of possibility. But whenever there is a question of necessity, there is als 0 one of possibility, for if we call something necessary, we deny the possibility of its opposite. It therefore suffices to demonstrate the necessary connections between things and their consequences in this way: by deducing them from a clear and distinct intuition (that is, from a definition when this intuition is expressed in words), through a continuous series of definitions which imply them; that is, through a demonstration. Therefore since the doctrine of Law is a science, and the basis of science is demonstration, and definition is the principle of demonstration, it follows that we must first of all investigate the definitions of the words Right, just, and justice, that is, the clear ideas by which we usually estimate the truth of propositions or of the right use of words in speech, even when we do not know we are doing SO. 5 2. The method of our investigation is to gather the more important and distinctive examples of the use of these terms and to set up some meaning consistent with these and other examples. For just as we construct a hypothesis by induction from observations, so we construct a definition by comparing propositions; in both cases we make a compendium of all other instances, as yet untried, out of the most important given cases. This method is necessary whenever it is not desirable to determine the use of terms arbitrarily for one's self. For as long as we are speaking only to ourselves or to our special group, or about something not generally known, it is in our power to assign to any definite idea whatever the word which will serve to arouse our memory, so that it will be unnecessary for us always to repeat the definition, that is to say, ten other words. But when we are writing for the public and on a commonly discussed matter in which we do not lack terms, it is either the folly of one who does not want to be understood, or the malice of a deceiver, or the pride of one who seeks to bring others to his own views without offering any reasons, to think up words or usages private and peculiar to one's self. This is a matter which I have discussed at length in the preface to Nizolius. 3. From the beginning, however, both our own good and that of others are involved in the question of right. For as concerns our own good, it is universally admitted that what one does out of the necessity of protecting his own security seems to be done justly. In the next place, no one is willing to separate justice from prudence, for, as For references see p. 138
134 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS everyone agrees, justice is a definite virtue, but every virtue restrains the affections so that nothing can obstruct the dictates of right reason. But the right reason for our actions is the same as prudence. It follows, therefore, that there can be no justice without prudence. Prudence, furthermore, cannot be separated from our own good, and any statement which contradicts this is empty and foreign to the actual practice of those who utter it, whatever they may say against it. There is no one who deliberately does anything except for the sake of his own good, for we seek the good also of those whom we love for the sake of the pleasure which we ourselves get from their happiness. To love is to find pleasure in the happiness of another. We love God himself above all things because the pleasure which we experience in contemplating the most beautiful being of all is greater than any conceivable joy. It follows from this, if you consider the matter completely, that no one can be obligated to do evil to himself. What is more, no one can be obligated except for his own good. For since justice is something of which a prudent man can be convinced, and since no one can be convinced of anything except for reasons of his own utility, it follows that every duty must be useful. We therefore derive two propositions from the common agreement of those who use these terms: first, that everything necessary is just and, second, that every duty (or injustice) is useful (or harmful). It remains to see to what extent there is in justice a basis for considering the good of others. 4. In the first place, however, all men proclaim that an injury has been done and, indeed, that nature has been violated if anyone seeks to harm others without gaining any advantage for himself, or if he refuses to do something useful to others which involves no harm to himself, or if he chooses to let a person die whom he could save at no cost to himself; but also if he places some advantage of his own, which does not bear upon the common good, above the misery or happiness of others, if he feasts his cruel eyes on the dead, if he achieves his ends by resorting to murder and torture, if he prefers to let a servant be destroyed rather than his own vice. Furthermore, there is no one who approves making a profit at the expense of others. Finally, there is also another ground for complaint if the same misfortune afflicts two people, but one of them assumes that only he is to be recompensed, for when the cause is alike in equivalent cases, the right is equal. In all these cases men find not only the deed blameworthy but also the will. Hence these propositions: First, it is unjust to will to harm another except for one's own good. Second, it is unjust to will the cause of another's destruction unnecessarily. Third, it is unjust to will harm to another for one's own gain. Fourth, it is unjust to be unwilling to bear a common injury. 5. Since it is agreed in summary, therefore, that the just consists of having a reason for the good of one's self and of others, let us try to define this step by step. Whether perhaps the just is to be defined as willing what is harmful to no one? But then it will not be just to seek one's own harm that other harm may be avoided. Whether then that is just which is done for the sake of avoiding harm to one's self? But then it would be just to prefer one's vice even though a servant perish. Whether just is what happens by reason of its own necessity? But then it would not be permissible to prefer one's own gain to that of another. Whether the just is what is publicly approved? But then my security should be postponed by public misfortune. Whether just is whatever is not a cause of war? But then it would not be just, in case of assault, to prefer that someone else be destroyed rather than myself.
MAINZ AND PARIS, 1666-76 135 Whether the just is whatever does not deserve censure by a prudent man? Certainly. But the injustice makes the censure; the censure does not make the injustice. This argument is also valid if you define the just as whatever prudent men do not regard as punishable; or as whatever can be defended in the assemblies of wise men in general; or as what is in conformity with the best commonwealth; or as whatever conforms to nature; or whatever pleases a wise and powerful man; or whatever is of advantage to the stronger. Likewise the view that you should be sure to do, yourself, what you demand of others; that you demand nothing of others which you would not do yourself; and that each one should do what, if done by all, is useful to each. Nor is the just whatever is not contrary to the social good. For even Curtius could justly have refused to make his horrible leap, though the security of his country was involved, if all hope after death had been denied him. 6 Nor is the just whatever is congruent with a rational nature. For what would such a nature wish for itself? Whether the just is whatever can exist together without deformity? For that would be congruent in the popular sense. But then the sick would be unjust. Whether the just is rather whatever is congruent with right reason? But then every error, even if no harm results to the one who errs, would be a crime. Whether justice is virtue preserving the mean between two affections of man toward man - love and hate? As a boy I myself supported this opinion enthusiastically, for being fresh from the Peripatetics, I failed thoroughly to digest the fact that all the other virtues governing our affections have themselves one governess - the justice of things. But I put aside this convincing rather than sound view without difficulty when it became clear that the whole basis of virtue is found in the fact that the affections can do nothing but obey and that there can thus be only one moral virtue, as it is called: to be the master of one's own spirits and blood, so to speak; to be able to glow, to rise up, to cool off, to rejoice, and to grieve when we wish and as long and as strongly as we wish. This balancing of contraries, however, usually turns out to be mixed. To this we may add that to be ineptly profuse or unseasonably persist ought not to be ascribed to the breaking-off of an affection, since men reason falsely that a kind of honor comes to them from luxury or prodigality or from promising more than one's capacities or uneasy fortunes justify, or on the other hand, from being unreasonably diffident about one's abilities and fortunes. So I can be unjust, not because of the hate of him whom I harm, but because my love for myself or for a third person prevails over my love for you. But to love myself and you, or you and a third person, are not affections opposed to each other, although they may accidentally conflict, since both can exist together in the highest degree. Yet although we may assign this latitude of love and hate to justice, it would be unjust to love another too much to one's own injury. This is inept rather than unjust, however, for whom does it injure save him who does it? But to injure one's self is not, strictly speaking, injustice. The value of such a different use of words would be less than the resulting confusion between just and good, and we should have to form new words, whereas we are trying not to resort to such aids. Therefore the just will not be whatever does not conflict with prudence in aiding and harming others. For it would follow that, where the right to harm someone is once admitted, he is unjust who fails to do this harm in conformity with the strictest rules. Whether just is really what is not contrary to conscience? But what does it mean to be contrary to conscience, since conscience is the memory of one's own deeds? Whether that deed of ours is unjust whose memory is burdensome, i.e., for which we are sorry? For references see p. 138
136 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS If SO, every harm which we inflict upon ourself through our own fault will be unjust. Therefore we do ourselves an injury, contrary to our earlier view. But you say there are certain innate concepts, and there has been placed within us a certain witness of the just and the unjust, stronger than all our protests, which tortures the wicked by the mere consciousness of crime, our nature being so formed by the wonderful wisdom of its creator that, if there were no other punishment, this would certainly be the punishment of sinners, the grief of the perpetrator. But let those consult this oracle who will. They will find that this internal torturer is fear; fear, I say, of punishment by a judge who can be neither deceived nor escaped and whose opinion impressed on even the most simple by the aspect of this universe, not even the most profligate can put aside, however much they may wish. Just, therefore, will be that whose punishment is not to be feared, and this basis for defining it we now judge to have been established. Where, then, do we stand after so many attempts? Whether justice is the habit of willing the good of others for the sake of our own? This is nearest to the truth, but a little distorted. There is in justice a certain respect for the good of others, and also for our own, but not in the sense that one is the end of the other. Otherwise it may follow that it will be just to abandon some wretched person in his agony, though it is in our power to deliver him from it without very much difficulty, merely because we are sure that there will be no reward for helping him. Yet everybody abominates this as criminal, even those who find no reason for a future life; not to mention the sound sense of all good people which spurns so mercenary a reason for justice. And what shall we say of God; is it not unworthy to hold him an instrument to this? But how reconcile these views to those given above, where se said that we do nothing deliberately except for our own good, since we now deny that we should seek the good of others for the sake of our own? They are to be reconciled, beyond doubt, by a certain principle which few have observed, but from which a great light can be thrown upon true jurisprudence as well as upon theology. The answer certainly depends upon the nature of love. There is a twofold reason for desiring the good of others; one is for our own good, the other as iffor our own good. The former is calculating, the latter loving. The former is the affection of a master for his servant, the latter that of a father for his son; the former that of one in need toward the instrument for meeting his need, the latter that of a friend for his friend; the former for the sake of some other expected good, the latter for its own sake. But, you ask, how is it possible that the good of others should be the same as our own and yet sought for its own sake? For otherwise the good of others can be our own good only as means, not as end. I reply on the contrary that it is also an end, something sought for its own sake, when it is pleasant. For everything pleasant is sought for its own sake, and whatever is sought for its own sake is pleasant; all other things are sought because of the pleasure they give or conserve or whose contrary they destroy. All people sense this, whatever they may say; or at least they act according to it, whatever they may believe. Ask the Stoics, those airy dreamers, cloud-dwellers, star-gazers, those enemies, professedly of joy, but really of reason. Observe, pry into their acts and movements. You will find that they cannot stir a finger without pointing out the falsehood of their own foolish philosophy. Honor [honestas)' itself is nothing but pleasure of mind. If you listen more carefully to Cicero when he declaims in favor of honor and against pleasure, you will hear him plead magnificently for the beauty of virtue, the deformity of wickedness, the conscience quiet and at peace with itself in the bosom of the joyous mind, the good of uninjured
MAINZ AND PARIS, 1666-76 137 reputation, the triumph of glory. 8 But what is sought in all these things in themselves, save pleasure? I say in themselves, f or there is still another fruit of glory - it increases power. For it makes us loved or feared. We seek beautiful things because they are pleasant, for I define beauty as that, the contemplation of which is pleasant. Pleasure, however, is doubled by reflection, whenever we contemplate the beauty within ourselves which our conscience makes, not to speak of our virtue. But as a double refraction can occur in vision, once in the lens of the eye and once in the lens of a tube, the latter increasing the vision of the former, so there is a double reflection in thinking. For every mind is something like a mirror, and one mirror is in our mind, another in the mind of someone else. So if there are many mirrors, that is, many minds recognizing our goods, there will be a greater light, the mirrors blending the light not only in the eye but also among each other. The gathered splendor constitutes glory. There is an equal reason for deformity in the mind; otherwise there would be no shadows to be increased by the reflection of the mirrors. 9 But to return to our path, in the consensus of mankind everything pleasant in itself is sought after in itself, and everything sought after in itself is pleasant. We can therefore readily understand how we not only can achieve the good of others without our own but can even seek it in itself; namely, insofar as the good of others is pleasant to us. A true definition of love can be built from this. For we love him whose good is our delight. Therefore we have confirmed (as I have already said) that everything which is loved is beautiful, that is, delightful to a sentient being, but not that everything beautiful is loved. For we do not really love nonrational beings, since we do not seek their good in itself, except those who make the popular mistake of imagining that there is some reasonable element - I know not what - in animals which they call sense. Since justice, therefore, demands that we seek the good of others in itself, and since to seek the good of others in itself is to love them, it follows that love is of the nature of justice. Justice will therefore be the habit ofloving others (or of seeking the good of others in itself and of taking delight in the good of others), as long as this can be done prudently (or as long as this is not a cause of greater pain). For even the joy which we take in our own good must be curbed by prudence, lest it sometime become the cause of greater pain; how much more then the joy we take in that of others. Yet it may not be pertinent to call in prudence here, for even one who believes, though foolishly, that the good of others is unrelated to his own pain is nonetheless obligated to them. Therefore justice will be the habit of deriving pleasure from an expectation of the good of others, even to the expectation of our own pain. But these last words can be extended even further, for even though our own pain intervenes, nothing prevents our taking pleasure in an expectation of the good of others, though our act itself may follow the greater pleasure or the lesser pain. To reach a conclusion at last, the true and perfect definition of justice is therefore the habit of loving others, or of finding joy in the expectation of the good of others whenever an occasion arises. It is equitable to love everyone else whenever an occasion arises. We are obligated (we ought) to do that which is equitable. It is unjust not to be delighted in the good of others when an occasion arises. The just (the permissible) is whatever is not unjust. Therefore the just is not merely what is equitable - to delight in the good of others when the issue arises - but also what is not unjust - to do what you will when no issue is involved. Right is the power of doing what isjust. 1o For references see p. 138
138 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS REFERENCES 1 The title we use is that in PA.; MoUat, who first published the paper, gives the title as Elements of Law and Equity (Mitteilungen aus Leibnizens ungedruckten Schri/ten, Leipzig 1893, pp.19-36). 2 The allusion is to gunpowder; cf. Leibniz's epigram in verse on the bombs developed by the technicians of Louis XIV (Klopp, V, 636). 3 Cf. note 1, above. Depending upon the context, we shaU translate Jus either by Law (as opposed to laws), or Right (as distinct from rights). 4 MoUat appropriately documents this passage with Plato's Republic 507b. The influence of Plato's logic and ethics is apparent throughout the work. S Leibniz's theory of demonstration is stated more clearly and completely in Nos. 18 and 25. His view that principles of justice are truths of reason or of possibilities which condition but do not completely determine existence already presupposes the distinction between possibility and existence made in his later thought, though his logical theory still concerns only the former. What are here called clear and distinct intuitions (imaginationes) are the simple, primary concepts to which Leibniz believed all knowledge may be reduced by analysis and out of which all demonstration is therefore built. 6 See Liyy vii, 6. 7 See p. 58, n. 5. 8 De finibus bonorum et malorum v; De officiis iii. 9 In the selection in note 10, below, Leibniz extends this argument for the social multiplication of pleasure to God, making it a moral argument for creation and plurality. Here is implied also his argument for the necessity of evil as the source of variety in value. The mirror analogy was a favorite with Leibniz; it must be borne in mind that the mirrors of the 17th century were still imperfect reflectors, containing much materia prima or indistinctness and inertness, and that Leibniz may have had in mind concave focusing mirrors, of the kind he advocated for scientific uses and his friend Tschirnhaus was later to experiment with. 10 The following selection, from a somewhat earlier study in the Elements of Law, expounds another dimension of social harmony, namely praise, and also portrays its divine basis (PA., VI, i, 437-38 [from 1669 or 1670]): "How few men there are who do not attribute some sense and a kind of reason to beasts, almost as to an infant who cannot be said to think. Yet they do not shrink from inflicting misery upon beasts for the sake of even the smallest benefit to themselves, and hardly anyone, in any age, with the exception of a few Pythagoreans, has charged that it is an injustice to kill beasts for the sake of our appetites, for the obvious reason that we are not afraid that they will plot against us. H is to be noted, however, that there is still another reason [i.e., besides fear of reprisal]. Concern for security is to be placed above concern for praise; one does not place acclaim higher than security. Hence tyrants care very little about being hated when they are safe, for they say, 'They may hate me, if only they fear me.' But even if we are beyond fear, we all seek praise. No wise man fails to desire praise, because he desires harmony. Praise is a kind of echo and duplication of harmony. If God had no rational creatures in the world, he would still have the same harmony, but alone and devoid of echo; he would still have the same beauty, but devoid of reflection and refraction or multiplication. Hence the wisdom of God demanded rational creatures in which things may multiply themselves. So one mind may be a kind of world in a mirror, as it were, or in a lens or some kind of point collecting visual rays. Therefore if we are prudent we try to give satisfaction to those whom we believe to be in a position to judge our actions as good and evil. Thus I hold that he is the most powerful or inviolable being of all who will seek as much of the highest good as possible." Cf. also the following: "Harmony is diversity compensated by identity; or the harmonious is the uniformly difform" (PA., VI, i, 484 [from 1671]).
8 STUDIES IN PHYSICS AND THE NATURE OF BODY 1671 It is not until the Paris period that Leibniz, under the particular tutelage of Huygens, developed any adequate understanding of the issues in modern mathematics and physics. His first interest in these fields came earlier, however, as a result of philosophical and theological problems, and in ''proud ignorance "1 he not only answered most controversial questions to his own satisfaction but ventured to enter into the jealous public discussions then at their height between English and French scholars. In 1669 he had proposed corrections to the laws of motion worked out by Huygens and Wren. The New Physical Hypothesis, published in 1671, outlined a somewhat incoherent program of new physical and cosmological principles. This work appeared in two parts, one of which, The Theory of Abstract Motion, he dedicated to the French Academy, the other, The Theory of Concrete Motion, to the British Royal Society. The Fundamental Principles presented in the former treatise, though an unassimilated combination of Cavalierian, Hobbesian, Cartesian ideas, suggest a number of his own later metaphysical principles, though the central concept offorce is still lacking. The second selection, written late in 1671, shows Leibniz's skill in constructing empirical definitions and reveals the motives for his phenomenalism. His criticisms of Descartes are already wellformulated. 1. THE THE OR Y OF ABSTRACT MOTION: FUNDAMENTAL PRINCIPLES, [PRAEDEMONSTRABILIA]2 [G., IV, 228-32] 1. There are actually parts in a continuum, though the learned Thomas White believes the contrary. 2. And these are actually infinite, for the indefinite of Descartes is not in the thing but in the thinker. 3. There is no minimum in space or in a body, that is, no part of which the magnitude would be zero; for such a thing cannot have any position, since whatever has a position can be in contact at the same time with several things which do not touch each other and hence will have many faces. Nor can a minimum be assumed without it following that there are as many minima in the whole as in the part, which implies a contradiction. 4. There are indivisibles or unextended beings, for otherwise we could conceive neither the beginning nor the end of motion or body. The proof of this is as follows. There is a beginning and an end to any given space, body, motion, and time. Let that whose beginning is sought be represented by line ab, whose middle point is c, and let the middle point of ac be d, that of ad be e, and so on. Let the beginning be sought at the left end, at a. I say that ac is not the beginning, because cd can be taken from it without For references see p. 144
140 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS destroying the beginning; nor is it ad, because ed can be taken away, and so forth. So nothing is a beginning from which something on the right can be removed. But that from which nothing extended can be removed is unextended. Therefore the beginning of body, space, motion, or time - namely, a point, conatus, or instant - is either nothing which is absurd, or unextended, which was to be demonstrated. 5. There is no point whose part is 0, or whose parts lack distance; whose magnitude is inconsiderable; incapable of being designated, less than that which can be expressed by a ratio not infinite to another sensible magnitude; less than any which can be given. This is the foundation of the method of Cavalieri 3 , in which its truth is obviously demonstrated so that we must think of certain rudiments, so to speak, or beginnings of lines and figures, as smaller than any given magnitude whatever. 6. The ratio of rest to motion is not that of a point to space but that of nothing to one. 7. Motion is continuous or not interrupted by little intervals of rest. 8. For where a thing is once at rest, it will always remain at rest unless a new cause of motion occurs. 9. Conversely, a thing once moved will always move with the same velocity and in the same direction if left to itself. to. Conatus is to motion as a point to space, or as one to infinity, for it is the beginning and end of motion. 4 11. Hence whatever moves, no matter how feeble, and no matter how large may be the obstacle it meets, will propagate its conatus in full against all obstructions into infinity, and furthermore it will impress its conatus on all that follows. For though it cannot be denied that a moving body does not proceed in its motion even when it has been stopped, it at least strives to do so, and what is more, it strives, or what is the same thing, begins to move the obstructing bodies, however large, even though they may exceed it. 12. There can therefore be many contrary conatuses in the same body at the same time. For given the line ab, and c moving from a to b, and d, on the other hand, moving from b to a, and colliding with c; then at the moment of collision c will strive against b even though it is thought to stop moving, because the end of motion is conation. But it will also strive in the opposite direction if the opposing body is thought to prevail, for it will begin to move backward. But even if neither should prevail over the other, this will still be the same, because every conatus is continued through the resisting bodies to infinity, and so, that of each one in the other. And if equal velocities accomplish nothing, neither will a double or any greater velocity, for two times nothing is nothing. 13. One point of a moving body at the time of conatus, or in a time less than any assignable time, is in many places or points of space, i.e., the body will fill a part of space greater than itself, or greater than it would fill at rest or if moving more slowly, or if striving in one direction only. Yet this space is still inassignable or consists in a point, although the ratio of the point of the body (or the point it would fill at rest) to the point of space it fills in motion is like that of an angle of tangential contact to a rectilinear angle or of a point to a line. 14. In general, too, whatever moves is never in one place when it moves, nor indeed in one instant or least moment of time, because whatever moves in time strives, or begins and stops moving, in that instant, that is, it changes its place. It is also irrelevant
MAINZ AND PARIS, 1666-76 141 to say that, when it strives in a time less than any given time, it is in a minimum space, for there is no minimum of time, otherwise there would also be one of space. For whatever moves through a line in a time less than any given time moves through a line in space less than any given line, or a point, and therefore through an absolutely minimum part of space in an absolutely minimum time. But by the third principle, there is no such thing. 15. On the contrary, at the time of impulsion, impact, or collision, the boundaries or points of two bodies either penetrate each other or are in the same point of space. For when one of two colliding bodies strives into the position of the other, it begins to be in it, that is, it begins to penetrate or to be united. For conatus is beginning, penetration, union. The bodies are therefore in the beginning of union, or their boundaries are one. 16. Therefore bodies which push or impel each other are in a state of cohesion, for their boundaries are one, for as Aristotle too defines them, bodies whose limits are one [wv 'Co. BtTxarex BV] are continuous or are in cohesion. s For if two things are in one place, one cannot be put in motion without the other. 17. No conatus without motion lasts longer than a moment except in minds. For what is conatus in a moment is the motion of a body in time. This opens the door to the true distinction between body and mind, which no one has explained heretofore. For every body is a momentary mind, or one lacking recollection [recordatio], because it does not retain its own conatus and the other contrary one together for longer than a moment. For two things are necessary for sensing pleasure or pain - action and reaction, opposition and then harmony - and there is no sensation without them. Hence body lacks memory; it lacks the perception of its own actions and passions; it lacks thought. 6 18. One point is greater than another point, one conatus is greater than another conatus, but every instant is equal to every other one. Hence time is measured by uniform motion in the same line, although its parts do not stop in an instant but are dense [indistantes], as are angles in a point. 7 These parts the Scholastics, perhaps after the example of Euclid, called signs, because there appear in them things that are simultaneous in time but not in nature, since one is the cause of the other. Likewise in accelerated motion, which increases at every instant and therefore at the very beginning; but to increase presupposes an earlier and a later. So one sign is necessarily earlier than another at the same given instant, even though without distance or extension.... No one can easily deny the inequality of conatuses, but from this the inequality of points follows. One conatus is obviously greater than another, or one body, moving more rapidly than another, obviously passes through more space from the beginning, for if it passes through the same amount at the beginning, it will always continue to pass through the same amount, for motion continues as it begins unless some external cause changes it, by No.9. Then, too, if the beginnings are equal, the ends are also equal; therefore, at the moment of collision the fast one will act upon the slow one only as much as the slow one on the fast, which is absurd. They must therefore be unequal. The stronger body will therefore pass through more space than the slower at a given instant. But in one instant no conatus can pass through more than a point, or a part of space less than any given part, otherwise it would pass through an infinite line in time. Therefore one point is greater than another. 8 •.• 19. If two conatuses occurring at the same time can be conserved, they are compounded into one, and the motion of each is conserved. This is clear in a sphere rolled along a For references see p. 144
142 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS plane, where the motion of each point designated on the surface of the sphere is compounded from a straight line and a circle, combined through minima or conatuses into a cycloid. 9 ••• This argument deserves to be treated more carefully by geometricians, so that it may be made clear what new curves may be produced by combining the conatuses of any given curves; thus many new geometric theorems could perhaps be demonstrated. . 20. A moving body impresses upon another, without any diminution of its own motion, whatever the other can receive without losing its own earlier motion .... 21. If there is not something which can act simultaneously upon everything else, and be the cause of everything equally, and if there is no third thing involved, there is no action. This is the cause of rest .... 22. If conatuses that cannot be compounded are unequal, they are subtracted from each other, the direction of the stronger being conserved .... For two conatuses can be subtracted from each other, since the less is equal to a part of the greater, and hence, as long as a resolution of the problem is found in a part of either conatus, there is no reason for choosing a third solution. 23. If two conatuses that cannot be compounded are equal, the directions of both will be destroyed, or a third will be chosen intermediate between the two, the velocity of conatus being conserved. This is, so to speak, the peak of rationality in motion, since the problem is solved not merely by a crude subtraction of equals but also by the choice of a more fitting third possibility, and so by a kind of remarkable but necessary wisdom, such as is not easily shown in the whole of geometry or phoronomy.lo Therefore, since everything else depends on the one principle that the whole is greater than its part, Euclid prefaced the Elements by saying that the rest can be solved by addition and subtraction alone. But this principle, along with No. 20, depends on the noblest of all, namely: 24. That there is nothing without a reason. The consequences of this principle are that as little as possible should be changed, that the mean is to be chosen between contraries, that whatever is added to one thing need not even be subtracted from another, and many other things that are important in civil science as well. II. AN EXAMPLE OF DEMONSTRATIONS ABOUT THE NATURE OF CORPOREAL THINGS, DRAWN FROM PHENOMENA Late 1671 [K., pp. 141-42] By the word thing we mean that which appears, hence that which can be understood; because when we are deceived and recognize our error, we may still rightly say that something has appeared to us but not that it has existed. The nature of a thing is the cause, in the thing itself, of its appearances. Hence the nature of a thing differs from its phenomena as a distinct appearance differs from a confused one, and as the appearance of parts differs from the appearance of their positions or their relations to the outside; or as the plan of a city, looked down upon from the top of a great tower placed upright in its midst differs from the almost infinite horizontal perspectives with which it delights the eyes of travelers who approach it from one direction or another. This analogy has always seemed excellently fitted for understanding the distinction between nature and accidents. 11
MAINZ AND PARIS, 1666-76 143 What men call a body must be investigated carefully, for a clear and distinct idea of this gives us access to demonstrations. First of all, men agree that only what is thought of as extended can be called a body. Yet all men hold that wherever they think of empty extension alone, there is no body but only empty space. And they think that the space remains when one body leaves it and another takes its place, even if they sense the contrary. Whether this derives from the prejudices of childhood needs to be made clear. Moreover, they think of a body whenever they think of something else besides space or extension alone which appears to them, for mere extension never appears to them without being invested with some color, or conatus, or resistance, or some other quality. At first glance it occurs to no one that these are merely species of extension, and therefore we must' not assume it any more than we assume that all bodily changes are merely local movements. This must be demonstrated. Therefore we think of a body whenever we think of extension being somewhere but at the same time think of a phenomenon. We can, of course, think of bodies which are not perceptible to us. But we think of all these as imperceptible, either because they are not located conveniently to us or because they are too large or too small. Bu t for these same reasons we can also certainly say that bodies are perceptible (even if not in themselves but merely in their externals), if we think we should see them even if nothing were changed in them, but only in things external to them, as in us and the medium. So for example, we believe we should be able to see fish in the bottom of the sea if we could descend there; hence we also believe that they are there. Men call space something which they think is extended but nothing else, unless it be immutable. For they think that when everything else is changed, that is, is sensed to have stopped or begun, space is sensed as neither stopping nor beginning but that it is always sensed as long as sentient beings are attending to it (that is, want to sense it) and as long as they retain the faculty of sense or are able to sense. Indeed, they think that this is the only way in which they can sense it and that, even if they might wish to, they can never think of it as anything but what would be sensed never to move as long as they attended to it. Space is therefore something extended which we see that we cannot think of as changing. A body is something in space (that is, something not apart from some space), which we perceive we cannot think of without space, though we can think of space without it, But can we think of space without any body? We can, but only in the same way that we think of God, the mind, the infinite. These are kno wn, and hence thought of, but without any image. We think of space in a body, but because we think of space remaining the same when a body changes, we percei ve space and body to be distinct. However, space and body are distinct. For we perceive that we think of space as the same when bodies change, and what we perceive ourselves to be thinking or not thinking we perceive truly.12 The perception of thought is immediate to the thought itself in the same subject, and so there is no cause of error. Therefore it is true that we think of space remaining the same when bodies change and that we can think of space without a body which is in it. Now two things are diverse if one can be thought of without the other. Therefore space and body are diverse. Let no one think that this demonstration is like Descartes's effort to demonstrate the existence of God from the idea in his mind. It will be worth while to show the difference briefly. Descartes's argument reduces to this. I think (clearly and distinctly) of a perfect being. Whatever I think (clearly and distinctly) is possible. Therefore a perfect For references see p. 144
144 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS being is possible. Again, if something is possible, that without which it cannot be thought (that is, that without which it is impossible) is necessary. But a perfect being cannot be thought of without its existence. Therefore the existence of a perfect being is necessary. The perfect being is God. Therefore the existence of God is necessary. He could have condensed this as follows. An existing being is possible. That without which it is not possible is necessary. An existing being without existence is not possible. Therefore the existence of an existing being is necessary. Who would deny it? But also, who would conclude from it that God is, since, namely, we have already assumed that he is? But Descartes's entire reason obviously reduces to this. For he asserts that God is perfect only because he thinks that this proposition contains the proposition that God exists. But he has not yet proved that God is perfect in the sense that he already exists; this in turn rests on the question whether he exists. Our reasoning is entirely different, although it does proceed from an idea in our mind to the truth of things. For it rests on these two propositions: whatever is perceived clearly and distinctly is possible, and whatever is immediately sensed is true. Or whatever the mind perceives within itself, it perceives truly. Hence if the mind dreams that it is thinking, it will be truly thinking; however, it will not be truly seeing if it dreams it is seeing. Therefore, when I sense that I am thinking clearly and distinctly of space remaining the same when a body changes, I am sensing truly. What I sense clearly and distinctly is possible; therefore it is possible for space to remain the same when a body changes. Therefore space and body are different. ... REFERENCES The phrase is in J. E. Hofmann, Die Entwicklungsgeschichte der leibnizschen Mathematik wiihrend des Aufenthaltes in Paris, Munich 1949, p. 4. This work describes Leibniz's efforts to 1 establish his reputation at this time and the unhappy effects upon his later relations with the Royal Society. 2 This section is preceded by definitions of the concepts involved in the laws of bodily impact. The title implies that Leibniz considers them as demonstrable, though they are treated as postulates. In his mature period such principles would be 'subordinate maxims' (No. 35, Sec. 17) or principles of existence and therefore not completely reducible to the general laws of being by human minds. Here they illustrate Leibniz's a priori and synthetic approach to scientific laws, though the basic principles of being (except for the law of sufficient reason in Sec. 24) are not yet formulated. 3 Leibniz had read Uotaud's Examen circuli quadraturae and Cavalieri's Geometria indivisibilibus continuorum nova quadam ratione promota and is here struggling with the latter's indivisibles and the paradoxes involved in them. He makes no headway with the possible elements of a calculus of infinitesimaIs, however, until after he has read Pascal in Paris. His concern here is rather with the place of Hobbes's conatus as beginning of motion, in relation to geometric and phoronometric relations. 4 Cf. p. 101, note 3. Conatus is here an element of motion at a point; Leibniz does not distinguish force from motion until the period in which he criticized Descartes's theory of the conservation of quantity of motion (No. 34). 5 See p. 103, note 11. 6 The reflective perception of its own processes is thus the basis of memory and thought in the mind. Leibniz has here moved beyond the mind-body dualism of Descartes to a position in which both are analyzed into elementary motions endowed with feeling. 7 The difficulties which Hobbes's theory of the conatus crea tes with respect to the whole-part
MAINZ AND PARIS, 1666-76 145 axiom of Euclid lead Leibniz eventually to distinguish between the relations of containing and inclusion, on the one hand, and part-whole, on the other. The Scholastic doctrine of signs, which he here introduces as elements wherein greater and smaller points or conatuses differ, is fruitful in the further development of Leibniz's thought, for it suggests the internal complexities of any particular value of y = I(x), the petites perceptions in a present mental state, and the relations within a momentary impulse of force. S Contrary to Euclid's definition of a point as that which has no parts. The rest of this section contains applications to the geometry of angles, circles, regular polygons, and circular motion. 9 Thus Leibniz knew of the construction of the cycloid before studying Pascal, as well as the principle of compounding and resolving quantities of motion. 10 Phoronomy is the abstract theory of motion, or the interpretation of motion in terms of the general principle of the equivalence of preceding and succeeding states of motion. It thus adds to geometry the temporal dimension and lies midway between that science and Leibniz's later science offorce, or dynamics. 11 See p. 103, note 12. 12 Leibniz uses sentio throughout this study for the fundamental mental act of apprehension; for the sake of clarity we have used, variously, 'to see', 'to perceive', and 'to sense'.
9 LETTER TO MAGNUS WEDDERKOPF May, 1671 Leibniz's starting point in the principle of harmony, and the metaphysical consequences which he draws from it, are explicit in this letter to a jurisconsult in Kiel with whom he corresponded briefly. The implications of Leibniz's determinism for the problems of freedom and of evil are briefly treated. [PA., II, i, 117-18] Fate is the decree of God or the necessity of events. Those events are fatal which will necessarily happen. Both views are difficult - that a God who does not decide everything, or that a God who does decide everything, should be the absolute author of all. For if he does decide everything, and the world dissents from his decree, he will not be omnipotent. But if he does not decide everything, it seems to follow that he is not omniscient. For it seems impossible that he should suspend his omniscient judgment about anything. If we frequently suspend our judgments, this happens out of ignorance. Hence it follows that God can never be purely permissive. It follows also that there is no decree of God which is really not absolute. For we suspend our judgments with conditions and alternatives because we have insufficiently explored the circumstances of the problem. Is this conclusion hard? I admit it. What of it? Pilate is condemned. Why? Because he lacks faith. Why does he lack it? Because he lacks the will to attention. Why this? Because he has not understood the necessity of the matter (the utility of attending to it). Why has he not understood it? Because the causes of understanding were lacking. For it is necessary to refer everything to some reason, and we cannot stop until we have arrived at a first cause - or it must be admitted that something can exist without a sufficient reason for its existence, and this admission destroys the demonstration of the existence of God and of many philosophical theorems. What, therefore, is the ultimate reason for the divine wiII? The divine intellect. For God wiIIs the things which he understands to be best and most harmonious and selects them, as it were, from an infinite number of all possibilities.! What then is the reason for the divine intellect? The harmony of things. What the reason for the harmony of things? Nothing. For example, no reason can be given for the ratio of 2 to 4 being the same as that of 4 to 8, not even in the divine wiII. This depends on the essence itself, or the idea of things. For the essences of things are numbers, as it were, and contain the possibility of beings which God does not make as he does existence, since these possibilities or ideas of things coincide rather with God himself. Since God is the most perfect mind, however, it is impossible for him not to be affected by the most perfect harmony, and thus to be necessitated to do the best by the very ideality of things. This in no way detracts from freedom. For it is the highest freedom to be impelled
MAINZ AND PARIS, 1666-76 147 to the best by a right reason. Whoever desires any other freedom is a fool. Hence it follows that whatever has happened, is happening, or will happen is best, and also necessary, but as I have said, with a necessity which takes nothing away from freedom because it takes nothing from the will and from the use of reason. No one has the power to will what he wills, even though he can somethimes do what he wills. Indeed, no one wants this Ii berty of willing what to will for himself, but rather of willing the best. Why then do we invent for God that which we do not want for ourselves? It is thus clear that an absolute will which does not depend upon the goodness of things is a monstrosity; there is, on the contrary, no permissive will in an omniscient being, except insofar as God makes himself conform to the ideality or the bestness [optimitate] of things. Therefore nothing is to be considered absolutely evil; otherwise God would not be supremely wise in grasping it or supremely powerful in eliminating it. I have no doubt that this was the opinion of Augustine. Sins are evil, not absolutely, not to the world, not to God - for otherwise he would not permit them - but only to the sinner. God hates sins, not in the sense that he cannot bear the sight of them as we cannot bear the sight of things we detest - otherwise he would eliminate them - but in the sense that he punishes them. Sins are good, that is, harmonious, taken along with their punishment or expiation. For there is 110 harmony except through contraries. But this is said to you; I should not like to have it get abroad. For not even the most accurate remarks are understood by everyone. 2 REFERENCES The distinction between possibility and existence and the principle of the best possible were thus taking form in Leibniz's mind before he read MaJebranche in Paris and before he criticized Spinoza's view that all possibles exist (No. 14, II, and No. 20). But there is no evidence that he has worked out the logical foundations of the distinction. 2 Later note by Leibniz: "I later corrected this, for it is one thing for sins to happen infallibly, another for them to happen necessarily." Whether Leibniz later succeeds in softening the harshness of his determinism is doubtful (see No. 29). 1
10 LETTER TO ANTOINE ARNAULD Early November, 1671 (Selection) 'The great Arnauld', Jansenist opponent of the Jesuits and acknowledged to be the outstanding philosophical and theological controversialist of the time, was at the height of his fame and activity when Leibniz addressed his first letter to him. The occasion was a plan to promote Catholic support for the proposed Catholic Demonstrations (No.5). Arnauld's criticisms in his later correspondence were to be influential in sharpening Leibniz's thought (Nos. 35 and 37), but there is no evidence that he replied to this letter. Only that part of this long and rather boastful writing is here translated which outlines Leibniz's intellectual opinions and motives. The section on physiCS restates some of the conclusions in the New Physical Hypothesis (No.8, J) and further sections build his psychology upon it. [G., I, 71-74] ... Amid so many distractions, there is nothing, I think, upon which I have brooded more earnestly over the course of my life, however short, than the problem of assuring my security in the future, and I confess that by far the greatest cause of my philosophizing as well has been the hope of winning a prize not to be disdained - peace of mind and the ability to say that I have demonstrated certain things which have heretofore merely been believed or even, in spite of their great importance, ignored. I saw that geometry, or the philosophy of position, is a step toward the philosophy of motion and of body and that the philosophy of motion is a step toward the science of mind. Therefore I have demonstrated some propositions of great importance about motion, of which I shall here state two. First, there is no cohesion or consistency in bodies at rest, contrary to what Descartes thought, and furthermore, whatever is at rest can be impelled and divided by motion, however small. This proposition I later extended still further, discovering that there is no body at rest, for such a thing would not differ from empty space. From this there follows a demonstration of the Copernican hypothesis and many other novelties in natural science. The other proposition is that all motion in a plenum is homocentric circular motion and that no rectilinear, spiral, elliptical, oval, or even circular motion around different centers can be understood to exist in the world, unless we admit a vacuum. It is unnecessary to speak of the rest here. I mention these because something follows from them which is useful for my present purpose. From the latter principle it follows that the essence of body does not consist in extension, that is, in magnitude and figure, because empty space, even though extended, must necessarily be different from body. From the former it follows that the essence of body consists rather in motion, since the concept of space involves nothing but magnitude and figure, or extension.
MAINZ AND PARIS, 1666-76 149 In geometry I have demonstrated certain fundamental propositions on which depends a geometry of indivisibles, that is, a source of discoveries and demonstrations. These are that any point is a space less than any given space; that a point has parts, though these are dense [indistantes]; that Euclid was not wrong in speaking of parts of extension; that there are no indivisibles, yet there are non-extended beings; that one point is greater than another point, but in a relation less than any which can be expressed, or incomparable to any sensible difference; that an angle is the quantity of a point. From the phoronomy of indivisibles I added to these that the relation of rest to motion is not that of a point to space but that of nothing to one; that a conatus is to motion as a point is to space; that there can be several conatuses at once in the same body but not several contrary motions; that at the time of its conatus a single point of a moving body may sometimes be in many places or many points of space or in a part of space greater than itself; that whatever moves is never in one place, not even in an infinitesimal instant; that, if one body strives against another, this is the beginning of mutual penetration or union or that the boundaries of the two are one, as Aristotle defines a continuum (ov TO. laxaTa BV). Hence all those bodies - and only those - cohere which press upon each other. There are also certain momentary parts or signs, a conception which can be understood from continuously accelerated motion which increases at every instant and hence at the very beginning. For to increase connects the earlier and the later state. At a given instant one sign is necessarily prior to another, but without extension, that is, without any distance between the signs whose ratio to any sensible time whatever is greater than any given quantity, or as that of a point to a line. 1 From these propositions I reaped a great harvest, not merely in proving the laws of motion, but also in the doctrine of mind. For I demonstrated that the true locus of our mind is a certain point or center, and from this I deduced some remarkable conclusions about the imperishable nature of the mind, the impossibility of ceasing from thinking, the impossibility of forgetting, and the true internal difference between motion and thought. Thought consists in conatus, as body consists in motion. Every body can be understood as a momentaneous mind, or2 mind without recollection. Every conatus in bodies is indestructible with respect to direction [determinatio] 3; in mind it is also indestructible with respect to the degree of velocity. As the body consists in a sequence of motions, so mind consists in a harmony of conatuses. The present motion of a body arises from the composition of preceding conatuses; the present conatus of a mind, that is, will, arises from the composition of preceding harmonies into a new one or through pleasure. If this harmony is disturbed by another conatus impressed upon it, the result is pain. I hope to demonstrate these and many other matters in the Elements of Mind which I am undertaking. From this I make bold to promise some light for the defense of the mysteries of the Trinity, the Incarnation, Predestination, and the Eucharist, of which I shall speak last of all. My mode of life has itself compelled me to try to investigate moral problems and to establish the foundations of justice and equity with somewhat more clarity and certainty than is usual. I am working on a Nucleus of Roman Law, which presents in its own words, concisely and in good order, that which is truly law in the entire Corpus, both what is new and what is purviewed - all this as a sample of a new Perpetual Edict which can be enacted even now. In addition, I am thinking of recapitulating the Elements of Roman Law in a short table which presents, at a single glance, the few clear For references see p. 150
150 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS rules the combination of which can solve all cases, and furthermore, new arguments for abridging lawsuits - all these far more expediently, efficiently, thoroughly, and naturally [ollcelCh"ep(n], so to speak, than has been proposed anywhere, in my opinion. In addition to these, I am planning to treat the Elements 0/ Natural Law in a short book in which everything will be demonstrated from definitions alone. I define a good man or a just man as one who loves all men; love as pleasure derived from the happiness of others, and pain from the unhappiness of others; happiness as pleasure without pain; pleasure as the sense of harmony; pain as the sense of disharmony [inconcinnitas]; sense as thought with will or with a conatus to act; harmony as diVersity compensated by identity. For variety always delights us if it is reduced to unity. From these I deduce all the theorems of justice and equity. That is permitted which a good man can do. That is duty which a good man must do. Hence it is clear that the just man, the man who loves all, necessarily strives to please all, even when he cannot do so, much as a stone strives to fall even when it is suspended. I show that all obligation is fulfilled by the supreme conatus; that to love others and to love God, the seat of universal harmony, is the same; indeed, that it is the same to love truly or to be wise, and to love God above all things; this is to love all or to be just. If the benefits of several people interfere with each other, that person is to be preferred from whose help the greater good in the end follows. Hence in case of conflict, other things being equal, the better man, that is, the one who loves more generally, is to be preferred. For whatever is given him will be multiplied by reflection so as to benefit many people, and therefore many will be helped by helping him. In general, other things being equal, he is to be preferred who is already satisfied. For it may be shown that benefiting others proceeds at the rate, not of addition but of multiplication. If two numbers, one greater than the other, are multiplied by the same number, multiplication adds more to the larger.... Therefore the larger the number that is multiplied by the same multiplier, the greater is our gain. This difference between addition and multiplication has important applications in the doctrine of justice. For to benefit is to multiply, to harm is to divide, for the reason that the person benefited is a mind, and mind can apply each thing in using it to everything, and this is in itself to expand or to multiply it .... REFERENCES That is, the ratio approaches zero. On Leibniz's use of the doctrine of signs see p. 144, note 7. Reading seu for sed (as in No.8, I, and following G.'s suggestion, p. 73). 8 Determinatio is generally the logical condition for a complete or existent notion, as opposed to incomplete or abstract notions. In his physical writings, however, Leibniz uses it in the sense of determined direction, as here interpreted. 1 2
11 LETTER TO SIMON FOUCHER WITH NOTES ON FOUCHER'S REPLY TO DES GABETS 1675 Leibniz's intellectual achievements during the four years he spent in Paris, from March, 1672, to September, 1676 1 , cannot befully appraised until his papers from that period are completely published. The general impression that he forsook philosophy for mathematics is wrong; indeed, it contradicts his whole conception of the relation between the two fields. While his mathematical studies were advancing under the guidance of Huygens and by the reading of Pascal and Descartes, his philosophical conceptions were also being subjected to new tests and problems ,for it is in this period that Malebranche produced the Recherche de la verite and that Leibniz had opportunity for discussions with him, with Arnauld, with Foucher, and with other intellectual leaders. Now, too, he undertook a careful study of Descartes and Plato, whose Phaedo and Theaetetus he paraphrased during this period. Simon Foucher, canon of Dijon (1644-97), had written a criticism of Malebranche's work in 1675 from the point of view of the ancient Academy; in the following year he replied to a defense of that author by Dom Robert des Gabets. Leibniz's letter to Foucher in 1675 concerns questions of subjectivism and our knowledge of the external world. His notes to Foucher's reply to Dom Robert show that his own doctrine of ideas is now related explicitly to the problems of epistemology and logic. [G., I, 369-74] I I agree with you that it is important once and for all to examine all our presuppositions in order to establish something sound. For I hold that it is only when we can prove everything we assert that we understand perfectly the thing being considered. I know that such studies are not very popular, but I also know that to take the pains to understand matters to their roots is not very popular. As I see it, your purpose is to examine those truths which affirm that there is something outside of us. You seem to be most fair in this, for thus you will grant us all hypothetical truths which affirm, not that something does exist outside of us, but only what would happen if anything existed there. So we at once save arithmetic, geometry, and a large number of propositions in metaphysics, physics, and morals, whose convenient expression depends on arbitrarily chosen definitions, and whose truth depends on those axioms which I am wont to call identical; such, for example, as that two contradictories cannot exist and that at any given time a thing is as it is; that it is, for example, equal to itself, as great as itself, similar to itself, etc. But although you do not enter explicitly into an examination of hypothetical propositions, I am still of the opinion that this should be done and that we should For references see p. 155
152 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS admit none without having entirely demonstrated and resolved it into identities. It is the truths which deal with what is in fact outside of us which are the primary subject of your investigations. Now in the first place, we cannot deny that the very truth of hypothetical propositions themselves is something outside of us and independent of us. For all hypothetical propositions assert what would be or would not be, if something or its contrary were posited; consequently, they assume two things at the same time which agree with each other, or the possibility or impossibility, necessity or indifference, of something. But this possibility, impossibility, or necessity (for the necessity of one thing is the impossibility ofits contrary) is not a chimera which we create, since all that we do consists in recognizing them, in spite of ourselves and in a constant manner. So of all the things which actually are, the possibility or impossibility of being is itself the first. But this possibility and this necessity form or compose what are called the essences or natures and the truths which are usuaIly called eternal. And we are right in calling them this, for there is nothing so eternal as what is necessary. Thus the nature of the circle with its properties is something which exists and is eternal, that is, there is some constant cause outside of us which makes everyone who thinks carefully about a circle discover the same thing, not merely in the sense that their thoughts agree with each other, for this could be attributed solely to the nature of the human mind, but also in the sense that phenomena or experiences confirm them when some appearance of a circle strikes our senses. These phenomena necessarily have some cause outside of us. But although the existence of necessities comes before all others in itself and in the order of nature, I nevertheless agree that it is not first in the order of our knowledge. For you see that in order to prove its existence, I have taken for granted that we think and that we have sensations. So there are two absolute general truths; truths, that is, which teIl of the actual existence of things. One is that we think; the other, that there is a great variety in our thoughts. From the former it foIlows that we are; from the latter, that there is something other than us, that is to say, something other than that which thinks, which is the cause of the variety of our experiences. Now one of these truths is just as incontestable and as independent as the other, and having stressed only the former in the order of his meditations, Descartes failed to attain the perfection to which he had aspired. If he had foIlowed with exactness what I calI a filum meditandi 2 , I believe that he would reaIly have achieved the first phiiosophy.3 But not even the greatest genius can force things; we must of necessity enter through the openings which nature has made, in order to avoid being lost. What is more, one man alone cannot do everything all at once, and for myself, when I think of all that Descartes has said that is exceIlent and original, I am more amazed at what he has done than at some things which he failed to do. I admit that I have not yet been able to read his writings with all the care that I had intended to give them, and as my friends know, it happened that I read most of the other modern philosophers before I read him. Bacon and Gassendi were the first to faIl into my hands. Their familiar and easy style was better adapted to a man who wanted to read everything. It is true that I have often glanced through Galileo and Descartes, but since I have only recently become a geometrician, I was soon repeIled by their style of writing, which requires deep meditation. Personally, though I have always loved to think by myself, I have always found it hard to read books which one cannot understand without much meditation, for in following one's own thoughts one follows a certain natural inclination and so gains profit with pleasure. One is
MAINZ AND PARIS, 1666-76 153 violently disturbed, in contrast, when compelled to follow the thoughts of someone else. I always liked books which contained some good thoughts, but which I could run run through without stopping, for they aroused ideas in me which I could follow up in my own fancy and pursue as far as I pleased. This also prevented me from reading the books on geometry carefully; I freely admit that I have not yet been able to make myself read Euclid in any other way than one usually reads history. I have learned from experience that this method is good in general, yet I have recognized nevertheless that there are authors for whom one must make an exception, such as Plato and Aristotle among ancient philosophers, and GaIileo and Descartes among our own. Yet what I know of the metaphysical and physical meditations of Descartes has come almost entirely from the reading of a number of books written in a more popular style which report his opinions. And perhaps I have not as yet understood him well. To the extent that I have read him over myself, however, it seems to me that I have at least been able to discover what he has not done or tried to do, and among other things, this is to analyze all our assumptions. This is why I am inclined to applaud all who examine even the smallest truth to the end, for I know that it is much to understand something perfectly, no matter how small or easy it may seem. One can go very far in this way and finally establish the art of discovery, which depends on knowledge of the simplest things, but on a distinct and perfect knowledge of them. It is for this reason that I have found no fault with the plan of De Roberval, who tried to demonstrate everything in geometry, even some of the axioms. 4 I grant that we should not enforce such exactness upon others, but I believe that it is good to demand it of ourselves. But I return to these truths which are primary with respect to ourselves, and first to those which assert that there is something outside of us; namely, that we think and that there is a great variety in our thoughts. This variety cannot come from that which thinks, since one thing by itself cannot be the cause of the changes occurring in it. For everything remains in the state in which it is, unless there is something which changes it. And since it has not been determined by itself to undergo certain changes rather than others, we cannot begin to attribute any variety to it without saying something which admittedly has no reason, which is absurd. Even if we tried to say that our thoughts have no beginning, we should be obliged to assert that each of us has existed from all eternity; yet we should not escape the difficulty, for we should always have to admit that there is no reason for this variety which would have existed from all eternity in our thoughts, since there is nothing in us which determines us to one variety rather than another. Thus there is some cause outside of us for the variety of our thoughts. And since we agree that there are some subordinate causes of this variety which themselves still need a cause, we have established particular beings or substances to whom we ascribe some action, that is, from whose change we think that some change follows in us. So we make great strides toward fabricating what we call matter and body. S But at this point you are right in stopping us for a while and renewing the criticisms of the ancient Academy. For at bottom all our experiences assure us of only two things: first, that there is a connection among our appearances which provides the means to predict future appearances successfully; and, second, that this connection must have a constant cause. But it does not follow strictly from this that matter or bodies exist but only that there is something which gives us appearances in a good sequence. For if some invisible power were to take pleasure in giving us dreams that are well tied into our preceding life and in conformity with each other, could we distinguish them from For references see p. 155
154 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS reality before we had awakened? Now, what prevents the course of our life from being one long well-ordered dream, about which we could be undeceived in a moment? Nor do I see that such a power would be imperfect just on this ground, as Descartes asserts, to say nothing of the fact that its imperfection is not involved in tbe present question. For it might be a kind of subordinate power, or a demon who for some unknown reason could interfere with our affairs and who would have at least as much power over us as that caliph had over the man whom he caused to be carried, drunk, into his palace, and let taste of the paradise of Mohammed after he was awakened; after which he was once more made drunk and returned in that condition to the place where he had been found. When this man came to himself, he naturally interpreted this experience, which seemed inconsistent with the course of his life, as a vision, and spread among the people maxims and revelations which he believed he had learned in his pretended paradise; this was precisely what the caliph wished. Since reality has thus passed for a vision, what is to prevent a vision from passing for reality? The more consistency we see in what happens to us, it is true, the more our belief is confirmed that what appears to us is reality. But it is also true that, the more closely we examine our appearances, the better ordered we find them, as microscopes and other means of observation have shown. This permanent consistency gives us great assurance, but after all, it will be only moral until somebody discovers a priori the origin of the world which we see and pursues the question of why things are as they appear back to its foundations in essence. For when this is done, he will have demonstrated that what appears to us is reality and that it is impossible for us ever to be deceived in it. But I believe that this would very nearly approach the beatific vision and that it is difficult to aspire to this in our present state. Yet we do learn therefrom how confused the knowledge which we commonly have of the body and matter must be, since we believe we are certain that they exist, but eventually find that we could be mistaken. This confirms Mr. Descartes's excellent thought concerning the proof of the difference between body and soul, since one can doubt the one without being able to question the other. For even if there were only appearances or dreams, we should be nonetheless certain of the existence of that which thinks, as Descartes has very well said. I may add that one could still demonstrate the existence of God by ways different from those of Descartes but, I believe, leading farther. For we have no need to assume a being who guarantees us against being deceived, since it lies in our power to undeceive ourselves about many things, at least about the most important ones. I wish, Sir, that your meditations on this matter may have all the success you desire; but to accomplish this, it is well to proceed in order and to establish your propositions. This is the way to gain ground and make sure progress. I believe you would oblige the public also by conveying to it, from time to time, selections from the Academy and especially from Plato, for I know that there are things in them more beautiful and substantial than is usually thought. II. NOTES ON THE REPLY OF FOUCHER TO THE CRITICISM OF HIS CRITICISM OF THE 'RECHERCHE DE LA VERITE'6 1676 On page 30. An idea is that by which one perception or thought differs from another with respect to its object.
MAINZ AND PARIS, 1666-76 155 On page 33. Though they are not extended, ideas can serve the mind to know extension, for there can be a relation between what is extended and what is not, as for example, between an angie and the arc by which it is measured. On page 39. Idea can be taken in two senses; namely, for the quality or form of thought, as velocity and direction are the quality and form of movement; or for the immediate or nearest object of perception. Thus the idea would not be a mode of being of our soul. This seems to be the opinion of Plato and the author of the Recherche. For when the soul thinks of being, identity, thought, or duration, it has a certain immediate object or nearest cause of its perception. In this sense it is possible that we see all things in God and that the ideas or immediate objects are the attributes of God himself. These formulas or modes of speaking contain some truth, but to speak correctly it is necessary to give constant meanings to the terms. 7 On page 56. The author says that traces are necessary for us to conserve a memory of things. But this does not seem so certain to me. Those who ascribe memory to the separate soul will not agree to it. By what trace does the soul remember that it has beC¥1 and has thought? On page 63. The author seems to reason as follows. When we speak of being, thought, etc., the traces of these words are not naturally joined to the ideas. Therefore there must be some traces which are joined immediately to the ideas. But perhaps they can be joined immediately without being joined naturally. One must investigate the means we might use to make men who do not understand our language grasp the meaning of the words: to be and to think. This would be done, it seems to me, by showing them specimens and giving them negatively to understand that the words which we use signify what they experience or perceive in themselves or in the things, over and above what they see, hear, or touch. Thus they can be made to understand these words, not through traces but through the negation of traces. Once understood, these words will serve as traces, though arbitrary, for the future. It would be necessary to observe more exactly how infants learn language by hearing adults and without an interpreter .... On page 120. The author is right in saying that thought is not the essence of the soul, for a thought is an act, and since one thought succeeds another, that which remains during this change must necessarily rather be the essence of the soul, since it remains always the same. The essence of substances consists in the primitive force of action, or in the law of the sequence of changes, as the nature of the series consists in the numbers.8 REFERENCES For an account of Leibniz's activities in Paris see L. Daville, 'Le Sejour de Leibniz a Paris', Archiv fiir Geschichte der Phil. 32 (1920), 142ft'.; 33 (1920), 67ft'., 165ft'. This letter is in French, a new accomplishment of Leibniz. The date follows PA., rather than G., who surmises 1676. 1 2 The figure of Ariadne's thread, by which Theseus made his way out of the Cretan labyrinth, served Leibniz to illumine the purpose of his proposed universal characteristic and general science. S That is, metaphysics. The allusion is clearly to the Meditations on First Philosophy. 4 Giles Personne de Roberval (1602-75) was for over 40 years the occupant of the famous chair established by Ramus at the Royal College. S Leibniz here puts the argument for an external world in its causal form, which will have to be
156 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS modified after his later view of the self-determination of individual substances has been developed. But he always argues that the complex and coherent nature of our perceptions is the evidence for an external world. 6 The text of these notes is taken from F. Rabbe, L 'Abbe Simon Foucher, Paris 1867, Appendix p. xIii. In his letter to Foucher, Leibniz has virtually admitted that human analysis cannot advance from truths of fact to the simple primary truths upon which they rest. These notes, on the other hand, show that he has not abandoned the realm of ideas and absolute truths as a foundation for all knowledge. 7 Leibniz's own view of ideas, to judge by his later definition in No. 21, includes both senses given here, if 'form' is taken in a Platonic sense. S If this sentence is not a later revision note, it is an early appearance of Leibniz's conception both ofthe individual law or notion (cf. No. 35) and of primitive force.
12 SELECTIONS FROM THE PARIS NOTES 1676 The many philosophical notes which Leibniz made in Paris have been only imperfectly and very incompletely published. Those translated here were edited by 1. Jagodinski in 1913. Written hastily, often rej/ecting the excitement of initial, untested exploration, with sentences incomplete and opinions sometimes reversed within the same fragment, they indicate the entire range of Leibniz's metaphysical problems - that of the infinite in space and time, that of the metaphysical foundations of a logic of analysis and synthesis and its compatibility with a genuine individualism. Leibniz takes a critical attitude toward the Cartesian and Spinozistic dualism of extension and thought. There is a strong interest in self-experience, which serves to offset the continuing trend toward monism and immanentism. February 11, 1676 [Jag., pp. 28-40] After rightly weighing matters, I set up as a principle the harmony of things, that is, the principle that the greatest possible quantity of essence exists. It follows that there is more reason for the existent than for the nonexistent and that all things would exist if this were possible for them. For since something exists, but all possibles cannot exist, it follows that those things exist which contain the most essence, since there is no other reason for choosing them and excluding others.l So there will exist, before all things, the being that is the most perfect of all possible beings. The reason is obvious, moreover, why most perfect beings should exist before all things, because, being at once both simple and perfect or including a maximum, they leave most room for others. Hence one perfect being is to be preferred to many equivalent imperfect beings, because since the latter occupy space and time, they impede the existence of others. From this principle it already follows that there is no vacuum offorms; likewise there is no vacuum in space and time to the extent that this is possible. Hence it follows that no time can be designated in which something does not occur, and no space which is not as full as it can be. We must therefore see what follows from the fulness of the world. But above all we will prove that besides fluids there must also exist solids, for these are more perfect than fluids, since they contain more essence. But not all things can be solid, for then they would impede each other. There are therefore solids mixed in with fluids. It does not seem possible to explain the origins of solids from the motion of fluids alone. All solids seem (if I may say so in passing) to be informed with a certain mind .... Whether atoms seem consistent with reason? If any atom once subsists, it will always subsist, for the surrounding liquid matter will strive to dissipate it because its motion is agitated, as can easily be shown. If any large body which resists dissipation to some For references see p. 164
158 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS extent moves in a liquid, it will at once form a kind of island and a vortex. It seems to follow from a solid in a liquid that perfectly fluid matter is nothing but a multitude of infinitely small points or of bodies less than any assignable ones, or that there is necessarily an interspersed metaphysical vacuum; this does not conflict with a physical plenum. A metaphysical vacuum is an empty place, however small, yet true and real. A physical plenum is consistent with an unassignable metaphysical vacuum. Perhaps it follows from this that matter is divided into perfect points or into all the parts into which it can be divided. No absurdity follows from this, for it would follow that a perfect fluid is not a continuum but discrete or a multitude of points. From this it does not further follow that the continuum is composed of points, since liquid matter will not be a true continuum, though space will be. Hence it is clear, further, how great the difference between space and matter. Matter alone can be explained by a plurality without continuity. And matter seems in fact to be a discrete being. For though it is assumed to be solid, matter taken without a cement, through the motion of another body, for example, will be reduced to a state of liquidity or divisibility. Hence it follows that it is composed of points. This I prove as follows: every perfect liquid is composed of points, because it can be dissolved into points, namely, by the motion of a solid within it. Matter therefore is discrete being, not continuous. It is merely contiguous and is united by motion or by some mind. There seems to be a certain center to the whole universe, and an infinite general vortex, and a most perfect mind, or God. And this mind is a whole in the whole body of the world; to it is due also the existence of the world. It itself is its own cause. Existence is nothing but that which is the cause of sensations agreeing among themselves. The reason for the world is the aggregate of requisites of all things. Concerning the one, concerning God. The whole infinite is one. That particular minds exist amounts merely to this - that the highest being judges it conducive to harmony that there should be somewhere something that understands, i.e. some intellectual mirror or a reduplication of the world. To exist is nothing other than to be harmonious; the mark of existence is organized sensations. From the fact that something exists, it follows that there is some necessity for it, and hence either that all things are necessary in themselves (which is false) or that their ultimate causes are necessary. Hence it follows that an absolutely necessary being is possible or does not imply a contradiction. It follows therefore that it exists. Whence it is to be seen whether this being can be demonstrated to be unique, etc. Furthermore, since some things exist, and certain things do not exist, it follows that there must exist most perfect Elements 0/a Secret Philosophy 0/ the Whole o/Things, geometrically demonstrated. " . God is not a kind of imaginary metaphysical being. incapable of thought, will, and action, as some make him. This would be the same as to say that God is nature, fate, fortune, necessity, or the world. But God is a definite substance, a person, a mind. These meditations could be entitled On the Secrets o/the Sublime, or also De summa rerum. It was the extreme abstractions of certain imagined philosophers, who reduced God to a kind of imperceptible nothing, that caused Vorst, indignant against opinions so chimerical and contrary to the divine honor, to make God corporeal and enclose him in a definite place in order to show that he is a substance and a person. 2 It must be shown that God is a person or substance, an intelligence. It must be demonstrated rigorously that he feels himself to act upon himself. For there is nothing more admirable than for the same being to feel and to be acted upon by himself.
MAINZ AND PARIS, 1666-76 159 The whole labyrinth about the composition of the continuum must be unraveled as rigorously as possible; see the book of Fromond. 3 Treatment of the angle of the tangent, for this discussion belongs not to geometry but to metaphysics. We must see whether it can be demonstrated that there is something infinitely small yet not indivisible; from the existence of such a being there follow wonderful things about the infinite; namely if we assume creatures of another, infinitely small world, we will be infinite in comparison with them. Hence we can clearly be assumed to be infinitely small in comparison with another world of infinite magnitude, yet bounded. Hence it is clear that the infinite is other than the unbounded, as we surely assume popularly. This unbounded infinite should more rightly be called the immensum. It is remarkable that one who has lived an infinite number of years can have had a beginning and that one who lives a number of years greater than any finite number can sometime die. From this it would follow that there is an infinite number. From another viewpoint, it is clear that there must be infinite number if a liquid is really divided into parts infinite in number. But if this is impossible, it will follow too that a liquid is impossible. Since we see that the hypothesis of infinites and infinitesimals turns out to be consistent in geometry, this also increases the probability that it is true. All possibilities cannot be understood distinctly by anyone, for they imply a contradiction. The most perfect being is that which contains the most. Such a being is capable of ideas and thoughts, for this multiplies the varieties of things like a mirror. Hence God is necessarily a thinking being, and if he is not a thinking being, the whole will be more perfect than he. An omniscient and omnipotent being is the most perfect. A thinking being is therefore even necessary, and some things which do not exist are at least thought - those, namely, worthy to be thought above others; and so, since every possible event is thinkable, some are nonetheless chosen which will be thought in reality. There are beautiful discoveries and clever images of the harmony of things. That has most harmony which is most pleasing to the most perfect of minds. If God is mind or person, it follows by reason of God and of the other minds that there must exist whatever can be demonstrated about the supreme State, whose King is most wise and most powerful. Hence no one in the world need ever be wretched unless he wills to be. It seems consistent with our reason that only he will remain wretched who wills to do so .... All things are good for him who believes, who loves God, who trusts in God. All things are good, not merely in general but also in particular, to whoever understands this. I do not see why eternal damnation is not consistent with the harmony of things. It is possible for this damnation to be of infinite duration but not unterminated. That this is probable is consistent with the harmony of things. It does not seem credible that any mind whatever should undergo all possible variations and sometime be wretched and evil; for it also does not seem that the fates of all are equalized, since whatever displeases the understanding of the wise man should, it seems, also displease God. For it seems to be reasonable that the wise man should be content. It does not seem that the wise man will be content, however, if he knows that he will sometime be wretched, or if he doubts whether he has not already been wretched sometime or will be hereafter - unless we say that this can be understood only of the past. And anyone whatever who is wise and happy at the present moment ought to be certain that he never will be either unwise or unhappy. Every relapse is a sign that he who has relapsed never was truly wise. From this it follows that all happiness is unbounded but that no wretchedness is without limits, though it For references see p. 164
160 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS can be eternal. And so the blessed will be happy for a longer time than the doomed will be unhappy, since the grace of God consists of the abundant gift of the will. For happiness is in the power of him who has a good will .... Every mind is of unbounded duration. Every mind also is implanted indissolubly in certain matter. This matter is of definite magnitude. Every mind has a vortex around it. All the mundane spheres are perhaps endowed with mind; such intelligences do not seem absurd. The objection too is that they will not have sufficiently free motion, but since they understand their duty (officium) and communicate with God through the mutual influences of the bodies which they sense, they will not affect a variety of motion. Everywhere there are innumerable minds. There are minds in the human egg even before conception, and they are not lost even if conception never takes place. We are ignorant of the wonderful uses to which things are destined by providence .... II April,1676 [Jag., pp. 94-99] Extension and thought are complex forms, for existence, duration, etc., are common to them. 4 Both thinking and extension have duration in common, but what it is for one form to be more highly structured than another is a strange thing. Thus forms differ in this respect: some involve more relations and some less. For example, thought has both subject and object, extension has merely a subject. Yet it seems that selfconsciousness is something per se, just as is extension per se, namely, a state; for in self-consciousness subject and object are the same. It if is true that there is no memory without traces and that the traces in bodies of thoughts about incorporeal things are not natural but arbitrary, or characters 5 (for there is no necessary connection of representation between the incorporeal and the corporeal), it follows that there is no knowledge or reasoning without characters, because all reasoning or demonstration takes place through a memory of premises. But as we have assumed, there is no memory without characters or images .... A remarkable thing, that the subject is something other than forms or attributes. This is necessary because nothing can be said about forms because of their simplicity. Therefore no proposition would be true unless forms are united in a subject. Thought is not duration, but a thinking being is an enduring one. And in this consists the difference between substance and forms. It is to be seen whether thought is rightly said to endure, to change, to be .... Any simple form whatever is an attribute of God. There are necessarily simple forms or perceptions per se, because if things are perceived only through others, and these others again are perceivable only through others still, and so forth, nothing at all will be perceived. In those things in which there is variety, such as color, there is a reason why this variety is not perceived distinctly by us. This is because we perceive color in a definite period of time. But this time can be subdivided into infinite parts, in each of which we do something pertaining to the perception, which we do not remember, however, because of a defect in our organs. But the things which are perceived in a single act, such as being, perception, extension, are understood perfectly.... ... Rightly understood, forms are conceived per se, and subjects through forms. This is what subjects are. But that whose modifications depend on the attributes of
MAINZ AND PARIS, 1666-76 161 something else, in which, namely, all its requisites are contained, is certainly conceived through something else; that is, it cannot be perfectly understood except by understanding another. Two things are connected if one cannot be understood without the other. Those things are requisites which connect something else, but not the converse. A reason is the sum of requisites. Sensible things cannot be perfectly understood by us, because an infinite number of things concur in constituting them, since time and space are infinitely divisible. Hence the perception of a sensible quality is not one perception but an aggregate of infinites .... ... Aristotle saw that a separate intellect does not remember, because there is no memory without imagination. For my part, it seems to me that there is some memory per se of our perception but not of a perception of variety. And so there will be neither joy nor grief without images, and no images without reminiscence.... It seems to me that without memory nothing that happens after death pertains to us. So there will be some memory after death, such as there is in faIling asleep. This operation of the mind seems most remarkable to me. It seems that when I think of myself thinking and already know, between the thoughts themselves, what I think of my thoughts, and a little later marvel at this triplication of reflection, then I turn upon myself wondering and do not know how to admire this admiration. ... It sometimes happens that I cannot forget something, but involuntarily think of the same thing for almost an hour, and then think of this difficulty in thinking and stupefy myself into reflections through perpetual reflections, so that I almost begin to doubt that I shall ever think of anything else and begin to fear that this direction of mind has harmed me. ... Anyone who desires an experience of these matters should begin to think of himself and his thinking sometime in the middle of the night, perhaps when he cannot sleep, and think of the perception of perceptions and marvel at this condition of his, so that he comes gradually to turn more and more within himself or to rise above himself, as if by a succession of spurts of his mind. He wiII wonder that he has never before experienced this state of mind. We are thus never without other perceptions than sense, for we sense within ourselves this direction of the mind by which we are led back within ourselves and suppress externals. The fatigue which accompanies pure thought certainly often arises from this. I have noticed further that this perception of perception also occurs without characters and therefore that memory does also. For to perceive perception, or to sense that I have sensed, is to remember, as Hobbes says. I do not yet adequately experience how these different acts of the mind take place in this continually reciprocating reflection, as it were, in the intervals between these acts, but they seem to be made by a distinguishing sense of the bodily direction. But if you observe well, this act wiII merely make you remember that you already had this in mind a little previously, that is, this reflection of reflection, and so you observe it and designate it by a distinct image accompanying it. Therefore it already was in your mind earlier, and so perception of perception goes on perpetually in the mind to infinity. In it consists the existence of the mind per se and the necessity of its continuation. III April 15, 1676 [Jag., pp. 108-10] In our mind there is perception or a sense of itself as of a certain specific thing; this is For references see p. 164
162 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS always in us, because, as often as we use the name, we at once recognize it. As often as we will, we recognize that we perceive our thoughts, that is, that we have thought a little earlier. Therefore intellectual memory consists not in what we sense but in that we sense - that are we those who sense. This is what we commonly call identity. This faculty in us is independent of externals. I do not see how a man or a mind can die or be extinguished while these reflections last. Something remains in modifications, not as extension in itself remains in space, but as a certain particular thing endowed with definite modifications, since, namely, it perceives one thing or another. This sense of one's particular self is without other characters, which I have well noted when I was thinking and reflecting.... If this is the nature of mind, and it consists in the perception of itself, I do not see how it can ever be impeded or destroyed, as I have said earlier, because the identity of the mind is not destroyed by any modifications and therefore is not destroyed by anything - as can easily be shown. I therefore believe that solidity or unity of body comes from the mind and that there are as many minds as vortices, as many vortices as there are solid bodies. A body resists, and this resistance is sense. The body namely resists what attempts to divide it. Sense is a kind of reaction. An incorruptible body and mind alike. Various organs around it are changed variously. . .. My opinion is that all true beings or minds, which alone are unities, increase always in perfection and that every impression which is made on the body has an effect into infinity. Minds will be for a while reduced into themselves; then they will retum, perhaps to the sense of external things, perhaps to some far different nature. Sometime there will be an intercourse of all the spheres of the world with each other. Once brought into this theater minds will advance to more and more perfection. It is impossible to believe that the effect of all perceptions will ever disappear, since the effect of all other actions lasts always. This would happen only if the mind were obliterated. So I do not accept Spinoza's opinion that the individual mind is extinguished with the body, for mind somehow remembers what has preceded, and this is over and above what is merely eternal in mind - the idea of the body, or its essence .... IV April,1676 [Jag., pp. 1200.] Simple forms: perception and situs. But change and matter, or modifications, themselves are resultants from all the other forms taken at the same time. For they vary infinitely in matter and motion. This infinite variety can arise only from an infinite cause, that is, from various forms. It is easily understood from this that Simple forms are infinite. The modifications, however, which result from all forms, when related to individuals, constitute the variety in them .... Perception and situs seem to be everywhere, but matter seems to be diversified into this order or that, and thus there arises this set of laws or that; as for example, the law in our order that the same quantity of motion is always conserved. There can be another order of things, in which there are also other laws. But one space nonetheless differs from another, for there will be a certain position and plurality, but will not necessarily be width, breadth, or depth. We already see that in time, in the angle, and in other things, the kinds of quantities have new varieties .... Everywhere there seems to be perception, joy, happiness. For this is the remarkable nature of it - that it duplicates, indeed multiplies into infinity the
MAINZ AND PARIS, 1666-76 163 variety of things. But diversity seems to be possible in other ways which do not occur to our minds. God is the subject of all absolute simple forms; absolute, that is, affirmative. There are therefore two things in God: that which is one in all forms, and essence or the collection of forms. Obviously one and the same God is absolutely ubiquitous or omnipresent, absolutely enduring or eternal, absolutely active or omnipotent, and absolutely existent or perfect. To be is in some way to think in relation to something. No one is unless he is something. To whatever existence is absolutely ascribed, i.e., existence without a determinate addition, to that as much existence must be ascribed as possible, that is, the maximum . ... As space is to the immensum, so the collection of all minds is to the active intellect. God is primary intelligence insofar as he is omniscient, or insofar as he contains that absolute affirmative form which is ascribed by limitation to all others who are said to perceive something. In this manner God is the immensum itself, insofar as a perfection is ascribed to him (that is, this absolute affirmative form) which is discovered in things when they are said to be somewhere, to be present.... God is not a part of our mind, just as the immensum is not a part of a certain place or interval. Just as God is that which perceives perfectly whatever can be perceived, or is intelligence, so God is also that which is somewhere perfectly wherever something can be. Just as God is intelligence, therefore, he is also this immensum. Furthermore, universal space is being by aggregation, just as is the universal state, or the society of all minds. But there is a difference here, since position or a spatial interval can be destroyed ... but the soul cannot be destroyed. Whatever acts cannot be destroyed, for at least it lasts while it acts; therefore it wiII last always. Whatever suffers and does not act can be destroyed; so place, figure, body, and every aggregate can be destroyed. There seem to be elements or indestructible bodies because there is mind in them. As a figure is already in the immensum before it is marked off, so an idea or the differentia of thoughts is already in the primary intelligence. As a figure is in space, just so an idea is in our mind. There is no world soul, because there can be no continuum composed of minds, as there can be of spaces. '" Ideas are in our mind as differentiae of thoughts. Ideas are in God insofar as the most perfect being consists in the conjunction of all absolute forms or possible perfections in the same object. But from this conjunction of possible simple forms there result modifications, that is, ideas, as properties from essence. Simple forms are infinite because our perceptions are infinite, and they cannot be explained out of the mutual relation of the two. Thus no one can explain from the knowledge of perception and extension alone, what we sense in red, bright, hot, nor can this ever be done except then, when . ... In us joy is a sense of increased perfection; in God joy is perfection itself, the whole possessed together.... It seems that the total perfection of minds always increases, while that of bodies is not increased, for such increase would be in vain, and this is the true reason a priori why forces always remain constant, powers always remaining the same while our knowledge does not. Whether mind is the idea of the body? This cannot be, because mind remains while the body continuously changes. And of what body should it be the idea; why not rather of all that it perceives? ... The idea of existence and identity does not come from the body; neither does that of unity. A remarkable thing, that mind remembers negatives, or is conscious that it has not thought of something. For references see p. 164
164 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS It seems so me that the origin of things from God is like the origin of properties from essence; since 6 is 1 + 1 + 1 + 1 + 1 + 1, it follows that 6 = 3 + 3 = 3 x 2 = 4 2, etc. And we cannot doubt that one of these expressions differs from another, for thinking in one way we think expressly of 3 or 2, and in another way we do not think of the same numbers. ... Just as these properties differ from each other and from their essence, therefore, so also do things differ from each other and from God. I use the word 'thing' deliberately, for we customarily say that God is a being; we do not usually call him a thing. 6 ••• + REFERENCES 1 Cf. p. 147, note 1. The principle of the best possible is here given its mathematical scientific force as the principle of the maximum or extremum. 2 Conrad von dem Vorst, Protestant theologian banished from Holland in 1619 for his heterodoxy, published his Tractatus theologicus de Deo in 1610. 3 On Fromond see p. 60, n. 22. 4 Thus extension and thought are not simple attributes, as in Descartes and Spinoza. Yet Leibniz's theory of the immensum as the basis of extended beings, and active intellect as the basis of minds, as developed in these notes, carries signs of the influence of Spinoza as well as of Malebranche. 5 Characters are signs or symbols; they are here treated as physical but subjective and the basis of memory and thought. 6 It is significant that these notes were written soon after Leibniz had devised the symbols and operations of the calculus of differentials. The simple illustration of the different number sets emerging from 6 serves to illustrate his metaphysics of individual series, sharing some simple essences, but each a different functional expression of the underlying harmony of ideas in God.
13 LETTER TO HENRY OLDENBURG December 28, 1675 Henry Oldenburg was one of the secretaries of the London Royal Society and a correspondent of Spinoza and other scholars. Leibniz had exchanged letters with him intermittently since 1670, receiving from him important information about the affairs of the Royal Society and other matters of scholarly interest in England. It was Oldenburg who in 1676 transmitted the two letters of Newton upon which the later charge ofplagiarism of the calculus was based. The present letter is an early proposal by Leibniz of his plan for a universal characteristic or science of symbols. It also suggests that a casual reading of Robert Boyle prompted him to return to his earlier project of an Elementa de mente. [GM., I, 83-84] I am indebted to you for your two letters, and I ask you not to take my silence too ill. For I am often interrupted and take up these studies only at intervals. Your sending Tschirnhaus to us is a token of your friendship, for I take great delight in his company and recognize outstanding ability in the youth. His discoveries are very promising, and he has shown me a number of elegant ones in analysis and geometry. I can easily judge from this what may be expected from him. Long ago he asked me, in writing to you, to beg your indulgence for his silence. And I should add in his behalf that he has not lacked diligence in searching for the manuscripts of Roberval, Pascal, and Fermat, though he has in part lacked success. l ••• I ask you to commend me to the illustrious Mr. Boyle when occasion offers. I esteem him as highly as the virtue and learning of man can be esteemed. I recently read his diatribe, 'That Theological Studies Are Not To be Condemned'; it made a deep impression on me and confirmed me in the purpose, which you know I already had a long time ago, of treating the science of mind through geometric demonstrations. I have made many remarkable observations in this field and shall sometime publish them, presented with the rigor which they deserve. I cannot reconcile myself to certain Cartesian views on this subject. Descartes builds many things upon ideas which I suspect of being sophisms. But in the body, too, there is something necessary besides extension. The distinction between mind and matter is therefore not yet clear from the distinction between thought and extension. But another principle has been given us by the nature of things, from which the perennial duration of the mind can be established by direct demonstration. Whatever the conclusions which the Scholastics, Valerianus Magnus, Descartes, and others derived from the concept of that being whose essence it is to exist, they remain weak as long as it is not established whether such a being is possible, provided it can be thought. To assert such a thing is easy; to understand it is not so easy. Assuming that such a being is possible or that there is some idea corresponding to these words, it certainly follows that such For references see p. 166
166 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS a being exists. But we believe that we are thinking of many things (though confusedly) which nevertheless imply a contradiction; for example, the number of all numbers. We ought strongly to suspect the concepts of infinity, of maximum and minimum, of the most perfect, and of allness [omninitas] itself. Nor ought we to believe in such concepts until they have been tested by that criterion I seem to recognize, and which renders truth stable, Visible, and irresistible, so to speak, as on a mechanical basis. Such a criterion nature has granted us as an inexplicable kindness. Algebra, which we rightly hold in such esteem, is only a part of this general device. Yet algebra accomplished this much - that we cannot err even if we wish and that truth can be grasped as if pictured on paper with the aid of a machine. I have come to understand that everything of this kind which algebra proves is only due to a higher science, which I now usually call a combinatorial characteristic 2, though it is far different from what may first occur to someone hearing these words. I hope sometime, given health and leisure, to explain its remarkable force and power by rules and examples. I cannot encompass the nature of the method in a few words. Yet I should venture to say that nothing more effective can well be conceived for perfecting the human mind and that if this basis for philosophizing is accepted, there will come a time, and it will be soon, when we shall have as certain knowledge of God and the mind as we now have of figures and numbers and when the invention of machines will be no more difficult than the construction of geometric problems. And when these studies have been completed - though there will always remain to be studied the choicest harmonies of an infinity of theorems, but by observation from day to day rather than by toil- men will return to the investigation of nature alone, which will never be entirely completed. For in experiments good luck is mixed with genius and industry. Once men carry our method through to the end, therefore, they will always philosophize in the manner of Boyle, except insofar as nature itself, to the degree to which it is known and can be subjected to this calculus and to the degree that new qualities are discovered and reduced to this mechanism, will also give to geometricians new material to which to apply it. But the enthusiasm of writing is carrying me further than I intended and makes me speak somewhat incoherently. REFERENCES Walter von Tschirnhaus came to Paris with Oldenburg'S recommendation and worked with Leibniz during the winter in which his discoveries of the calculus were made. It was he who brought Leibniz his first information about Spinoza's Ethics. 2 The term shows a transition from the Ars combinatoria of 1666 to the Ars characteristica of 1678 and the years following. 1
14 TWO NOTATIONS FOR DISCUSSION WITH SPINOZA 1676 On his prolongedjourney from Paris to Hanover by way of England and Holland, Leibniz visited Spinoza and as he wrote to the Abbe Gallois in 1677, "spoke with him several times andfor very long".1 The terminology and ideas in the following notations correspond closely to those of the Paris notes, but the problems arise out of Spinoza's views. They contain an effort to find a firmer basis for the ontological argument and point to the distinction between logical possibility and compossibility in existence. 1. THAT A MOST PERFECT BEING EXISTS November, 1676 [G., VII, 261-62; PA., II, i, 271-72] By a perfection I mean every simple quality which is positive and absolute or which expresses whatever it expresses without any limits. 2 But because a quality of this kind is simple, it is unanalyzable or indefinable, for otherwise either it will not be one simple quality but an aggregate of many or, if it is one, it will be contained within limits and hence will be understood through negation of what is beyond these limits; which is contrary to hypothesis, since it is assumed to be purely positive. From this it is not difficult to show that all perfections are compatible with each other or can be in the same subject. For let us assume that there is a proposition of this kind: A and B are incompatible, understanding by A and B two simple forms or perfections of this kind. It makes no difference if more than two are assumed simultaneously. It is clear that this proposition cannot be demonstrated without an analysis of the terms A and B, either or both, for otherwise their nature would not enter into the reasoning, and incompatibility could be demonstrated equally as well about any other things as about themselves. And by hypothesis they are unanalyzable. Therefore this proposition cannot be demonstrated about them. But it could certainly be demonstrated about them if it were true, since this proposition is not true by itself. For all propositions which are necessarily true are either demonstrable or known per se. Therefore this proposition is not necessarily true, or it is not necessary that A and B should not 3 be in the same subject. Therefore they can be in the same subject. And since this reasoning is the same for any other assumed qualities of this kind whatsoever, it follows that all perfections are compatible. Therefore there is, or can be conceived, a subject of all perfections or a most perfect being. Hence it is clear that this being exists, since existence is contained in the number of perfections. 4 [Leibniz later added the following notes.] For references see p. 169
168 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS The same can be shown also offorms compounded out of absolutes, provided there are any. I showed this reasoning to Mr. Spinoza when I was in The Hague. He thought it sound, for when he contradicted it at first, I put it in writing and gave him this paper. Scholium. Descartes's reasoning about the existence of a most perfect being assumed that such a being can be conceived or is possible. If it is granted that there is such a concept, it follows at once that this being exists, because we set up this very concept in such a way that it at once contains existence. But it is asked whether it is in our power to set up such a being, or whether such a concept has reality and can be conceived clearly and distinctly, without contradiction. For opponents will say that such a concept of a most perfect being, or a being which exists through its essence, is a chimera. Nor does it suffice for Descartes to appeal to experience and allege that he experiences this very concept in himself, clearly and distinctly. This is not to complete the demonstration but to break it off, unless he shows a way in which others can also arrive at an experience of this kind. For whenever we inject experience into our demonstrations, we ought to show how others can produce the same experience, unless we are trying to convince them solely through our own authority. Propositions for which a demonstration is needed. Prop. 2. Two substances with diverse attributes have nothing in common with each other. Prop. 5. There cannot be in the universe two or more substances with the same attribute. Prop. 10. Every attribute of a single substance must be conceived through itself. Prop. 22, 23. About infinite modes. Sch. 31. Intellect and will must be referred to natura naturata and not to natura naturans. Part 2: 19,20 seem to conflict. However, 26: Therefore there is an idea of an idea. 29,49. II December 2,1676 5 [Cout. OF., pp. 529-30] There is no need of many worlds to increase the multitude of things, for there is no number which is not contained in this one world and, indeed even in anyone of its parts. To introduce another kind of existing things, and another world, so to speak, which is also infinite, is to abuse the word 'existence', for we cannot say whether or not these things exist now. But existence as it is conceived by us involves some determinate time, or we say that a thing exists precisely if we can say about it at some definite moment of time, 'This thing exists now.' 6 A multitude of things is greater in the whole than in a part; this is true in an infinite multitude as well. It is not useless to discuss the vacuum of forms, in order to show that not all possibles per se can exist along with others; otherwise many absurdities would follow. Nothing, however unreasonable, could be conceived which would not be in the world, not merely monsters but evil and wretched minds, and injustices, and there would be no reason for calling God good rather than evil, just rather than unjust. There would be some world in which all good people would be punished by eternal punishments, and all bad people rewarded, or wickedness expiated by happiness.
MAINZ AND PARIS, 1666-76 169 The immortality of the mind must be taken as proved at once by my method, because it is possible within itself and compossible with all other things, or it does not impede the course of things. For minds have no volume. My principle, namely, is that whatever can exist and is compatible with other things does exist, because the reason for existing in preference to other possibles cannot be limited by any other consideration than that not all things are compatible. Thus there is no other reason for determining existences than that the more perfect shall exist, that is, those things which involve the greatest possible reality. If all possibles existed, no reason for existing would be needed, and possibility alone would suffice. Therefore there would be no God except insofar as he is possible. But such a God as the pious hold to would not be possible if the opinion of those is true who believe that all possibles exist. REFERENCES PA., II, i, 379. Leibniz also refers to his visit with Spinoza in the Theodicy, III, Sec. 376, and in later letters (G., VI, 339; PA., II, i, 535). 2 Leibniz's argument therefore rests on his identification of the simple concepts of his combinatoriallogic with the perfections of God. Sense data are not simple but infinitely complex. That degrees of perfection and degrees of reality correspond is the common Neo-Platonic assumption of Leibniz and Spinoza. But the ontological argument fails when Leibniz adInits that not all possible essences attain existence, so that though God remains the seat of all perfections, existence is but the best possible of these. For the further development of this difficulty see Nos. 16, 20, and 31, I, ii. 3 The non is misplaced in G., VII, 261, with a distortion of the meaning. 4 Leibniz's original note ends here. What follows was added later. S This was the day after an interview with Spinoza. Cf. Couturat, 'Sur la metaphysique de Leibniz', Revue de mbaphysique et de morale 10 (1902), 12. 6 Time is thus the principle of the existence of compossible events which would involve contradiction if regarded as eternal essences. 1
PART II HANOVER TO THE ITALIAN JOURNEY 1676-87
15 ON A METHOD OF ARRIVING AT A TRUE ANALYSIS OF BODIES AND THE CAUSES OF NATURAL THINGS May, 1677 The first of the three rulers under whom Leibniz served at Hanover also allowed him the greatest freedom for his own intellectual activities. The few years preceding John Frederick's death late in 1679 were among the most creative in his life, involving many studies for the revived Catholic Demonstrations and for the new projects of a universal characteristic, a logical calculus, and an encyclopedia. Among these studies is a short paper applying the method of analysis and synthesis to phYSical and chemical problems, in which the empirical and utilitarian motives in his thought are expressed. Leibniz's conception of experimental controls and of the pragmatic limits of chemical as opposed to phYSical analysis is noteworthy. His interest in chemistry may have been revived at this time by the discovery ofphosphorus, on which he first reported in the same year. 1 [G., VII, 265-69] First of all, I take it to be certain that all things come about through certain intelligible causes, or causes which we could perceive if some angel wished to reveal them to us. And since we may perceive nothing accurately except magnitude, figure, motion, and perception itself, it follows that everything is to be explained through these four. But because we are now speaking of those things which seem to take place without perception, such as the reactions of liquids, the precipitations of saIts, etc., we have no means of explaining them except through magnitude, figure, and motion, that is, through mechanism. What cannot be explained in this way will here be referred to the action of some perceiving being. Let us imagine, therefore, that some angel comes to explain to me the true cause of magnetic declination and the periods observed in it. He will surely not really satisfy me by saying that this is the nature of the magnet or that there is a certain sympathy or a kind of soul in the magnet by which it happens. Rather he must explain some cause to me, such that, if I understand it, I can see that the phenomena follow from it as necessarily as the cause of the hammer stroke when a given time has elapsed follows from my knowledge of a clock. Bodies that are composite in appearance, such as a plant or an animal, are to be reduced to bodies simple in appearance, such as flesh, tendons, glands, blood. Bodies that are simple in appearance are to be reduced to those out of which or by the combination of which they can be produced. Thus brass, as it is called, is made out of copper and zinc under the action of fire and air, and vitriol from sulfur or some other acid, and copper or iron. Since there is a circle involved in the processes of composition and production - for example, sulfur can be produced again from vitriol, and we do not yet know whether For references see p. 176
174 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS vitriol is prior in nature to sulfur or sulfur to vitriol - it should be sufficient for us to determine a certain few classes [species] from which we can artificially produce a variety of other classes and sensible qualities. For an effect is understood when its cause is understood. Hence we can explain all remaining classes perfectly and mechanistically from these few classes, if we know accurately what happens in the process of preparation. Among the other ingredients we must also count the general agents and instruments - fire, air, water, earth - without which we cannot treat or prepare anything. We must note also which kinds of fire, air, water, and earth intervene, and reduce these also to a few simple ones. For it is certain that air contributes considerably to fire, that lime increases its weight by fire, that some subtle force penetrates even glass, as in congealment, and that crystals take on something from water, since they spring up in solutions. The vessels also contribute something to changes in preparations. Finally, the effect of coal fire is different from that of the fire of a torch. When the same effect is produced by the use of different ingredients or instruments, this effect is to be explained by something which they have in common. When all things, or at least most of them, have been reduced to certain few classes such as saltpeter, common salt, sulfur, potash, soot, spirit of wine, then it will be necessary merely to institute or describe as many experiments as possible to observe what happens when these classes are combined with each other; for example, when common salt is put into soap, which is made by using potash and fat, earth is precipitated and the fat floats on the water. As many experiments as possible are to be carried out isolatedly, that is, as experiments in which, besides one single homogeneous body, nothing enters into the process but the general and necessary agents. Next, after the isolated experiments are completed, as many experiments as possible are to be tried with only two kinds taken together, as with saltpeter and common salt alone, treating them in various ways by fire, water, air; and by combining various products thus made, for instance, combining the products made with salt with each other as well as with those made with saltpeter. After combinations, one should go on to the contemations, etc., or to the temions and quaternions of the classes. 2 All experiments in which only a few elements are brought together are more useful for science than others, because it is easier to discover in which element the cause lies hidden. In experiments made by the combination of ~everal bodies, one must see whether anything can be altered or eliminated without changing the results of the experiment, as linseed oil, for example, from the ironmaking experiment. Those experiments are to be tried first in which the analogy to other experiments promises some special effect. It is likely that things which are similar in many known factors will also be similar, or at least approximately so, in other factors not yet examined, but which seem to have a connection with the factors already tried. But whether or not the result does show such similarity in the remaining factors, we will always profit. It is possible that bodies which are exceedingly subtle and cannot be caught or perceived by sense in one substance can be caught in another. Thus the gas of wine cannot yet be captured, but one can catch the gas of other bodies. In animals, too, we find certain vessels and organs to be invisible in some species but distinctly noticeable in others.
HANOVER TO THE ITALIAN JOURNEY, 1676-87 175 Especially are those experiments to be interpreted the success of which is reliable and infallible. All experiments reported by others are also to be entered in a catalogue, provided these experiments are certain and approved by common consent and very distinctly described. 3 Bodies and preparations made from them are to be examined by means of the instruments 0/ experimentation - scales, thermometers, hygrometers, pneumatic pumps - and also by vision, whether naked or fortified, by smell, and by taste. I believe there is no medium more effective than taste for discerning the essential nature of bodies, because taste brings bodies to us in their substance and dissolves them in us so that we may percei~e the whole solution closely. ' Not only microscopes are to be used but perfectly polished concave and spherical mirrors of very large radius. The magnifying power of lenses varies inversely with their diameters; that of mirrors, on the contrary, in direct proportion. Now diameters can be increased to infinity but not decreased. Hence mirrors are more useful. Then too, only the surface needs to be good in mirrors, and last of all, the whole body can be made visible in one mirror, which is not possible in a microscope. Probably the causes of what happens in bodies - especially in those homogeneous in appearance - are not very complex, and if some angel were to unveil them and explain them to us, we should perhaps be astonished that we had not discovered them earlier ourselves. So it is also probable that those bodies which are homogeneous in appearance are not so complex that we must despair of discovering their inner structure insofar as this is necessary for our many purposes. Although bodies may be divided into other subtler bodies to infinity, and it is incredible that there should be any primary elements, this ought not to prevent us from seeking causes. He who uses stones in architecture does not mind the bits of earth interposed between them; he who uses water in hydraulics pays no attention to the air in it, which can afterward be extracted by the Guericke pump; and he who uses earth to raise a rampart does not think of the small stones scattered about in it but which do not bother him. So we may believe that the effect of those very subtle bodies within the bodies which we handle are no more relevant to the phenomena than are stones, or even the imperceptible corpuscles which compose earth, to the strength of a bulwark. If the invisible bodies which are hidden in visible ones and which enter noticeably into the effect of our experiments were of so many kinds, then they would also be very subtle. And if they w~re so subtle, they would change in the briefest moment, and bodies such as saltpeter an~ sulfur would not remain so long in the same state or continue to produce the same experimental results. If those bodies which contribute in causing the phenomena were so inaccessible to us and so subtle, then some slight and superficial mixture of two liquids could not produce such great effects, or else it would follow that any mixture whatever could also produce the greatest effects. The physical effects may be considerably intensified and reduced through slight mechanical manipulations, such as shaking, stirring, beating, blowing, pouring in water; for example, water suddenly poured over oil of vitriol produces amazing heat which it does not make when slowly added in drops. Bodies are greatly changed by trituration. All of these things are sure indications that the bodies which our crude manipulations make perceptible so easily are not so inaccessible to us. Analysis is of two kinds - one of bodies into various qualities, through phenomena or experiments, the other of sensible qualities into their causes or reasons, by ratioFor references see p. 176
176 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS cination. So when undertaking the most accurate reasoning, we must seek the formal and universal causes of qualities which are common to all hypotheses and must begin accurate but universal enumerations of all possible modifications, such as those of weight, elasticity, light or heat, coldness, liquidity, firmness, tenacity, volatility, fixity, solubility, precipitation from menses, crystallization. If we combine these analyses with experiments, we shall discover in any substance whatever the cause of its qualities. But this can be very effectively achieved through definitions and a philosophic language. 4 REFERENCES Leibniz published 'Le phosphore de M. Krafft, ou liqueur de terre seiche de sa composition qui jettent continuellement de grands eclats de lumiere' in the Journal des savants, August 2, 1677. Not only Krafft but the original discoverer, Brand, visited Hanover to promote the manufacture of phosphorus. See also Leibniz's letter to Huygens, 1679 (No. 27, I). Fontenelle considered Leibniz's description of phosphorus, in his eulogy at John Frederick's death in 1679, as one ofthe finest productions of modem Latin poetry. 2 The terminology and the method of applying the theory of combinations are still those of the De arte combinatoria (1666). 3 On the nature of distinct knowledge see No. 33, below. 4 The last sentence is a later notation in Leibniz's handwriting (the text is in the copy of a secretary, with some corrections by Leibniz). His account of the role of material analysis in technology may be compared with his later discussions of conceptual analysis in Nos. 18, 25, 32, and 69, II. 1
16 LETTER TO ARNOLD ECKHARD Summer, 1677 Soon after his arrival in Hanover, Leibniz was sought out by a zealous Cartesian, Arnold Eckhard, professor of mathematics at Rinteln. Gerhard Molanus, the genial and learned abbot of Loccum, near Hanover, brought the two men together for a philosophical discussion of the Cartesian conception of being, particularly of the argument from God's essence to his existence. Eckhard is one of the Cartesian Scholastics to whom Leibniz later refers as the first recipients ofhis criticisms of Descartes. This letter is a careful reply to a very long one by Eckhard in May, 1677, and contains the essence of the extensive comments which Leibniz made on that letter, several of which are given here as notes.! Leibniz was as much concerned as Eckhard to find a sound basis for the ontological argument, but his objections are a step in the clarification of his own logical and metaphysical pluralism. [G., I, 266-70] As soon as I received your most learned and weighty, rather than lengthy, letter, I at once consumed the whole. For there is nothing which I will read with more pleasure than things written so elegantly and soundly about an argument of such importance. I should have replied more fully had not the most reverend Abbot of Loccum given me the hope that a formal demonstration would follow. I preferred to wait for this, but since the demonstration has not yet arrived, I have decided to make this brief reply meanwhile, so that you may understand that I have received your letter and have read it studiously. 2 Several of my objections have ended since you have explained that in your usage, perfection is being insofar as it is understood to differ from nonbeing, or, as I should prefer to define it, perfection is degree or quantity of reality or essence, as intensity is degree of quality, and force is degree of action. It is clear, also, that existence is a perfection or increases reality, that is: when A is thought of as existing, more reality is thought of than when A is conceived as possible. 3 But it still seems to follow from this that there is more perfection or reality in a mind which suffers than in an indifferent one which is neither e~oying nor suffering, so that in a metaphysical sense, pain too is a perfection. But since pleasure is also a metaphysical perfection, it seems that we must ask whether pain or pleasure is the greater perfection, metaphysically speaking. It seems that pleasure is the greater perfection, because it is the consciousness of power, while pain is the consciousness of powerlessness. But powerlessness, again speaking metaphysically, is an imperfection, and the consciousness of metaphysical imperfection is less perfect, again speaking metaphysically, than the consciousness of metaphysical perfection. So pain implies a certain imperfection in the suffering subject. But there remain certain scruples even here, which I pass over for now. I hasten to the heart of the question, which is whether a most perfect being does not For references see p. 180
178 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS imply a contradiction. You have undertaken to prove this because neither Descartes nor any of the Cartesians have done it, though I have often urged them to do so. You have chosen the best way to prove it, for if you show that the concept of the most perfect is not composite, you will have concluded also that it does not imply a contradictio~. Therefore you promise to set up a certain concept which is known to be the most simple yet also to contain all of reality. The concept which you set up is this: a most perfect being is either a being by itself [a se] or a necessary being, because it is self-determined to everything of which it is capable. This concept, you say, does not imply a contradiction (1) because it is distinct, for its individual parts are clear, (2) especially since everyone classifies being into that which is by itself and that which is through something else, and there must therefore necessarily be some idea underlying these two; otherwise men would speak like parrots. (3) Besides, we know what it means to be through something else or to be determined to something by something else; therefore we must also know what it means not to be determined by something else. (4) Furthermore, we know by experience that the concept to be determined by itself does not imply a contradiction, for we experience this every day in our own volitions. (5) Also, pure actuality is simpler than an actuality mixed with potentiality. Therefore, since the latter does not contain an implied contradiction, the former will much less contain one. (6) Nothing more is even required for a most perfect being, you add, than that it be a most perfect mind, that is, a mind to which belong all the perfections which are found in any mind. For every substance is either mind or body; but a being which determines itself is not a body, therefore it will be a mind. A most perfect mind, that is, a mind which understands and wills most perfectly, most certainly does not imply a contradiction. To understand most perfectly, or to understand all things, does not imply a contradiction, because to understand implies none. Likewise, to understand all things at any time in a single act does not imply a contradiction, because to understand many things sometimes in a single act does not imply one. Nothing conflicts with understanding itself but non-understanding, perfect non-understanding. Also, a mind endowed with the most perfect will, or a mind whose power reaches as far as his will, does not imply a contradiction. For the contrary of power is not omnipotence but impotence. Because therefore a being which determines itself to everything of which it is capable is a most perfect mind, and hence most perfect in its willing, or omnipotent, it follows that all other realities come from it. So you also prove the second part of your assertion, namely, that the concept which you set up of a most perfect being not only implies no contradiction but also produces every other perfection or contains it virtually. Having shown these points, (7) you also prove the existence of a most perfect being by a different method, from the existence of certain contingent beings; for example, from the existence of our minds or of the world. For such beings must necessarily have received their existence from one whose nature is such that all things come from it. If I am not mistaken, these points, which you have expounded very clearly and elegantly, contain a summary of your reasoning. I shall state frankly and sincerely what I find still to be desired for a demonstration of absolute perfection. To (1) I reply that for a distinct concept it is not enough that all its parts are clear, unless it is also clear that they can be combined with each other. Thus whoever speaks of a maximum velocity knows what velocity is and what a maximum is, yet he cannot understand maximum velocity, for it is easy to demonstrate that this implies a contra-
HANOVER TO THE ITALIAN JOURNEY, 1676-87 179 diction. To (2): just as those who speak of a maximum velocity do not speak like parrots, although they are speaking of something for which there is no possible concept, so, it may be objected, do also those who speak of being by itself. To (3): it does not follow that if the existence of one of two opposite terms is intelligible, the other is also intelligible, for it is possible that the opposite term implies a contradiction. This happens, for instance, if you classify men into rational and irrational, or bodies into mobile and immobile. So too if you classify being into that which is through something else and that which is not through something else. For your opponents may say that whatever is, is necessarily through something else. To (4): so far it is very doubtful whether our will is determined by ourselves or not rather by the impressions of objects.4 To (5): this seems to be a sophism. By the same reasoning a maximum velocity would be pure and therefore simpler in kind than a velocity combined with slowness; yet the former velocity implies a contradiction, while a velocity combined with slowness does not. If the matter is rightly considered, pure actuality involves many important things, namely, as many powers as there are things to which the being must determine itself, and also the power to exclude and, so to speak, repel external powers. Hence you see how slippery the argument is that only nonactuality is incompatible with actuality and that therefore pure actuality is not, as if it were certain that all acutalities and all potentialities are compatible with each other. The opponents believe that such beings, in which we accumulate, as it were, all perfection and all actuality, are chimerical. To (6): this assumes without proof that all substance is either mind or body. But this is not certain, even though we may never have thought of any other substance. For perhaps there can be others of which we can no more think than a blind man thinks of colors. To prove that a mind which understands all things and wills most perfectly or is omnipotent does not imply a contradiction, you make use of the same paralogism which you use above, if I am not mistaken, namely, that nonunderstanding is opposed to understanding, but that to understand everything at once and always is not. By the same argument you may prove that an eye which would see everything always and at once is possible. S It is the same when you say that the opposite of power is impotence, not omnipotence. So much about your proof that the concept of a being which determines itself does not imply a contradiction. The proof by which you maintain that the being which determines itself also determines all other beings seems to be weaker, however, and less well formulated. For it reduces to this: a being which determines itself to everything of which it is capable cannot be a body. Therefore it is a mind, etc. (Here you assume what is not at all demonstrated, namely, that every substance is either a body or a mind.) Furthermore, since it is a mind, and not just any mind, it must be some particular mind; therefore what other than the most perfect one? (That this mind is possible, you tried to prove by the paralogism which I have mentioned.) But this does not follow, for it is possible that the property of determining itself to everything of which it is capable may belong to other minds in common with a perfect mind. For a being determining itself is not by that fact alone the most perfect, since it is possible that there may be some other being more perfect than it, which also determines itself to everything of which it is capable. For a more perfect mind, capable of more things, would also determine itself to more things. But, you say, the most perfect mind is omnipotent; it can do everything or determine all other things. Therefore there cannot be more than one self-determining mind. J reply that you have not proved that such a most perfect mind For references see p. 180
180 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS is possible, and, besides it is enough for the perfection of a mind to know everything and be able to do everything that it wills. But it does not follow therefrom that it should be able to do everything, because it may not will everything, for it may not will what it understands is not within its power; that is, it may not will to determine those things which are already determined by themselves. 6 The reasoning in (7) assumes that such a most perfect being, source of all being, is possible, and so it does not need a separate reply. These are the answers which can be given summarily in reply to your argument, so that you may see the scruples which I have so far had about the whole thing almost visually tabulated. As for the rest, you have made many fine comments on which I shall not now touch. To many of the ideas which you have mixed in throughout, I cannot give my assent; for instance, the Cartesian doctrine that eternal truths depend on the will of God. In my opinion this is either error or a mere play of words. 7 You offer many clear considerations on the nature of action, power, necessity, immutability, eternity, will, thought, pleasure, and pain which must be praised, not refuted. But I have made note of a few things here and there which will, I believe, be welcome to you, and which I shall send you some other time so that you may have a richer material on which to exercise the gifts of genius. In short, I believe that Descartes does not prove the possibility of a most perfect being, which is the first desideratum in this argument; indeed he does not even try. So I hold that what you have done here is not Cartesian but your own. I do not see that you have done this, as you say, by the Cartesian method. What, I pray, is this Cartesian method which some people boast about so frequently? And what does he have of which the rest of us are ignorant or which all good thinkers born before Descartes did not use? Were Archimedes and Galileo Cartesians, perchance? I admit that Descartes founded a method in geometry, though one not so very different from Vieta's, and far from perfect. For it cannot touch innumerable problems which are both most important and most useful. It is false that every problem can be reduced to an equation which can then be represented by a curve of the kind admitted by Descartes. I esteem the genius and the discernment of Descartes highly, but he tried to convince the world that the things which he achieved by virtue of his outstanding ability were done solely through the use of a certain unique method which he had established, so that men were drawn to the hope of discovering an art by which mediocre minds could equal excellent one. In fact, it seems to me that almost no Cartesian has produced anything which even remotely approaches the discoveries of the master. The outstanding advances which have been made since Descartes are not due to his method; by some ill chance, in fact, they seem to have been made by almost anyone rather than Cartesians. Therefore, distinguished Sir, I am unwilling to do you and other excellent philosophers the injury of regarding as Cartesian any outstanding work which you produce. I observe that whenever men become too devoted to one author, they usually block the paths of further progress for themselves .... REFERENCES The following comment of this kind, on a point omitted in the present letter, is regarded by Mahnke as the first explicit recognition by Leibniz of unconscious mental processes. "It is assumed here that there is nothing actually in our minds of which we are not conscious; this I seriously doubt" (G., 1,261, n. 92). 1
HANOVER TO THE ITALIAN JOURNEY, 1676-87 181 Reading studiose for sudiose (G., I, 266). See above, p.169, note 2. 4 In his notes Leibniz had said "by impressed species", that is, "from without" (G., 1,261). Note that Leibniz here still uses the language of interaction. 5 Note to Eckhard's letter: "Even if 'all things' is not inconsistent with 'to understand', it is inconsistent with itself when combined with 'to understand'. Just so, 'to see' is not inconsistent with eyes, nor is 'to see everything' inconsistent with 'to see'. Yet 'to see everything' is inconsistent with eyes. So it must be demonstrated that it does not conflict with the nature of mind to understand everything" (G., I, 250). 6 This already points, not only to a pluralism of self-determining beings, but to the distinction between the two levels of being, that of possibilities determined by God's intellect and that of existence determined by God's will. 7 Note to Eckhard's letter: "I know that it is the opinion of Descartes that the truth of things depends on the divine will; this has always seemed absurd to me. For thus the necessity of the divine existence, and therefore of the divine will, itself depends on the divine will. Thus it will be a nature prior, yet posterior to itself. Besides, the principle of necessary truths is only this: that the contrary implies a contradiction in terms .... Since then the incompossibility of contradictories does not depend on the divine will, it follows that neither does truth depend on it. Who would say that A is not non-A because God has decreed it?" (G., I, 253). 2 3
17 DIALOGUE August, 1677 The dialogue form had interested Leibniz in Paris, where he had paraphrased Plato, and he tried his hand at it frequently during the following years. Be. fittingly calls the present one a "Dialogue on the Connection between Things and Words". Aimed explicitly at Thomas Hobbes's position that truth is arbitrary, but also indirectly at Descartes's view that truth rests upon God's arbitrary will, the dialogue probably grew out of the correspondence with Eckhard. It develops the theory of characters, their use in reasoning, and their bearing upon the nature of truth. The problem of error is lost sight of as the dialogue progresses. As the use of the term 'express' suggests, the position reached here is important in the development of the theory of representation. [G., VII, 190--93] A. If you were given a thread and told to bend it in such a way that it shall form a closed line and shall include the greatest possible inclosed space, how would you bend it? B. In a circle, for the geometricians show that a circle is the most spacious of figures of the same circumference. If there are two islands, one circular and the other square, around which one can walk in the same time, the circular one contains more land. A. Do you consider that this is true even if you were never to think of it? B. Certainly, and even before the geometricians had proved it or men observed it. A. So you think that truth and falsehood are in things, and not in thoughts. B. By all means. A. But can any thing be false? B. I do not think that things are false, but thoughts or propositions about things. A. Then falsehood is a property of thoughts and not of things. 1 B. I am forced to agree. A. Why not truth also, then? B. So it seems, but I am inclined to doubt whether this conclusion is valid. A. When a question is proposed, do you not doubt whether or not some answer is true or false until you are certain of your opinion? B. Of course. A. You admit, therefore, that it is the same subject which is capable of truth or falsehood, until one or the other is established by the particular nature of the question. B. I admit it and acknowledge that if falsehood is a property of thoughts, then truth is also and not of things. A. But this contradicts what you said before, that there is also truth which no one has thought. B. You have confused me.
HANOVER TO THE ITALIAN JOURNEY, 1676-87 183 A. Yet we must attempt to reconcile the two views. Do you think that all the thoughts that can be made are actually formed? Or, to put it more clearly, do you think that all propositions are thought? B. I do not. A. It seems then that truth is a quality of propositions or thoughts, but of possible thoughts, so that what is certain is only that if anyone should think in this way or in the opposite way, his thought would be true or false. B. You seem to have succeeded in getting us over a slippery place. A. But since there has to be a cause for the truth or falsity of any thought, I ask you where we shall seek this cause? B. In the nature of things, I think. A. But what if it arises from your own nature? B. Certainly not from my nature alone. For my own nature and the nature of the things of which I think must be such that when I proceed by a valid method I shall necessarily infer the proposition concerned or find it true. 2 A. Your reply is excellent, but there are still difficulties. B. Of what kind, I beg of you? A. Certain men of learning believe that truth arises from the human will and from names or characters. 3 B. Such an opinion is certainly most paradoxical. A. But they prove it in this way. Isn't definition the principle of demonstration? B. I admit this, for certain propositions can be demonstrated solely by joining definitions together. A. Hence the truth of such propositions depends upon definitions. B. Granted! A. But definitions depend upon our will. B. Howso? A. Don't you see that it is within the choice of mathematicians to use the word 'ellipse' to signify a certain figure? And that it was within the choice of the Latins to ascribe that meaning to the word 'circle' which its definition expresses? B. What of it? Thoughts can occur without words. A. But not without some other signs. Try, I pray, whether you can begin any arithmetical calculation without numerical signs.· B. You disturb me very much, for I did not think that characters or signs are so necessary for ratiocination. A. You grant then that arithmetical truths presuppose some signs or characters? B. That can't be denied. A. Therefore such truths depend on the human will? B. You seem to be getting me tied up by a kind of sleight of hand. A. These are not my ideas, but those of a very gifted writer. B. But can anyone depart so far from a sound mind as to persuade himself that truth is arbitrary and depends on names, though he knows that the geometry of the Greeks, Latins, and Germans is the same? A. You are right; yet the difficulty needs to be resolved. B. There is just this one thing that makes me pause. I notice that no truth is ever known, discovered, or proved by me except by the use of words and other signs presented to the mind. For references see p. 185
184 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS A. In fact, if tltere were no characters, we could neither think of anything distinctly nor reason about it. B. Yet when we examine the figures of geometry, we sometimes establish truths merely by contemplating them accurately. A. True, but we must recognize that these figures must also be regarded as characters, for the circle described on paper is not a true circle and need not be; it is enough that we take it for a circle. B. Nevertheless, it has a certain similarity to the circle, and this is surely not arbitrary. A. Granted; therefore, figures are the most useful of characters. But what similarity do you think there is between ten and the character 10? B. There is some relation or order in the characters which is also in things, especially if the characters are well invented. A. That may be, but what similarity do the first elements themselves have with things; for example, 0 with nothing, or a with a line? You will have to admit, therefore, that in these elements at least, there is no need of similarity to things. This is true, for example, in the words lux andferens; even though their compound lucifer has a relation to these two words, light and bearing, which corresponds to that which the thing signified by lucifer has to the things signified by lux andferens. B. But the Greek rpwarpopO!; has the same relation to rpw~ and rpipw. 5 A. The Greeks might have used another word than this, however. B. True. Yet I notice that, if characters can be used for ratiocination, there is in them a kind of complex mutual relation [situs] or order which fits the things; if not in the single words at least in their combination and inflection, although it is even better if found in the single words themselves. Though it varies, this order somehow corresponds in all languages. This fact gives me hope of escaping the difficulty. For although characters are arbitrary, their use and connection have something which is not arbitrary, namely a definite analogy between characters and things, and the relations which different characters expressing the same thing have to each other. This analogy or relation is the basis of truth. For the result is that whether we apply one set of characters or another, the products will be the same or equivalent or correspond analogously. But perhaps certain characters are always necessary for thinking. A. Excellent! You have extricated yourself clearly and fully. And the analytic or arithmetical calculus confirms this view. For in numbers the problem always works out in the same way whether you use the decimal system or as some mathematician did, the duodecimal. Mterward, if you apply the solution you have reached by calculation in several different ways, by arranging kernels or some other countable objects, the answer always comes out the same. In analysis as well, even though different properties of the subject are more easily apparent when different characters are used, the basis of truth is always found in the connection and coordination of these characters. So calling the square of a, a 2, and substituting b + C for a, we have b 2 + C 2 + 2bc as the square. But if we substitute d - e for a, we will have d 2 + e 2 - 2de as the square. In the former case we express the relation of the whole, a, to its parts band c; in the latter the relation of the part, a, to the whole, d, and the excess, e, of the whole over the part, a. Yet by substitution it becomes apparent that the calculation always leads to the same result. For if we substitute in the formula d 2 + e 2_ 2de (which equals a 2 ), its equivalent a +eford, we shall have a 2 + e 2 +2ae for d 2 , and- 2ae-2e 2 for- 2de.
HANOVER TO THE ITALIAN JOURNEY, 1676-87 185 So, adding these together, +d 2 =a 2 +e 2 +2ae +e 2 = e 2 -2de = -2e 2 -2ae the sum produced is. . .. = a 2. You see then that however arbitrarily the characters may be chosen, if you observe a certain order and rule in their use, they always agree. Therefore though truths necessarily presuppose some characters, and are indeed sometimes asserted about these characters themselves (as in the theorem about casting off nines), yet they consist not in the arbitrary element in their characters but in the permanent element in them, namely, in their relation to things. It is always true, without any arbitrary choice of ours, that if certain characters are adopted, some definite argument must proceed, and if others are adopted whose relation to the things signified is known but different, the resulting relation of the new characters will again correspond to the relation of the first characters, as appears by a substitution or comparison. REFERENCES The discussion of truth and falsehood and their relation to thought and things in The Art of Thinking (,The Port Royal Logic') by Arnauld and Nicole is similar to this, and Leibniz may have been influenced by this source. See The Art of Thinking, Part II, chap. V, 'On the Falsity 1 To Be Found in Complex Terms and in Incident Propositions'. 2 Leibniz's position here implies his opinions expressed in the letter to Foucher (No. 11), where he distinguished the purely formal logical necessity inherent in hypothetical truths when their relations to an external order are neglected from their material and hypothetical truth which depends upon the relation to a'suppositum'. 3 Thomas Hobbes, De corpore, Book I, chaps. III, VII-IX. Cf. the analogous position of Descartes concerning the divine will, criticized on p. 181, note 7. 4 Note on the margin of the manuscript: "When God calculates and exercises his thought, the world is made." 5 See p. 176, note 1.
18 LETTER TO HERMAN CONRING March 19, 1678 Herman Conring (1606-81), professor at Helmstadt, was one of the outstanding scholars and controversialists of his day, active in such diverse fields as medicine, jurisprudence (a founder of the history of law), philosophy, history, and theology. His correspondence with Leibniz had begun in 1670, when his friend Boineburg sent him a copy of the New Method of Learning and Teaching Jurisprudence. At first (before Leibniz's Paris sojourn) their letters were concerned primarily with the theory of law; even here Conring was inclined to defend the old philosophy, especially Aristotle, against Leibniz's appreciation of the new, so that this period of the correspondence ended with the impatient protest and exhortation to the venerable Aristotelian, "Let us dismiss our prejudices and honor the geniuses of all ages" (G., I, 175). Conring was engaged in theological controversy with the Capuchins at the court of Hanover when Leibniz came there in 1676 and soon resumed the correspondence. The present letter returns to the problem of the validity of Aristotle and the Scholastics and the usefulness of substantial forms for a mechanistic philosophy of nature. But it is most important for Leibniz's theory of method, particularly in the verification oftruths offact and the use ofhypotheses. [G., I, 193-99] ... I do not think that the function of respiration and the way in which it is necessary for life have as yet been explained satisfactorily. No one who has carefully observed the anatomy of living animals will say that respiration is the cause of the motion of the heart. Even if the heart really beats because of heat, as experience confirms, it is not yet clear where heat comes from in an animal, how it is conserved, and how it acts. To derive heat from the motion of the blood and thus from the motion of the heart again would be to commit a vicious circle. It seems therefore that the phenomenon must be reduced to some kind of fermentation, or to a reaction and conflict, which, some authors think, arises from the mixture of old blood and new chyle. I should have liked your opinion about this rather than about the question of whether the motion of the heart comes from respiration, which I had not raised. But it remains to ask whether the air in the lungs supplies something to the blood, or whether it merely supports the temperature, somewhat in the way in which chemical furnaces need some ventilation. I come to your criticisms regarding analysis and demonstration. You think that I have added some very paradoxical novelties to this matter, and you sometimes doubt whether I am writing seriously. But I have in fact said only things that I have concluded about this matter from many years of experience and from instances of the reasoning of myself and others as well; things, moreover, that are consistent with what men do every day, even though they are not always aware that they are doing it. What I have proposed is effective, too, in discovery and judgment and not, like the methods
HANOVER TO THE ITALIAN JOURNEY, 1676-87 187 and precepts of certain other men, barren and remote from applications and facts. Demonstration is reasoning by which some proposition is made certain. This is achieved whenever it is shown that the proposition necessarily follows from certain suppositions (which are assumed to be certain). By necessarily I mean in such a way that its contrary implies a contradiction; this is the true and unique mark of impossibility. Just as necessity corresponds to impossibility, furthermore, so an identity corresponds to a proposition which implies a contradiction. For the primary impossibility in propositions is this: A is not A; just so the primary necessity in propositions is this: A is A. Hence only identities are indemonstrable, but all axioms are demonstrable, even though they are mostly so clear and easy that they do not need demonstration; nevertheless, they are demonstrable in the sense that if their terms are understood (i.e., by substituting the definitions for the terms defined), it becomes clear that they are necessary or that their contrary implies a contradiction in terms. This is also the opinion of the Scholastics. But we know that identical propositions are necessary propositions without any understanding or analysis of their terms, for I know that A is A, whatever may be understood by A. All propositions, however, whose truth must be shown by further analyzing and understanding their terms are demonstrable by such analysis, that is, by definitions. So it is clear that demonstration is a chain of definitions. For in the demonstration of any proposition, nothing is used but definitions, axioms (with which I here include postulates), theorems which have been demonstrated previously, and observations. Since the theorems again must themselves be demonstrated, and axioms, except for identities, can also all be demonstrated, it follows that all truths can be resolved into definitions, identical propositions, and observations - though purely intelligible truths do not need observations. Mter the analysis has been completed, it will become manifest that the chain of demonstration begins with identical propositions or observations and ends in a conclusion but that the beginning is connected with the conclusion through intervening definitions. In this sense I said that a demonstration is a chain of definitions. The definition of a compound idea, moreover, is an analysis of it into its parts,just as a demonstration is nothing but the analysis of a truth into other truths which are already known. And the solution of any problem which is to be worked out is the reduction of the problem to others which are easier or already known to be within one's power. This is my analysis, which has been tested in mathematics and in other sciences and will succeed. If anyone has another, I shall be surprised if it does not reduce finally to this one, or prove to be a part or corollary ofit. Synthesis, on the other hand, is the process in which we begin from principles and compound theorems and problems, whichever the natural order of thought presents to us, while analysis is the process in which we begin with a given conclusion or proposed problem and seek the principles by which we may demonstrate the conclusion or solve the problem. 1 Thus synthesis does not help to solve questions which tum up accidentally (except when tables of truths can be established); yet it is useful in diccovering many excellent things which we may set aside for later use when some question happens to arise. For it is certain that a man who knows many of the theorems in Euclid, Archimedes, Apollonius, and others will perform the analysis more briefly than one who knows only a few fundamental propositions, even though the latter can always achieve his aim as well as the former, if he uses a sure method and is industrious enough. I have made many fine discoveries about these matters and could For references see p. 191
188 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS illustrate them with excellent examples if I had enough time. When we arrive eventually at already known truths by starting from an assumption of whose truth we are uncertain, we cannot conclude from this that the assumption is true, as you rightly warn, unless we make use in our reasoning of pure equations or propositions that are convertible or whose subject and predicate are equally inclusive. We must take care, that is, not merely that the predicate is as inclusive as the subject in each proposition, and the converse (which is true in reciprocal propositions), but also that subject and predicate in one proposition are as inclusive as the subject and predicate in all the other propositions occurring in the same proof. 2 But though my comment may seem new to you, the practice of the ancients shows that they were not ignorant of this principle, for they guarded against errors adequately, even though they did not record their rules of analysis distinctly enough - not to mention the fact that their analytic writings have been lost. Equations of this kind have a place, moreover, not merely in mathematics but in all other reasoning that is, wherever, definitions occur. But those who deduce known phenomena from some physical hypothesis which has been taken for granted without demonstration cannot by this process demonstrate that their hypothesis is true, unless they have observed the condition which we have just set down. This they have not done, nor perhaps, have they wanted or been able to do it. Yet it must be admitted that a hypothesis becomes the more probable as it is simpler to understand and wider in force and power, that is, the greater the number of phenomena that can be explained by it, and the fewer the further assumptions. It may even tum out that a certain hypothesis can be accepted as physically certain [pro physice certa] if, namely, it completely satisfies all the phenomena which occur, as does the key to a cryptograph. Those hypotheses deserve the highest praise (next to truth), however, by whose aid predictions can be made, even about phenomena or observations which have not been tested before; for a hypothesis of this kind can be applied, in practice, in place of truth. But the Cartesian hypothesis is still far from deserving this praise; I have often raised this objection with the chief Cartesians of France and Belgium - that until now nothing new has ever been discovered by the use of Descartes's principles, whether in nature or in the mechanical arts. What is more, none of the discoverers of important things was a Cartesian. By Cartesian principles, however, I do not mean those which are common to Descartes and Democritus 3, but only his physical hypothesis and elements. You need not wonder that Descartes should have found so many disciples all at once. For except for GaIileo, you will find no one in our century who can be compared with him, whether in genius for discovering the causes of things, in judgment in explaining the senses of the mind lucidly, or in ready eloquence in capturing the minds of more discerning men. To these things was added the fame of his profound mathematical knowledge; and though we know today that it has not been as great as the crowd of Cartesians now believe, yet it was greater than that of any other man of his time, for Vieta and GaIileo had died when Descartes was flourishing. Besides, there were many people at that time who were disgusted with the Scholastic program of studies and sought to be freed from it, for Bacon and others had already prepared them for freedom. For the rest, neither Galileo, Descartes, nor Gassendi was ignorant of Aristotle's doctrines. Gassendi had certainly read the ancients more carefuIly than did many Aristotelians. It seems to me that no one is more ignorant of Aristotle's teachings than the so-called Aristotelians. I have always admired Aristotle's Organon, Rhetoric,
HANOVER TO THE ITALIAN JOURNEY, 1676-87 189 and Politics. I understand that his zoOlogy is esteemed by the experts and think that there are many things which we ought not to spurn in his eight books on physics, as well as in his books on the soul and on metaphysics. But I cannot value his works on the heavens and on generation and corruption highly, and I do not believe that you disagree. That the whole new philosophy is soon to be rejected by a learned posterity, as you say, is very unlikely if the world continues to advance as it has begun, unless you think, perhaps, that men will tum back again from the full fruits of discovery to their little acorns, and from things to words. This we need not fear unless a new barbarism should break out which would bring darkness into human affairs. Who would deny substantial forms, that is, essential differences between bodies? You say that I have somewhere wrongly ascribed to you the view that forms originate out of nothing. 4 I do not remember where I did this; nor do I know why you should consider as most absurd the view that everything happens mechanically in nature, that is, according to certain mathematical laws prescribed by God. I recognize nothing in the world but bodies and minds, and nothing in minds but intellect and will, nor anything in bodies insofar as they are separated from mind but magnitude, figure, situation, and changes in these, either partial or total. Everything else is merely said, not understood; it is sounds without meaning. Nor can anything in the world be understood clearly unless it is reduced to these. Suppose that some angel wishes to explain the nature of color to me distinctly. He will accomplish nothing by chattering about forms and faculties. But if he shows that a certain rectilinear pressure is exerted at every sensible point and is propagated in a circuit through certain regular permeable or diaphanous bodies, and then teaches me exactly the cause and the mode of this pressure, and deduces the laws of reflection and refraction from it, thus explaining everything in such a way that it is clear that it could not even happen otherwise, then at last he will have increased my knowledge, since he has treated physics mathematically. Who has ever said that all the affections of natural things are quantities? Motion is not a quantity, nor is figure, though both are subjects of quantity, for figure and motion can be measured. You challenge me to reduce any genuinely sensible quality to common quantities. What else do mathematicians do when dealing with sight and hearing, where they reduce everything, as far as possible, to mechanical laws? There is still some doubt about odor and taste. Furthermore, what is more probable than that all sensible qualities are merely tactual qualities varying according to the variety of sense organs? But touch recognizes only magnitude, motion, situation, or figure and various degrees of resistance in bodies. It is always true in every science, certainly, that special qualities are nothing but common qualities, variously complicated. If these considerations do not convince you, I should like you to think of this one thing: that unless physical things can be explained by mechanical laws, God cannot, even if he chooses, reveal and explain nature to us. For what would he say, I ask you, about vision and light? That light is the action of a potentially transparent body? Nothing is truer, even though it is almost too true. But would this make us any wiser? Could we use this to explain why the angle of reflection of light is equal to the angle of incidence, or why a ray should be bent more toward the perpendicular in a denser transparent body, though it would seem that the opposite should happen? There are other phenomena of this kind, and if we understood their causes, I believe we should understand the nature oflight. But how can we hope to explain the causes of such things except by mechanical laws, that is, by concrete mathematics or geometry applied to motion? For references see p. 191
190 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS I do not think that we disagree on the demonstration of special matters. You say that my estimate of the Schoolmen's metaphysics would be more favorable if I had read them. Yet I esteemed them most favorably, for I had written you, if I remember well, that I believe many excellent metaphysical demonstrations are to be found in them which deserve to be purged of their barbarisms and confusion. I could not have said this if I had not wanted you to believe that I have read them. And I did in fact read them, more immoderately and eagerly than my teachers approved, when I began to study philosophy at the universities. They feared, indeed, that I should cling too tightly to these rocks. You would have found me, then, making some original and profound comments (for so they seemed to others as well) on the principle of individuation, the composition ofthe continuum, and the concourse of God. And I have never since regretted having sampled these studies. I am unwilling to agree with you that Descartes only pretended to defend the existence of God and the immortality of the soul, and I do not see your grounds for inferring this. His arguments are not sophistical but imperfect; that is, he assumes some things which he has not demonstrated but which are nonetheless demonstrable, though they could not easily be demonstrated by his principles. It is certain, however, that most of his metaphysics is already found, partly in Plato and Aristotle and partly in the Scholastics. So far I have been convinced that my friend in Rinteln 5 holds the best doctrine about God and the soul, and I have no ground for changing my opinion. So I do not want you to become fixed in the opinion which you seem to have gathered from false stories which others have told about a good and scholarly man. Whether there is some incorporeal substance in beasts which is called a sentient soul is something to be investigated by experiments, for it is a question of fact. Yet if I am not mistaken, God could certainly have created a kind of machine similar to an animal which carries out, without sensibility, all the functions, or at least most of them, which we see in beasts. Conversely, we cannot assert with certainty that there is a sentient soul in beasts unless we observe phenomena which cannot be explained mechanically. If I were shown an ape who plays the game of highwayman or chess skilfully and successfully, even with men as opponents, I should certainly be forced to admit that there is something in him greater than a machine. But from that time on I should become a Pythagorean and like Porphyry, condemn the eating of animals and the tyranny which men exercise against them. I should also provide for a place for their souls after death, for no incorporeal substance can be destroyed. But enough of these matters for now. I have gone into greater detail about them, both to clear myself of a suspicion of being thoughtlessly inclined to adopt absurd beliefs merely because their novelty pleases me, and also to see whether a man of such great genius and discernment as yourself can voice any objection to my findings. I am concerned, as are all who wish to hold a middle ground, not to seem too much inclined toward either of the two opposed adversaries. Whenever I discuss matters with the Cartesians, certainly, I extol Aristotle where he deserves it and undertake a defense of the ancient philosophy, because I see that many Cartesians read their one master only, ignoring what is held in high esteem by others, and thus unwisely impose limits on their own ability. I do not at all approve of throwing words around too freely against the old philosophy, nor do I approve of the argument which a certain friend in this neighborhood has divulged; I have told him so in a letter, I think that the two philosophies should be combined and that where the old leaves off, the new should begin.
HANOVER TO THE ITALIAN JOURNEY, 1676-87 191 Perhaps my tetragonism will some day be published in France, where I have abandoned my demonstrations. 6 It is not such as mathematicians usually desire, but such as they ought to desire, for since it is impossible to express the ratio between a circle and a square in one number, a series of numbers continued to infinity is required. I do not think a series can be given that would be simpler than mine. I greatly regret that your work on the boundaries of the German Empire has met with a delay, for I know that you can say some excellent things on this. 7 I hope that soon, after you have completed these and other matters which you have in hand, you may be able to write down some things in medicine and publish your praiseworthy findings in this field, which is so difficult and yet so important. Above all, I wish that a correct doctrine of the use of parts could be set up, and a pathology treating the causes and symptoms of diseases and based on observation constructed upon it. I know no one who can do this more accurately than you. But that you may be able to achieve these and other outstanding services, I wish you, from the bottom of my heart, sound health, prolonged for a very long time. REFERENCES It must be noted that analysis and synthesis cannot be correlated with deduction and induction, or the converse. Leibniz thinks of all ratiocination as deductive, the role of analysis or synthesis depending upon whether the simpler and more abstract, or the compound and more concrete concepts are known (cf. Introduction, Sec. IV). 2 In Leibniz's final copy this sentence was changed as follows: "We must take care, that is, not merely that the predicate is in the subject but also that subjects and predicates, not only in the same proposition but in all the propositions occurring in the same proof, are equally extended." The use of the principle that the predicate is in the subject begins in this period, but it is here clear that this principle is subordinate to the principle of identity. Though Leibniz, here regarding an algebraic solution as a special case of logical demonstration, already conceives of the equivalence of subject and predicate in a proposition, this is always in an essential and intensional sense rather than an extensional interpretation. 3 That is, mechanistic interpretations of nature in general, which Leibniz sometimes identifies as the corpuscular philosophy (see p. 349, note 14). 4 SeeNo.3andp.l03,notel0. 5 Arnold Eckhard (see No. 16). 6 Leibniz did not, in fact, publish his findings on the quadrature of the circle until 1682, and then in the Leipzig Acta eruditorum; in the same journal he first published his findings on the differential calculus in 1684. 7 Conring's important study of the Empire, De /inibus imperii Germanici Libri II (1654), appeared in a new edition in 1693. 1
19 LETTER TO WALTER VON TSCHIRNHAUS May, 1678 (Selection) After their winter of collaboration in Paris, Leibniz and Tschirnhaus continued to discuss mathematicalandphilosophicalproblemsby letter.! On April 30, 1678, the latter wrote a long letter from Rome, in which the solution of higher equations was discussed, along with other mathematical questions. In the course of the letter it was proposed that algebra is the universal science of symbols, of which the art of combinations is but one part. Leibniz's reply contained a criticism of Tschirnhaus' proposed solution of algebraic equations, an exposition of some of the fundamental principles of the calculus, and a clear statement of the scope of his proposed characteristic science and the relation of algebra to it. Only the philosophical section of the letter is here reproduced. 2 [GM., IV, 451-63] ... As I run through the rest of your letter, I notice incidentally that you write: Many people quite falsely believe that the art of combinations is a separate science, to be mastered before algebra and other sciences. Indeed, some people believe that there is more in the art of combinations than in the art commonly called algebra; in other words, that the daughter knows more than her mother. But it is certainly obvious, from the composition of powers alone if by nothing else, that the art of combinations is mastered through algebra. These are your words which are undoubtedly aimed at me, for the 'many' who, as you say, think in this way are few, I believe, besides myself. However, I believe that your opinion is right because you do not seem to have understood me. For if you hold the art of combinations to be the science of finding the number of variations, I freely admit that it is subordinate to the science of numbers and consequently to algebra, since the science of numbers is also subordinate to algebra. For certainly you do not find these numbers except by adding, multiplying, etc., and the art of multiplying is derived from the general science of quantity, which some call algebra. But for me the art of combinations is in fact something far different, namely, the science offorms or of similarity and dissimilarity, while algebra is the science of magnitude or of equality and inequality. The combinatory art seems little different, indeed, from the general science of characteristics, by the use of which fitting characters have been or can be devised for algebra, for music, and even for logic itself. 3 Cryptography is also a part of this science, although the difficulty here lies not so much in compounding as in analyzing what has been compounded, or in investigating its roots, so to speak. What a root is in algebra a key is in cryptographic divination. Taken by itself algebra has only rules of equality and proportion but, when the prob-
HANOVER TO THE ITALIAN JOURNEY, 1676-87 193 lems are more difficult and the roots of equations very involved, algebra is forced to draw something again from the higher science of similitude and dissimilitude or from the science of combinations. 4 For a device to compare similar equations or equations of the same form was already known to Cardan and others and very distinctly described by Vieta; it has properly been taken from the art of combinations. But this art can be and ought to be used not only when our concern is with formulas which express magnitudes, and with the solution of equations, but also when the involved key is to be developed for other formulas which have nothing in common with magnitude. The art of finding progressions and of establishing tables of formulas is also purely combinatorial, for these have a place not only in formulas expressing magnitude but in all others as well. For formulas can also be derived from them which express situation [situs] and the construction of lines and angles without considering magnitude. More elegant constructions can be discovered by this method, and more easily, than through the computing of magnitudes. With the help of combinatorial theorems (that is, involving similarity and dissimilarity) it can be proved far more naturally than Euclid has done that the sides of triangles having equal angles are proportional. 5 Meanwhile I admit that no more beautiful example of the art of combinations can be found anywhere than in algebra and that therefore he who masters algebra will the more easily establish the general art of combinations, because it is always easier to arrive at a general science a posteriori from particular instances than a priori. But there can be no doubt that the general art of combinations or characteristics contains much greater things than algebra has given, for by its use all our thoughts can be pictured and as it were, fixed, abridged, and ordered; pictured to others in teaching them,fixed for ourselves in order to remember them; abridged so that they may be reduced to a few; ordered so that all of them can be present in our thinking. And though I know you are prejudiced, by reasons which I do not know, to look rather adversely upon these meditations of mine, I believe that when you examine the matter more seriously, you will agree that this general characteristic will be of unbelievable value, since a spoken and written language can also be developed with its aid which can be learned in a few days and will be adequate to express everything that occurs in everyday practice, and of astonishing value in criticism and discovery, after the model of the numeral characters. We certainly calculate much more easily with the characters of arithmetic than the Romans did either with pens or in their heads, and this is undoubtedly because the Arabic characters are more convenient, that is, because they better express the genesis of numbers. No one should fear that the contemplation of characters will lead us away from the things themselves; on the contrary, it leads us into the interior of things. For we often have confused notions today because the characters we use are badly arranged; but then, with the aid of characters, we will easily have the most distinct notions, for we will have at hand a mechanical thread of meditation, as it were, with whose aid we can very easily resolve any idea whatever into those of which it is composed. In fact, if the character expressing any concept is considered attentively, the simpler concepts into which it is resolvable will at once come to mind. Since the analysis of concepts thus corresponds exactly to the analysis of a character, we need merely to see the characters in order to have adequate notions brought to our mind freely and without effort. We can hope for no greater aid than this in the perfection of the mind. I wanted to write this to you a little more fully, my friend, to find out whether reasons do not carry For references see p. 195
194 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS more weight with you than prejudiced opinions. If you reply that the matter is clear but difficult, this is all I ask of you, for the difficulties do not frighten me, since I see certain, and unless I am mistaken, very appropriate means for overcoming them. You will have learned that the posthumous works of Spinoza have appeared. There is among them a fragment On the Improvement of the Intellect, but he stopped just where I most expected something. He does not always sufficiently explain his opinions in the Ethics, but I need not pursue this. Sometimes he commits paralogisms, the cause being that he departs from rigorous demonstrations. 6 I certainly believe that it is useful to depart from rigorous demonstration in geometry because errors are easily avoided there, but in metaphysical and ethical matters I think we should follow the greatest rigor, since error is very easy here. Yet if we had an established characteristic we might reason as safely in metaphysics as in mathematics. You say that it is difficult to set up definitions of things; perhaps you mean in the most simple and the primitive concepts, so to speak. These, I admit, it is difficult to give. We must realize, indeed, that there are several definitions of the same thing, that is, reciprocal properties which distinguish one thing from all other things and that from each one we can derive all the other properties of the thing defined. You are not unaware of this, but some of these definitions are more perfect than others, that is, they come nearer to the primary and adequate notions. Indeed, I hold this to be a certain criterion of a perfect and adequate definition: that when the definition is once grasped. we cannot further doubt whether the thing defined in it is possible or not. Besides, anyone who wishes to construct a characteristic or universal analytic can use any definitions whatever in the beginning, since all will eventually lead to the same result when the analysis is continued. You are entirely of my opinion when you say that in very composite matters a calculus is necessary. For this is the same as if you had said that characters are necessary, for a calculus is nothing but operation through characters, and this has its place not only in matters of quantity but in all other reasoning as well. Meanwhile I have a very high regard for such problems as can be solved by mental powers alone insofar as this is possible, without a prolonged calculation, that is, without paper and pen. For such problems depend as little as possible on external circumstances, being within the power even of a captive who is denied a pen and whose hands are tied. Therefore we ought to practice both in calculating and in meditating, and when we have reached certain results by calculation, we ought to try afterward to demonstrate them by meditation alone, which has in my experience often been successful. But since we think the same about many things, I have no doubt that if we differ it is with reason. I do not want this to cause dissension between us, nor dissension to diminish our friendship. I hope therefore that you will not be displeased with my frankness in expressing my opinion about your extraction of the roots of equations, for I think you have missed the mark and want to indicate this to you to save you labor. I in tum await your opinion about my own views, for I have great confidence indeed in you and have no doubt of profiting. I have learned many things from you, and I can learn even now. You are capable of great discoveries and can do the things which have already been presented by others, even by me, if you give your mind to them. But, in the public interest, I should prefer to have you apply your mind to untouched problems which are not yet in our power. I hope also that several prejudices which you seem to hold against some of my opinions will more and more disappear....
HANOVER TO THE ITALIAN JOURNEY, 1676-87 195 REFERENCES On Tschimhaus see the letter to Oldenburg (No. 13) and p.166 note 1. Leibniz later wrote at the head of this letter, "To Mr. Tschimhaus at Rome, end of May, 1678. Tschirnhaus received the letter, for he answered it and repeated my words in his reply. In it I already explained to Tschirnhaus my general method for investigating quadratures; also the mark of a real definition, which is possibility. He later attributed both to himself." It was Tschirnhaus' publication of some of these results that caused Leibniz to publish his methods in the differential calculus in 1684. 3 The logical calculus (Nos. 26 and 41) is thus only an application of the universal characteristic, other phases being algebra, cryptography, the geometry of situation, the universal language, etc. 4 Both correspondents had been trying to find the roots of higher algebraic equations by applying their combinations to the coefficients of the terms of the equation. 5 See No. 27 and the criticism of Euclid contained in it. 6 In June, 1682, Leibniz said that Tschirnhaus was now freed "from some prejudices drawn from Descartes and Spinoza, against which I once preached on various occasions, since I have always held that neither thought nor extension are primitive or perfectly understood terms" (PA., II, i, 528). But Tschirnhaus' Medicina mentis (1687), in which he proposes a mathematical logic as the medicine of the mind, was influenced by Spinoza's De emendatione intellectus as well as by Leibniz. A more positive judgment on Spinoza is found in Leibniz's letter to Henry Justel, earlier in the same year (February 4/14,1678 [PA., II, i, 393]): "The posthumous works ofthe late Mr. Spinoza have at last been published. The most important part is the Ethics, composed of five treatises: on God, on mind, on human servitude to affections or on the force of the affections, and on human freedom or the power of the understanding. I have found there a number of excellent thoughts which agree with my own, as some of my friends know who have also learned from Spinoza. But there are also paradoxes which I do not find true or even plausible. As for example, that there is only one substance, namely God; that creatures are modes or accidents of God; that our mind perceives nothing further after this life; that God himself does indeed think but neither understands nor wills; that all things happen by a kind of fatal necessity; that God does not act for the sake of ends but only from a certain necessity of nature. This is to retain in word but to deny in fact, providence and immortality. I consider this book dangerous for those who wish to take the pains to master it. For the rest will not make the effort to understand it." 1 2
20 ON THE ETHICS OF BENEDICT DE SPINOZA 1678 As the letters to Tschirnhaus and Justel show (No. 19 and p. 195, note 6), Leibniz received a copy of Spinoza's Opera posthumafrom G. H. Schuller, the literary executor, immediately after their publication, and assumed a critical attitude toward both the Ethics and the essay On the Improvement of the Understanding from the start. His reading notes on Book Iof the Ethics are particularly detailed and show how his concern to establish a sound logical basis for his own pluralistic view of substance impelled him to search out and criticize the logical gaps and implicit assumptions in Spinoza's arguments. [G., I, 139-50] PART I. ON GOD Definition 1. Cause of itself is that whose essence involves existence. Definition 2. To say that a thing is finite if it can be limited by another thing of the same nature involves obscurity. For what does it mean to say that a thought is limited by another thought? Does this mean that the other one is greater, in the sense that he says that a body is limited because another can be conceived which is greater than it? See Proposition 8, below. Definition 3. Substance is that which is in itself and is conceived through itself. This definition too is obscure. For what does 'to be in itself' mean? Then we must ask: Does he relate 'to be in itself' and 'to be conceived through itself' cumulatively or disjunctively? That is, does he mean that substance is what is in itself and also that substance is what is conceived through itself? Or does he mean that substance is that in which both occur together, that is, that substance is both in itself and conceived through itself? But then it would be necessary for him to prove that whatever has one property also has the other, while the contrary seems rather to be true, that there are some things which are in themselves though they are not conceived through themselves. 1 And this is how men commonly conceive of substances. He continues: substance is that whose concept does not need the concept of any other thing upon which it must rest. But there is also a difficulty in this, for he says in the next definition that an attribute is perceived by the understanding as belonging to substance and as constituting its essence. Therefore the concept of the attribute is necessary to form the concept of the substance. If you reply that an attribute is not a thing and that you merely mean that a substance does not need the concept of any other thing, I answer that it is then necessary to explain what 'thing' means, in order to understand the definition and see why an attribute is not a thing. Definition 4. It is also obscure to say that an attribute is that which the understanding perceives about substance as constituting its essence. For the question arises whether he understands by attribute every reciprocal predicate, or every essential
HANOVER TO THE ITALIAN JOURNEY, 1676-87 197 predicate whether reciprocal or not, or finally, every primary essential or indemonstrable predicate of substance. 2 See Definition 5. Definition 5. A mode is that which is in something else and is conceived through something else. It seems therefore to differ from an attribute in this - that an attribute is indeed in a substance but is conceived through itself. And with the added explanation here the obscurity of Definition 4 disappears. Definition 6. He says: I define God as the absolutely infinite being, or as the substance which consists of infinite attributes, each of which expresses an eternal and infinite essence. He ought to show that these two definitions are equipollent 3 ; otherwise the one cannot be substituted for the other. They will be equipollent if it is shown that there is a plurality of attributes or predicates in the nature of things which are conceived through themselves; but also that the several predicates are compatible with each other. Besides, every definition is imperfect, however true and clear it may be, which permits some doubt, even when it is understood, about whether the thing defined is possible. Now this is such a definition, for it still can be doubted whether a being having infinite attributes does not imply a contradiction. Furthermore, it can be doubted whether the same simple essence can be expressed through many different attributes. There are in fact many definitions of composite things, but only one of a simple thing, and its essence can be expressed, it seems, only in one way.4 Definition 7. A being is free which exists and is determined to action by the necessity of its own nature; a being is coerced whose existence and action are determined by another. Definition 8. By eternity I mean existence itself insofar as it is conceived to follow from the essence of a thing. I approve of both of these definitions. As for the axioms, I make the following comments. The first is obscure as long as what it means 'to be in itself' is not stated. No comment is necessary on the second and the seventh. The sixth hardly seems consistent, for every idea agrees with that of which it is the idea, and I do not see what a false idea can be. I believe that the third, fourth, and fifth axioms can be proved. Proposition 1. Substance is by nature prior to its affections, that is, to its modes, for he has said in Definition 5 that by the affections of a substance he means the modes. But he has not explained what the term 'prior by nature' means, and so this proposition cannot be demonstrated from what precedes it. But it seems that by 'something prior to another thing by nature' he means that through which the other thing is conceived. Yet I confess that I find some difficulty in this too, for it seems that what is posterior cannot only be conceived through what is prior, but also the prior through the posterior. 'To be prior by nature' can be defined in this way, however: as that which can be conceived without the other being conceived, while the other thing cannot, on the contrary, be conceived without the concept of the former. But to tell the truth, to be prior by nature is a little more general even than this. For example, the property of the number 10 to be 6 + 4 is posterior to that of being 6 + 3 + 1, because this latter property is closer to the first property of all; ten is 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1. Still it can be conceived without the second property, and what is more, it can be proved without it. I add another example. In a triangle the property that the three internal angles equal two right angles is posterior in nature to the property that two internal angles are equal to the exterior angle of the third. Yet the former can be understood without the latter and, indeed, can be demonstrated without it, though not as easily. For references see p. 205
198 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Proposition 2. Two substances with different attributes have nothing in common. If by attributes he means predicates which are conceived through themselves, I grant the proposition, assuming that there are two substances A and B and that c is the attribute of substance A and d the attribute of substance B, or that c and e are all the attributes of substance A, and d and/all the attributes of substance B. But the case is different if these two substances have some attributes different and some in common, as when c and d are the attributes of A, and d and/the attributes of B. Ifhe denies that this is possible, he must demonstrate its impossibility. Perhaps he would demonstrate the proposition against this objection, as follows. Since d and c alike express the same essence (being attributes of the same substance A, by hypothesis), and d and / also express the same essence, for the same reason (being by hypothesis attributes of the same substance B), c and/must also. Hence it follows that A and B are the same substance, which is contrary to hypothesis, and it is therefore absurd that two distinct substances can have anything in common. I reply that I do not concede that there can be two attributes which are conceived through themselves and yet can express the same substance. For whenever this happens, these two attributes expressing the same thing in different ways can be further analyzed, or at least one of them. S This I can easily prove. Proposition 3. If two things have nothing in common, one cannot be the cause of the other, by Axioms 5 and 4. Proposition 4. Two or more distinct things are distinguished either by the diversity of the attributes of their substances or by the diversity of affections. He proves this as follows. Everything that is, is either in itself or in something else, by Axiom 1; that is, outside of the understanding there is nothing besides substances and their affections, by Definitions 3 and 5. Here I am surprised at his forgetting attributes, for in Definition 5 he understands merely modes by the affections of substances. It follows either that he speaks ambiguously or that he does not include attributes among the things that exist outside the understanding, but merely substances and modes. 6 For the rest, he could have shown the proposition more easily by adding that things which can be conceived through their attributes or affections are necessarily known and therefore also distinguished from each other. Proposition 5. In the nature of things there cannot be two or more substances with the same nature or attribute. Here I point out that what is meant by 'in the nature of things' seems obscure. Does he mean in the whole of existing things or in the region of ideas or of possible essences? Then it is not clear whether he meant to say that there are not many essences with the same common attribute or that there are not many individuals with the same essence. I also wonder why he here takes the word 'nature' and the word 'attribute' as equivalent,. unless he means by attribute that which contains the whole nature. If this is assumed, I do not see how there can be many attributes of the same substance which are conceived through themselves. His proof of the proposition is as follows. If the substances were distinct, they would be distinguished either by affections or by attributes; if by affections, then since a substance is by nature prior to its affections, by Proposition 1, they must also be distinguished apart from their affections, and therefore they are distinguished by their attributes. If by their attributes, then there are no two substances with the same attribute. I reply that there seems to be a concealed fallacy here. For two substances
HANOVER TO THE ITALIAN JOURNEY, 1676-87 199 can be distinguished by their attributes and still have some common attribute, provided they also have others peculiar to themselves in addition. For example, A may have the attributes c and d, and B the attributes d and e. I note further that Proposition 1 is useless except for proving this proposition. It might have been omitted, for it is enough that substance can be conceived without its affections, whether it be prior to them by nature or not. Proposition 6. One substance cannot be produced by another substance. For by Proposition S, two substances do not have the same attribute; therefore they can have nothing in common, by Proposition 2, and therefore the one cannot be the cause of the other, by Axiom S. To prove the same thing otherwise and more briefly: What is conceived through itself cannot be conceived through something else as its cause, by Axiom 4. For the rest, I grant the demonstration if substance be taken as something which is conceived through itself. The case is different if substance is taken to be something which is in itself, as this is commonly understood, unless he shows that to be in itself and to be conceived through itself are the same thing. Proposition 7. To exist pertains to the nature of substance. One substance cannot be produced by another, by Proposition 6. Therefore it is the cause of itself, that is, by Definition 1, its essence involves existence. Here he is rightly to be criticized for using the term 'cause of itself' sometimes in the special sense which he has given it in Definition 1 and sometimes in its common and popular meaning. Yet it is easy to remedy this, if he transforms Definition 1 into an axiom and says: Whatever is not from something else is from itself, or from its own essence. But then there remain other difficulties here. For the reasoning is valid only on the assumption that substance can exist. For since it cannot be produced by something else, it must exist by itself, and hence exist necessarily. But it must be demonstrated that substance is possible, that is, that it can be conceived. This, I think, can be demonstrated: for, if nothing can be conceived through itself, nothing will be conceivable through something else either, and therefore nothing will be conceivable at all. To show this more distinctly, we must consider that if a is assumed to be conceived through b, the concept of b must be contained in the concept of a. And, again, if b is conceived through c, the concept of c must be contained in the concept of b, and thus the concept of c will be contained in the concept of a; and so on, to the last concept. If someone answers that there is no last concept, I reply that then there is no first one either, and I prove it as follows. Since there is nothing except alien elements in the concept of that which is conceived through something else, then proceeding by stages through many concepts, it will have either nothing whatever in it or nothing except what is conceived through itself. I believe that although this demonstration is new, it is infallible. With its aid it can be proved that what is conceived through itself is possible. Yet we can still doubt whether it is possible in the sense in which it is here assumed to be possible, namely, not merely for that which is conceivable, but for that of which some cause can be conceived which is eventually reducible to a first cause. For not everything which is conceivable by us can therefore be produced, because of other more important things with which it may be incompatible. Thus, to prove that a being conceived through itself actually exists, we must resort to experience, because, since things exist which are conceived through other things, a thing exists through which they are conceived. So you see that an entirely different kind of reasoning is necessary to prove accurately that there is a thing which exists through itself. 7 But perhaps there is no need of this extreme caution. For references see p. 205
200 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Proposition 8. Every substance is necessarily infinite, because otherwise it would be limited by another substance of the same nature, by Definition 2, and there would be two substances of the same nature, which contradicts Proposition S. This proposition must be understood as follows. A thing which is conceived through itself is infinite within its own kind; this must be admitted. But the demonstration suffers from obscurity as to the term 'to be limited' and also from uncertainty, by reason of Proposition S. In the scholium he gives an elegant proof that there is only one thing that is conceived through itself (within its own kind, that is), because, assuming that there is a plurality of individuals, there must be some reason in nature why there should be just so many and no more. But the reason for there being exactly so many is the same as that for there being this one and that one, and therefore the same as the reason for there being this particular one. But this reason is not to be found in one of them rather than another; therefore the reason is outside all of them. One objection is possible, namely, that the number of individuals is unlimited or no number at all, or that it exceeds any number. But this could be avoided if we take only some of them and ask why these exist, or if we take several of them having a common property such as existence in the same place, and ask why they exist in this place. Proposition 9. The more reality or being a thing possesses, the more attributes belong to it. (He should have explained what is meant by reality or being, for these terms are subject to equivocation.) His demonstration: it follows from Definition 4. Thus our author. But it does not seem to me to follow from it. For one thing can have more reality than another for the reason that it is greater in its own kind or has a greater share in some attribute. For example, the circle has more extension than the inscribed square. And it can still be doubted that several attributes may belong to the same substance, in the sense in which the author understands attributes. Meanwhile I admit that if his meaning of attributes is accepted and attributes are supposed to be compatible, a substance is the more perfect, the more attributes it has. Proposition 10. Each attribute of the same substance must be conceived through itself, by Definitions 4 and 3. But then it follows, as I have several times objected, that one substance can have only one attribute if this attribute expresses its whole essence. Proposition 11. God, or the substance which consists of infinite attributes, each of which expresses an eternal and infinite essence, necessarily exists. He gives three demonstrations. First, because God is a substance and therefore exists, by Proposition 7. But this assumes that a substance necessarily exists, which was not sufficiently proved in Proposition 7, and that God is a possible substance, which is not so easy to prove. The second proof is that there must always be a cause for the being of a thing as well as for its nonbeing. But there can be no reason why God should not exist - not in his own nature, for this implies no contradiction; not in anything else, for that something else would either be of the same nature and attribute, and therefore would be God, or it would not, in which case it would have nothing in common with God and so could neither support nor prevent his existence. To this I reply (1) that he has not yet proved that God's nature does not imply contradiction, even though the author says without proof that it is absurd to say that it does, and (2) that another being could have the same nature as God in some things but not in all. His third argument: finite beings exist, by experience. Therefore, if an infinite being did not exist, the finite beings would be more potent than the infinite being. To this I reply: If the infinite
HANOVER TO THE ITALIAN JOURNEY, 1676-87 201 being implies a contradiction, it will have no power at all; not to mention that the capacity to exist cannot properly be called a power. Propositions 12 and 13. No attribute of substance can truly be conceived from which it would follow that substance is divisible; or taken absolutely, substance is indivisible. For it will be destroyed by division; the parts will not be infinite and therefore not substances. Or else there would be several substances of the same nature. I grant this argument for a thing existing through itself. Hence the corollary follows that no substance is divisible, and therefore the corporeal substance, too, is indivisible. Proposition 14. There is no substance besides God, and none can be conceived. Because all attributes pertain to God and there is no plurality of substances with the same attribute, there are no substances besides God. All this presupposes the definition of substance as a being which is conceived through itself, as well as many other propositions, already noted, which cannot be granted. (It does not yet seem certain to me that bodies are substances; with minds the case is different.) Corollary 1. There is only one God. Corollary 2. Thinking being and extended being are either attributes of God or, by Axiom 1, affections of the attri butes of God. Here he speaks confusedly; besides he has not yet shown that extension and thought are attributes or can be conceived through themselves. Proposition 15. Whatever is, is in God, and nothing exists or can be conceived without God. For since there is no substance besides God, by Proposition 14, all other things are affections or modes of God, because there is nothing besides substances and modes. (Again he omits attributes.) Proposition 16. From the necessity of the divine nature there must follow an infinite number of things in infinite modes, that is, everything which can be an object of an infinite intellect, by Definition 6. Corollary 1. Hence it follows that God is the efficient cause of everything which is the object of his intellect. Corollary 2. God is a cause through himself and not by accident. Corollary 3. God is absolutely the first cause. Proposition 17. God acts solely according to the laws of his own nature and is coerced by no one, since there is nothing outside of him. Corollary 1. Hence it follows, first, that there is no cause which moves God to act, either extrinsically or intrinsically, except the perfection of his own nature. Corollary 2. Only God is a free cause. In the scholia he explains in more detail that God has created everything which is in his intellect (though it would seem that he has created only what he wills). He also says that the intellect of God differs in essence from our intellect and that the name 'intellect' can be ascribed to both only equivocally, like calling both the heavenly constellation and a barking animal a dog. The thing caused differs from its cause in that which it receives from its cause. One man differs from another with respect to the existence which he receives from him; he differs from God with respect to the essence which he receives from God. Proposition 18. God is the immanent, not the transeunt, cause of all things. This follows from the proposition which he thinks he has proved above, namely, that only God is a substance, and all the rest his modes. For references see p. 205
202 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Proposition 19. God or all his attributes are eternal. For his essence involves existence, and his attributes involve his essence. In addition, the author refers to the proof given in Proposition 19 of his work on the Principles of Descartes and approves of the way he demonstrated it. 8 Proposition 20. The essence and the existence of God are one and the same thing. He proves this as follows: all that can be attributed to God belongs to his essence; all his attributes are eternal (Proposition 19) and therefore express existence (by the definition of eternity). But the same attributes also express essence, by the definition of attributes. Therefore essence and existence are the same in God. I reply that this does not follow but only that essence and existence are expressed by the same thing. I note also that this proposition presupposes the preceding one; if, therefore, the demonstration of the preceding proposition were applied instead of the proposition itself to the demonstration of the present one, an awkward circle would become apparent, as follows. I prove that God's essence and existence are one and the same, because the attributes of God express both essence and existence. They express essence by the definition of an attribute, and they express existence because they are eternal. But they are eternal because they involve existence, since they express the essence of God, which involves existence. What need, then, of mentioning the eternity of attributes and Proposition 19, since the matter reduces to nothing more than a proof that the existence and essence of God are one and the same thing, because the essence of God involves existence. All the rest is introduced as an empty pretentious device to twist the whole into the form of a demonstration. Reasoning of this kind is very common among men who do not know the true art of demonstration. Corollary 1. Hence it follows that God's existence, as well as his essence, is an eternal truth. I do not see how this proposition follows from the preceding one; in fact, it is far more true and clear than the preceding. For it becomes evident at once, if we assume that God's essence involves existence, even if essence and existence are not admitted to be one and the same. Corollary 2. God and all his attributes are immutable. The author's statement and proof of this are both obscure and confused. Proposition 21. All that follows from the absolute nature of some attribute of God must exist always and be infinite or is eternal and infinite through this same attribute. He demonstrates this obscurely and at length, though it is easy. Proposition 22. Whatever follows from some attribute of God, inasmuch as it is modified by such a modification as exists necessarily and is eternal through this attribute, must also exist necessarily and be infinite. He says the demonstration proceeds as in the preceding. So it too is obscure. I wish he had given an example of such a modification. Proposition 23. Every mode which exists necessarily and is infinite must follow necessarily either from the absolute nature of some attribute of God or from some attribute modified by a mode which exists necessarily and is infinite. That is, such a mode follows from the absolute nature of some attribute, either immediately or by the mediation of some other such mode. Proposition 24. The essence of the things produced by God does not involve existence, for otherwise they would be the causes of themselves, by Definition 1, which is contrary to hypothesis. This proposition is obvious on other grounds, but this demonstration is fallacious. For in Definition 1, 'being the cause of itself' has taken on
HANOVER TO THE ITALIAN JOURNEY, 1676-87 203 a particular sense which is not its common meaning. The author therefore cannot substitute the common meaning of the word in place of his own arbitrary meaning without showing that the two are equivalent. 9 Proposition 25. God is the efficient cause not only of the existence of things but of their essence as well. Otherwise the essence of things could be conceived without God, by Axiom 4. But this proof carries no weight. For even admitting that the essence of things cannot be conceived without God, by Proposition 15, it would not follow that God is the cause of their essence. For the fourth axiom does not say that 'the cause of a thing is that without which it cannot be conceived'. (This would be false, for a circle cannot be conceived without a center, or a line without a point, yet the center is not the cause of the circle, nor the point of the line.) The fourth axiom says merely that 'the knowledge of the effect involves the knowledge of the cause', which is something far different. Nor is this axiom convertible - not to mention the fact that to involve something is one thing and to be inconceivable without it is another. The knowledge of a parabola involves the knowledge of its focus, yet the parabola can be conceived without it. Corollary. Particular things are nothing but the affections or modes of the attributes of God, which express these attributes in a definite and determinate way. He says this is evident from Definition 5 and Proposition 15, but the connection between this corollary and the present Proposition 25 is not clear. Spinoza is certainly not a great master of the art of demonstrating. This corollary is evident enough from what was said above, but it is true only if it is understood in the right sense; that is, in the sense not that things are such modes but that the ways in which we conceive particular things are determinate ways of conceiving the divine attributes. 1o Proposition 28. Any individual thing, or anything which is finite and has a determinate existence, cannot exist or be determined to act unless it is determined to exist and to act by some other cause which is also finite and has a determinate existence, and this in turn by another, and so on to infinity. For nothing limited, finite, and existing in a definite time can follow from the absolute essence of God. Rightly understood, this opinion leads to many absurdities. According to it, things would not truly follow from the nature of God. For the determining thing is in its tum determined by another thing, and so on to infinity; thus things are in no way determined by God. God merely contributes something absolute and general of his own. It would be more correct to say that one particular thing is not determined by another in an infinite progression, for in that case things would always remain indeterminate, no matter how far you carry the progression. All particular things are rather determined by God.l l Prior things are not the full cause of the posterior 1Z, but God rather creates posterior things so that they are connected with the prior according to certain rules of wisdom. If we say that prior things are the efficient causes of posterior, the posterior will in tum be the final causes of the prior, in the opinion of those who hold that God operates according to purposes. Proposition 29. There is nothing contingent in the nature of things, but everything is determined to a certain way of existence and action by the necessity of the divine nature. The demonstration is obscure and abrupt, being carried through by means of the abrupt, obscure, and questionable propositions which have preceded it. The matter depends on the definition of 'contingent', which he has given nowhere. I use the term 'contingent', as do others, for that whose essence does not involve existence. In For references see p. 205
204 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS this sense particular things are contingent according to Spinoza himself, by Proposition 24. But if you take contingent in the sense of some of the Scholastics, a usage unknown to Aristotle and to common life, as that which happens in such a way that no reason of any kind can be given why it should have happened thus rather than otherwise, and as that whose cause is equally disposed to act and not to act when all the conditions, both internal and external, have been fulfilled, then I think that such contingency implies a contradiction; for according to the hypotheses of a divine will and a given state of things, everything is defined and determined by its own nature, even though this nature may be unknown to us and is determined not by itself but, according to the supposition or hypothesis, by the external conditions. Proposition 30. Both the actually finite intelkct and the actually infinite intellect must comprehend the attributes of God and the affections of God and nothing else. This proposition, which is clear enough from the preceding, and true if taken in the right sense, our author proves in another obscure, questionable, and devious way, as is his wont. He says, namely, that a true idea must agree with its object; that is, as is self-evident (so he says, though I am unable to understand why it is self-evident or even true), that what is contained in the intellect as its object must necessarily exist in nature but that there is only one substance in nature, namely God. These propositions, however, are obscure, questionable, and far-fetched. Our author's mind seems to have been most tortuous; he rarely proceeds by a clear and natural route but always advances in disconnected and circuitous steps, and most of his demonstrations surprise the mind instead of enlightening it. Proposition 31. The intellect, whether actually finite or infinite, along with the will, desire, love, etc., must be ascribed to the natura naturata and not to the natura naturans. By natura naturans he means God and his absolute attributes; by natura naturata, his modes. But he regards intellect as nothing but a certain mode of thinking. Hence he says elsewhere that strictly speaking, God has neither intellect nor will. I do not agree with this. Proposition 32. Will cannot be called a free cause but only a necessary one, because 'only that which is determined by itself is free. But will is a mode of thought and is therefore determined by something other than itself. Proposition 33. The world could not have been produced by God in any other way than it has been produced, for it follows from the immutable nature of God. This proposition may be true or false, depending on how it is explained. On the hypothesis that the divine will chooses the best or works in the most perfect way, certainly only this world could have been produced; but, if the nature of the world is considered in itself, a different world could have been produced. Thus we say that confirmed angels cannot sin, in spite of their freedom. They could if they willed, but they do not will. Speaking absolutely, they can will to sin, but in this existing state of things they no longer can so will. In his scholium the author rightly recognizes that something may be rendered impossible for two different reasons - either because it implies contradiction or because there is no external cause apt to produce it. He denies, in his second schoHum, that God does all things in view of the good. He has already denied God a will, it is true, and he thinks that those who disagree make God subject to fate, though he himself admits that God does all things according to the principle of perfection. Proposition 34. The power of God is his essence itself, because it follows from his essence that he is the cause of himself and of the other things.
HANOVER TO THE ITALIAN JOURNEY, 1676-87 205 Proposition 35. Whatever is in God's power exists necessarily, that is, it follows from his essence. 13 Proposition 36. Nothing exists from whose nature some effect does not follow, because it expresses the nature of God, that is his power, in a certain and determined way, by Proposition 34. This proposition does not follow, but it is nonetheless true. He adds an appendix in which he attacks those who believe that God acts according to purposes. The appendix is a mixture of truth and falsehood. Even though it is true that not everything happens for the sake of men, it does not follows that God acts without will or knowledge of the good. REFERENCES An important distinction for Leibniz, as the following comments show, for the individual monad is in itself but cannot be conceived adequately except in terms of its relations to God and to other monads. This criticism of Spinoza may be regarded as clearing the way for his own solution of the problem of the one and the many and therefore for his theory of representation. 2 For Leibniz's conception of attribution see No. 35, Sec. 8. A reciprocal predicate is one which mutually implies and is implied by the substance and is therefore complete enough to include the total meaning of the subject. An essential predicate may be any component of this, while a primary essential predicate is one not further reducible, or one of the 'simple' concepts out of which the law of the individual nature is compounded. 3 The principle of equipollence is a methodological application of the law of identity to particular fields of knowledge, in the realms of both the possible and the existent. In general, it is defined in terms of successful substitution; for example, in mathematics, a function for its dependent variable; in logic, a definition for its definitum; in geometry, congruent or (in less complete concepts) similar relations; in dynamics, the quantitative relations among effects for those among causes, or work done for energy expended, and the converse. 4 This is reminiscent of No. 14, I, and the discussion with Spinoza which it involved. In this discussion it should be remembered that Leibniz frequently shows that neither extension nor thought is a simple concept. But Leibniz's difficulty here is with the issue whether substance is simple or not, as his comments on Propositions 9 and 10 below, show. Leibniz dislikes the term 'attribute' and is not sure whether to equate it with a primary essence or with a total or complete essence. 5 And are therefore not attributes as simple primary concepts (see No. 25 and p. 169, note 2). Ultimately every substance has only one essence, though this is complex and complete, taking the form of the individual notion or law. The use of the term 'express' is not yet Leibniz's but suggests a duality of essence and attribute (see note 6 beloW). 6 Leibniz was thus one of the first to note that Spinoza's attributes may be taken in a subjective sense. 7 Note that Leibniz here sharply differentiates logical possibility and necessity from existence and thus rejects the general ontological principle that essences exist, though they demand or strive for existence. Instead he here appeals to experience to establish existence. Though he has not yet rejected the ontological argument for God, therefore, he here admits that it does not establish the existence of primary concepts in the commonly accepted sense of existence. See note 13, below. 8 See Spinoza's R. Descartes Principia philosophiae more geometrico demonstrata, Book I, Proposition 19, together with 5 and 6. The proof referred to is the ontological argument. 9 Marginal note: "It follows from this proposition, contrary to Spinoza himself, that not all things are necessary. For if the essence of a thing does not involve its existence, it is not necessary. " 1
206 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS The pivotal term here is 'express', which Leibniz is already interpreting to involve an epistemology of symbolic representation, a view which supports his pluralism and phenomenalism (see Proposition 30, below). 11 This general argument is refined in No. 51. Leibniz here reasons from his own pluralism, finding the basis for unity (i.e., harmony) in the conditions of our knowledge of things or specifically, in the interrelations of representation by which each individual reflects the entire universe. 12 Leibniz miswrote: "nec posteriora priorum esse causam plenam", an obvious slip of the pen. 18 See Proposition 33 above. This is the point to which many of Leibniz's comments have been leading; not all possibilities exist, as Spinoza holds (see No. 31, I and II). 10
21 WHAT IS AN IDEA? 1678 In the marginal notes in his copy of Spinoza's Ethics, to Definition 4 ofPart II, Leibniz commented: "Explicandum ergo erat, quid sit vera idea." An earlier answer to the question had been given in his theological and legal writings (Nos. 5 and 6, II) and in his comments on criticisms of Malebranche (No. 11, II). But his earlier theory was metaphysical and needed to be related to the epistemological questions which were now foremost in philosophical discussion. This Leibniz did in his theory of expression or representation, for which his criticism of Spinoza prepared the way and which was clearly stated, with both epistemological and methodological applications, in this short paper from the same year. [G., VII, 263-64] First of all, by the term idea we understand something which is in our mind. Traces impressed on the brain are therefore not ideas, for I take it as certain that the mind is something other than the brain or a more subtle part ofthe brain substance. There are many things in our mind, however, which we know are not ideas, though they would not occur without ideas - for example, thoughts, perceptions, and affections. In my opinion, namely, an idea consists, not in some act, but in the faculty of thinking, and we are said to have an idea of a thing even if we do not think of it, if only, on a given occasion, we can think of it. Yet there is one difficulty in this view, for we have a 'remote' faculty for thinking of all things, even those of which we may, perhaps, not have ideas, because we have the faculty of receiving ideas of them. Idea therefore requires a certain 'near' faculty or ability to think about a thing.! This does not quite suffice, however, for he who has a method which will lead him to some object if he follows it does not therefore have an idea of the object. So if I enumerate the conic sections in order, I shall certainly come to the knowledge of the opposite branches of the hyperbola, even though I do not yet have an idea of them. Hence there must be something in me which not merely leads me to the thing but also expresses it. That is said to express a thing in which there are relations [habitudines] which correspond to the relations of the thing expressed. But there are various kinds of expression; for example, the model of a machine expresses the machine itself, the projective delineation on a plane expresses a solid, speech expresses thoughts and truths, characters express numbers, and an algebraic equation expresses a circle or some other figure. What is common to all these expressions is that we can pass from a consideration of the relations in the expression to a knowledge of the corresponding properties of the thing expressed. Hence it is clearly not necessary for that which expresses to be similar to the thing expressed, if only a certain analogy is maintained between the relations. For references see p. 208
208 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS It is also clear that some expressions have a basis in nature, while others are arbitrary, at least in part, such as the expressions which consist of words or characters. Those which are founded in nature either require some similarity, such as that between a large and a small circle or that between a geographic region and a map of the region, or require some connection such as that between a circle and the elIipse which represents it optically, since any point whatever on the eIlipse corresponds to some point on the circle according to a definite law. Indeed, a circle would be poorly represented by any other figure more similar to it in such a case. Similarly every entire effect represents the whole cause, for I can always pass from the knowledge of such an effect to a knowledge of its cause. So, too, the deeds of each one represent his mind, and in a way the world itself represents God. It may also happen that the effects which arise from the same cause express each other mutually, as for example, gesture and speech. So deaf people understand speakers, not by sound, but by the motion of the mouth. That the ideas of things are in us means therefore nothing but that God, the creator alike of the things and of the mind, has impressed a power of thinking upon the mind so that it can by its own operations derive what corresponds perfectly to the nature of things. Although, therefore, the idea of a circle is not similar to the circle, truths can be derived from it which would be confirmed beyond doubt by investigating a real circle. REFERENCE The 'nearfacuIty' is defined in No. 11, II (comment on page 39 of Foucher's reply to Gabets). The 'near' or immediate faculty of thinking seems to be that of the intuited pattern of thought itself, while the 'remote' ability involves the reference of this given unity of symbol and objective structure to further objects not yet known. When these are known through rational deduction or inference, we have new ideas. 1
22 LETTERS TO NICOLAS MALE BRANCHE 1679 (Selections) The acquaintance between Leibniz and Nicolas Malebranche, member of the Oratory and distinguished Cartesian and Platonist, began in Paris around 1675; the first volume of the Recherche de la verite (1674) had then evoked both criticism and qualified defense by Leibniz (cf No. 11, IJ). Their early correspondence had been concerned with the Cartesian theory of body and extension, which Leibniz was already criticizing. On receiving a copy of Malebranche's Conversations chretiennes, published in 1677, from the Princess Elizabeth, Countess Palatine and sister of the Duchess Sophia of Hanover, Leibniz seized the opportunity to revive the correspondence. Letters between the two men continued intermittently until 1711. Many personal references and items of current intellectual gossip have been omitted in these translations. [G., I, 327-28] Hanover, January 13/23, 1679 ... Through the favor of her highness, the Princess Elizabeth, who is celebrated as much for her learning as for her birth, I have been able to see your Christian Conversations. 1 Her judgment on it is very favorable, and indeed, it contains many things that are very penetrating and very sound. I have grasped your opinion better through it than I had done in the past in reading the Recherche de la verite, because I did not have enough leisure then. I wish you had not written solely for Cartesians, as you say you have done, for all sectarian labels should be odious, it seems to me, to a lover of the truth. Descartes has said some fine things; his was a most penetrating and judicious mind. But it is impossible to do everything at once, and he has given us only some beautiful beginnings, without getting to the bottom of things. It seems to me that he is still far from the true analysis and the general art of discovery. For I am convinced that his mechanics is full of errors, that his physics goes too fast, that his geometry is too narrow, and that his metaphysics is all these things together. As for his metaphysics, you yourself have shown its imperfection, and I am entirely of your opinion concerning the impossibility of conceiving that a substance which has nothing but extension, without thought, can act upon a substance which has nothing but thought, without extension. But I believe that you have gone only halfway and that still other consequences can be drawn than those which you have made. In my opinion it follows that matter is something different from mere extension, and I believe, besides, that this can be demonstrated. I agree with you completely when you say that God acts in the most perfect manner For references see p. 212
210 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS possible. 2 And when you say in one particular passage that "it is perhaps a contradiction that man should be more perfect than he is in relation to the bodies which surround him", you have only to strike out the perhaps. I find also that you make a most beautiful use of final causes; I have had a bad opinion of Mr. Descartes for rejecting them and also for certain other passages of his in which the depths of his soul seem to be exposed. I beg you to commend me to Mr. Arnauld when you have occasion and to bear him witness that I shall honor his virtue and his equally incomparable learning all my life. I should like to know whether your Mr. Prestet continues his work in analysis. 3 I hope so, for he seems fitted for it. I recognize more and more the imperfection of what we now have. For example, it gives us no way to solve the problems of Diophantine arithmetic; it can provide no method 0/ inverse tangents, that is, of finding the curve from the given property 0/ its tangent; it supplies no way of extracting the irrational roots of equations of higher degree; it is far removed from quadrature problems. In short, I could write a scholarly work on what it has not done and on what no Cartesian, whoever he may be, can succeed in doing without discovering some method which goes further than that of Descartes. If I have the leisure, I hope some day to show, by some effective evidence, how far Descartes was from giving us the foundations of the true method. And not to mention other matters, it will then be seen that we are already able to take a bigger step beyond his own geometry than his takes beyond the geometry of the ancients. Though I do not agree with all your opinions, I nevertheless find so many excellent thoughts in your works that I hope you will continue to produce them for us. II [G., I, 330-31] June 22jJuly 2, 1679 I have received your letter, for which I am obliged to you. 4 Shortly afterward I also received the Meditations on Metaphysics, which I can also attribute only to you, or at least to this Abbe Catelan to whom you ascribe the Christian Conversations.' He must be an able man and completely familiar with your opinions. I have read these Meditations, not as one reads an ordinary book, but carefully, and if you will permit my frankness, I shall tell you what ideas I have formed about them. I approve most heartily these two propositions which you advance: that we see all things in God and that strictly speaking, bodies do not act upon us. I have always been convinced of this for important reasons which seem to me indisputable and which rest on certain axioms which I do not as yet see used anywhere, though they could be most serviceable in proving some other theses no less important than those I have just mentioned. As for the existence and nature of what we call body, we dec.!ive ourselves even more than you say, and I agree with you that it would be hard to prove that there is extension outside of us in the sense in which this is usually understood. But as for other spirits than ourselves, their existence can be demonstrated, and there must be more of them than is commonly believed. There is little difficulty concerning the perpetuity of all these spirits once they exist, but there is much difficulty concerning their beginning as this is commonly imagined. I find very true, also, what you say about the simplicity of God's decrees being the
HANOVER TO THE ITALIAN JOURNEY, 1676-87 211 cause of the existence of certain particular evils, since God would otherwise be obliged to change the laws of nature at each moment. But something more must be said about this, and I remember once having shown a little dialogue to Mr. Arnauld and Mr. des Billettes which went much further and left no more doubt about freedom, in my opinion, unless one adopts an absurd and contradictory notion of it. Whatever acts is free insofar as it acts. We must also say that God makes the maximum of things he can, and what obliges him to seek simple laws is precisely the necessity to find place for as many things as can be put together; if he made use of other laws, it would be like trying to make a building with round stones, which make us lose more space than they occupy. As for the soul of beasts, I believe that you would judge quite differently from Descartes about them if you were to regard your own positions from the same point of view as I do, who am convinced of them, but for reasons which differ from yours. The reasons which you give in your Meditations do not seem convincing enough and do not lead where they should. I do not say this out of vanity or a spirit of contradiction, b'\lt I hold the remark to be necessary. For long experience has shown me that our thoughts are confused as long as we do not have rigorous demonstrations. This, I think, is why we can reason a little more loosely in mathematics, where matters are self-regulating, but that we should reason with greater rigor in metaphysics, because we lack the aid of imagination and experience there and because the slightest lapse in that field produces bad effects which it is hard to notice. I believe the fact that you approve in Mr. Descartes what I am unable to appreciate results from our not understanding each other well. I consider it certain that the proofs which he produces for the existence of God are imperfect as long as he does not prove that we have an idea of God or of the greatest of all beings. You may reply that, if we did not, we could not reason about him. But one can also reason about the greatest of all numbers, an idea which nevertheless implies a contradiction, as does also the greatest of all velocities. This is why we still need much deep meditation to complete this demonstration. Someone may say: I conceive the most perfect of all beings because I conceive my own imperfection and that of the other imperfect beings, though they may be more perfect than I, and I would not know this without knowing what an absolutely perfect being is. But this is still not sufficiently convincing, for I can judge that two is not an infinitely perfect number, because I have, or can perceive in my mind, the idea of another number more perfect than it, and still another more perfect than this. Yet after all, I still do not get from this any idea of an infinite number, though I see very well that I can always find a number greater than any given number whatever. 6 The distinction between soul and body is not yet entirely proved. For since you admit that we do not conceive distinctly what thought is, it is not enough that we are able to doubt the existence of extension (that is, of the extension which we conceive distinctly) without being able to doubt thought. This, I say, is not enough to draw a conclusion as to how far the distinction can be carried between what is extended and what thinks, since it can be said that perhaps it is only our ignorance which distinguishes them and that in some way unknown to us thought includes extension. Nevertheless I am convinced of all these aforesaid truths, in spite of the imperfection of their ordinary proofs, instead of which I think I can give rigorous demonstrations. Since I began to meditate when I was not yet imbued with Cartesian opinions, For references see p. 212
212 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS I penetrated into the nature of things by another door and discovered new lands. So strangers making a tour of France who follow the paths of those who have preceded them never experience anything unusual unless they are very careful or very lucky, while those who take the side roads, even at the risk of getting lost, are more likely to meet with things which other travelers do not know. You have delighted me with your information that Mr. Arnauld is perfectly restored to health. God grant that he may enjoy it a long time still, for where should we find a person like him? I beg you to assure him of my respect. 7 ••• REFERENCES The work appeared anonymously. It contained an apology for Christianity in dialogue form, and from the Cartesian point of view. Leibniz made extensive notes on it (PA., II, i, 442-54). 2 Malebranche, however, supplied merely a confirmation of this Leibnizian opinion and was not its source, as some interpreters have held (see above, p. 147, note 1). 3 Jean Prestet (d. 1690) published his Elements des mathematiques in 1675. Wallis and others regarded Malebranche as the author of the anonymous work, to which Prestet, however, attached his name in the second edition, in 1689. Though he distinguished himself in theory of numbers, of combinations, and of equations, Malebranche reported in his next letter that Prestet had withdrawn from mathematical work and entered the Oratory but was preparing a revision of his Elements. 4 In his brief reply (G., I, 329), Malebranche ascribed the authorship of the Conversations chretiennes to his pupil, the Abbe Catelan (who was later to take issue with Leibniz's criticism of the Cartesian principle of the conservation of quantity of motion). Malebranche defended Descartes but was not inclined to enter into an argument. That this did not deter Leibniz. the following letter shows. Meanwhile another anonymous work, which Leibniz assumed also to be Malebranche's, also reached Hanover. 5 In his briefreply of July 31, 1679, to this letter (G., I, 339-40), Malebranche wrote: "The author of the Meditations on Metaphysics is the Abbe de Lanion. Although he did not set his name to it, he is not concealing it; I know this because he has told me so, and many other people whom I know. So please do not ascribe this work to me." The Meditations sur la metaphysique, according to Pierre Bayle, appeared with the author given as Guillaume Wander. It was purportedly printed in Cologne but apparently actually printed in Paris itself in 1678. Bayle's edition, in Recueil de quelques pieces curieuses concernant la philosophie de Monsieur Descartes (1684), is the best available, since the first edition was withdrawn, and copies were scarce even when Bayle prepared his edition. The influence of Malebranche is obvious. 6 Marginal note on Leibniz's copy: "However, I conceive the highest perfection absolutely; otherwise I could not apply it to a number, where it is applied unsuccessfully." 7 The warm friendship between Malebranche and Arnauld was to end in 1683 in the celebrated controversy over the nature of ideas (cf. No. 33 and p. 276, note 13). 1
23 TWO DIALOGUES ON RELIGION Ca. 1678 (Selections) There are many evidences of a heightened interest in religion during the first years which Leibniz spent at Hanover; among them are four dialogues on religion written around 1678. Parts of two of these are here translated. The first is satirical in mood and contrasts the true love of God with ecclesiastical fashions and superstitions. It may be considered as the literary account of discussions between Leibniz himself and Nicolas Steno, apostolic vicar at Hanover at that time. 1 The second, without title, but with a marginal note saying, .. Written before the death of Duke John Frederick", ends in a mood of deep exaltation. It describes the moral effects of the religious faith which Leibniz's work was to establish (cf. No. 28). Both dialogues are takenfrom Jean Baruzi's incomplete copies in 'Trois dialogues mystiques inedits de Leibniz', Revue de metaphysique et de morale 13 (1905) 1-38. I. DIALOGUE BETWEEN POLIANDER AND THEOPHILE Some months ago I found myself in the same coach with an apostolic missionary and a very honorable man [homme honnete] of the Augsburg Confession who had had important duties at the court but had retired from the world to look after his salvation. The missionary was named Poliander. He had grown old in controversy and had no hesitation in starting in on people on this subject. So he at once attached himself to Theophile (this was the gentleman's name), seeing him in a humor to listen peaceably. Poliander deployed all his rhetoric and made use of the devices customary to those of his kind. Theophile defended himself with a certain self-effacement and simplicity which gave ample evidence of great resources and an enlightened and tranquil soul. The discussion had already lasted a whole morning, and they had got no further than ever, when Theophile, taking the lead with the purpose of changing the conversation a little, began as follows. Th. I am surprised that people are more strongly attached to these disputes than to the practice of piety, Poliander. You agree that those who love God above all things are in the state of salvation. Why is it necessary to entangle one's self further in so many difficult problems? What end is gained? Po. It is not enough to love God; it is necessary to obey his wishes, that is to say, the church which interprets them. Th. Whoever truly loves God above all things will not fail to do what he knows to conform to his commands. This is why it is necessary to begin with this love, since charity and justice are its inescapable results. Po. A pagan philosopher can love God above all things, since his reason can teach For references see p. 220
214 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS him that God is an infinitely perfect and a supremely lovable being. But this will not make him a Christian, for he may not have heard anything about Jesus Christ, without whom there is no salvation. So the love of God is not enough. Th. This question of the salvation of pagans is too much for me. However, I have much liking for the ideas of certain learned and pious theologians who believe that God will illumine all those who sincerely seek him, at least at the point of death, and will reveal to them, even internally, what it is necessary to know about Jesus Christ, following the incontestable rule that God does not deny his grace to those who do their part. Po. I have no desire to fight opinions which seem quite fitting to reconcile piety with reason, and I should agree with you that the love of God above all things does suffice when the matter is understood in this way. But this love must necessarily be true, serious, sincere, ardent, and active. For we try to learn the wishes of the person whom we love and to conform to them. A true lover has regard for the slightest movements of the person on whom his happiness depends. And yet the rest of you believe you can dispense with learning the orders which God has made so very clear that no one can claim grounds for ignorance of them. There is nothing more clear and more conspicuous than his church, which may be seen afar off, like a city set upon a hill. Yet you close your eyes in order not to see it. Th. I confess that it is necessary to learn the will of him whom one loves and honors, for the purpose of carrying it out. But since there is an order in everything, and one cannot respond equally to diverse concerns, I believe at the same time that we must begin our obedience with the first of his wishes, which is well enough known to us. Reason and Scripture both tell us that we must love God above all things and our neighbor as ourself. It even appears that this love suffices for salvation and that everything else is but a result, following what we have just said. Po. I assume that God is truly loved; I now ask what he who loves God ought to do. And I maintain that the first concern we should have after the love of God is to search for the true church. Th. Good enough. But the assumption that you make is a great one and very rare here below. What, Poliander! Do you really think that God is loved above all things? I maintain that few people know what the love of God is.... Po. Perhaps the love of God is not as necessary as you think, and it suffices to fear him. For, according to our teaching, attrition, that is penitence bestowed through fear of punishment, suffices, along with the sacrament of absolution, even though one does not love God above all things; that is, even though there is no contrition, for you know the difference which exists between these two kinds of penitence. 2 Th. I am amazed that an opinion as dangerous as this is accepted among people who confess Christianity. The Jansenists show us its absurdity, the Holy Fathers and even the old Schoolmen are ignorant of it, and since God has commanded us to love him above all things, it is very clear that whoever does not is in a state of mortal sin. Po. Don't mention the Jansenists to me, Theophile. They are considered by Rome as heretics. As for the Fathers, we study them very little; in fact, we have done away with them, except for the many fine collections we have drawn from their writings, which serve us to combat you. This is the whole use we make of the Fathers. What is more, the ancients are eclipsed by the beautiful subtleties and unusual questions of the modems. In a word, since the church is infallible, every opinion which is today public-
HANOVER TO THE ITALIAN JOURNEY, 1676-87 215 ly accepted in our chairs of theology cannot but be good, as is every practice publicly received and approved by our flood of doctors. The doctrine of attrition is one of this number, and we need seek no other proof of it. Th. Yet there are men of piety and learning among you who speak of reform, who try to call you back to the simplicity of doctrine and the exactitude of discipline which was apparent in the primitive church. Po. Such people are only visionaries or ambitious men who are scarcely better than heretics, since they have the presumption to reform the holy church. Can infants reform their mother? Nothing is more insupportable. But if you insist in wishing for reformers, we have a good number of them, but they take care not to give offense to the opinions received by the doctors. Th. I see that you have no desire for reformers, if the matter is taken in a right sense, for the church and what it teaches and approves are for you beyond reform. What you would have are people who dote upon the mode 3 , and you call them reformers in the sense that they are the founders and renovators of religious orders. Po. If you mean by 'mode' what we call the accepted practice of the church in conformity with the century in which we live, this is true. For since the church is infallible, it cannot but choose a mode which is fitting for the time. So when hermits are in vogue, we must conform to the Thebaid; when Scholastic theology reigns, we must quibble as much as possible; when casuists take their place, it is meritorious to be a casuist. For though the casuists may have been in error when they diminished the number of sins, this did not prevent their being useful, for men who believe that what they are doing is not sinful, are not as great sinners as when they know they are sinning. But if the casuists diminish the number of sins which are contrary to moral virtues, they compensate for this by leading men to the Christian virtues, that is, they teach them to have regard for sacred ceremonies and all sorts of religious observances accepted today, for we must push things as far as we can. This is why the true reformers are those who introduce certain fashions and modes of praying and of honoring God, such as rosaries, chaplets, scapulars, and a thousand other sacred inventions, for they teach people to conform to the mode which reigns in the church, which is the interpreter of God's will. Th. But you make no mention of charity or justice, and I do not see many reformers who take up these things and stilI fewer who succeed with them in the minds of men of the times - perhaps because this is not the mode. Po. Take good care not to confuse such purely moral reforms with Christian reforms. Justice and charity are things which we can have in common with pagans; it takes other pious practices to please God. That is, we need fastings, hair shirts, disciplines, gratings, books of hours, the Ave Maria, and similar things; as for the Lord's Prayer, I see nothing in it which a pagan cannot also say. This is why we make much more of a case for the Ave Maria. Th. I might well agree with all that you have said, Poliander, if we assumed the infallibility of the practice which reigns in your church. But it seems to me that this pushes infallibility a little too far. Many able men among you, besides, recognize no other infallible Catholic doctrine than that coming from tradition. They give the church the right to witness, not to rule. 4 This being so, it is not necessary to hold to the practice which rules today but rather to that which the church received traditionally from Jesus Christ and the apostles .... But let us leave the court of Rome, with all For references see p. 220
216 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS its infallibility, since you have not proved it, and long discussion would be necessary to reach the end. Let us return to what is more certain. This is that we must love God above all things and our neighbor as ourselves. It is in this that the law consists; it is in this that true active faith also consists, in conformity to the teaching of Jesus Christ. For he has taught us this great secret; he has been not only the preceptor but also the redeemer of mankind. The divinity which dwells in the human nature of Jesus Christ has established reunion between God and men. There is no salvation at all except in Jesus Christ. ... You call yourself an apostolic missionary, and we call ourselves evangelicals. Let us agree with the evangelist and apostle Saint John, who proclaimed nothing but this charity full of faith, and this divine love which enlightens through good deeds, and we shall have enough to save ourselves and to win souls. Po. I have received no instruction from Rome about that. However, I approve your reasons in part, and I shall have a little more consideration for them in the future than I have in the past. But you who have thought so well about the divine love, carry out your promise as well. You have agreed with me that the first thing which we should seek, after this love, is the true church. This is the true union of all the living members of Jesus Christ; in a word, it is the universal charity. Th. If you put it on that basis, I am already one of you. But it seems to me that you demand something more which I can hardly grant you. You wish us to be convinced of a great number of new and doubtful things and to condemn absolutely all who dare to doubt them. Besides, you are too ceremonious, and you engage souls with so many superfluous cares that they tum away from him who ought to be their chief care. All this hurts this universal charity, it seems to me. But here is the inn; we can speak more at our ease after we have refreshed ourselves a little from the fatigues of the journey. II. DIALOGUE BETWEEN POLIDORE AND THEOPHILE Theophile. I have found you somewhat changed for some time, my dear Polidore, and it seems to me that your usual gaiety is lacking. Yet your affairs are prospering, your prudence has been helped by fortune, and you lack none of the things which men seek with such eagerness. You have wealth, you have acquired fame, and God has given you so vigorous a constitution that we may hope to enjoy you for many more years. So I cannot understand the cause of the change which I observe. Polidore. I know that you love me, Theophile, and I esteem you enough to enlighten you. I will tell you then, that what you see in me is not sadness but an indifference which I feel about many of the things which once appealed to me. Now that I have attained the things I wanted, I have come to recognize their vanity, and finding myself at the peak of the joys to which men aspire here below, I recognize better than ever the imperfection of human nature, which is incapable of solid happiness. You know that gross lusts do not much move me, but a short time ago I found more and more that the most refined pleasures of the mind are only pleasing deceptions which disappear when closely examined. Is there anything on earth to which great spirits are more sensitive than glory and the immortality of name which we like to imagine? And yet what good will they do me when I am reduced to dust? These reasons will not keep me from doing things worthy of approbation, for it is my habit to do them and I could hardly do otherwise, but I shall no longer exert myself to acquire so chimerical an immortality. My intellectual curiosity is thus diminished by half; I no longer enjoy the
HANOVER TO THE ITALIAN JOURNEY, 1676-87 217 beauties of nature and of art; and I find even less satisfaction in beautiful discourses, for they often consist only in an outburst of weIl-arranged words. And though I recognize that there are solid sciences like mathematics and mechanics, I observe that these are of use only to those who maktl a profession of them, for they take too much work. Since we shaIl lose the fruits of all our labors in a moment, let us not embarrass ourselves with anything whatever but foIlow an easy path oflife and arm ourselves with indifference against the deceptive charms of enterprise. Th. I am sorry for you, Polidore, for I stle that you are depriving yourself of the greatest satisfaction of life just when you are in the best circumstances to enjoy it. But I am still more sorry for the public and for posterity, which will be deprived ofthe great and exceIlent things you planned at a time when your affairs did not permit you to carry them out. It makes me wonder at the conduct of men, who seek only what is far off. But I perceive only that you have changed your maxims, that you no longer believe that you are under obligation to trouble yourself for the public, and find it ridiculous to work for a time when you will no longer exist. Yet I believe that you would judge otherwise if you were convinced that there is a great monarch of the universe, who takes everything done for the public as done for himself; and that if you were convinced of the immortality of our souls, then you would take an interest in the state of future centuries. Po. If you are speaking to me as a theologian, I shaIl stop, for I submit to the faith. But if you are limiting yourself to philosophical boundaries, I see great reasons for doubting these beautiful things, which serve only to soften our misery by false hopes. I admit that I should like to be one of those who are happy through their errors, but since I see clearly that they are errors, it no longer rests with me but to tum my eyes away. Th. But you, who have such exceIlent knowledge and have so often admired the wisdom of nature, can you doubt a governing providence when you consider the machine of the universe, which moves with such regularity? Po. It seems to me no great wonder that the sun, turning about its center, carries with it the liquid matter which surrounds it and is caIled ether and that this in tum also carries along some great baIls caIled planets, which float in this ether and foIlow its motion with greater or less speed in proportion to their solidity and distance. And since they meet with no resistance, we need not be astonished that their periods are regular, with no noticeable change for a long period oftime. Th. What you say is reasonable. Once assume the motion of this ether as weIl as the baIls of different solidity and volume around the sun, and the rest foIlows mechanicaIly. But tell me how it happens that there is a sun, ether, and planets. Could not the world have been made in an entirely different way? And who has made things this particular way? Assuming even the choice of these bodies explained, whence comes the principle of motion which we observe in them? ... [In a long discussion Theophile brings Polidore to assent at last to Leibniz's principle of the maximum compossible determination of existence, on the simplest assumptions.] Th. See now if what we have just discovered ought not to be caIled God. Po. The reasoning is excellent and sound, and I am most surprised. After this I will not wonder at the marvelous structure of organic bodies, the smaIlest part of which surpasses in craftsmanship all the machines which man can invent. But it seems that this wisdom, which reveals such economy in each animal or organic body considered For references see p. 220
218 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS separately, has left them afterward to attack each other in the greatest confusion imaginable. A wretched sheep is tom apart by a wolf, a pigeon falls prey to some vulture, the poor flies are exposed to the malice of spiders, and men themselves - what a tyranny they exercise over the other animals, and even among themselves they are more than wolves and more than vultures. What appearance of order is there in all this? Or rather, since we have agreed on the sovereign wisdom of the Author of things, we must say that he cares not at all for what we call justice and that he takes pleasure in destruction as we take pleasure in hunting the beasts which prey on each other. Individuals must give way; there is room only for the species, some of which subsist through the misfortune of others. And we in our folly are presumptuous enough to imagine that he will exempt us from these universal cycles by means of an immortality which is without example in nature and is all the more incredible, since a beginning must be followed by an end. Th. Your argument is plausible, and many persons of intelligence are unfortunately impressed by it, but thank God, there is a way of meeting it. We have agreed that God made everything in the greatest perfection of which the universe is capable. Consequently each thing in it, or will have, as much perfection as it is capable of claiming in proportion to what it already has, without doing violence to other things. But since pleasure is nothing but the feeling of an increase of perfection, it follows that God will give all creatures as much pleasure as they are capable of, so that those who are reasonable find themselves as happy as possible, consistent with the harmony of the universe, which demands that when the books are balanced there must be found the greatest perfection and the greatest happiness possible in the whole. Perhaps this is impossible without the misery of some who deserve it. Now of all the creatures which surround us, it is only the spirit of man which is capable of a true happiness. It can be said that the difference between God and man is only one of more or less, though the ratio is infinite. Man demonstrates truths; he invents machines and is capable of containing within himself the perfections of the things whose ideas he conceives; he knows the great God, he honors him, he loves him, and he imitates him. He exercises dominion over some things with a detachment and an elevation like that of God, though his decisions meet with obstacles in their execution. One can say that with regard to the perfection of spirit, there is at least as much difference between man and the other creatures in relation to God as there is between God and man. In short, there is some community between God and men. For since both are reasonable and have some commerce with each other, they compose a City which must be governed in the most perfect manner. This is why, if God is sovereign wisdom, as his admirable works show, and if wisdom seeks perfection everywhere insofar as it is possible, we cannot doubt that the most perfect beings and those who most nearly approach God are the ones most considered in nature, and that God is concerned for their happiness in preference to everything else. Finally, this is possible, and the order of the universe does not oppose it. It is true that our bodies are subject to the impact of other bodies and hence to dissolution. But the soul is a substance entirely different from matter and space and hence cannot be destroyed. And since this is so, it is capable of subsisting and of being happy in spite of the destruction in the world. Provided that God leaves it memory and thoughts, the soul can be happy and unhappy, punished and rewarded, according to the laws of this City of which God is the monarch ....
HANOVER TO THE ITALIAN JOURNEY, 1676-87 219 Po. Your reasons are effective and permit no reply, and I admit that I am moved by them, all the more since you have most remarkably anticipated the objections of those who believe that all souls must be reunited to the soul of the universe, as the body is lost in the general mass. For as you have well said, that which is once a body apart will always remain so and carry out its own functions in such a manner that it will be united with something else. Besides, this union of souls with the universal soul consists in a play on words only, which mean nothing, for souls are not like raindrops or brooklets which return to the ocean. If this comparison were good, it could stilI be said that each atom of the raindrop does not cease to subsist in the ocean as well and that souls as well never cease to have each its own thoughts when reunited to the universal soul of God.... [In the following section Theophile gains Polidore's assent to the view that the will of God, the universal monarch, is reflected in the kingdom of spirits.] Th. Since you have acknowledged this great point, let us draw its practical consequences. First, it follows that the world is governed in such a way that a wise person who is well informed will have nothing to find fault with and can find nothing more to desire. Second, every wise man ought to be content, not only out of necessity as if he were compelled to be patient, but with pleasure and a kind of extreme satisfaction, knowing that everything happens in such a way that the interests of each individual person who is persuaded of this truth will be achieved with every possible advantage. For when God admits us a little further into his secrets than he has until now, then among other surprises, there will be that of seeing the wonderful inventions which he has used to make us happy beyond our possible conception. Third, we ought to love God above all things, since we find everything with greater perfection in him than in things themselves, and since his goodness provides us with our whole power. For it is by this goodness that we obtain everything we can wish for our happiness. Fourth, with these opinions we can be happy in advance here below, before enjoying everything which God has prepared for us; those who are discontent, on the other hand, expose themselves to losing voluntarily everything that God has tried to give them. It can be said that this resignation of our will to that of God, whom we have every reason to trust, follows from the truly divine love, whereas our dissatisfaction and even our disappointment in mundane matters contain something of hatred toward God, which is the ultimate of misery. Fifth, we ought to give witness of the supreme love which we bear toward God through the charity we owe to our neighbor. And we ought to make every effort imaginable to contribute something to the public good. For it is God who is the Lord; it is to him that the public good pertains as his own. And all that we do unto the least of these, his subjects, whom he has the goodness to treat as brothers, we have done unto him; all the more will he receive as brother whoever contributes to the general good. Sixth, we must try to perfect ourselves as much as we can, and especially the mind, which is properly what we call ourself. And since perfection of mind consists in the knowledge of truth and the exercise of virtue, we should be persuaded that those who in this life have had the best entrance into eternal truths and the most transparent and clearest knowledge of God's perfection, and as a result have loved him more and witnessed with more ardor for the general good, will be susceptible of greater happiness in the life to come. For finally, nothing is neglected in nature; nothing is lost with God; all our hairs are numbered, and not a glass of water will be forgotten; qui ad justitiam erudiunt multos /ulgebunt quasi stellae 5; no good action For references see p. 220
220 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS without reward, no evil one without some punishment; no perfection without a series of others unto infinity. Po. Most truly beautiful and generous maxims! I see that they directly combat this indifference into which I should have plunged without your help .... You have restored me to life, my dear Theophile, for the sluggish and negligent life which I was about to lead was worth no more than death. Now my vigor returns; I shall go back to my plans. I see that virtue and glory are not chimeras. I recognize that the general lament about the misery of life poisons our satisfaction and strangely deceives us. Instead we must remember that we are the most perfect and happiest of all known creatures, or at least that it takes only us to become so. Felices nimium sua qui bona norint. 6 Hereafter let us no longer complain of nature; let us love this God who has so loved us, and know once for all that the knowledge of great truths, the exercise of divine love and charity, the efforts which one can make for the general good - by assuaging the ills of men, contributing to the happiness of life, advancing the sciences and arts and everything that serves to acquire a true glory and immortalize oneself through good deeds all these are pathways to this felicity, which lead us as far as we are capable of going toward God and which we may take as a kind of apotheosis. 7 REFERENCES Nicolas Steno (1638-87) was a Danish anatomist and physician of distinction who had abandoned his science upon entering the church in 1667. Leibniz had more regard for his past science than for his present theology. On his biological achievements see E. Nordenskiold, The History o/Biology, New York 1928, pp. 155-58. His paleontological studies are reflected in Leibniz's own studies in the Harz Mountains, reported in the Protogaea. 2 This paragraph and what follows echo the well-known controversy which Richelieu's Catechism (1637) had aroused. Poliander proposes essentially the view there formulated, which was attacked by Seguenot and other early Jansenists. 8 On the spirit of the phrase 'ida mode' see Hazard, op. cit., I, 81-82. 4 Leibniz had written 'to judge' but struck it and substituted 'to rule'. 5 "They who lead many into righteousness shall shine forth as stars." 6 "Most blessed they who know their own good." 7 Baruzi comments on the evidences of religious exaltation in the last two speeches, reflected even in the handwriting of the manuscript itself, which overflows its margins. Of the last page he says: "The appearance of this page is admirable. Very few periods. The rhythm is visible even in the writing." The ease with which Leibniz slips into scriptural phrases should refute the opinion that he was unfamiliar with the Bible. 1
24 ON THE GENERAL CHARACTERISTIC Ca. 1679 The year 1679 was one of the most creative in Leibniz's life and the last he was to enjoy under the patron who had called him to Hanover. In this year the detailed plans for two projects formulated much earlier were revived, and many studies written in preparation for their execution. These were the universal encyclopedia and the great apologetic work, the Catholic Demonstrations (No. 28). For his encyclopedia as he planned it at this time, Leibniz chose the title Plus ultra (G., VII, 49-53), borrowed from Glanvill. Many of the preliminary drafts which Lejbniz made for this work have been published in G., Volume VII. and in Couto OF. The following selections (Nos. 24, 25, and 26) are arbitrary but give a conception of his plan and the state ofhis notions in logic. They may be regarded as belonging to the introductory section of the work, to be called 'Initia et specimina scientiae generalis', Nos. 24 and 25 belonging to the 'Initia' and Nos. 26 and 27 to the 'Specimina'.l The long lists of definitions on which Leibniz worked intermittently over a long period of time are not represented. The following two selections are obviously closely related, the first discussing the origins and values of the general characteristic; the second, the general logical principles to be assumed as axiomatic in it. [G., VII, 184-89] There is an old saying that God created everything according to weight, measure, and number. But there are things which cannot be weighed, those namely which have no force or power. There are also things which have no parts and hence admit of no measure. But there is nothing which is not subordinate to number. Number is thus a basic metaphysical figure, as it were, and arithmetic is a kind of statics of the universe by which the powers of things are discovered. Men have been convinced ever since Pythagoras that the deepest mysteries lie concealed in numbers. It is possible that Pythagoras brought over this opinion, like many others, from the Orient to Greece. But, because the true key to the mystery was unknown, more inquisitive minds fell into futilities and superstitions, from which there finally arose a kind of popular Cabbala, far removed from the true one, and that multitude of follies which is falsely called a kind of magic and with which books have been filled. Meanwhile there remained deep-rooted in men the propensity to believe that marvels can be discovered by means of numbers, characters, and a certain new language, which some called the Adamic language; Jacob B6hme called it the Natursprache. But perhaps no mortal has yet seen into the true basis upon which everything can be assigned its characteristic number. For the most scholarly men have admitted that they did not understand what I said when I incidentally mentioned something of the For references see p. 227
222 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS sort to them. z And although learned men have long since thought of some kind of language or universal characteristic by which all concepts and things can be put into beautiful order, and with whose help different nations might communicate their thoughts and each read in his own language what another has written in his 3, yet no one has attempted a language or characteristic which includes at once both the arts of discovery and of judgment, that is, one whose signs or characters serve the same purpose that arithmetical signs serve for numbers, and algebraic signs for quantities taken abstractly. Yet it does seem that since God has bestowed these two sciences on mankind, he has sought to notify us that a far greater secret lies hidden in our understanding, of which these are but the shadows. Some unknown fate has brought it about, however, that when I was a mere boy I became involved in these considerations, and as first inclinations usually do, they have remained strongly fixed in my mind ever since. Two things which are otherwise of doubtful merit and are harmful to many people, proved wonderfully useful to me: first, I was self-taught, and second, I looked for something new in every science when I first studied it, often before I even understood its already established content. But so I gained a double reward: first, I did not fill my head with empty and cumbersome teachings accepted on the authority of the teacher instead of sound arguments; second, I did not rest until I had traced back the tissues and roots of every teaching and had penetrated to its principles. By such training I was enabled to discover by my own effort everything with which I was concerned. When I turned, therefore, from the reading of history, which had delighted me from my earliest youth, and from the cultivation of style, which I carried out with such ease both in prose and in more restricted forms that my teachers feared that I might remain stuck in such frivolities, and took up logic and philosophy and had barely begun to understand something about these fields, what a multitude of fancies came to birth in my brain and were scratched down on paper to be laid before my astonished teachers. Among other things I once raised a doubt concerning the categories. I said that just as we have categories or classes of simple concepts, we ought also to have a new class of categories in which propositions or complex terms themselves 4 may be arranged in their natural order. For I had not even dreamed of demonstrations at that time and did not know that the geometricians do exactly what I was seeking when they arrange propositions in an order such that one is demonstrated from the other. My question was thus superfluous, but when my teachers failed to answer it, I pursued these ideas for the sake of their novelty, attempting to establish such categories for complex terms or propositions. Upon making the effort to study this more intently, I necessarily arrived at this remarkable thought, namely that a kind of alphabet of human thoughts can be worked out and that everything can be discovered and judged by it comparison of the letters of this alphabet and an analysis of the words made from them. This discovery gave me great joy though it was childish of course, for I had not grasped the true importance of the matter. But later, the more progress I made in my thinking about these things, the more confirmed I was in my decision to carry the problem further. It happened that as a young man of twenty I had to prepare an academic treatise. So I wrote a Dissertation on the Art 0/ Combinations, which was published in book form in 1666, and in which I laid my remarkable discovery before the public. This dissertation was in fact such as might be written by a youth just out of the schools who was not yet conversant with the real sciences. For mathematics was
HANOVER TO THE ITALIAN JOURNEY, 1676-87 223 not cultivated in those parts; if I had spent my childhood in Paris, as did Pascal, I might have advanced these sciences earlier. There are two reasons, however, why I do not regret having written this dissertation; first, it pleased many very gifted men greatly; and second, in this dissertation I already then served notice to the public of my invention, so that it will not look as ifI had thought ofit only recently. Why, within the memory of mankind as preserved by records, no mortal has ever essayed so great a thing - this has often been an object of wonder to me. For to anyone who proceeds according to an order in thinking, these considerations should have occurred from the very first, just as they occurred to me as a boy interested in logic, before I had even touched on ethics, mathematics, or physics, solely because I aJways looked for first principles. The true reason for this straying from the portal of knowledge is, I believe, that principles usually seem dry and not very attractive and are therefore dismissed with a mere taste. Yet I am most surprised at the failure of three men to undertake so important a thing - Aristotle, Joachim Jung, and Rene Descartes. For when Aristotle wrote the Organon and the Metaphysics he laid open the inner nature of concepts with great skill. Joachim Jung of Lubeck is a man not well known even in Germany but of such rare judgment and breadth of mind that I cannot think of anyone, not even excepting Descartes himself, from whom a great revival of science might better have been expected, if only he had been known and supported. 5 He was already an old man, however, when Descartes began his activity, and it is regrettable that these men could not have known each other. As for Descartes, this is of course not the place to praise a man the magnitude of whose genius is elevated almost above all praise. He certainly began the true and right way through the ideas, and that which leads so far; but since he had aimed at his own excessive applause, he seems to have broken off the thread of his investigation and to have been content with metaphysical meditations and geometrical studies by which he could draw attention to himself. For the rest, he set out to discover the nature of bodies for the purposes of medicine, rightly indeed, if he had completed the task of ordering the ideas of the mind, for a greater light than can well be imagined would have arisen from these very experiments. His failure to apply his mind to this problem can be explained by no other cause than that he did not adequately think through the full reason and force of the thing. For had he seen a method of setting up a reasonable philosophy with the same unanswerable clarity as arithmetic, he would hardly have used any way other than this to establish a sect of followers, a thing which he so earnestly wanted. For by applying this method of philosophizing, a school would from its very beginning, and by the very nature of things, assert its supremacy in the realm of reason in a geometrical manner and could never perish nor be shaken until the sciences themselves die through the rise of a new barbarism among mankind. As for me, I kept at this line of thought, in spite of the distraction of so many other fields, for no other reason than that I saw its entire magnitude and detected a remarkably easy way of following it through. For this is what I finally discovered after most intent thought. Nothing more is necessary to establish the characteristic which I am attempting, at least to a point sufficient to build the grammar of this wonderful language and a dictionary for the most frequent cases, or what amounts to the same thing, nothing more is necessary to set up the characteristic numbers for all ideas than to develop a philosophical and mathematical 'course of studies', as it is called, based on a certain new method which I can set forth, and containing nothing more difficult For references see p. 227
224 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS than other courses of study, or more remote from use and understanding, or more alien to the usual way of writing. Nor would it require more work than is already being spent on a number of courses, or encyclopedias, as they are called. I think that a few selected men could finish the matter in five years. It would take them only two, however, to work out by an infallible calculus the doctrines most useful for life, that is, those of morality and metaphysics. 6 Once the characteristic numbers for most concepts have been set up, however, the human race will have a new kind of instrument which will increase the power of the mind much more than optical lenses strengthen the eyes and which will be as far superior to microscopes or telescopes as reason is superior to sight. The magnetic needle has brought no more help to sailors than this lodestar will bring to those who navigate the sea of experiments. What other consequences will eventually follow from it must be left to the decree of the fates; however, they cannot be the great and good. For men can be debased by all other gifts; only right reason can be nothing but wholesome. But reason will be right beyond all doubt only when it is everywhere as clear and certain as only arithmetic has been until now. Then there will be an end to that burdensome raising of objections by which one person now usually plagues another and which turns so many away from the desire to reason. When one person argues, namely, his opponent, instead of examining his argument, answers generally, thus, 'How do you know that your reason is any truer than mine? What criterion of truth have you?' And if the first person persists in his argument, his hearers lack the patience to examine it. For usually many other problems have to be investigated first, and this would be the work of several weeks, following the laws of thought accepted until now. And so after much agitation, the emotions usually win out instead of reason, and we end the controversy by cutting the Gordian knot rather than untying it. This happens especially in deliberations pertaining to life, where a decision must be made; here it is given to few people to weigh the factors of expediency and inexpediency, which are often numerous on both sides, as in a balance. The more strongly we are able to present to ourselves, now one circumstance and now another, in order to balance the varying inclinations of our own minds, and the more eloquently and effectively we can adorn and point them out for others, the more firmly we shall act and carry the minds of other men with us, especially if we make wise use of their emotions. There is hardly anyone who could work out the entire table of pros and cons in any deliberation, that is, who could not only enumerate the expedient and inexpedient aspects but also weigh them rightly. Thus two disputants seem to me almost like two merchants who are in debt to each other for various items, but who are never willing to strike a balance; instead, each one advances his own various claims against the other, exaggerating the truth and magnitude of certain particular items. Their quarrel will never end on this basis. And we need not be surprised that this is what has happened until now in most controversies in which the matter is not clear, that is, is not reduced to numbers. Now, however, our characteristic will reduce the whole to numbers, so that reasons can also be weighed, as if by a kind of statics. For probabilities, too, will be treated in this calculation and demonstration, since one can always estimate which of the given circumstances will more probably occur. Finally, anyone who is certainly convinced of the truth of religion and its consequences, and so embraces others in love that he desires the conversion of mankind, will surely admit, if he understands these matters,
HANOVER TO THE ITALIAN JOURNEY, 1676-87 225 that nothing will be more influential than this discovery for the propagation of the faith, unless it be miracles, the holiness of an apostle, or the victories of a great monarch. Where this language can once be introduced by missionaries, the true religion, which is in complete agreement with reason, will be established, and apostasy will no more be feared in the future than would an apostasy of men from the arithmetic or geometry which they have once learned. So I repeat what I have often said: that no man who is not a prophet or a prince can ever undertake anything of greater good to mankind or more fitting for the divine glory. But we must go further than words! Since the admirable connection of things makes it most difficult to give the characteristic numbers of a few things separated from others, I have thought of an elegant device, if I am not mistaken, by which to show that ratiocination can be proved through numbers. Thus I imagine that these most remarkable characteristic numbers are already given, and, having observed a certain general property to be true of them, I set up such numbers as are somehow consistent with tIns property, and applying these, I at once demonstrate through numbers, in wonderful order, all the rules of logic and show how we can know whether certain arguments are in good form. 7 But the material soundness or truth of an argument can be judged without much mental effort and danger of error only when we have the true characteristic numbers of things themselves. II [G., VII, 299-301] When I observed that almost all who think about principles follow the example of others rather than the nature of things, and even their prejudices when this is of great advantage, I concluded that it is not enough to avoid this error but that I should undertake some higher order with respect to my own opinions. One cannot go to infinity in his proofs, however, and therefore some things must be assumed without proof - not silently and by stealth, indeed, dissimulating our own laziness as philosophers customarily do, but keeping clearly in mind what we have used as first assertions, after the example of geometricians who, to show their good faith, acknowledge at the very start the assumed axioms they are to use, so that they may be sure that all the conclusions are proved at least hypothetically from these assumptions. First of all, I assume that every judgment (i.e., affirmation or negation) is either true or false and that if the affirmation is true the negation is false, and if the negation is true the affirmation is false; that what is denied to be true - truly, of course - is false, and what is denied to be false is true; that what is denied to be affirmed, or affirmed to be denied, is to be denied; and what is affirmed to be affirmed and denied to be denied is to be affirmed. Similarly, that it is false that what is false should be true or that what is true should be false; that it is true that what is true is true, and what is false, false. All these are usually included in one designation, the principle of contradiction. Now we must see what can truly be affirmed and denied, so that its contradiction may also be known to be false. The first of the true propositions are those which are commonly called identical; such as A is A, non-A is non-A, and if the proposition L is true, it folIows that the proposition L is true. And however much useless 'coccysm'S For references see p. 227
226 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS there seems to be in these judgments, they nevertheless give rise to useful axioms by a slight change. Thus from the fact that A is A, or for example, that three-legged is three-legged, it is obvious that anything is as much as it is or is equal to itself. Hence (to show how useful identities are by an example) philosophers have long ago demonstrated that a part is less than the whole by assuming only this definition; that is less which is equal to a part of another (the greater). The demonstration is as follows. A part is equal to a part of the whole (namely, to itself), by the axiom of identities. What is equal to a part of the whole is less than the whole, by the definition of less. Therefore a part is less than the whole, Q.E.D. Subalternation, or the derivation of a particular from a universal, may be proved similarly. All A is B; therefore some A is B using a syllogism of the first figure. The derivation is as follows. All A is B, by hypothesis. Some A is A, by identity. Therefore some A is B. I offer these examples, though they do not belong here, to show that identities do indeed have a use and that no truth, however slight it may seem, is completely barren; on the contrary, it will soon be apparent that these identities contain the foundations of the rest. 9 Just as identical propositions are the primary propositions of all, and are incapable of proof and thus true per se, for of course nothing can be found to serve as a middle term to connect something with itself, so as a result, truths are virtually identical which can be reduced to formal or explicit identities through an analysis of their terms, if we substitute for the original term either an equivalent concept or a concept included in it. It is obvious that all necessary propositions, or propositions which have eternal truth, are virtual identities and can be demonstrated or reduced to primary truths by ideas or definitions alone, that is, by the analysis of terms, so that it is made clear that their opposite implies a contradiction and conflicts with some identity or primary truth. Hence the Scholastics also observed that truths which are absolute or have metaphysical necessity can be proved by their terms alone, since the opposite involves a contradiction. In general, every true proposition which is not identical or true in itself can be proved a priori with the help of axioms or propositions that are true in themselves and with the help of definitions or ideas. For no matter how often a predicate is truly affirmed of a subject, there must be some real connection between subject and predicate, such that in every proposition whatever, such as A is B (or B is truly predicated of A), it is true that B is contained in A, or its concept is in some way contained in the concept of A itself. And this must be either by absolute necessity, in propositions which contain eternal truth; or by a kind of certainty which depends upon the supposed decree of a free substance in contingent matters, a decree, however, which is never entirely arbitrary and free from foundation, but for which some reason can always be given. This reason, however, merely inclines and does not truly necessitate. 10 Such truth could itself be deduced from the analysis of concepts, if this were always within human power, and will certainly not escape the analysis of an omniscient substance who sees everything a priori from ideas themselves and from his decrees. It is certain, therefore, that all truths, even highly contingent ones, have a proof a priori or some reason why they are rather than are not. And this is what is commonly asserted: that
HANOVER TO THE ITALIAN JOURNEY, 1676-87 227 nothing happens without a cause, or these is nothing without a reason. Yet however strong this reason may be - though whatever kind it is, it is enough to effect a greater inclination in one direction or the other - even if it establishes certainty in a predicting being, it does not place necessity in the thing itself, because its contrary would still remain possible per se and implies no contradiction. Otherwise what we call contingent would rather be necessary or of eternal truth.ii This axiom, however, that there is nothing without a reason, must be considered one of the greatest and most fruitful of all human knowledge, for upon it is built a great part of metaphysics, physics, and moral science; without it, indeed, the existence of God cannot be proved from his creatures, nor can an argument be carried fom causes to effects or from effects to causes, nor any conclusions be drawn in civil matters. So true is this that whatever is not of mathematical necessity, as for instance are logical forms and numerical truths, must be sought here entirely. For example, Archimedes, or whoever is the author of the book on equilibrium, assumes that two equal weights placed in a balance in the same relation to its center or axis will be in equilibrium. This is merely a corollary of our axiom, for since everything is assumed to be related in the same way on each side, there is no reason why the balance should tip to one side rather than the other. 12 But with this assumption Archimedes in turn proves other mathematical matters by necessity. REFERENCES See Couto L., pp. 134--40. Neither Oldenburg nor Tschirnhaus fully grasped Leibniz's descriptions in his letters. Huygens failed to take seriously both his universal characteristic and his new geometry of situation. Not until the late nineteenth century was the significance of Leibniz's efforts understood. 3 See Couto L., chap. III. The allusion is probably to Dalgamo and John Wilkins, in whose proposals for a universal language Leibniz early became interested (cf. New Essays, III, ii, l). 4 Note that Leibniz has here resolved the distinction between terms and propositions. Thus "man is a reasonable immortal animal", to use the example in No. 25, may be treated conceptually or as a structure of propositions inherent in the definition; in either case the expression is x = abc, which implies such propositions as all men are rational, immortal, animal, and also some animals are immortal, rational, men, etc. o See p. 130, note 4. Leibniz highly esteemed Jung's discovery and analysis of nonsyllogistic forms of inference (cf. New Essays, IV, xvii, 4). 6 One of the delusions under which Leibniz continued to labor much of his life was the simplicity of this project; this was the result of his conviction that the simple concepts are independent of each other and relatively few in number. 7 See Nos. 26 and 40 for examples of the logical calculus, which Leibniz thus considers as the formal development of his general characteristic and upon which he depends to prove his case. But compare the statement to Tschimhaus (No. 19 and p. 195, note 3). 8 'Coccysm' was proverbial for wordiness or redundancy, from the reputation of John Cocceius, professor of theology at Leyden, and his followers. 9 In what follows Leibniz makes an early attempt to show that identity, contradiction, and sufficient reason, and the operations with them, apply to judgments of existence as well as to truths of reason. In general, his view is that these principles have particularized application to contingent truths, though the complete analysis lies beyond us. But he fails to show why the application of the subject-predicate proposition to created substances allows for freedom; the several parts of his explanation do not cohere, especially since the factor of incompleteness in i 2
228 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS contingent truths is placed in the predicting agent and his limitations rather than in the nature of the substance to be known. 10 For the reason that causes which we may discover for existing events are only partially determinant; complete causality would involve the infinite analysis of which we are incapable. Yet the individual substance seems to be itself completely determined. 11 AIl propositions are thus analytic, though all factual judgments whose subjects are not substances but mere partial concepts are only virtually so. See No. 26 for the sense in which Leibniz regards particular judgments as analytic. 12 The general principle of equipollence or equivalence (cf. p.205, note 3) is thus derivable from the principle of sufficient reason.
25 ON UNIVERSAL SYNTHESIS AND ANALYSIS, OR THE ART OF DISCOVERY AND JUDGMENT 1679(?) Couturat has established the probability that this important paper on method, whose date is uncertain, belongs to the logical writings of 1679 or the years following and is "the sketch ofa chapter of the Plus ultra ".1 [G., VII, 292-98] As a boy I learned logic, and having already developed the habit of digging more deeply into the reasons for what I was taught, I raised the following question with my teachers. Seeing that there are categories for the simple terms by which concepts are ordered, why should there not also be categories for complex terms, by which truths may be ordered? I was then unaware that geometricians do this very thing when they demonstrate and order propositions according to their dependence upon each other. It seemed to me, however, that this could be achieved universally if we first had the true categories for simple terms and if, to obtain these, we set up something new in the nature of an alphabet of thoughts, or a catalogue of the highest genera or of those we assume to be highest, such as a, b, c, d, e,/, out of whose combination inferior concepts may be formed. For we must note that genera may serve as differentiae to each other, so that every difference can be conceived of as a genus, and every genus as a difference. It is as right to say 'rational animal' as 'animal rational being', if such a concept can be formed. 2 But since our common genera do not reveal the species in their combination, I concluded that they were not correctly formed and that the genera next below the highest should be binions, such as ab, ac, bd, cf; the genera on the third level would be ternions, such as abc, bd/, and so on. But if the highest genera, or those assumed to be highest, should happen to be infinite, as is the case with numbers, we should only have to establish the order of these highest genera, and some order would then become apparent in the lower genera. For in the case of numbers, the prime numbers can be taken as the highest genera, since all even numbers can be called binaries, all divisible by three, ternaries, and so forth. Then every derivative number can be expressed through prime ones as genera. Thus every multiple of six [senary] is a binary ternary. So if some particular species is proposed, the propositions which are demonstrable about it could be enumerated in order, or all its predicates could be listed, whether broader than it or convertible with it, and the more meaningful could then be selected from these. Thus assume that there is a species y, whose concept is abed; and for ab substitute I; for ac, m; for ad, n; for be, p; for bd, q; for cd, r, which are binions. Then come ternions; for abc substitute s; for abd, v; for Qed, w; for bcd, x. These would all be predicates of y, but only the following would be convertible with y: ax, bw, CV, ds, Ir, mq, np. I have said more about this in my little treatise on the For references see p. 233
230 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Art of Combinations, which I brought out soon after my adolescence, before the longpromised work of the same title by Kircher had appeared. I hoped to find similar matters discussed in it, but when it did appear later, I found that it had merely revived the LuIIian art or something similar to it but that the author had not even dreamed of the true analysis of human thoughts any more than had the others who have tried to reform philosophy. 3 The primary concepts from whose combination the rest are made are either distinct or confused. Those are distinct which are understood through themselves, such as 'being'. Those are confused though clear, which are perceived through themselves, such as color, because we can only explain them to someone else by showing them to him. For though the nature of color is analyzable since it has a cause, we cannot sufficiently describe or recognize it by any concepts that are separately explained; it is known only confusedly and hence cannot be given a nominal definition. A nominal definition consists in the enumeration of signs or elements sufficient to distinguish the thing defined from everything else. If we proceed to seek the elements of the elements, we shall come at last to primitive concepts which have no elements at all, or none which we can explain to a sufficient degree. This is the art of dealing with distinct concepts. The art of dealing with confused concepts, however, must discover the distinct concepts which accompany the confused ones, whether these distinct concepts can be understood through themselves or can at least be resolved into such as are understood, for with their help we can sometimes arrive at some cause or resolution of the confused notion. All derivative concepts, moreover, arise from a combination of primitive ones, and the more composite concepts from the combination of less composite ones. But one must take care that the combinations do not become useless through the joiningtogether of incompatible concepts. This can be avoided only by experience or by resolving them into distinct single concepts. One must be especially careful, in setting up real definitions, to establish their possibility, that is, to show that the concepts from which they are formed are compatible with each other. So while every reciprocal property of a thing can serve as its nominal definition, since all the other attributes of the thing can always be demonstrated from it, not every such property suffices for a real definition. For as I have pointed out, there are certain properties which I call paradoxical, whose possibility can be doubted. For example, it can be doubted whether there is a curve for which it is true that given any segment and any point on the curve, the lines connecting this point with the ends of the segment will always form the same angle. For assuming that we have so adjusted the points of the curve to one segment, we still cannot foresee that what may seem to have succeeded by chance in one case will succeed in others, namely that the same points on the curve will satisfy this condition with respect to another segment as well, since all of the points are now determined and no further ones can be assumed. Yet we know that this is the nature of a circle. 4 So, although someone might give a name to the curve having this property, it would not yet be certain that such a curve is possible, and hence that its definition is real. But the concept of the circle set up by Euclid, that of a figure described by the motion of a straight line in a plane about a fixed end, affords a real definition, for such a figure is evidently possible. Hence it is useful to have definitions involving the generation of a thing, or if this is impossible, at least its constitution, that is, a method by which the thing appears to be producible or at least possible. I have already
HANOVER TO THE ITALIAN JOURNEY, 1676-87 231 used this observation in the past to examine the imperfect demonstration which Descartes proposed of the existence of God, about which I have often argued in writing with the most learned Cartesians. Descartes argues as follows. Whatever can be demonstrated from the definition of a thing can be predicated of that thing. Now from the definition of God - that he is the most perfect being, or as certain Scholastics said, a being than whom no greater can be thought - there follows his existence, for existence is a perfection, and whatever possesses existence will therefore be greater or more perfect than it would be without it. Therefore existence can be predicated of God, or God exists. This argument, revived by Descartes, was defended by one of the old Scholastics in a special book called Contra insipientem. 5 But following some others, Thomas replied to it that this presupposes that God is, or as I interpret this, that he has an essence, at least in the sense that the rose has an essence in winter, or that such a concept is possible. This therefore is the privilege of the most perfect being, that, given its possibility, it at once exists or that its existence follows from its essence or its possible concept. But to make this demonstration rigorous, the possibility must first be proved. Obviously we cannot build a secure demonstration on any concept unless we know that this concept is possible, for from impossibles or concepts involving contradictions contradictory propositions can be demonstrated. This is an a priori reason why possibility is a requisite in a real definition. A difficulty raised by Hobbes can also be answered on this basis. For Hobbes saw that all truths can be demonstrated from definitions but held that all definitions are arbitrary and nominal, since we impose arbitrary names upon things. He therefore concluded that truths also consist merely in names and are arbitrary.6 But we must recognize that if we are to have a real definition, we cannot combine notions arbitrarily, but the concept we form out of them must be possible. Hence every real definition must contain at least the affirmation of some possibility. Furthermore, although names are arbitrary, once they are adopted, their consequences are necessary, and certain truths arise which are real even though they depend on the characters which have been imposed. For example, the rule of nines depends on characters imposed by the decimal system, yet it contains real truth. Moreover, to set up a hypothesis or to explain the method of production is merely to demonstrate the possibility of a thing, and this is useful even though the thing in question often has not been generated in that way. Thus the same ellipse can be thought of either as described in a plane with the aid of two foci and the motion of a thread about them or as a conic or a cylindrical section. Once a hypothesis or a manner of generation is found, one has a real definition from which others can also be derived, and from them those can be selected which best satisfy the other conditions, when a method of actually producing the thing is sought. Those real definitions are most perfect, furthermore, which are common to all the hypotheses or methods of generation and which involve the proximate cause of a thing, and from which the possibility of the thing is immediately apparent without presupposing any experiment or the demonstration of any further possibilities. In other words, those real definitions are most perfect which resolve the thing into simple primitive notions understood in themselves. Such knowledge I usually call adequate or intuitive, for, if there were any inconsistency, it would appear here at once, since no further resolution can take place. 7 From such ideas or definitions, then, there can be demonstrated all truths with the exception of identical propositions, which by their very nature are evidently indemonstrable and can truly be called axioms. What are popularly called axioms, however. Po r references see p. 233
232 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS can be reduced to identities by analyzing either the subject or the predicate or both, and so demonstrated; for by assuming the contrary, we can show that the same thing would at the same time be and not be. Hence it is evident that in the last analysis the direct and indirect methods of demonstration coincide and that the Scholastics were right in observing that every axiom, once its terms are understood, may be reduced to the principle of contradiction. Thus any truth whatever can be justified, for the connection of the predicate with the subject is either evident in itself as in identities, or can be explained by an analysis of the terms. This is the only, and the highest, criterion of truth in abstract things, that is, things which do not depend on experience - that it must either be an identity or be reducible to identities. From this can be derived the elements of eternal truth in all things insofar as we understand them, as well as a method for proceeding demonstratively, as in geometry. In this way God understands everything a priori and through eternal truth, since he does not need experience and knows all things adequately, whereas we know hardly anything adequately, few things a priori, and most things through experience. In this last case other principles and other criteria must be applied. In factual or contingent matters, therefore, which do not depend on reason but on observation and experiment, primary truths (for us) are those that are perceived immediately within us or those of which we are conscious within ourselves. For it is impossible to prove these to ourselves through other experiences nearer or more intrinsic to us. But within myself I perceive not only myself who thinks but also many differences in my thoughts, from which I conclude that there are other things outside of me and gradually gain faith in my senses in opposition to the skeptics. For in matters which do not possess metaphysical necessity, we must regard the agreement of phenomena as truth, since such agreement does not occur by chance but has a cause. 8 Certainly it is only through this agreement among phenomena that we distinguish dreams from waking, and we predict that the sun will rise tomorrow only because it has fulfilled our faith so often. To this is added the great power of authority and of public testimony, since it is not likely that so many should conspire to deceive us. To these factors can be added what Saint Augustine has said on the utility of faith.9 The authority of the senses and of other witnesses once established, we may prepare a record of phenomena from which a mixed knowledge can be formed by combining with them truths abstracted from experience. But we need a particular art for arranging as well as for ordering and combining our experiments, so that useful inductions can be made from them, causes discovered, and general truths and postulates [aphorismi et praenotiones] set up. The carelessness of men is amazing, wasting their time in trifles and neglecting the matters by which they could take care of health and well-being. For perhaps they would have within their power the remedies for a great part of their ills if only they would make right use of the great wealth of observations already available to our century and of the true analysis. Our human knowledge of nature seems to me at present like a shop well provided with all kinds of wares but without any order or inventory. The distinction between synthesis and analysis also becomes apparent from these considerations. Synthesis is achieved when we begin from principles and run through truths in good order, thus discovering certain progressions and setting up tables, or sometimes general formulas, in which the answers to emerging questions can later be discovered. Analysis goes back to the principles in order to solve the given problems only, just as if neither we nor others had discovered anything before. 10 It is more im-
HANOVER TO THE ITALIAN JOURNEY, 1676-87 233 portant to establish syntheses, because this work is of permanent value, while we often do work that has already been done in beginning the analysis of a particular problem. But it is a lesser art to use syntheses already set up by others and theorems already discovered, than to achieve everything through one's own work, by carrying out analyses, especially since we do not always remember or have at hand the truths which we ourselves or others have already discovered. Analysis is of two kinds. The common type advances by leaps and is used in algebra. The other is special and far more elegant but less well known; I call it 'reductive' analysis.u Analysis is more necessary in practice, in order to solve problems that are given to us. But whoever is capable of more theoretical pursuits will be content to practice analysis only far enough to master the art but will then prefer to synthesize and will willingly tackle only such questions to which he is led by the order of research itself. In this way he will always progress pleasantly and easily and will not feel any difficulties or be disappointed in the outcome, for in a short time he will achieve much more than he could ever have hoped at the start. But ordinarily people destroy the fruits of their thinking through undue haste and attack too difficult problems at a leap, thus achieving nothing despite great effort. It must be realized that our method of inquiry is at last perfected when we can foresee whether it will lead us to a solution. Those who think that the analytic presentation consists in revealing the origin of a discovery, the synthetic in keeping it concealed, are in error.12 I have often observed that of the great geniuses of discovery, some are more inclined to analysis, others to the art of combinations. Combination or synthesis is the better means for discovering the use or application of something, as for example, given the magnetic needle, to think of its application in the compass. Analysis, on the contrary, is best suited for discovering the means when the thing to be discovered or the proposed end is given. Analysis is rarely pure, however, for usually, when we search for the means, we come upon contrivances which have already been discovered by others or by ourselves either accidentally or by reason, and which we find stored up as in a table or inventory, either in our own memory or in the accounts of others, and which we now apply for our purpose. But this is synthesis. For the rest, the art of combinations in particular, as I take it (it can also be called a general characteristic or algebra), is that science in which are treated the forms or formulas of things in general, that is, quality in general or similarity and dissimilarity; in the same way that ever new formulas arise from the elements a, b, c themselves when combined with each other, whether these elements represent quantities or something else. This art is distinct from common algebra, which deals with formulas applied to quantity only or to equality and inequality. This algebra is thus subordinate to the art of combinations and constantly uses its rules. But these rules of combination are far more general and find application not only in algebra but in the art of deciphering, in various games, in geometry itself when it is treated linearly in the manner of the ancients 13 , and finally, in all matters involving relations of similarity. REFERENCES Couto L., p. 189, n.l; p. 323 n. See also the introduction to No. 24, above. See p. 227, note 4. This is in effect a criticism of Aristotle's theory of the definition and of the hierarchical implications of a subject-predicate viewpoint. If carried through, this change would have led to a purely relational logic. The unsolved problem in Leibniz's logic is thus the 1 2
234 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS reduction of complex terms, or relational propositions, which apply to existence, to propositions whose predicates are all included in their substantial subjects. 3 Athanasius Kircher's Ars magna sciendi sive combinatoria appeared in Amsterdam in 1669, 3 years after Leibniz's De arte combinatoria. 4 Euclid's Elements, Book iii, Prop. 20. 5 Leibniz has in mind Anselm's Liber apologeticus adversus respondentem pro insipiente, a reply to Gaunilo's attack on the argument of the Proslogium in the Liber pro insipiente adversus Anselmi in proslogio ratiocinationem. 6 See above, p. 185, note 3. 7 Cf. New Essays, IV, ii, 1: "In this way all adequate definitions contain primitive truths of reason and consequently intuitive knowledge. It can be said in general that all primitive truths of reason are immediate with respect to an immediateness of ideas." In No. 33, where the kinds of knowledge and definition here described are discussed in more detail, Leibniz suggests that though we cannot give good examples of adequate intuitive knowledge on the part of man, there is a kind of adequate knowledge in which we use symbols to retain the primitive elements which we cannot retain in an intuited whole. S For a further development of this criterion of the truth of contingent propositions see No. 39. 9 De utilitate credendi ad Honoratum. Like Hume, Leibniz recognizes psychological grounds for empirical judgments. But unlike him, he holds that logical analysis and synthesis, aided by real definitions, reveal an inhering but abstractly necessary order within these judgments, so that scientific analysis proceeds from observations to causal judgments and functional laws. 10 Thus both analysis and synthesis rest upon a demonstrative structure of truth and upon an analytic theory of meaning; the direction is determined by whether the unknown is the relatively simple or the relatively complex. It is noteworthy that Leibniz subordinates both perceptual data and hypotheses to his analytic conception of truth. Synthesis proceeds from the simple, whether abstract or concrete, to the more complete, from a plurality of predicates to the determined subject which is equivalent to them; analysis in the opposite direction. Leibniz would recognize no induction by simple enumeration but would insist that scientific generalization involves intensional meanings and that abstract analysis of observations must precede synthesis. Cf. Introduction, Sec. IV. 11 Cf. Couto OF., p. 351: "Analysis is through a leap, when we begin to solve the problem itself, with no other assumptions; ... analysis is by degrees when we reduce the proposed problem to an easier one, and this to an easier still, etc., until we arrive at one which is within our power." See also ibid., p. 558, where the latter method is called 'anagogic analysis'. Leibniz's own examples include the reduction of quartics to quadratics and the analysis of higher curves by decomposition into simpler ones. 12 Descartes, Responsio ad secundas objectiones (Adam and Tannery, VII, 155-56). 13 See No. 27.
26 TWO STUDIES IN THE LOGICAL CALCULUS 1679 In 1679 Leibniz thought of the logical calculus as an application of the more general science of characters to the problems of formal logic. Such an application would, he was convinced, put logic on a more universal basis and serve to convince men of the value of applying symbols to material truth as well. Of the two studies given here, the first was written in April, and the second probably later in the same year. In the former, the Elements of Calculus, he attempted to use numerical symbols, as he had suggested in Nos. 24 and 25, and to restrict logical operations to mUltiplication and division. His analysis was extended, in other studies dated in April, to the proof of the rules of immediate inference and the syllogism. In the second paper he abandoned numerical symbols and used letters, addition. and the simple relation esse. This approach was carried further in the later studies of the 1690's (No. 40).1 Significant in the second selection is the beginning of an attempt to interpret the predicables in terms of his calculus. I. ELEMENTS OF CALCULUS [Cout. OF., pp. 49-57] 1. A term is the subject or predicate of a categorical proposition. Thus I include neither the sign 2 not the copula among the terms. So when it is said, 'The wise man believes', the term is not believes, but a believer,just as ifI say, 'The wise man is a believer'. 2. In what follows, I understand propositions to be categorical when I do not specifically indicate otherwise. But the categorical proposition is the basis of the rest, and all modal, hypothetical, disjunctive, and other propositions presuppose the categorical. I call A is B categorical, or A is not B, or it is false that A is B. When a variation in sign is added, the proposition is either universal and understood to apply to all of the subject or particular, applying to some. 3. To every term whatever may be assigned its characteristic number, which we may use in calculating, as we use the term itself in reasoning. I choose numbers in writing; in time I shall adapt other signs both to numbers and to speech itself. For the present numbers are the most useful because of their accuracy and the ease with which they are handled and because it is thus clear to the eye that all of the relations of concepts are certain and determined after the likeness of numbers. 4. The rule for discovering fitting characteristic numbers is this one only: when the concept of a given term is composed directly [in casu recto] 3 out of the concepts of two or more other terms, then the characteristic number of the given term is to be produced by multiplying the characteristic numbers of the terms composing it. For example, since man is a rational animal, if the number of animal is a, for instance, 2 and the number of rational is r, for instance 3, the number of man, or h, will be 2 x 3 or 6. 4 For references see p. 246
236 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 5. We shall introduce letters (such as a, r, and h here) when the numbers are not given or at least need not be considered specifically but are dealt with in general, as it is proper for us to do here in dealing with the elements. Like the practice in symbolic algebra or the arithmetic of figures, this is a way of avoiding the effort to try to do for each individual case what can be shown at one and the same time for an infinite number of instances. I shall explain the manner of using these letters below. 6. The rule given in Article 4 suffices to include everything in the whole world in our calculus, insofar as we have distinct notions of it, that is, insofar as we know certain of its constituents and can distinguish them from all others after examining them by their parts; in other words, insofar as we can assign a definition to them. For these constituents are nothing but the terms whose concepts compose the concept which we have of the thing. Moreover we can distinguish most things from others by their constituents, and if it is hard to decide which are requisite or prior to which, we can assign them some prime number temporarily and use it to designate other things by means of them. In this way we could at least discover all propositions by a calculation and show which ones can at least be demonstrated analytically when taken as primary for the time being, without actually being so. Thus Euclid nowhere uses the definition of a straight line in his demonstrations but presents something taken as axiomatic in place of it. 5 But when Archimedes tried to go further, he was compelled to analyze the straight line and to define it as the least distance between two points. In this way we may thus discover, not all truths, indeed, but at least innumerable truths, those which are already demonstrated by others as well as those which could be demonstrated by others through definitions, axioms, and observations that are already known. And this is the advantage of our method - we can judge at once, through numbers, whether proposed propositions are proved, and so we accomplish, solely with the guidance of characters and the use of a definite method which is truly analytic, what others have scarcely achieved with the greatest mental effort and by accident. And therefore we can succeed in presenting conclusions within our own century which would scarcely be provided for mortals in many thousands of years otherwise. 7. To make clear the use of characteristic numbers in propositions, the following must be kept in mind. Every true categorical proposition, affirmative and universal, signifies nothing but a certain connection between the predicate and the subject - in the direct case, that is, of which I am always speaking here. This connection is such that the predicate is said to be in the subject, or to be contained in it, and this either absolutely and viewed in itself, or in some particular case. Or in the same way, the subject is said to contain the predicate; that is, the concept of the subject, either in itself or with some addition, involves the concept of the predicate. And therefore the subject and predicate are mutually related to each other either as whole and part, or as whole and coinciding whole, or as part to whole. 6 In the first two cases the proposition is universal affirmative. So when I say, 'All gold is a metal', I mean by this only that the notion of metal is contained in the notion of gold in a direct sense, for gold is the heaviest metal. And when I say, 'All pious people are happy', I mean only that the connection between piety and happiness is such that whoever understands the nature of piety perfectly will see that the nature of happiness is involved in it in the direct sense. But in every case, whether the subject or the predicate is a part or a whole, a particular affirmative proposition always holds. For example, some metals are gold; even if metal per se did not include gold, yet some metal with an added or special
HANOVER TO THE ITALIAN JOURNEY, 1676-87 237 quality (such as what makes up the greater part of an Hungarian ducat) is of a nature that involves the nature of gold. But a distinction between the subjects of a universal and a particular proposition is found in the manner of this inclusion. For the subject of a universal proposition, viewed in itself and taken absolutely, must contain the predicate; so that the concept of gold, viewed in itself and taken absolutely, involves the concept of metal, since the notion of gold is that of the heaviest metal. 7 But in an affirmative particular proposition it suffices that the inclusion is successful when something is added to the subject. The concept of metal, viewed absolutely and in itself, does not involve the concept of gold; something must be added to involve it, namely, the sign of particularity. For it is some certain metal which contains the concept of gold. In the future, however, when we say that a term is contained in another or a concept in another concept, we understand this to mean simply and in itself. 8. Negative propositions, however, merely contradict affirmative ones and assert that they are false. Thus a particular negative proposition does nothing but deny that there is an affirmative universal proposition. So when I say, 'Some silver is not soluble in common aqua fortis [nitric acid]', I mean this one thing: the universal affirmative proposition that all silver is soluble in common aqua fortis is false. For if we may believe certain chemists, there is an instance to the contrary, namely that which they call luna jixa. A universal negative proposition, moreover, merely contradicts a particular affirmative. For example, if I say, 'No wicked people are happy', I mean that it is false that some wicked people are happy. Thus it is clear that negatives can be understood from affirmatives, and affirmatives from negatives. 8 9. Further, every categorical proposition has two terms. Any two terms whatever may differ in the following ways, insofar as they are said to be in, or not to be in, or to be contained in, or not contained in. Either one is contained in the other, or neither. If one is contained in the other, it may either be equal to the other, or they may differ as whole and part. If neither is contained in the other, then either they contain something in common or they differ entirely in genus. But we will explain these cases individually. 10. Two terms containing each other and yet equal, I call coincidents. For example, the concept of a triangle coincides in fact with the concept of trilateral; that is, exactly what is contained in one is also contained in the other, even though it may not sometimes appear so at first glance. But if both terms are analyzed, they will coincide. Thus heaviest of metals and most stable of metals coincide, even though speaking absolutely, heaviest and most stable do not coincide. This is clear from the example of mercury. for between the two metals, copper and quicksilver, the former is obviously the most stable, the latter the heaviest. But this is merely in passing. 11. Two terms, one of which contains the other but which are not coincident, are commonly called genus and species. Considered as concepts or component terms as I am here viewing them, these dyrer as part and whole, so that the concept of genus is part, the concept of species the whole, for it consists of genus and differentia. For example, the concept of gold and the concept of metal differ as whole and part, for the concept of metal and something more is contained in the concept of gold; for example, the concept of the heaviest among metals. Thus the concept of gold is greater than the concept of metal. 12. The schools speak otherwise, because they are considering not concepts but instances subsumed under universal concepts. Thus they say that metal is wider than gold, since it contains more species than does gold. If we were to count the individuals For references see p. 246
238 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS made of gold on the one hand, and those made of metal on the other, there would certainly be more of the latter than of the former, and hence the former would be contained in the latter as part in a whole. In fact, by applying this observation and using fitting characters, we could demonstrate all the rules of logic by another kind of calculus than the one developed here, merely by an inversion of our own calculus. But I prefer to consider universal concepts or ideas and their composition, for these do not depend on the existence of individuals. 9 So I say that gold is greater than metal, because more constituents are required for the concept of gold than for that of metal, and more is needed to produce gold than to produce just a metal. Thus our phrases here and the Scholastic phrases do not contradict each other but must nevertheless be carefully distinguished. It will be clear to the careful student that I make no innovations in my way of speaking which do not have a definite reason and application. 13. If neither term is contained in the other, they are called disparate. In that case, to repeat what I have already said, either they have something in common or they differ entirely in genus. Terms have something in common when they fall under the same genus. These can be called conspecies; thus man and beast have the common concept animal, gold and silver that of metal, gold and vitriol that of mineral. Hence two terms clearly have more or less in common according as their genus is more or less remote. For if the genus is very far removed, it will also be a very smaIl part of what the species symbolize. And when the genus is most remote, as for example, substance, we say that the things are heterogeneous, or differ entirely in genus, as body and mind, not because they have nothing in common, since both are substances, but because this common genus is so far removed. From this it follows that whether two terms are to be called 'heterogeneous' or not is a comparative matter. It suffices for our calculus that two things have in common none of a particular set of notions specified by us, even though they may have others in common. 14. Everything that we have so far said about terms that contain or do not contain each other in various ways, we may now transfer to their characteristic numbers. This is easy because, as we said in Article 4, when a term helps to constitute another term, that is, when the concept of one term is contained in that of another, then the characteristic number of the one enters by multiplication into the characteristic number assumed for the term so constituted. Or what amounts to the same thing, the characteristic number of the term to be constituted (or that which contains the other) is divisible by the characteristic number of the constituting term (or that which is in the other). For example, the concept of animal enters into the formation of the concept of man, and so the characteristic number of animal, a (for example, 2), combines with some other number r (such as 3), to produce the number ar or h by multiplication (2 x 3); that is, the characteristic number of man. Hence number ar or h (or 6) must necessarily be divisible by a (or by 2). 15. When two terms are coincident, however, for example man and rational animal, their numbers too (h and ar) are in fact coincident. But since each term still contains the other in this case, that is reciprocally, for man contains rational animal (but nothing more) and rational animal contains man (and nothing more which is not already contained in man), hand ar must necessarily contain each other (6 and 2 x 3), and this is indeed true, since they are coincident and the same number is contained in itself. Besides, one must necessarily be divisible by the other, and this is true also, for when any number is divided by itself, the quotient is one. What we said in the pre-
HANOVER TO THE ITALIAN JOURNEY, 1676-87 239 ceding section is therefore true for coincident terms as well; whenever one term contains another, its characteristic number is divisible by the characteristic of the other. 16. Hence we can also determine through characteristic numbers which term does not contain another. One has merely to test whether the number of one term can be divided exactly by the number of the other. For example, if the characteristic number of man is found to be 6, and that of the ape is 10, it is obvious that the concept of ape does not include that of man, nor that of man the ape, since 10 cannot be divided evenly by 6, nor 6 by 10. So if you wish to know whether the concept of wisdom is contained in that of a just being, that is, whether nothing more is required for wisdom than what is already contained in justice, you need merely to examine whether the characteristic number of just can be divided exactly by the characteristic number of wise. If the division is impossible, it will be clear that something more is required for wisdom than what is in justice, namely, a knowledge of reasons. For one can be just by custom or habit, even though he cannot give a reason for what he does. I will show later how that minimum which is necessary or must be added for the purpose can be discovered by characteristic numbers. 17. So we can learn in this way whether any universal affirmative proposition is true. For in such a proposition the concept of the subject, taken absolutely and indefinitely and in general viewed in itself, always contains the concept of the predicate. For example, all gold is a metal, that is, the concept of metal is contained in the concept of gold generally and viewed in itself, so that whatever is assumed to be gold is by this fact assumed to be metal, since all the constituents of metal, such as being homogeneous to sense, becoming a liquid when fire is applied in a certain degree, and then not wetting other things immersed in it, are contained in the essentials of gold. (We have explained how in Article 7.) Thus if we wish to know whether all gold is a metalfor it can be doubted whether fulminating gold is a metal, since it is in the form of powder and explodes rather than liquifies when fire is applied in a certain way - we merely see whether the defiinition of metal is contained in it; that is, by a very simple procedure when characteristic numbers are introduced, we see whether the characteristic number of gold can be divided by the characteristic number of metal. 18. But in the particular affirmative proposition it is not necessary for the predicate to be contained in the subject per se and viewed absolutely, or for the concept of the subject per se to contain the concept of the predicate. It suffices that the predicate be contained in some species of the subject or that the concept of some instance or species of the subject contain the concept of the predicate; of what kind the species must be, the proposition need not express. Hence, if you say, 'Some expert is prudent', this does not assert that the concept of prudence is contained in the concept of expert viewed in itself, though this is not denied, either. It suffices for our purpose that some species of expert has a concept which contains the notion of prudence, even though it is not made explicit what sort of species this may be, for instance, even if the proposition does not express that the expert who also possesses natural judgment is prudent. It is enough to understand that some species of expert involves prudence. 19. If the concept of the subject, viewed in itself, contains the concept of the predicate, then certainly the concept of the subject with additions, or the concept of a species of the subject, will contain the concept of the predicate. This is enough for us, for we do not deny that the predicate is in the subject itself when we say it is in a species of it. So we can say, 'Some metal in fire (rightly applied) is a liquid', although For re/eren ces see p. 246
240 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS we could express this more generally and usefully thus: 'All metal in fire is a liquid.' But a particular assertion has its uses, as when it is more easily demonstrated than a general one or when the hearer may accept it more readily than the universal, and the particular serves our purpose. 20. Since nothing more is required in a particular affirmative proposition than that a species of the subject contains the predicate, the subject will itself be related to the predicate either as species to genus, or as species to something coinciding with it or a reciprocal attribute, or as a genus to a species. That is, the concept of the subject will be related to that of the predicate, either as whole to part, or as whole to a coinciding whole, or as part to whole. (See above, Arts. 7 and 11.) It will be related as whole to part when the concept of the predicate as a genus is in the concept of the subject as a species (for example, if 'bernicle' is the subject and 'bird' the predicate). It will be related as whole to coinciding whole when two equivalents are asserted of each other mutually, as is the case when 'triangle' is the subject and 'trilateral' the predicate. And finally, it will be related as part to whole, as when 'metal' is the subject and 'gold' the predicate. Thus we can say, 'Some bernicles are birds', 'Some triangles are trilaterals' (though we might have affirmed these two propositions as universals as well), and finally, 'Some metal is gold.' No particular affirmative proposition is possible in any other cases. I prove this as follows. If the species of the subject contains the predicate, it will certainly contain it in such a way that it coincides with it, or as a part. If equal or coincident with it, the predicate is certainly a species of the subject. If however the species of the subject contains the predicate as a part, the predicate will be a genus of the species of the subject, by Article 11. Thus the predicate and the subject will be two genera of the same species. Now two genera of the same species either coincide or if they do not coincide, are necessarily related as genus and species. It is easy to show this, for the concept of a genus is formed from that of a species merely by casting off; therefore, if both genera are produced from the common species of two genera by a process of continued casting off, i.e. if both genera remain after the superfluous has been rejected, one will be produced before the other, and so one will be a whole, the other a part. But this is a fallacy, and at once many things fail which we have said so far. For I now see that there are particular affirmative propositions also when neither term is genus or species, or when the terms are compatible, as some animals are rational. Hence it appears that the subject need not be divisible by the predicate or the predicate by the subject. We have obscured many things by the discussion so far, though we have been right about special cases; so we may now begin with the whole. 10 II. SPECIMEN OF UNIVERSAL CALCULUS [G., VII, 218-27] 1. A universal affirmative proposition is here expressed in this way: a is b, or (all) man is animal. 11 So we always understand the universal sign to be prefixed. We are not now discussing negative propositions or particular and hypothetical propositions. 2. Aproposition true in itself: ab is a, or (all) rational animal is animal. ab is b, or (aU) rational animal is rational.
HANOVER TO THE IT ALlAN JOURNEY, 1676-87 241 Or omitting b, a is a, or (all) animal is animal. 3. Conclusion true in itself: If a is b, and b is c, then a is c. If (all) man is animal, and (all) animal is substance, then all man is substance. 4. From this follows: If a is bd and b is c, then a is c. (All) man is rational animal; (all) animal is substance; hence (all) man is substance. This may be demonstrated as follows. If a is bd, by hypothesis, and bd is b, by No.2, then a is b, by No.3. Further, if a is b (as we have proved), and bc is c, by hypothesis, then a is c, by No.3. 5. A proposition is true which arises through logical conclusions from given propositions which are true in themselves. Note. Although some propositions are to be assumed arbitrarily, such as definitions of terms, truths follow from them which are not arbitrary; for at least it is absolutely true that conclusions arise from such assumed definitions or what amounts to the same thing, that the connection between conclusions, whether theorems and definitions or arbitrary hypotheses, is absolutely true. This is apparent in numbers for instance, whose signs and decimal order are established by the will of man. Yet the calculations based on them signify absolute truths; that is, the connection between the assumed characters and the formulas deduced from them signify also the connections between things, which remain the same regardless of what characters are assumed. Moreover, it is useful to science to assume characters in this way, so that many conclusions may be drawn from few assumptions, which is the case when characters are assigned to the simplest elements of thought. 6. If one thing can be substituted anywhere in place of another without destroying truth, the other thing can be substituted conversely in place of the first. For example, since trilateral can be substituted in place of a plane triangular figure, a triangle can be substituted in place of a trilateral. For assuming two terms a and b, such that b can be substituted anywhere for a, then I say, a can be substituted anywhere in place of b. This I prove as follows. Assume the proposition b is c, or dis b; I say a can be substituted for b in these. For let us assume that it cannot be substituted, or that one cannot say that a is c and d is a; then these propositions are false. Then at least these two propositions are true: it is false that a is c and it is false that dis a. But by hypothesis, b can be substituted for a; therefore these two propositions would also be true: it is false that bis c, and it is false that dis b. But this contradicts the hypothesis by which these are assumed to be true. So the proposition is proved. It can also be proved in other ways. 7. Terms are the same [eadem] if one can be substituted in place of the other without destroying truth, as triangle and trilateral, quadrangle and quadrilateral. 8. All propositions (i.e. universal affirmative propositions; we are here dealing only with them) of which a given letter a is a part can be reduced to the following forms, however many others may seem enumerable. aisd abis e cis a a isfg is reducible to a is d, assumingfg to be d. a is fhp is reducible to a is d, assumingfhp to be d, or hp to be g, andfg to be d, etc. For references see p. 246
242 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS ab is ik is reducible to ab is e, assuming ik to be e, etc. aIm is e is reducible to ab is e, assuming b to be 1m. b is 1m, hence ab is aIm. aim is ik is reducible to ab is e, for ik is e, and ab is aim, etc. np is a is reducible to c is a, assuming c to be np, etc. q is ab (abc, etc.) is reducible to q is a, because ab is a. rs is ab (abc, etc.) is reducible to q is a, assuming rs to be q etc. a is a is reducible to d is a, assuming d to be a, or to a is c, assuming a to be c. a is at (aB A, etc.) is reducible to a is d, assuming at to be d, or to a is a, because at is a. a ab is ) av awx 1az (etc.) a abc is ap,w All these can be analyzed in two ways from the foregoing ones, retaining a either in the subject or in the predicate. (etc.) All forms are reducible to the three given above, however, provided that we observe that for d/or dig or bc or en, ab, abc, etc., can be placed one letter equal to this combination of more than one. So for the term 'rational animal', for the sake of compactness, we place one term 'man', and for the composite ab or abc in the given predicate we can substitute the simple term a. For if you say c is ab, or 'Man is a rational animal', you can certainly say that c is a, or 'Man is an animaL' But it is otherwise in the subject, for although I may say that all rational animals are man, I cannot say that all animals are men. Thus I cannot reduce the proposition ab is c to a more simple one in which a remains an ingredient. The others I can, as appears from what has been said. 9. If a island/is a, a and/are the same, or one can be substituted in place of the other. I prove this as follows. I will show first that/can always be substituted in place of a itself. By the preceding section, namely, all propositions which contain a can be reduced to three forms: a is d, ab is e, and c is a. From this I show that the following three can be substituted:/is d,fb is e, and c is/. For since/is a and a is d,fwill also be d. Likewise, since/is a,fb will be ab (by demonstration through addition), and since ab is e,fb will be e. Finally, since c is a, and a is/. c will be/. In the same manner, moreover, in which I show that/can be substituted in place of a, it can also be shown that a can be substituted for /. since a and/are chosen arbitrarily, and also, since we showed substitution to be reciprocal, in Section 6, above. A being is what is signified by any term such as a or b or abo Additions to the Specimen 0/ Universal Calculus To understand the nature of this calculus, we must note that whatever we express by certain letters which are assumed arbitrarily must be understood to be expressible in the same way by any others which we may assume. So when I say that this proposition, ab is a, is always true, I mean not merely that the example, 'A rational animal is an animal', is true, assuming 'animal' to be signified by a and 'rational' by b, but I mean also that the example, 'A rational animal is rational', is true, assuming 'rational' to be signified by a and 'animal' by b. And so we may proceed to any other example, such as an organic body is organic. And therefore we may also say bd is b instead of ab is a.
HANOVER TO THE ITALIAN JOURNEY, 1676-87 243 It is to be noted also that it makes no difference whether you say ab or ba, for it makes no difference whether you say 'rational animal' or 'animal rational being'. The repetition of any letter in the same term is useless, and it is adequate to retain it only once; for example, aa or man man. Hence if a is be, and b is d, and e is also d, it is useless to say that a is dd; it suffices that a is d. For example, man is a rational animal; all animals are sentient, and all reasoning beings are sentient; but it useless to say that therefore man is a sentient sentient, for this is saying no more than that man is sentient. However, if one wishes to say that man is sentient in a double sense, this can itself be expressed in another way, following the rules of our characteristic. Different predicates can be combined into one; if it is established that a is b, and also that a is e, it can be said that a is be. So if man is an animal, and man is rational, man is a rational animal. Conversely, one composite predicate can be divided into many. Thus a is bd; therefore a is b and a is e. For example, man is a rational animal; therefore man is animal and man is rational. When this division is noted in itself, the composition can be demonstrated from it. For let us assume that man is an animal, and man is rational, but that man is nevertheless not a rational animal. Then the proposition would be false that man is a rational animal. This falsity can be proved only in three ways: one by showing that man is not an animal, which is contrary to hypothesis; another by showing that he is not rational, which is also contrary to hypothesis; the third that he cannot be both together or that the two are incompatible, which is also contrary to hypothesis, since we assumed that he is at once animal and rational. Composition is possible in the subject, but not division. For if b is a, and e is a, be is also a. If all animals live, and all reasoning beings live, surely all rational animals live. This is proved as follows. be is b, b is a, therefore be is a. be is e, e is a, therefore be is a. Also, if we mix the composition and division of terms in various ways, there arise many results until now untouched by logicians, especially if we add negative and particular propositions besides. If b is e, then ab is ae, or if man is an animal, it follows that a wise man is a wise animal. This is proved as follows. ab is b, b is e; therefore ab is e, by the first rule of conclusions. ab is e, ab is a; therefore ab is ae, through the above demonstration. But one cannot reason backward that ab is ae, therefore b is c. For it may happen that a is ad, and bd is a. Yet if a and e have nothing in common, the conclusion would be valid that ab is ae. We propose here, however, to pursue only general consequences. Afterwards we will proceed to the more special ones, which are of greater importance than the general ones, and have not been treated heretofore according to their importance. For the whole analysis rests upon 'certain conclusions which seem to violate form but do not in fact violate the general c'onditions always observed in terms. If a is b, and a is d, and d is b, ad is bd. This is demonstrable from the preceding. a is b, a is e, dis b, dis e, therefore ad is be, assuming that e is d. It seems true from For references see p. 246
244 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS the preceding that so many assumptions are unnecessary, and that it suffices that a is b; hence ad is bd. If a is b, and dis c, then ad is bc. This is an admirable theorem, which can be demonstrated in this way. a is b, therefore ad is bd, by the above. dis c, therefore bd is bc, also by the above. ad is bd, and bd is bc, therefore ad is bc, which was to be demonstrated. In general, if there is any number of propositions whatever: a is b, c is d, e is I, then one can be made from them: ace is bdl, by addition of the subjects on one side and the predicates on the other. 12 In general, if there is a proposition m is bdl, three can be made from it, m is b, m is d,misf. All these things are easily proved if only this one thing be assumed - that the subject be the container, and the predicate at the same time be the contained or joined to the subject; or on the contrary, that the subject be the contained and the predicate the alternative or conjunctive containerP A term is a, b, ab, bcd; such as man, animal, rational animal, rational visible mortal. I designate a universal affirmative proposition thus: a is b, or (all) man is animal. I wish this always to be the sign of universality, where a is the subject, b the predicate, and is the copula. Postulate. It is permissible to assume a letter to be equivalent to one or more letters at once (so d is equal to a) and that it can be substituted in place of the other. c is equivalent to the term ab, or for example, man is the same as rational animal. I mean this to hold, if nothing contrary to these assumptions has already been assumed. Propositions true in themselves: (1) a is a. Animal is animal. (2) ab is a. Rational animal is animal. (3) a is not non-a. Animal is not nonanimal. (4) Non-a is not a. Nonanimal is not animal. (5) What is not a is non-a. What is not an animal is nonanimal. (6) What is not non-a is a. What is not a nonanimal is an animal. From these many others can be derived. Consequences true in themselves: a is b, and b is c, therefore a is c. God is wise, wise is just; therefore God is just. This chain can be continued further. For example, God is wise, wise is just, just is austere; therefore God is austere. Principles of the calculus. (1) Whatever is concluded in certain indefinite letters must be understood to be concluded in whatever other letters have the same relation. Thus, since it is true that ab is a, it is also true that bc is b and that bcd is bc. For substituting e for bc (by the postulate), it is the same as if we said, edis e. (2) The transposition of letters in the same term changes nothing; thus ab coincides with ba, or rational animal with animal reasoner. (3) The repetition of the same letter in the same term is useless; thus b is aa, or bb is a; man is an animal animal, or man man is an animal. It suffices to say that a is b, or man is an animal. (4) From any number of propositions whatever one can be made by adding all the subjects into one subject and all the predicates into one predicate. a is b, and c is d, and e is f.' hence ace is bdf. Thus God is omnipotent, man is endowed with a body. To be
HANOVER TO THE ITALIAN JOURNEY, 1676-87 245 crucified is to suffer. Therefore a God-man crucified is an omnipotent being endowed with a body and suffering. It makes no difference if the terms sometimes combined in this way are inconsistent. Thus a circle is a null-angle. A square is a quadrangle. Therefore a square circle is a null-angled quadrangle. For the proposition is valid, though from an impossible hypothesis. This observation is especially useful in chains extended to more length, for example in this way: God is wise, God is omnipotent, a just omnipotent being punishes the wicked. God does not punish some wicked people in this life. He who punishes but does not punish in this life, punishes in another life. Therefore God punishes in another life. (5) From any proposition whose predicate is composed of many terms, many propositions can be made of which each will have the same subject as the original but will have some part of the original predicate in place of the predicate. a is bed; therefore a is b, and a is c, and a is d. Or man is a rational, mortal, visible being. Therefore man is rational, man is mortal, and man is visible. If a is band b is a, then a and b are said to be the same. Thus every pious man is happy, and every happy man is pious. Therefore pious and happy are the same. Hence it can easily be proved that one can be substituted anywhere in the place of the other without destroying truth. Thus if a is band b is a; and b is e, or d is a, then a is also e, and dis b. Thus all pious are happy, and all happy are pious, and all the happy are elect, and all martyrs are pious. Therefore all the pious are elect, and all martyrs are happy. (Note. By the pious I mean those persevering or dying in grace.) Terms are diverse which are not the same, as man and animal, for even though all men are animals, not all animals are men. a and b are disparate if a is not band b is not a; as man and stone. For man is not a stone, and a stone is not a man. Thus all disparates are diverse, but not the converse. If a is m and b is m and a and b are the same, then m is said to be one. Thus Octavianus is Caesar and Augustus is Caesar. But since Octavianus and Augustus are the same, only one Caesar will be counted.... ... If we assume any simple term whatever equivalent to any composite one, or expressing the same thing, the simple term will be defined, the composite term will be the definition. This defined term expressed by a character we will henceforth call the name of a thing. Thus if for ab we should say a rational animal, and for the sake of brevity, say e for man, then e, or the word 'man', would be the name of the thing whose definition is rational animal, or the word 'man' would be the name of men. If in a universal affirmative proposition, the subject is a thing but the predicate is neither a thing nor a definition but some other term, then this term is said to be an attribute. Thus the definition of God, whose name is 'God', is a most perfect being. His attributes are pity, omnipotence, creativity, being, being by itself. Thus if c is a thing and ab is its definition, and e is d (where d is not the term ab), then d is called the attribute of e. If in a universal affirmative proposition the predicate is a thing, but the subject is not a thing or the definition of a thing but some other term, this term is called a property (propriumJ. For example, all man is animal; thus man is 'proper to' animal. For only an animal can be a man, even though all animal may not be man. We are not defining property here in the fourth mode, but in general, in the sense of what belongs to something alone. So if e is a thing and ab the definition of a thing, and the universal For references see p. 246
246 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS affirmative proposition dis c is given, d will be the property of, or proper to, c, though neither c nor ab is to be understood by the term d. A genus is a common attribute. Thus the genus of the terms d and e is a, if d is ab and e is ac, or if d is a but a is not d. The proprium genus is the attribute common to many, but of them alone. Thus animal is the proprium genus of men and beasts, or if d is a and e is a, and if what is non-d and non-e is non-a, a will be the proprium genus of the species d and e. An accident is a subject both in a particular affirmative proposition and in the negative with the same subject. So some men are learned and some men are not learned, therefore learning is an accident of man. If some a is b and some a is non-b, b is an accident of a. Aproprium attribute is obviously what is at once an attribute and a property. Namely, if the definition of a thing c (as of man) is ab (rational animal) and there are given two propositions: c is d ('Man is a rational morta)'), in which d is an attribute, and d is c ('A rational mortal is man'): in which d is a property, it is obvious that d is a proprium attribute. It is also obvious that a name, a definition, and a proprium attribute are equivalent terms, or terms expressing the same thing. This is what is commonly called the property in the fourth mode, or the reciprocal property. A substantive 14 is that (name) which includes (the name of a) being or thing. An adjective is what does not include it. Thus animal is a substantive, or the same as an animal being. Rational is an adjective, but it can become a substantive if you combine it with being, and say a rational being or, briefly in a word (if a jest be permitted), a rational. Thus from the term 'animal being', the term 'animal'. A genus is a substantive which is an attribute common to many, which are called species. Attribute I Every differentia can be specific with another genus. A specific difference is an adjective which, with the genus, constitutes a term equi) valent to a species (or better, the definition of a species?). A generic difference is that which is the specific difference of a genus. A definition is a composite substantive term equivalent to a species. A property is an adjective, the subject of a universal proposition whose predicate is a substantive. An accident is an adjective, the predicate of a subject of a particular affirmative proposition only. REFERENCES Discussions of these papers may be found in Couto L., chap. VIII, and in the works by Durr, Matzat, and Parkinson given in the Bibliography. 2 That is, the syncategorematic sign, including that of quantity: all or some. Note that Leibniz neglects negative propositions, which he rules out below in Section 8. a The distinction between 'direct' and 'oblique' relations originates in Aristotle's Prior AnaIytics i. 36. Terms are directly related when they can be combined by multiplication (or addition) alone. Terms enter a proposition obliquely when they involve a relation other than combination. Leibniz's best definition of these relations is in the letter to Gabriel Wagner (No. 48). Though he often touches upon oblique relations, he never deals systematically with 1
HANOVER TO THE ITALIAN JOURNEY, 1676-87 247 them, because his logical calculus does not advance beyond the multiplication (or addition) and resolution of terms and categorical propositions. His recognition of oblique relations reflects the inadequacy of his theory of propositional inclusion to cover the existence of a plurality of substances and their interrelations. 4 To simplify the exposition, we omit Leibniz's second example (gold is the heaviest metal), which adds nothing to his analysis. 5 Elements, Book I, Definition 4: "A straight line is that which rests evenly between its extreme points." 6 Couturat notes: "All of these considerations are relative to the point of view of connotation (or intension)." 7 Leibniz, it must be remembered, is here and throughout this study (with the exception in Sec. 12, below) discussing intensional meanings, not classes. 8 Leibniz's reduction of negative logical relations between affirmative terms to the denial of an affirmative proposition supports his conception of the ontological significance of logic. It also saves him from an analogy between logical negation and physical resistance and opposition. 9 Leibniz therefore explicitly recognizes the possibility of an extensional logic of inclusion, with laws inverting his own intensional ones. His reason for clinging to the intensional position must be sought in his conviction that truths of reason are prior to truths of fact. 10 Leibniz seems to have found himself betrayed by too close adherence to a logic of genera and species and now seeks a more general treatment of particular propositions. In the papers which continue this study (not here translated) he analyzes the particular proposition mathematically as one whose terms have a common factor (Cout. OF., pp. 64-65). 11 The Latin is translated literally to avoid implying an extensional interpretation such as 'all men are animals' suggests. 12 Leibniz is thus interpreting the combination of terms as addition rather than multiplication, as he continues to do in the studies of the 1690's (No. 41). 13 What follows is a marginal summary and systematization. 14 Marginal note: "These definitions are adapted to the Scholastic usage, but the difference between substantive and adjective need not appear in characters, and it serves no purpose.'
27 STUDIES IN A GEOMETRY OF SITUATION WITH A LETTER TO CHRISTIAN HUYGENS 1679 Leibniz's interest in the application ofthe general characteristic to geometry seems to have been stimulated by a rereading of the first book of Euclid's Elements early in 1679. (His notes are given in GM., V, 183-211.) He proposed the new, nonquantitative approach in a letter to Huygens, which is also interesting for its report on the properties ofphosphorus, and sent with the letter (I) an essay in which he developed fundamental geometrical definitions and relations on the basis of the relationship of congruence and the operations involved in it (II).l In a later second paper he used the less determinate but more general relationship of similarity in his demonstrations (III). Both relations are particular derivatives of the logical principle of identity or equivalence. 2 Leibniz's efforts to found such a geometry met with no response until Riemann and Grassmann, in the 19th century, undertook related studies. He returned to it several times, however, particularly in 1698-99 and near the close ofhis life (No. 69). [GM., II, 17-20] September 8, 1679 One of my friends, Mr. Hansen, who has had the honor of speaking with you, assures me that you continue to have a good opinion of me, for which I am much indebted to you. And I want to use this opportunity to witness how much I honor your extraordinary worth, which everyone recognizes as I do, and which places you in the highest rank. I have learned from Mr. Mariotte that you will soon give us the dioptrics which we have so long desired. I am very eager to see it some day, and I should like to know in advance if you are satisfied with the reasons for refraction which Descartes proposes. I must admit that I am not entirely, any more than with Mr. Fermat's explanation in the third volume of Descartes's letters. 3 I have left my manuscript on arithmetical quadratures at Paris so that it may some day be printed there. But I have advanced far beyond studies of this kind and believe that we can get to the bottom of most problems which now seem to lie beyond our calculation; for example, quadratures, the inverse method of tangents, the irrational roots of equations, and the arithmetic of Diophantus. I have some general methods which solve most of these things in a way as determinate as that used in ordinary algebra to solve an equation. And I am not afraid to say that there is a way to advance algebra as far beyond what Vieta and Descartes have left us as Vieta and Descartes carried it beyond the ancients .... ... But in spite of the progress which I have made in these matters 4, I am still not satisfied with algebra, because it does not give the shortest methods or the most beautiful constructions in geometry. This is why I believe that, so far as geometry is
HANOVER TO THE ITALIAN JOURNEY, 1676-87 249 concerned, we need still another analysis which is distinctly geometrical or linear and which will express situation [situs] directly as algebra expresses magnitude directly. And I believe that I have found the way and that we can represent figures and even machines and movements by characters, as algebra represents numbers or magnitudes. I am sending you an essay which seems to me to be important. There is no one who can judge it better than you, Sir, and I should take your opinion in preference to those of many other men. I am also sending you a little of the corporeal fire, which can well be called a perpetual light, for when properly protected, it lasts many years without being consumed. It is a small piece but beautiful, for similar pieces are not always produced; usually the matter comes in small grains. I have put it in a bladder, and this is sealed in wax so that nothing can escape, and the piece will not take fire by motion or friction, as easily happens. Such a piece will be enough for many experiments, for the smallest particle is capable of making things radiant, and when one takes it into his hands, they remain luminous for some hours, yet there is nothing visible in daylight. One can write with it in luminous letters, and some hours later, when these seem dead, they become visible afresh if rubbed once more. I hold that there is a true fire inclosed with the matter, but not concentrated enough to make itself felt. When one blows against it, the light disappears but returns immediately afterward, which is a remarkable thing. However, I have seen its vapor alone light a piece of paper which I was using to wipe my fingers when I emptied the container after I had produced the fire. It is easy to ignite gunpowder, either by the sun or through friction, after a little of this phosphorus is mixed with it. It would be good to try it in a vacuum. For the rest, I refer you to the experiments which I have reported to the Duke of Chevreuse. In order better to preserve this piece, one must spill a little water on it and keep it in a small well-corked glass bottle; otherwise it will evaporate in the air. In the water it will emit light at intervals, particularly when it is moved or warmed a little by contact with the hand; but when it is dry and exposed to the air, it shines continuously. You need not be "paring with it, for I can let you have more, since I can make it. I beg you, Sir, to show its effects to Mr. Colbert, the Duke of Chevreuse, and the Academy. If you find them agreeable, I am inclined to communicate its composition to the Academy, though this would be difficult for me. I beg you, Sir, to tell me something about scientific happenings there. Mr. Brousseau, the resident of my prince, who lives in the Rue des Rosiers behind little S. Antoine, will send me your letter. You have heard mention of the attempt of Mr. Becher 5, in Holland, to extract gold from sand. There are persons here who think well of him. Mr. Hudde is, as you know, one of the commissioners. Mr. Becher says he is also dealing with the French. I should like to know if you have heard talk about it in Paris. As for me, I am skeptical of his success, for I believe I know a little about the nature of his experiment. He does find a vestige of gold, but I do not think he has gained any of it, for he claims that the proportion of gold is greater in large than in small amounts, which is paradoxical. II. SUPPLEMENT [GM., II, 20-27] I have discovered certain elements of a new characteristic which is entirely different For references see p. 257
250 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS from algebra and which will have great advantages in representing to the mind, exactly and in a way faithful to its nature, even without figures, everything which depends on sense perception. Algebra is the characteristic for undetermined numbers or magnitudes only, but it does not express situation, angles, and motion directly. Hence it is often difficult to analyze the properties of a figure by calculation, and stilI more difficult to find very convenient geometrical demonstrations and constructions, even when the algebraic calculation is completed. But this new characteristic, which follows the visual figures, cannot fail to give the solution, the construction, and the geometric demonstration all at the same time, and in a natural way and in one analysis, that is, through determined procedure. Algebra is compelled to presuppose the elements of geometry 6; this characteristic, instead, carries the analysis through to its end. If it were completed in the way in which I think of it, one could carry out the description of a machine, no matter how complicated, in characters which would be merely the letters of the alphabet, and so provide the mind with a method of knowing the machine and all its parts, their motion and use, distinctly and easily without the use of any figures or models and without the need of imagination. Yet the figure would inevitably be present to the mind whenever one wishes to interpret the characters. One could also give exact descriptions of natural things by means of it, such, for example, as the structure of plants and animals. With its aid people who find it hard to draw figures could explain a matter perfectly, provided they have it present before them or in their nlind, and could transmit their thoughts and experiences to posterity - a thing which cannot be done today because the words of our languages are not sufficiently fixed or well enough fitted for good explanations without figures. This is the least useful aspect of this characteristic, however, for if only description were involved, it would be better - assuming that we can and are willing to bear the expense - to have figures and even models or, better still, the original things themselves. But its chief value lies in the reasoning which can be done and the conclusions which can be drawn by operations with its characters, which could not be expressed in figures, and still less in models, without multiplying these too greatly or without confusing them with too many points and lines in the course of the many futile attempts one is forced to make. This method, by contrast, will guide us surely and without effort. I believe that by this method one could treat mechanics almost like geometry, and one could even test the qualities of materials, because this ordinarily depends on certain figures in their sensible parts. Finally, I have no hope that we can get very far in physics until we have found some such method of abridgment to lighten its burden of imagination. For example, we see what a series of geometrical reasoning is necessary merely to explain the rainbow, one of the simplest effects of nature; so we can infer what a chain of conclusions would be necessary to penetrate into the inner nature of complex effects whose structure is so subtle that the microscope, which can reveal more than the hundred-thousandth part, does not explain it enough to help us much. Yet there would be some hope of achieving this goal, at least in part, if this truly geometrical analysis were established. But since I have found no one else who has ever come upon this thought, and am therefore apprehensive that it will be lost if I do not have the time to carry it out, I shall here add an essay which seems to me to be important and which will at least suffice to make my plan more plausible and easier to understand. If therefore some circumstance
HANOVER TO THE ITALIAN JOURNEY, 251 1676-87 prevents its perfection at present, this essay will serve as a witness to posterity and give occasion for someone else to carry it through. It is well known that nothing is more important in geometry than the consideration of loci. I shall therefore express one of the simplest of these by characters of this kind. The letters of the alphabet will ordinarily signify the points of figures. Letters at the beginning, such as A and B, will express given points; letters at the end, such as X and Y, unknown points. Instead of using equalities or equations as in algebra, I shall here use relations of congruence, which I shall express by the character \:l • For example, in the first figure (Figure I), ABC \:l DEF means that the triangles ABC and DEF are congruent with respect to the order of their points, that they can occupy exactly the same place, and that one can be applied or placed on the other without changing ., o o A A b E C Fig. 1. F I , I I I I B ",.,"'\ ,' ,,..1 "" "' __________ ./ ",,"" A " \ C I I I I I , , \ , , \ , ' ' '\ L _____ ..... E F Fig. 2. anything in the two figures except their place. So if one places D upon A, E upon B, and F upon C, the two triangles, which are assumed to be equal and similar, obviously coincide. But without speaking of triangles, one can, in a way, still say the same thing about points, or about ABC \:l DEFin Figure 2; that is, one can at the same time place A upon D, B upon E, and C upon F without the situation of the three points ABC being changed in relation to each other or that of the three points DEF to each other, assuming in this that the first three points are connected by rigid lines (whether straight or curved does not matter) and the other three likewise. After this explanation of our characters, we develop the following loci. Let A \:l Y (Figure 3); that is, given a point A, to find the locus of all points Y, or (Y)7, which are congruent with A. I assert that the locus of all these Y's will be a (y). A y. Fig. 3. For references see p. 257 Fig. 4.
252 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS space infinite in all directions. For all the points in the world are congruent to each other; that is, one can always be put in place of another. But all the points in the world are in the same space. This locus can also be expressed thus: Y 8 (Y). This is all very obvious, but we must begin at the beginning. Let A Y 8 A (Y) (Figure 4). The locus of all Y's will be the surface of a sphere whose center is A and whose radius is A Y, which is always the same in length or equal to a given segment AB or CB. For this reason we can express the same locus as AB 8 A Y, orCB 8 AY. Let AX 8 BX (Figure 5). The locus of all X's will be a plane. Two points, A and B, being given, to find a third, X, which has the same situation in relation to A as it has to B (that is, AX shall be equal or congruent to BX, since all equal straight lines are congruent, or point B can be placed on point A without changing the situation it had in (X) _- .......... ...... A ... ---- -......- .... X--+-----=:"'-8 y Fig. 5. Fig. 6. relation to X). I assert that all points X, (X) of a single definite plane extending to infinity will satisfy this condition. For just as AX 8 BX, so A (X) 8 B (X). But there is no point outside the plane which will satisfy this condition. Therefore this infinitely extended plane will be the common locus of every point in the universe situated in relation to A as it is to B. (It follows that this plane will pass through the midpoint of the straight line AB, which is perpendicular to it. 8) Let ABC 8 ABY (Figure 6). The locus of all Y's will be circular. That is, given three points A, B, C; to find a fourth point Y which has the same situation as C in relation to AB. I assert that there is an infinity of points which satisfy this condition and that the locus of all these points is a circle. This description or definition of a circular line does not, as does Euclid's, presuppose a plane or even a straight line. Yet it is clear that the center of the circle is D, between A and B. This can also be said in this way: ABY 8 AB(Y); then the locus would be a circle that is not given. A given point must therefore be added. 9 We can imagine that the two points A and B remain fixed and that point C, attached to them by certain rigid lines, straight or curved, and consequently preserving the same situation in relation to them, is turned around AC so as to describe the circle CY(Y). We can conclude from this that the situation of one point in relation to another can be thought of without expressing the straight line joining them, provided they are thought of as joined by some line, whatever it may be; and if this line is assumed to be rigid, the situation of the two points in relation to each other will be immutable. Two points can be thought of as having the same situation in relation to each other as two other points have, if the one pair can be joined by a line which is congruent with the line joining the other pair. I say this so that it can be
HANOVER TO THE ITALIAN JOURNEY, 253 1676-87 seen that nothing which I have said so far depends on the straight line, whose definition I am about to give, and that there is a difference between the points A and C, the situation of A and C in relation to each other, and the straight line A e. Let A Y ~ BY ~ CY (Figure 7). Then the locus of all Y's will be a straight line. That is, given three points, to find a point Ywhich has the same situation in relation to A as A B .. /j •• --••••.•.••••.••..y ••......•••••••••.•. c B Fig. 7. A ,-,<::'~4:::::::o"o", c Fig. 8. it has to B and to C. I assert that all such points will fall on an infinite straight line Y(Y). If this were all limited to a plane, two given points would suffice to determine a straight line in this way.10 Finally, let AY ~ BY ~ CY ~ DY (Figure 8). The locus will be a single point, for we seek a point Ywhich has the same situation relative to each of the four given points A, B, C, and D. That is, the straight lines A Y, BY, CY, and D Y shall be equal to each other, and there is only one point which will satisfy this condition. These same loci can be expressed in many other ways, but these are the simplest and most fruitful and can pass for definitions. To show that these expressions are useful in reasoning, I shall, before closing, demonstrate the nature of the intersections between these loci by means of their characters. First, the intersection of two spherical surfaces is a circle. l1 The expression of a circle is ABC ~ ABY; hence A C ~ A Yand BC ~ BY. But the loci corresponding to these congruences are two spheres, one with center A and radius AC, the other with center B and radius Be. The intersection of a plane and a sphere is likewise a circle. For the expression of a sphere is AC ~ AY, and that of a plane is AY ~ BY. Hence AC ~ BC, since point C is one of the points Y. NowsinceBC ~ AC,andAC ~ AY, itfollows that BC ~ AY; and since A Y ~ BY, we have BC ~ BY. Joining these congruences together, we have ABC ~ ABYor AB ~ AB, BC ~ BY, and AC ~ AY. But ABC ~ ABYis the expression of a circle, which was here to be proved by this kind of calculus. In the same way it is shown that the intersection of two planes is a straight line. For let there be two congruences: AB ~ BY for one plane, and A Y ~ CY for another plane. Then we will have A Y ~ BY ~ CY, whose locus is a straight line. Finally, the intersection of two straight lines is a point. For let A Y ~ BY ~ CY, and BY ~ CY ~ DY;thenwehaveAY ~ BY ~ CY \) DY. I have only one comment to add; namely, that I see the possibility of extending the characteristic to things which are not subject to sensory imagination. But this is so important and has so many implications that I cannot explain it here in a few words. For references see p. 257
254 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS III. ON ANALYSIS SITUS 12 [GM., Y, 178-83] What is commonly known as mathematical analysis is analysis of magnitude, not of situation, and as such it pertains directly and immediately to arithmetic but is applicable to geometry only in an indirect sense. The result is that many things easily become clear through a consideration of situation, which the algebraic calculus shows only with greater difficulty. To reduce geometric problems to algebra, i.e., to reduce problems determined by figures to equations, is often a rather prolonged affair, and further complications and difficulties are necessary to return form the equation to the construction, from algebra back to geometry. Often, too, the constructions produced in this way are not entirely appropriate, unless we are lucky enough to stumble upon unforeseen postulates and assumptions. This Descartes himself tacitly admitted in solving a certain problem of Pappus in Book III of his Geometry. In fact algebra, whether using numbers or symbols, adds, subtracts, multiplies, divides, extracts roots, all of which are arithmetical. For logistics itself, or the science of magnitude and proportion in general, deals only with general or indeterminate number and with the species of operations performed on it, since magnitude is in fact measured by the number of determinate parts, yet this number may vary for the same fixed thing, depending upon which measure or unit is assumed. It is not surprising, therefore, that the science of magnitude in general is a kind of arithmetic, since it deals with indeterminate numbers. The ancients had another kind of analysis, different from algebra, which was concerned rather with considering situation. It deals with data and with the positions of unknown entities or their loci. This is the trend of Euclid's book De datis, on which there exists a commentary by MarinusP Apollonius particularly, but others as well, dealt with plane, solid, and linear loci; more recent thinkers have reconstructed the doctrine of plane and solid loci from his propositions as preserved by Pappus, but in such a way as to show merely the truth rather than the source of the ancient doctrine. Yet this kind of analysis does not reduce the matter to a calculation, nor is it carried through to the first principles and elements of situation, as is necessary for a perfect analysis. The true analysis of situation is therefore still to be supplied. This can be shown from the fact that all analysts, whether they use algebra in the new manner or deal with the given and the unknown after the ancient pattern, have to assume many things from elementary geometry which are not derived from the consideration of magnitude but from that of figure, and which have not yet been explained in any determinate way. Euclid himself was forced to assume certain obscure axioms, without proof, in order to proceed with the rest. And the demonstration of theorems and the solution of problems in his Elements sometimes seem to be achieved through hard labor rather than method and skill, even though he also seems sometimes to conceal the ingenuity of his method. Besides quantity, figure in general includes also quality or form. And as those figures are equal whose magnitude is the same, so those are similar whose form is the same. The theory of similarities or of forms lies beyond mathematics and must be sought in metaphysics. Yet it has many uses in mathematics also, being of use even in the algebraic calculus itself. But similarity is seen best of all in the situations or figures
HANOVER TO THE ITALIAN JOURNEY, 1676-87 255 of geometry. Thus a true geometric analysis ought not only consider equalities and proportions which are truly reducible to equalities but also similarities 'and, arising from the combination of equality and similarity, congruences. The true reason why geometricians have not made enough use of a theory of similarity is, I think, this. They did not have any general concept of it which was sufficiently distinct or adapted to mathematical investigation; this is a fault of philosophers, who usually are content, especially in metaphysics, with vague definitions which are fully as obscure as the thing defined. Hence it need not surprise anyone that this doctrine is usually barren and verbose. Thus it is not enough to designate objects as similar whose form is the same, unless a general concept is further given of form. In undertaking an explanation of quality or form, I have learned that the matter reduces to this: things are similar which cannot be distinguished when observed in isolation from each other. Quantity can be grasped only when the things are actually present together or when some intervening thing can be applied to both. But quality presents something to the mind which can be known in a thing separately and can then be applied to the comparison of two things without actually bringing the two together either immediately or through the mediation of a third object as a measure. Let us imagine that two temples or buildings are constructed according to this law: that nothing can be found in one which you do not also find in the other. The material is everywhere the same, white Parian marble, if you like; the proportions of walls, columns, and all the rest are everywhere the same; the angles are everywhere equal or in the same ratio to a right angle. If anyone is led into these two temples blindfolded, and his eyes are uncovered after he has entered and he walks about, first in one and then in the other, he will receive no clue from them by which to distinguish one from the other. Yet they may actually differ in magnitude, and might be distinguished if viewed at the same time from the same place, or also (assuming that they are some distance apart) if some third object be carried from one to the other and compared with them - if, for instance, some measure such as a yard or a foot or any other appropriate unit, be applied first to one and then to the other. Only then will there be a ground for distinguishing them with regard to the discovered inequality. Similarly, if the body of the spectator himself, or one of its members, which of course moves from place to place with him and may serve as a measure, is compared with these temples, then too their magnitudes will appear different and thus give a basis for distinguishing them. But if you consider the spectator only as a seeing mind concentrated at a point as it were, without any magnitude about him, either really or in his imagination, and have regard only for those aspects of things which the intellect can follow, such as numbers, proportions, and angles, no distinction will appear. These temples are therefore called similar, because they can be distinguished only by being observed together, either directly with each other or with a third something, but it is impossible to distinguish them singly and when seen by themselves. 14 This clear, practical, and universal description of similarity will be useful to us in geometrical demonstrations, as will appear directly. For we call two presented figures similar if nothing can be observed in one, viewed by itself, which cannot be equally observed in the other. Thus it follows that there should be the same ratio of proportion of parts in both cases; otherwise a distinction would appear even when each is viewed by itself, without any direct observation of both together. But lacking a general concept of similarity, geometricians have defined figures as similar whose For references see p. 257
256 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS corresponding angles are equal. This is a special case which does not reveal the nature of similarity in general. As a result they had to proceed indirectly to prove propositions which follow at the first glance from our definition. But let us come to examples. In the Elements it is shown that similar or equiangular triangles have proportional sides, and the converse. But Euclid uses many detours to achieve this demonstration, and then only in the fifth book, whereas he might have shown it in the first if he had used our concept. First we shall demonstrate that equiangular triangles are similar. Given two triangles ABC and LMN (Figure 9), whose angles A, B, and C and L, M, A L ~ M B Fig. 9. N and N are, respectively, equal. I say the triangles are similar. I use this new axiom: things which cannot be distinguished through their determinants (or through data adequate to define them) cannot be distinguished at all, since all other properties arise from these data. ls Now given the base BC and the angles Band C (and hence also the angle A), the triangle ABC is given; likewise, given the base MN and the angles M and N (and hence also the angle L), the triangle LMN is given. But from these properties sufficient to determine the triangles, they cannot be distinguished if viewed singly. For in each triangle the base and two adjacent angles are given, but the base cannot be compared with the angles. Therefore there remains nothing which can be examined in either triangle viewed singly by its determinants, except the ratio of each given angle to a right angle or to two right angles, that is, the magnitude of the angle itself. And since these are found to be the same in both triangles, it follows necessarily that the triangles singly cannot be distinguished and therefore are similar. For I may add as a scholium that although the triangles can be distinguished by magnitude, magnitude can be known only by observing together either both triangles at the same time or each with some other unit of measure. But in this case they would not be merely viewed separately, as was postulated. The converse is also clear, that similar triangles are equiangular. Otherwise, if there were some angle A in the triangle ABC to which no equal one is found in triangle LMN, there would be given an angle in ABC having a ratio to two right angles (or to the sum of the angles of the triangle) which no angle has in LMN, and this suffices to distinguish the triangle ABC, viewed separately, from triangle LMN. It is also shown that similar triangles have proportional sides. For if some two sides were given, such as AB and BC which have a ratio to each other which no two sides of LMN have, then one triangle could be distinguished from the other, even viewed singly. Finally, if their
HANOVER TO THE ITALIAN JOURNEY, 1676-87 257 sides are proportional, triangles are similar, for if the sides are given, the triangles are given, and it suffices (according to our axiom) that no basis for distinguishing them can be found in the ratio of the sides, so that we may conclude that such a distinction can be found in no other circumstance in the triangles viewed singly. It is also clear from this that equiangular triangles have proportional sides, and the converse. In the same way it is shown directly and at first glance from our concept of similarity that circles are to each other as the squares of their diameters, which Euclid shows only in his tenth book, and then by using inscribed and circumscribed figures and a reductio ad absurdum, whereas no such roundabout methods are necessary. Given a circle with a diameter AB (Figure 10) and CD, the square on the diameter Fig. 10. circumscribed about it. In the same way let a circle be described with a diameter LM, and the square NO, or its diameter, circumscribed about it. The determinants are similar in both figures, circle to circle, square to square, and relation of circle to square; so by the above axiom, figures ABCD and LMNO are similar. Therefore, by definition of similarity, the circle AB is to the square CD as the circle LM is to the square NO, and hence the circle AB is to the circle LM as the square CD is to the square NO, which was to be proved. In the same way it is proved that spheres are to each other as the cubes of their diameters and in general, that in similar figures lines, surfaces, and volumes are proportional, respectively, to lengths, squares, and cubes of corresponding sides. Until now this has been more generally assumed than proved. Furthermore, this point of view, which offers such facility in demonstrating truths which have been proved only with difficulty by other methods, also opens a new type of calculus to us which is far different from the algebraic calculus and is new both in its symbols and in the application it makes of them or in its operations. I like to call it Analysis Situs, because it explains situation directly and immediately, so that, even if the figures are not drawn, they are portrayed to the mind through symbols; and whatever the empirical imagination understands from the figures, this calculus derives by exact calculation from the symbols. All other matters which the power of imagination cannot penetrate will also follow from it. Therefore this calculus of situation which I propose will contain a supplement to sensory imagination and perfect it, as it were. It will have applications hitherto unknown not only in geometry but also in the invention of machines and in the descriptions of the mechanisms of nature. REFERENCES The essay (II) sent to Huygens is part of a more extensive study in geometry dated August 10, 1679, and published in OM., V, 141-71. 1
258 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 2 Cf. Couto OF., p. 152, from 1680: "We will reduce equality to congruence, and ratio to similarity. Two things are equal if one can be transformed into the other." There can be little doubt that Leibniz was first influenced to undertake the reform of geometry through his reading of Hobbes, though he recognized the latter's mathematical inadequacies (GM., VI, 71-72). But to Hobbes's effort to restore the Greek foundation to geometry, as against Cartesian analysis, he added something entirely new and fruitful, the logical analysis of the conditions of congruence and similarity and a rigorous synthesis of geometric truth with these determining conditions. See p. 130, note 8. a Huygens' Traite de la lumiere appeared in 1690. For Leibniz's analysis of refraction see No. SO. 4 The omitted paragraphs dealt with such mathematical problems as the solution of algebraic equations with the aid of tables, exponential equations, and the inverse tangent problem. 5 John Joachim Becher (1635-82) was an alchemistic adventurer and a founder of the phlogiston theory. Leibniz aroused his enmity by exposing his alchemical claims at Hanover. 8 For example, analytic geometry assumes the Pythagorean theorem in deriving the fundamental formula for the distance between two points and for the properties of straight lines based upon this. 7 (Y) is equivalent to Y1, Yz, Ya, etc. 8 Leibniz's parentheses indicate that the sentence contains an interpretation which is not a part of the demonstration, since it assumes a straight line, which is still to be defined. See note 10, below. S That is, to determine any specific member of the family of circles of whose centers the straight line AB is the locus. 10 That is, AY \:i BY. Leibniz thus defines the straight line as the locus of all points ( Y) whose relations to three fixed points (in space) are congruent. 11 At this point the text in G M. becomes inaccurate and incomplete, and we follow the German translation (BC., I, 83) in using the accurate text in Uylenbroeck's edition of Huygens' correspondence. The operational principles involved in determining the intersections which follow are (i) that corresponding parts of congruent figures are congruent; (ii) that any point can be substituted for another whose relations are congruent to its own; and (iii) that things congruent to the same thing are congruent to each other. 12 This essay is undated but belongs to the geometric studies of this period. Cf. Couto L., pp.396-97. 18 Euclid's 3e3opiva or Data, which was edited by Marinus of Neapolis, a pupil of Proclus, is discussed in Cantor, Vorlesungen fiber Geschichte der Mathematik (4th ed.), I, 282-83. 14 Note that Leibniz's definition of similarity can thus be derived from the principle of the identity of indiscernibles, applied abstractly to those related qualities which are not observed simultaneously or through a middle term, as his postulate requires. 15 This axiom relates Leibniz's analysis of similars in geometry with his more general theory of definition and of analysis and synthesis explained in No. 25. Determinants are the components of a concept adequate for its real definition. Note that the principle of equipollence (No. 205, n. 3) is here applied to equate the relations in known detenninants to the relations sought - an anticipation of its later application in the definition of continuity.
28 LETTER TO JOHN FREDERICK, DUKE OF BRUNSWICK-HANOVER Fall, 1679 The Treaty of Nijmegen, signed February 5,1679, and the concern of the reigning pope, Innocent XI, for a moral deepening of the Church of Rome and a return of Protestants from their apostasy, increased the spirit of tolerance between Catholic and Protestant branches of Christendom. Leibniz believed the time ripe for a revival of his great apologetic project, the Catholic Demonstrations, and he turned to his patron as the Catholic prince whose support would make it the spearhead of an effort to bring about church unity. The papal legate Spinola had visited Hanover for the second time with a message from the pope, and Leibniz had begun his long correspondence on the terms ofunion with Bossuet, whose Exposition de la foi de l'eglise catholique had won papal approval. After John Frederick's death late in the same year, Leibniz shifted his efforts to win princely patronage to another Catholic, Ernest of Hesse-Rheinfels, who was close to the great thinker, Antoine Arnauld, whom Leibniz had first sought to interest in his proposal (No. 10). [PA., II, i, 487-88] The departure of your serene highness and the conjuncture of the times compel me to touch upon a matter which I have weighed carefully. But lost time and opportunity never return, as I have already experienced on another occasion, and motives of piety and the public good must take precedence over all other considerations. Your serene highness should know, then, that I frequently examined the controversies of theology most throroughly with the late Baron von Boineburg and that we concluded at last that the Council of Trent can without difficulty be approved in its entirety except for three or four passages. It seems to me that in order to avoid opinions involving contradictions, we must give an interpretation to these which, I believe, is contrary neither to the words nor to the opinions of the Catholic church, though it is far removed from the common opinions of certain Scholastic theologians, especially from those of the monks. To speak candidly and without reservations: since these men have a great ascendancy over people's minds, as is testified by the trouble they gave Galileo, I told him frankly that I should have no difficulty in submitting and in making public avowal of this, if a declaration could be obtained from Rome assuring me that these interpretations, which seemed to me the true ones, are at least tolerable and contain nothing heretical or contrary to faith. Then, if this were done, I should set about arranging everything in so clear a light that my work could perhaps contribute something to reunion in its time. The late Baron was enthusiastic about this proposal, and when I made my journey to France, he gave me letters to Mr. Arnauld, for he believed that his opinions could For references see p. 262
260 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS carry great weight. But in order not to show myself ill-timed, I moved with all possible circumspection, and the death of the Baron came unexpectedly and removed my hope of succeeding along this path. So I did not explain my views to Mr. Arnauld but from that time on began to think of your serene highness, especially because I knew that the Baron von Boineburg had planned to speak to you, for still more particular reasons which I shall give in their place. Now assuming that these declarations were obtained from Rome, I had formed the plan of a work of first importance, which the Baron most heartily approved. Its title was Catholic Demonstrations. It was to contain three parts. The first was to deal with the demonstrations of the existence of God, of the immortality of the soul, and of all natural theology; for I did in fact have some surprising ones. The second part was to be about the Christian religion, or revealed theology, where I sought to demonstrate the possibility of our mysteries and to meet all the objections of those who claim to show the absurdity and the contradictions in the Trinity, the Incarnation, the Eucharist, and the resurrection of the body. For the proofs of the Christian religion are only moral, since it is impossible to give any other kind of proof in matters of fact. But every proof which carries only moral certainty can be destroyed by stronger contrary proofs; consequently, we must reply to objections in order to satisfy ourselves entirely, since a single impossibility proved of our mysteries would destroy the whole structure. The third part was to treat of the church; here I have convincing proofs that the church hierarchy is of divine right, and I distinguish the limits of secular and ecclesiastical power exactly. Churchmen themselves, namely, and all other men, owe an external obedience to sovereigns, but only usque ad aras 1 , and at least an unreserved suffrance to the rest. For example, the first Christians did not obey the most impious commandments of the pagan emperors, but they also did not oppose force to force. In exchange, all men, including sovereigns, owe an interior obedience to the church, that is, an unreserved deference in matters of faith, as far as this is possible for them. (This reservation is necessary, for if a man happens to believe that he sees a contradiction in what the church commands him to believe, it will be impossible for him to have faith in it, and he will be a heretic, though only materially. This alone will not prevent his being saved.) So we see that we owe a passive obedience, or nonresistance, to sovereigns, and an active obedience, so far as is in our power, to the church. In terms of these principles I give an easy and clear solution to the most disturbing questions. 2 But in order to lay the basis for these great demonstrations, I plan to preface them with the demonstrated elements of the true philosophy to help in understanding the main work. We need a new logic in order to know degrees of probability, since this is necessary in judging the proofs of matters of fact and of morals, where there are unusually good reasons on both sides and we are concerned only to know on which side to tip the scales. But the art of weighing probabilities is not yet even partly explained, though it would be of great importance in legal matters and even in the management of business. We must also push metaphysics further than has been done so far, in order to have true notions of God and the soul, of person, substance, and accidents. And unless we have a profounder insight into physics, we cannot meet the objections raised against the history of creation, the deluge, and the resurrection of the body. 3 In short, the true morality must be demonstrated, in order to learn what is justice, justification, freedom, pleasure, happiness, and the beatific vision. And to conclude, nothing conforms more truly with a true politics and the true happiness of mankind, even here
HANOVER TO THE ITALIAN JOURNEY, 1676-87 261 below and in this life, than does my proposal about the inviolable and irresistible power of the sovereign over external goods and of the internal rule which God exercises over souls through the church. It seems to me that I have already said to your serene highness on other occasions that nothing is more useful for the general good than the authority of a universal church which forms a body of all Christians, united by bonds of charity, and which can hold in sacred respect the greatest powers on earth as long as they are still sensible to the reproaches of their consciences. Every man of good will [homme de bien] should therefore desire that the luster of the church may everywhere be restored and that the spiritual power of its true ministers over the faithful may be more fully recognized than is often done, even among those who would pass as the most Catholic. But disputes are more customary than demonstrations in philosophy, morals, and theology, and most readers will have the prejudices about such a project that are usual about works dealing with these matters; for it will be thought that the author has merely transcribed and problematized and is probably a superficial mind little versed in the mathematical sciences and consequently hardly capable of true demonstration. In view of these considerations I have tried to disabuse everyone by pushing myself ahead a little further than is common in mathematics, where I believe I have made discoveries which have already received the general approval of the greatest men of the day and which will appear with brilliance whenever I choose. This was the true reason for my long stay in France - to perfect myself in this field and to establish my reputation, for when I went there I was not yet much of a geometrician, which I needed to be in order to set up my demonstrations in a rigorous way. So I want first to publish my discoveries in analysis, geometry, and mechanics, and I venture to say that these will not be inferior to those which Galileo and Descartes have given us. Men will be able to judge from them whether I know how to discover and to demonstrate. I did not study the mathematical sciences for themselves, therefore, but in order some day to use them in establishing my credit and furthering piety. There is another important thing in my philosophy which will give it access to the Jesuits and other theologians. This is my restoration of substantial forms, which the atomists and Cartesians claim to have exterminated. It is certain that without these forms and the distinction that exists between them and real accidents, it is impossible to explain our mysteries. For if the nature of body consists in extension, as Descartes claims, it involves a contradiction, beyond all doubt, to maintain that a body may exist in many places at once. But all that has been said about the essence of body until now is unintelligible, and it is not surprising that substantial forms have been taken for chimeras by the most able minds. What I shall say about them, among other things, will instead be as intelligible as anything that the Cartesians have ever proposed about other matters. Finally, to render my demonstrations absolutely incontestable, and as certain as anything that can be proved by arithmetical calculation, I shall offer an essay on my new writing or characteristic or, if you prefer, language. This is undoubtedly one of the greatest projects to which men have ever set themselves. It will be an instrument even more useful to the mind than telescopes and microscopes are to the eyes. Every line of this writing will be equivalent to a demonstration. The only fallacies will be easily detected errors in calculation. This will become the great method of discovering truths, establishing them, and teaching them irresistibly when they are established. For references see p. 262
262 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Nothing could be proposed that would be more important for the Congregation for the Propagation of the Faith. For when this language is once established among missionaries, it will spread at once around the world. It can be learned in several days by using it and will be of the greatest convenience in general intercourse. And wherever it is received, there will be no difficulty in establishing the true religion which is always the most reasonable and in a word everything which I shall develop in my work on Catholic Demonstrations. It will be as impossible to resist its sound reasoning as it is to argue against arithmetic. You can judge what advantageous changes will follow everywhere in piety and morals and in short, in increasing the perfection of mankind. But to achieve this end, I shall certainly need great assistance, and I see no better source for this than the Congregation for the Propagation of the Faith, which I mentioned above. All these projects, however, depend on the declarations from Rome, without which I could not contentedly submit, since I should otherwise be obliged to admit things which my demonstrations, and especially this characteristic, would refute in spite of myself and all the world. To obtain these declarations in the easiest way, we must undoubtedly act with great adroitness. There are many sides to everything, and the way it is first seen determines much. The most harmless proposals have often been rejected on false suspicions, and the most scabby ones accepted through the ability of their supporters. Men often do not take the pains to examine matters thoroughly, and however acceptable views may be, they are sometimes rejected at once on a false prepossession, if they are not recommended from some quarters which are respected. This is why I have concluded that it would be well to appeal to your most serene highness, who could direct the matter so skilfully that no one could perceive anything mysterious and raise difficulties where there are no true ones. This will be all the easier, since the present pope is not only a good man, but enlightened and fair-minded as well. 4 But there is still another outstanding reason which has obliged me to break silence and to make this proposal now. This is a most important one, and particularly concerns your serene highness. But since I cannot blurt it out suddenly, I shall speak of it distinctly later. 5 REFERENCES "As far as the altars." This outline of the Catholic Demonstrations differs in no essentials from that of the Mainz period given in PA., VI, i, 494-500 (cf. No.5), except that Parts I and II of the earlier plan have been combined into a demonstration of natural religion. S It may- be significant to note that Richard Simon's Histoire critique du Vieux Testament had appeared in 1678, one of the important beginnings of modem biblical criticism. 4 Innocent XI, pope from 1676 to 1689, opponent of the Jesuits and zealous worker for moral reform and the reconversion of Protestants. 6 Whatever this proposal may have been, it may never have been made, for John Frederick died on December 18 of the same year, on his way to the carnival at Venice. 1 2
29 ON FREEDOM Ca. 1679 On November 27, 1677, when he was stili occupied with Spinozistic approaches to metaphysics, Leibniz had had a discussion 0/ freedom with the apostolic missionary Steno. He had long been concerned with the problem. This paper, though undated, clearly belongs to the period 0/1679 or the years/ol/owing, when his position is modified by the distinction between necessary and contingent truths. It also presents a popular interpretation 0/ some 0/ the logical studies 0/ the period and relates them to the theological problems 0/ God's omnipotence, human/reedom, and sin. [F. de C., pp. 178-85] One of the oldest doubts of mankind concerns the question of how freedom and contingency are compatible with the chain of causes and with providence. And Christian investigations of the justice of God in accomplishing man's salvation have merely increased the difficulty of the matter. When I considered that nothing occurs by chance or by accident unless we resort to certain particular substances, that fortune apart from fate is an empty word, and that nothing exists unless certain conditions are fulfilled from all of which together its existence at once follows, I found myself very close to the opinions of those who hold everything to be absolutely necessary; believing that when things are not subject to coercion even though they are to necessity, there is freedom, and not distinguishing between the infallible, or what is known with certainty to be true, and the necessary. But I was pulled back from this precipice by considering those possible things which neither are nor will be nor have been.l For if certain possible things never exist, existing things cannot always be necessary; otherwise it would be impossible for other things to exist in their place, and whatever never exists would therefore be impossible. For it cannot be denied that many stories, especially those we call novels, may be regarded as possible, even if they do not actually take place in this particular sequence of the universe which God has chosen - unless/someone imagines that there are certain poetic regions in the infinite extent of space and time where we might see wandering over the earth King Arthur of Great Britain, Amadis of Gaul, and the fabulous Dietrich von Bern invented by the Germans. A famous philosopher of our century does not seem to have been far from such an opinion, for he expressly affirms somewhere that matter successively receives all the forms of which it is capable (Principles 0/ Philosophy, Part III, Art. 47).2 This opinion cannot be defended, for it would obliterate all the beauty of the universe and any choice of matters, not to mention here other grounds on which the contrary can be shown. Having thus recognized the contingency of things, I raised the further question of a clear concept of truth, for I had a reasonable hope of throwing some light from this upon the problem of distinguishing necessary from contingent truths. For I saw that For references see p. 266
264 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS in every true affirmative proposition, whether universal or singular, necessary or contingent, the predicate inheres in the subject or that the concept of the predicate is in some way involved in the concept of the subject. I saw too that this is the principle of infallibility for him who knows everything a priori. But this very fact seemed to increase the difficulty, for, if at any particular time the concept of the predicate inheres in the concept of the subject, how can the predicate ever be denied of the subject without contradiction and impossibility, or without destroying the subject concept? A new and unexpected light arose at last, however, where I least expected it, namely, from mathematical considerations of the nature of the infinite. For there are two labyrinths in which the human mind is caught. One concerns the composition of the continuum; the other concerns the nature of freedom. And both arise from the same source, namely, the infinite. 3 Since he could not unravel these two knots, or would not express his opinions of them, the famous philosopher whom I cited above chose to cut them with his sword, for he says (Principles 0/ Philosophy, Part I, Arts. 40 and 41) that we can easily become involved in great difficulties if we try to reconcile God's foreordination with the freedom of the will but that we ought to refrain from such discussions because we cannot comprehend the nature of God. In the same work (Part II, Art. 35) he says that we ought not to doubt the infinite divisibility of matter, though we cannot grasp it. But this will not do, for it is one thing not to comprehend a thing, but another to comprehend its contradictory. It is therefore necessary at least to answer those arguments from which it seems to follow that freedom and the infinite divisibility of matter imply a contradiction. It must be understood, then, that all created beings have a certain mark of the divine infinity impressed upon them and that this is the source of many wonderful matters which astound the human mind. For example, there is no portion of matter, however tiny, in which there is not a world of creatures, infinite in number. And there is no created substance, however imperfect, which does not act upon all the others and suffer action from all the others, and whose complex concept as this exists in the divine mind does not contain the whole universe, with all that ever is, has been, and will be. And there is no truth of fact or of individual things which does not depend upon an infinite series of reasons, though God alone can see everything that is in this series. This is the cause, too, why only God knows the contingent truths a priori and sees their infallibility otherwise than by experience. A careful consideration of these matters revealed a very essential difference between necessary and contingent truths. Every truth is either original or derivative. Original truths are those for which no reason can be given; such are identities or immediate truths, which affirm the same thing of itself or deny its contrary of its contrary. There are in tum two genera of derivative truths, for some can be reduced to primary truths; the others can be reduced in an infinite progression. The former are necessary; the latter, contingent. A necessary proposition is one whose contrary implies a contradiction; such are all identities and all derivative truths reducible to identities. To this genus belong the truths said to be of metaphysical or geometrical necessity. For to demonstrate is merely, by an analysis of the terms of a proposition and the substitution of the definition or a part of it, for the thing defined, to show a kind of equation or coincidence of predicate and subject in a reciprocal proposition, or, in other cases, at least an inclusion of the one in the other, so that what was concealed in the proposition or was contained in it only potentially, is rendered evident or explicit by the demon-
HANOVER TO THE ITALIAN JOURNEY, 1676-87 265 stration. For example, if we understand by a ternary, a senary, and a duodenary, numbers divisible by 3, 6, and 12, respectively, we can demonstrate this proposition: Every duodenary is a senary. For every duodenary is a binary-binary-ternary, since this is the reduction of a duodenary into its prime factors (12 = 2 x 2 x 3),4 or the definition of a duodenary. But every binary-binary-ternary is a binary-ternary (this is an identical proposition), and every binary-ternary is a senary (by the definition of a senary, since 6 = 2 x 3). Therefore every duodenary is a senary (12 is the same as 2 x 2 x 3, and 2 x 2 x 3 is divisible by 2 x 3, and 2 x 3 is the same as 6; therfore 12 is divisible by 6). In contingent truths, however, though the predicate inheres in the subject, we can never demonstrate this, nor can the proposition ever be reduced to an equation or an identity, but the analysis proceeds to infinity, only God being able to see, not the end of the analysis indeed, since there is no end, but S the nexus of terms or the inclusion of the predicate in the subject, since he sees everything which is in the series. Indeed, this truth itself arises in part from his intellect and in part from his will and so expresses his infinite perfection and the harmony of the entire series of things, each in its own particular way. For us, however, there remain two ways of knowing contingent truths. The one is experience; the other, reason. We known by experience when we perceive a thing distinctly enough by our senses; by reason, however, when we use the general principle that nothing happens without a reason, or that the predicate always inheres in the subject by virtue of some reason. So we can consider it as certain that God has made all things in the most perfect way, that he does nothing without a reason, and that nothing ever happens without its reason being understood by anyone who understands why the state of the world is as it is rather than otherwise. Sins arise from the aboriginal limitation of things; but God does not so much decree sins as he does the admission to existence of certain possible substances whose complete concept already involves the possibility of their freely sinning, and even connotes the whole series of events in which they figure as links. Nor should there be any doubt that God decrees only perfection or what is positive, while limitation with the sin which arises from it, is permitted only because it cannot be absolutely rejected if certain positive decrees are maintained. Nothing else would be congruent with wisdom than to compensate sin by a greater good that could not otherwise be obtained; but this cannot be discussed here. In order to fix our attention, however, so that our mind will not wrestle with vague difficulties, an analogy comes to my mind between truths and proportions which seems admirably to clarify the whole matter and put it in a clear light. Just as the smaller number is contained in the larger in every proportion 6 (or an equal in its equal), so in every truth the predicate is contained in the subject. And just as in every proportion between homogeneous quantities an analysis of equal or proportional terms can be carried out by subtracting the smaller from the larger, that is, taking away from the larger a part equal to the smaller, then subtracting the rest from the smaller, and so on, either until there is no remainder or to infinity; so also can we establish an analysis of truths, always substituting for a term its equivalent, so that the predicate will be resolved into elements already contained in the subject. But in proportions the analysis may sometimes be completed, so that we arrive at a common measure which is contained in both terms of the proportion an integral number of For references see p. 266
266 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS times, while sometimes the analysis can be continued into infinity, as when comparing a rational number with a surd; for instance, the side of a square with the diagonal. 7 Just so, truths are sometimes demonstrable or necessary, and sometimes free and contingent, so that they cannot be reduced to identities as if to a common measure, by any analysis. This is the essential distinction between truths as well as proportions. Yet the science of geometry has mastered incommensurable proportions, and we have demonstrations even about infinite series. All the more are contingent or infinite truths subject to the knowledge of God and known by him, not by demonstration for this would involve contradiction - but by an infallible vision. But this vision of God must not be thought of as a kind of empirical knowledge, as if he saw anything in the things distinct from himself, but as a priori knowledge in which he grasps the reasons for truths. For he sees possible things by considering his own essence; he sees those that have a contingent existence by considering his free will and his decrees, the first of which is that everything shall work in the best manner and with the highest reason. The so-called middle science is nothing but the knowledge of contingent possibles. 8 When all these matters are considered thoroughly, I do not think any difficulty can arise in this argument the solution of which cannot be derived from what has been said. If we admit this general concept of necessity - and everyone does admit it - namely, that all propositions are necessary whose contraries imply a contradiction, it is easily seen from a consideration of the nature of demonstration and analysis that there can and must be truths which cannot be reduced by any analysis to identities or to the principle of contradiction but which involve an infinite series of reasons which only God can see through. This is the nature of everything which is called free and contingent and especially of everything which involves space and time. As I have shown above, this follows from the very infinity of the parts of the universe and the mutual interdependence and nexus of all things. REFERENCES See the distinction between possibility and compossibility made against Spinoza in No. 14, II, and in No. 20. Cf. p. 205, notes 7 and 9. 2 This point is discussed in somewhat more detail in the letters to Philipp late in 1679 and early in 1680 (No. 31), where the same passage is cited. 3 On the source and meaning of Leibniz's figure of the labyrinth see the Introduction, Sec. V and p. 60, note 22. 4 Reading seu for sen. 5 Reading sed for sic; in the errata F. de C. givesseu. 6 Reading proportione for propositione. Leibniz's mathematical analogy will be simplified if the reader thinks of a ratio rather than a proportion (see note 7 below). 7 Basically, Leibniz here considers truths as analogous to the relations between numbers in the real number system, necessary truths corresponding to rational ratios between real numbers, and contingent truths to ratios involving irrationals which can be resolved only serially. Thus 6{5 is perfectly analyzable by division, but V2 or n involves an infinite series. 8 On the middle science see the Introduction, Sec. V and p. 61, note 35. 1
30 "FIRST TRUTHS" Ca. 1680-84 Among the papers of the period from 1679 to 1686 is this very important one, usually designated by its opening words, primae veritates, which Couturat has used to support his argument for the essentially logical foundation of Leibniz's metaphysics. 1 The student will discover, however, that though the principles of metaphysics, including that of individuality, are here developed a priori, the paper moves by means of definitions from an abstract principle of identity to more complete concepts and more concrete principles. Many of these definitions are basically metaphysical in character. The date is unknown. On the one hand, there are only references to the distinction between truths of reason and offact and between necessity and contingency, a distinction developed in detail in No. 29. On the other hand, the concepts and phrases of the Discourse of 1686 (No. 35) are already prominent, and Couturat considered it aforestudy for that work. [Cout. OF., pp. 518-23] First truths are those which predicate something of itself or deny the opposite of its opposite. For example, A is A, or A is not non-A; ifit is true that A is B, it is false that A is not B or that A is non-B. Likewise, everything is what it is; everything is similar or equal to itself; nothing is greater or less than itself. These and other truths of this kind, though they may have various degrees of priority, can nevertheless all be grouped under the one name of identities. All other truths are reduced to first truths with the aid of definitions or by the analysis of concepts; in this consists proof a priori, which is independent of experience. 2 I shall give as example this proposition which is accepted as an axiom by mathematicians and all other people alike: the whole is greater than its part, or the part is less than the whole. This is very easily demonstrated from the definition ofless or greater, with the addition of a primitive axiom or identity. For that is less which is equal to a part of another thing (the greater). This definition is very easily understood and is consistent with the general practice of men, when they compare things with each other and measure the excess by subtracting an amount equal to the smaller from the greater. Hence one may reason as follows. A part is equal to a part of the whole (namely, to itself, by the axiom of identity, according to which each thing is equal to itself). But what is equal to a part of a whole is less than the whole (by the definition of less). Therefore the part is less than the whole. The predicate or consequent therefore always inheres in the subject or antecedent. And as Aristotle, too, observed, the nature of truth in general or the connection between the terms of a proposition consists in this fact. 3 In identities this connection and the inclusion of the predicate in the subject are explicit; in all other propositions they For references see p. 270
268 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS are implied and must be revealed through the analysis of the concepts, which constitutes a demonstration a priori. This is true, moreover, in every affirmative truth, universal or singular, necessary or contingent, whether its terms are intrinsic or extrinsic denominations. 4 Here lies hidden a wonderful secret which contains the nature of contingency or the essential distinction between necessary and contingent truths and which removes the difficulty involved in a fatal necessity determining even free things. These matters have not been adequately considered because they are too easy, but there follow from them many things of great importance. At once they give rise to the accepted axiom that there is nothing without a reason, or no effect without a cause. Otherwise there would be truth which could not be proved a priori or resolved into identities - contrary to the nature of truth, which is always either expressly or implicitly identical. 5 It follows also that if the data contained a pair of identically related sets so will the consequences or quaesita. For no difference can be accounted for unless its reason is found in the data. 6 A corollary, or better, an example, of this is the postulate of Archimedes stated at the beginning of his book on the balance - that if the arms of a balance and its weights are supposed equal, everything will be in equilibrium. This also gives a reason for eternal things. If it be assumed that the world has existed from eternity and has contained only spheres, a reason should have to be given why it contains spheres rather than cube~. It follows also that there cannot be two individual things in nature which differ only numerically. For surely it must be possible to give a reason why they are different, and this must be sought in some differences within themselves. Thus the observation of Thomas Aquinas about separate intelligences, which he declared never differ in number alone, must be applied to other things also. 7 Never are two eggs, two leaves, or two blades of grass in a garden to be found exactly similar to each other. So perfect similarity occurs only in incomplete and abstract concepts, where matters are conceived, not in their totality but according to a certain single viewpoint, as when we consider only figures and neglect the figured matter. So geometry is right in studying similar triangles, even though two perfectly similar material triangles are never found. And although gold or some other metal, or salt, and many liquids, may be taken for homogeneous bodies, this can be admitted only as concerns the senses and not as if it were true in an exact sense. It follows further that there are no purely extrinsic denominations which have no basis at all in the denominated thing itself. For the concept of the denominated subject necessarily involves the concept of the predicate. Likewise, whenever the denomination of a thing is changed, some variation has to occur in the thing itself. The complete or perfect concept of an individual substance involves all its predicates, past,present, andfuture. For certainly it is already true now that a future predicate will be a predicate in the future, and so it is contained in the concept of the thing. Therefore there is contained in the perfect individual concepts of Peter or Judas, considered as merely possible concepts and setting aside the divine decree to create them, everything that will happen to them, whether necessarily or freely. And all this is known by God. Thus it is obvious that God elects from an infinity of possible individuals those whom he judges best suited to the supreme and secret ends of his wisdom. In an exact sense, he does not decree that Peter should sin or Judas be damned but only that, in preference to other possible individuals, Peter, who will sin - certainly, indeed, yet not
HANOVER TO THE ITALIAN JOURNEY, 1676-87 269 necessarily but freely - and Judas, who will suffer damnation - under the same condition - shall come into existence, or that the possible concept shall become actual. And although the future salvation of Peter is contained in his eternal possible notion, yet this is not without the help of grace, for in the same perfect notion of this possible Peter, there are contained as possibilities the helps of the divine grace to be granted to him. Every individual substance involves the whole universe in its perfect concept, and all that exists in the universe has existed or will exist. For there is no thing upon which some true denomination, at least of comparison or relation, cannot be imposed from another thing. Yet there is no purely extrinsic denomination. 8 I have shown the same thing in many other ways which are in harmony with each other. All individual created substances, indeed, are different expressions of the same universe and of the same universal cause, God. But these expressions vary in perfection as do different representations or perspectives of the same city seen from different points. Every created individual substance exerts physical action and passion on all others. For if a change occurs in one, some corresponding change results in all others, because their denomination is changed. This is confirmed by our experience of nature, for we observe that in a vessel full of liquid (the whole universe is such a vessel) a motion made in the middle is propagated to the edges, though it may become more and more insensible as it recedes farther from its origin. It can be said that, speaking with metaphysical rigor, no created substance exerts a metaphysical action or influence upon another. For to say nothing of the fact that it cannot be explained how anything can pas~ over from one thing into the substance of another it has already been shown that all the future states of each thing follow from its own concept. What we call causes are in metaphysical rigor only concomitant requisites. This is illustrated by our experiences of nature, for bodies in fact recede from other bodies by force of their own elasticity and not by any alien force, although another body has been required to set the elasticity (which arises from something intrinsic to the body itself) working. 9 If the diversity of soul and body be assumed, their union can be explained from this without the common hypothesis of an influx, which is unintelligible, and without the hypothesis of occasional causes, which calls upon a God ex machina. For God has equipped both soul and body from the beginning with such great wisdom and workmanship that through the original constitution and essence of each, everything which happens in one corresponds perfectly to whatever happens in the other, just as if something had passed over from the one into the other. I call thi.; the hypothesis of concomitance. This is true of all the substances in the whole universe but is not perceptible in all as it is in the soul and body. There is no vacuum. For the different parts of empty space would be perfectly similar and congruent with each other and could not by themselves be distinguished. So they would differ in number alone, which is absurd. Time too may be proved not to be a thing, in the same way as space. There is no corporeal substance in which there is nothing but extension, or magnitude, figure, and their variations. For otherwise there could exist two corporeal substances perfectly similar to each other, which is absurd. Hence it follows that there is something in corporeal substances analogous to the soul, which is commonly called form. 10 There are no atoms; indeed, there is no body so small that it is not actually subdiviFor references see p. 270
270 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS ded. By this very fact, since it is affected by all other things in the entire world and receives some effect from all, which must cause a change in the body, it has even preserved all past impressions and anticipates the future ones. If anyone says that this effect is contained in the motions impressed on the atom, which receives the effect in toto without any division in it, it can be replied that not only must an effect in the atom result from all the impressions of the universe but conversely, the entire state of the universe must be gathered from the atom. Thus the cause can be inferred from the effect. But from the figure and motion of the atom alone, we cannot by regression infer what impressions have produced the given effect on it, since the same motion can be caused by different impressions, not to mention the fact that we cannot explain why bodies of a definite smallness should not be further divisible. Hence it follows that every small part of the universe contains a world with an infinite number of creatures. But a continuum is not divided into points, nor is it divided in all possible ways. It is not divided into points, because points are not parts but limits. It is not divided in all possible ways, because not all creatures are in the same part, but only a certain infinite progression of them. Thus, if you bisect a straight line and then any part of it, you will set up different divisions than if you trisect it. There is no actual determinate figure in things, for none can satisfy the infinity of impressions. So neither a circle nor an ellipse nor any other line definable by us exists except in our intellect, or if you prefer, before the lines are drawn or their parts distinguished. i i Space, time, extension, and motion are not things but well-founded modes of our consideration. Extension, motion, and bodies themselves, insofar as they consist in extension and motion alone, are not substances but true phenomena, like rainbows and parhelia. For figures do not exist in reality and if only their extension is considered, bodies are not one substance but many. For the substance of bodies there is required something which lacks extension; otherwise there would be no principle to account for the reality of the phenomena or for true unity. There would always be a plurality of bodies, never one body alone; and therefore there could not, in truth, be many. By a similar argument Cordemoi proved the existence of atoms. But since these have been excluded, there remains only something that lacks extension, something like the soul, which was once called a form or species. 12 Corporeal substance can neither come into being nor perish except through creation or annihilation. For, once it does last, it will last always, for there is no reason for a change. Nor does the dissolution of a body have anything in common with its desstruction. Therefore ensouled beings neither begin nor perish; they are only transformed. REFERENCES 1 'Sur la metaphysique de Leibniz (avec un opuscule inedit)" Revue de metaphysique et de morale 10 (1902) 1-25. 2 Limiting itself to the a priori derivation of metaphysical principles, this paper illustrates Leibniz's inclination to view the universe from God's viewpoint rather than man's. Thus his failure to point out the empirical element which actually enters into his definitions and the assumptions implicit in them.
HANOVER TO THE ITALIAN JOURNEY, 1676-87 271 On the Aristotelian source of this principle, and Leibniz's interpretation of it, see p. 60, note 5. 4 See Introduction, Sec. V, and the correspondence with De VoIder (No. 54). There has been a tendency to interpret Leibniz's doctrine that there are no purely extrinsic denominations, expressed later in this paper, as an assertion of the internality of all relations, though it is sometimes accompanied with a distinction rather like G. E. Moore's between external relations and relational properties. Leibniz often says, it is true, that the relations between substances are added by the perceiving mind, as the term 'denomination' suggests. But in general, there are real relations between monads - those of representation - but every representative act involves an internal or intrinsic quality in the perceiving monad. The issue involves the nature of oblique relations discussed in note 246 on p. 3. 5 That all truth is resolvable to identities is the assumption which Leibniz does not prove. That there are identities involved in all truth is one thing; that truth reduces to them, another, which presupposes the existence of perfect essence. 6 Cf. p. 258, note 15. The axiom in No. 27, ill, and this are the first explicit statements, in these selections, of the principle of functional dependence, which becomes so important in Leibniz's conception of scientific method. Most compactly stated, the law is datis ordinatis, etiam quaesita sunt ordinata ("As the data are ordered, so the unknowns [or sought] are also ordered") (No. 37), and the law of continuity is usually interpreted by Leibniz in this functional sense. 7 Summa theol., i, quest. 50, ad 4. Cf. Discourse, Sec. 9 (No. 35). 8 After 1683 Antoine Arnauld was asserting, in controversy with Malebranche, that perceptions are essential modifications of the soul but that the soul can perceive external and even eternal objects. Leibniz himself anticipated this view with his own to the effect that external relations depend upon internal qualities or modes. 9 The distinction between physical action and metaphysical action is striking here; the theory of physical action between substances cannot be sustained after the nature of the monad is restricted to appetite and perception and after the physical studies of the 1690's. For the functional definition of external causality between substances see the Discourse, Sec. 15. 10 Forms are active principles. In an essay from the same period, called by Erdmann 'On the True Method of Dealing with Philosophy and Theology', Leibniz wrote, after criticizing Descartes's theory of matter: "What then shall we add to extension to complete the concept of body? Certainly nothing which sense does not verify. Sense, namely, establishes three things at once: that we sense; that bodies are sensed; and that what is sensed is varied and composite, or extended. To the concept of extension or variety, therefore, is to be added that of action. A body is therefore an extended agent. It can be said that it is an extended substance, only if it be held that all substance acts, and all agents are substances. It can be shown adequately from the essential principles of metaphysics that what does not act does not exist, for there is no power of acting without a beginning of action. You say there is no little power in a bent bow, yet it does not act. But I say, on the contrary, that it does act; even before it is suddenly released, it strives. But all striving [conatus] is action. For the rest, much that is excellent and certain can be said about the nature of conatus and the principles of action, or as the Scholastics called it, of substantial forms" (G., VII, 326-27). 11 Existence could therefore be derived analytically only through an infinite analysis. Insofar as they conform to logical laws, our scientific formulas apply exactly only to incomplete or abstract concepts, but they are incomplete simplifications of existence and therefore do not determine it completely. 12 Gerauld de Cordemoi, Le Discernement de I'time et du corps (1666). 3
31 SELECTIONS FROM LEIBNIZ'S CORRESPONDENCE 1679-84 The reign of Ernest August and his wife Sophia, 1680-97, was a period of aggressive political advancement for the Duchy of Hanover. Within the Empire it was elevated to an electorate. Marriage alliances with Celle, Prussia, Austria, and Modena shifted and strengthened political ties. Plans were laid in behalf of Sophia for the English succession. 1n the promotion of these aims Leibniz's efforts, too, were distracted from his intellectual projects and largely absorbed in the historical studies, diplomatic briefs, and efforts for church union which were involved in the ambitions of his patrons. 1n the years from 1681 to 1685 he was also engaged in the unsuccessful engineering project of freeing the Harz silver mines of excess water. The following selections are from his wide correspondence with scholars and men of affairs. They contain criticisms of the thought of others and reflect his efforts to gain general and influential support for his own ideas. I. TO CHRISTIAN PHILIPP 1 [G., IV, 281-82] Early December, 1679 As concerns the philosophy of Descartes, about which you ask my opinion, I hesitate to say absolutely that it leads to atheism. It is true that he says some things which I, who have studied him thoroughly, strongly suspect. For example, the two passages to the effect that one should not consider final causes in physics and that matter takes on, successively, all the forms of which it is capable. 2 There is an admirable passage in Plato's Phaedo in which he justly blames Anaxagoras for the same thing which di~ pleases me in Mr. Descartes. 3 For my part, I believe that the laws of mechanics which serve as foundation for the whole system depend on final causes, that is to say, on the wiII of God determined to do what is most perfect, and that matter takes on not all possible forms but only the most perfect ones. Otherwise we should have to say that there will be a time in which everything wiII be badly ordered, which is far removed from the perfection of the Author of all things. For the rest, if Descartes had relied less on his imaginary hypotheses and been more attached to experience, I believe that his physics would have been worth following, for it must be admitted that he had great penetration. As for his geometry and analysis, it is far from being as perfect as is claimed by those who have only applied themselves to the solution of minor problems. There are several errors in his metaphysics, and he did not know the genuine source of truths or the general analysis of concepts. In my opinion Jung understood this better than did he. 4 Yet I admit that it is very useful and instructive to read Descartes, and I prefer, beyond comparison, to deal with a Cartesian rather than with a partisan of some other school. In short, I consider this philosophy as the antechamber to the true one.
HANOVER TO THE ITALIAN JOURNEY, 1676-87 273 II. TO PHILIPP [G., IV, 283-84] End of January, 1680 ... I esteem Mr. Descartes almost as much as one can esteem any man, and though there are among his opinions some which seem false to me, and even dangerous, this does not keep me from saying that we owe nearly as much to Galileo and to him in philosophical matters as to the whole of antiquity. At present I recall only one of the two dangerous propositions, the location of which you want me to indicate. It is in the Principles ofPhilosophy, Part III, Article 47, in the following words: And after all, it makes very little difference what we assume in this respect, because it must later be changed according to the laws of nature. Hardly anything can be assumed from which the same effect cannot be derived, though perhaps with greater trouble. For due to these laws, matter takes on, successively, all the forms of which it is capable. Therefore if we considered these forms in order, we could eventually arrive at that one which is our present world, so that in this respect no false hypothesis can lead us into error. I do not believe that a more dangerous proposition than this could be formulated. For if matter takes on, successively, all possible forms, it follows that nothing can be imagined so absurd, so bizarre, so contrary to what we call justice, that it would not have happened and will not some day happen. These are precisely the opinions which Spinoza has expounded more clearly, namely, that justice, beauty, and order are things merely relative to us but that the perfection of God consists in that magnitude of his activity by virtue of which nothing is possible or conceivable which he does not actually produce. These are also the opinions of Mr. Hobbes, who asserts that everything that is possible is either past or present or future, and there will be no place for trust in providence if God produces everything and makes no choice among possible beings. Mr. Descartes was careful not to speak so plainly, but he could not keep from revealing his opinions incidentally, with such adroitness that he will be understood only by those who examine such matters carefully. In my opinion, this is the 'first falsehood' and the basis of atheistic philosophy, though it always seems to say the most beautiful things about God. The true philosophy, on the contrary, must give us an entirely different concept of God's perfection, one that will be of use in both physics and ethics. For my part, I hold that far from excluding final causes from physics, as Mr. Descartes tries to do in Part I, Article 28, it is rather by means of them that everything must be determined, since the efficient cause of things is intelligent, having a will and therefore striving for the good. But this too differs from Descartes's opinion, since goodness, truth, and justice are such, according to him, only because God has established them by a free act of his will- a most strange thing. For if things are good or evil only as the result of God's will, the good cannot be a motive of his will, being posterior to his will. His will, then, would be a certain absolute decree, without any reason .... 5 III. TO FRAN<';OIS DE LA CHAISE 6 [PA., II, i, 511-12] May, 1680 (?) Most reverend Father, I have always contemplated an art of discovery, and I believe I have made most For references see p. 276
274 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS unusual beginnings toward it. Algebra is but one example of it. I have a new kind of geometry as different from Mr. Descartes's as his is from the geometry of the ancients. For as Descartes has added supersolid lines and problems, or even problems of the fifth, sixth, seventh, and higher degrees to the plane and solid lines and problems of the ancients, so I have added transcendental problems which are of no degree, or rather of all degrees at once, to his. Of this kind is the cutting of an angle in a given ratio, or also the trigonometry without tables which I have, as well as the true area of a . 1· . I num bers. Thi· 1 - ;;1 + 9 1 - iT 1 +, etc., when the s IS I1 - :31 + 5 clrc e 10 ratlOna diameter or its square is 1. It is impossible to give the area in a single number, but this is its true value and contains at once all the approximations to it. I believe that men will now stop the useless effort to find the true ratio, which is none other than this. When the nicest problems of mechanics are reduced to the terms of pure geometry 7, one will usually find a transcendental problem where the geometry of Descartes is insufficient. I can give numberless examples of this. Until now the problems of mechanics could not be reduced to those of pure geometry, for the laws of motion had not been fixed. Now I have found a way of determining them all by a reductio ad absurdum. I demonstrate the rules of motion, in the same way that geometricians demonstrate their theorems, by showing that the contrary would imply that a thing is greater than itself; I show that to assume the contrary would make a thing more powerful than itself, that is to say, it would be possible to establish purely mechanical perpetual motion. 8 By this same method I demonstrate that Mr. Descartes's rules of motion are impossible. I believe that it can now be said that we have at last achieved pure mathematics, that is, mathematics which contains only numbers, figures, and motions; the rest will be a mere exercise for youngsters in developing their reason. For posterity there will remain only the task of turning its serious attention to physics. Perhaps we could also go much further in medicine, even in our own time, if we were to attack it in a better way. It depends only on a great king, like your own, to achieve this. For it seems to me that there is an analysis in physics as certain as that in geometry, not for the purpose of determining what experiments are fitting - for that is where chance plays a part, though one could still perform the proposed experiments by this method - but to draw from given experiments everything that an angelic spirit could draw from them and to determine those which remain to be made in order to resolve our doubts. I am greatly surprised that those who are called Cartesians have done almost nothing since the death of their master, who was undoubtedly a great man, though not as great as they think. Having considered everything, I find that we should retain the philosophy of Aristotle, St. Thomas, and that taught in your society: namely, that there are substantial forms and that the nature of body consists, not in extension, but in an action which is related to the extended, for I hold that there can be no body without effort. It follows from this that non corpus necessario determinatae extensionis esse sed ad eam habendam inclinari nisi superior potentia impediat. 9 If explained reasonably, this is in perfect agreement with the common philosophy, and the mystery of the Eucharist can be supported by it admirably. Those who believe that there is no difference between body and extension cannot defend this doctrine, though they say that the same body can be in many places. I am having my arithmetical machine worked on. It is entirely different from
HANOVER TO THE ITALIAN JOURNEY, 1676-87 275 Pascal's and from the sticks of Napier.... At present I am very busy, working out something that will succeed in drawing the water from our mines in the Harz..... IV. TO VEIT LUDWIG VON SECKENDORplO [PA., II, i, 533] June 1/11, 1683 Since you mention Blaise Pascal and Peter Daniel Huet l1 , whose writings in defense of religion deserve praise, I shalI telI you some things which I have learned about them. I have often spoken with Huet and saw his work when it existed only in manuscript; I have since received letters from him here in Germany. Pascal had recently died when I lived in Paris, but his sister was there, a learned and clever woman, and also his nephews, the sons of his sister,l2 I had many associations with them, as welI as with the illustrious Duke de Roanez, who had been a close associate of Pascal's and had been much influenced by these studies. From them I received some of Pascal's unpublished works to read, though they were mostly mathematical. I also learned some things about his life and the brilliant plans which he pursued for the propagation of piety; these I shall be able to relate more fully elsewhere. I will say one thing. Pascal paid attention only to moral arguments, such as he excellently presented in his little posthumous book of Thoughts, but he did not put much value on the metaphysical arguments which Plato and St. Thomas, and other philosophers and theologians, have used in proving the divine existence and the immortality of the soul. In this I do not agree with him. I think that God speaks to us, not merely in sacred and civil history, or even in natural history, but also internally, within our mind, through truths which abstract from matter and are eternal. Even if I should confess that these arguments have not been carried to the full force of a complete demonstration, they already seem to have as much force as the moral arguments; and I believe that men will gradually perfect them and that sometime, perhaps, they can be reduced to a rigorous demonstration. So I think we should disdain nothing which can be of use to us, even if alI things are not useful to alI men, and that each one should use those things rightly which best fit his own purpose. I do not think that Huet followed Pascal's Thoughts but that he anticipated their publication a long time in preparing his own work. His preface, if I am not mistaken, hints at nothing else, and since the whole basis of his work is his proof that the prophecies have been fulfilIed in Jesus Christ - arguments which the apostles themselves had already used but which he enriched with great learning and his many brilliant observations - I do not see how he can well be said to have followed Pascal. V. TO WALTER VON TSCHIRNHAUS [PA., II, i, 541-42] November (?), 1684 ... In Holland they are now disputing, loudly and soundly, whether beasts are machines. People are even amusing themselves by ridiculing the Cartesians for imagining that a dog that is clubbed cries in the same way as a bagpipe which is pressed. As for me, though I grant the Cartesians that all external actions of beasts can be explained mechanically, I nevertheless believe that beasts have some knowledge and that there For references see p. 276
276 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS is something in them, not itself extended, which can be called a soul, or jf you prefer, a substantial form .... ... I am astonished that Mr. Arnauld and Mr. Malebranche, who were such good friends when I was in Paris, are now attacking each other in their writings. 13 I have not yet read the books they have directed against each other, but so far as I can judge by their other works, Father Malebranche has much spirit but Mr. Arnauld writes with more judgment. There are many nice thoughts in the Recherche de la verite, but the author is far from having penetrated very deeply into analysis and the art of discovery in general. I could not help laughing when I saw that he thinks that algebra is the first and most sublime science and that truth is nothing but a relation of equality and inequality; that arithmetic and algebra are the only sciences which give the mind all the perfection and extension of which it is capable; and finally, that arithmetic and algebra together are the true logic. Yet I do not see that he himself has a great knowledge of algebra. The praise he bestows upon it should be given to symbolics in general, of which algebra is only a very particular and limited example. REFERENCES Philipp was the agent of the elector of Saxony in Hamburg and became librarian in Dresden in 1682. His interest in Descartes evoked Leibniz's criticism. 2 For the specific references in Descartes's Principles see the following letter. 3 Leibniz had written a paraphrase of the Phaedo in Paris and frequently cited and quoted this particular passage (Phaedo, 97-99) afterward. Cf. Discourse, Sec. 20, etc. (No. 35). 4 On Jung see p.130, note 4, and p. 227, note 5. 5 A criticism of Descartes's voluntarism follows. The whole letter is translated in The Philosophical Works of Leibnitz (trans. G. M. Duncan), New Haven, Conn., 1908. 6 La Chaise, the probable addressee of this letter, was the Jesuit father-confessor of Louis XIV. Leibniz was neglecting no approach to princes or pope for the theological approval he sought. His diplomatic flattery of Jesuit theology at the very time he was seeking Arnauld's support reveals the courtier at his most expedient. 7 The context indicates that this is not the new geometry of location (No. 27) but the algebraic analysis of transcendental functions after the pattern of Descartes's geometry. In spite of his recent emphasis on force (cf. p. 271, note 10), Leibniz here seems to be thinking of the analysis of motion only. 8 The test of Descartes's theory and laws of motion is developed in Nos. 34,42, and 46. 9 "A body is not necessarily of determinate extension but is inclined toward having one unless a stronger force impedes it." See the concluding paragraphs of No. 30. 10 Privy counsellor of Brandenburg and chancellor of the university at Halle; a distinguished scholar and statesman. 11 Together with Bossuet, Peter Daniel Huet was responsible for the education of the Dauphin and edited the celebrated classics In usum Delphini, for which Leibniz had worked on an edition of Martianus Capella while in Paris. The work here referred to is Huet's Demonstratio evangelica ad serenissimum Delphinum, Paris 1679. He was made bishop of Avranches after 1692. He had mediated the correspondence between Leibniz and Bossuet when it began in 1679. 12 Pascal died in 1662. The sister referred to was Gilberte, Mme Perier, who had cared for him until his death. 13 This controversy had begun with Arnauld's Des vraies et des fausses idees (1683); by the time of this letter Malebranche had published a Reponse (1684) and Arnauld a Defense (1684). Leibniz's notes on the controversy may be found in A. Robinet, Malebranche et Leibniz (Paris, 1955). 1
32 ON THE ELEMENTS OF NATURAL SCIENCE* Ca. 1682-84 Over 50 years ago Ernst Gerland published what was obviously a preliminary plan made by Leibniz in his early years at Hanover for a small work entitled the Elementa physicae (Ger., pp. 110-13). In a note Gerland expressed regret that Leibniz did not pursue this project, which promised so much. He seems not have observed that the folder of ten folio sheets of manuscript at Hanover among which he found the plan contained an extensive draft of a proposed popular introduction to the work, which was obviously intended for the two projects toward which he worked for so long - the encyclopedia and the Catholic Demonstrations. 1 We here offer translations of the prospectus published by Gerland (I) and of the Introduction (II), which is concerned with the human values of science and an account of the method of analysis and synthesis as it is used in the investigation of corporeal phenomena. As such it may well be regarded, not merely as one of the earliest attempts to give a popular introduction to science, but as a realistic companion piece to Nos. 25 and 33, with an objective reference to things and their attributes rather than to ideas. Leibniz's account of the significance ofphysical science is still timely. The influence ofFrancis Bacon, and particularly of Robert Boyle, is obvious. Both parts are here translated from the manuscript in Hanover; the Introduction has not yet been published in the original Latin. I. THE PLAN OF THE BOOK [Bod. LH., XXXVII, iv, 9-10] A small book is to be written on the Elements of Natural Science. To it may be added a description of phosphorus [pyropum], i.e., ofthe noctiluca which is a fire which does not consume and at the same time needs no fuel. 2 Our natural science will deal not with observations or a description 3 of nature but with principles [rationes] or with qualities and with what follows from the principles necessarily or with certainty per se (that is, if nothing impedes them). For only later will it be necessary to apply these reasonings to observations. The first part will therefore deal with qualities, but the second will deal with the subjects of qualities or with bodies which exist in the world, where description is combined with reasoning. Thus we shall deal with body and with its qualities, both the intelligible ones which we conceive distinctly and the sensible ones which we perceive confusedly.4 A body is extended, mobile, and resistant; that is, it is that which can act and suffer insofar as it is extended - acting when it is in motion, suffering when it resists motion. There are thus to be considered, first, extension; next, motion; and, third, resistance or impact. Extended is what has size and situation [situs]. Size is the mode by which all the parts of a thing, or all the entities by means of which the thing can be understood, are For references see p. 289
278 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS determined. Situation is the mode of determining with which qualities a thing can be perceived. The size of a thing is known exactly when the number of its parts is known which are congruent with some given measure. We must therefore deal with numbers, both with those that are definite or defined and which belong to arithmetic and those which are indefinite, belonging to algebra. Here we shall deal with equality and ratio. For those things are equal which can be made congruent, and ratio is to equality as number is to unity. The situation of parts among themselves is called figure. From this can be derived similars, which can be distinguished only if they are perceived together. Homogeneous things, however, are those which can be reduced to similars. All things that are similar and equal are congruent. 5 Before dealing with figure, we must deal with space itself and with the point; with the sphere and the intersection of two spheres or the circle; with the plane and the intersection of two planes or the straight line; with the intersection of three spheres or the point. From this it is clear why the position of a point is given if its distance from three other points and a plane besides is given, since three spheres can intersect in two points. Thus we shall also find the nature of a straight line and why two straight lines cannot have only two points in common. Thus a demonstration of the Elements [0/ Geometry] wiII now be easy. And so far this wiII involve a consideration of figures without any recourse to motion. 6 There follows then motion or change of situation; here the method of generating the circle and the straight line. Here we shall explicate the tomatorial science, or the science of the traces of motions. 7 On the method of getting a straight line, a plane, a sphere, a cone, the conic sections and their delineations on a plane; on still more complex figures; on the varied composition of motions. On impact or on motion and resistance combined. Here we deal with various machines, wheels, and vessels. 8 It is then to be demonstrated that space is indefinitely extended, for there can be no reason why it should end anywhere, because whatever can be concluded about any particular thing can likewise be concluded about anything similar to it. So one can conclude about a greater circle only what has already been concluded about a smaller. It is therefore impossible to designate any sphere beyond which no space exists. For if there were any reason for such a sphere, the same reason would be correspondingly valid for all other spheres. God, however, does nothing without reason. It is to be demonstrated also that every body is actually divided into smaller parts, or that there are no atoms, and that no actual continuum can be pointed out in any body. From the nature of this division arise fluidity and firmness. Empty space can in no way be distinguished from the perfectly fluid. There is no perfectly fluid body. There is no vacuum. In introducing his subtle matter, Descartes has done away with the vacuum in name only. There follows now a discussion of incorporeal matters. Certain things take place in a body which cannot be explained from the necessity of matter alone. Such are the laws of motion, which depend upon the metaphysical principle of the equality of cause and effect. Therefore we must deal here with the soul and show that all things are animated. Without soul or form of some kind, body would have no being, because no part of it can be designated which does not in tum consist of more parts. Thus
HANOVER TO THE ITALIAN JOURNEY, 1676-87 279 nothing could be designated in a body which could be called 'this thing', or a unity. On the nature of soul or form; that there is a kind of perception and appetite which are the passions and actions of the soul. And why; because souls result from God's knowledge of things, or they are imitations of the ideas. All souls are indestructible, but those especially are immortal which are citizens in the commonwealth of the universe, or those to whom God is not merely author but also king, for to them he is connected by an entirely special basis, and they are therefore called minds. These minds never forget themselves. They alone think of God and have distinct conceptions of things. It is improper to try to ascribe perception to man alone. Since all bodies are able to have some perception according to the measure of their perfection, they 'will have it, for whatever can happen without detriment to other things will in fact happen, because everything occurs in the most perfect way. Here too can be explained the nature of joy and grief, which is merely the perception of one's own success or perfection. Thus when a striving [conatus] is satisfied, the result is success; when it meets resistance, there arises grief. There are as many mirrors of the universe as there are minds, for every mind perceives the whole universe, but confusedly. Next we must deal with force or power. Here it must be recognized that it is to be estimated from the quantity of its effect. But the power of the effect and of the cause are equal to each other, for if the effect were greater, we should have mechanical perpetual motion, while if it were less, we should not have continuous [perpetuus] physical motion. It is worth showing here that the same quantity of motion cannot be conserved but that the same quantity of power is. Yet we must see whether there will not also be conserved in the universe the same quantity of motion also. 9 On perturbations and restitutions; on the vibratory motions arising from these. On the isochronism of free and of all kinds of vibrations. That the times are thus proportional to the forces. In every machine or composite structure the power tends at a constant ratio toward restitution. On weight or the solidity of a body and on the center of gravity. It is shown that there is a center of gravity in every body. On elastic force. On magnetic force. On impacts and reflections. On degrees of firmness; on fluid, rigid, flexible, tenacious bodies. On the motion of a solid in a fluid. On refraction in the transition from one fluid to another. All things seem in fact to be fluid but merely variously folded into each other without a break in the continuity. On what follows from certain definite laws of reflection and refraction. iO On tense bodies and their pulsations and vibrations. On a fluid within a fluid; a fluid within a solid which it cannot escape; a fluid outside a solid which it cannot enter; a permeating fluid. On an elastic fluid and the propagation of vibrations in it; and on bodies emitting the same tones. We must treat of meteors, crystals, and other bodily configurations. ii It will be best to postpone the details of definition and demonstration a little and to explain everything continuously and in clear language. So we will proceed as follows: Since our happiness consists in the perfection of the mind, but our mind is in this life affected in various ways by its body, and the human body is brought to enjoy and to suffer by other environing bodies, it follows that to know the nature of bodies For references see p. 289
280 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS should be considered a large part of wisdom, to the end that we may avoid their harmful, but experience their friendly, force .... II. AN INTRODUCTION ON THE VALUE AND METHOD OF NATURAL SCIENCE [LHS, XXXVII, iv, 1-6] On the utility of natural science Every science is to be sought after, not for the the sake of curiosity or ostentation, but for the sake of action. However, we act to attain happiness or a state of enduring joy, and joy is the sense of perfection. Every thing is to be held as more perfect to the degree that it is freer by nature; that is, to the degree that its power is greater over the things that surround it, and its suffering from external things is less. Hence, since the power proper to the mind is understanding, it follows that we will be the happier the clearer our comprehension of things and the more we act in accordance with our proper nature, namely, reason. Only to the extent that our reasonings are right are we free, and exempt from the passions which are impressed upon us by surrounding bodies. Yet it is impossible to evade these passions entirely, since the mind is affected in various ways by its body, while our body, which is but a small part of the universe can be helped and harmed by the bodies which surround it. The knowledge of bodies is therefore most important on two grounds - first, to perfect our mind through an understanding of the purposes and causes of things; second, to conserve and nurture our body, which is the organ of the soul, by furthering what is wholesome for it and reducing what is harmful. The greatest usefulness of theoretical natural science, which deals with the causes and purposes of things, isfor the perfection of the mind and the worship of God Of these two applications of this science, the former can be sought only in theoretical physics, the latter in empirical physics as well. For if a person should by accident or tradition secure a very important and useful secret of nature, such as the tincture of metals now being praised by so many authors, but did not understand its causes, he might be externally richer for it but not happier or wiser unless he used it to attain freedom of mind. But if someone were to discover some admirable device of nature and to learn its mode of operation, he would have achieved something great even if no application of his discovelY to common life could be shown. For though all science increases our power over external things provided a proper occasion arises for using it, there is nonetheless another use which depends on no such occasion, namely, the perfection of the mind itself. By understanding the laws or the mechanisms of divine invention, we shall perfect ourselves far more than by merely following the constructions invented by men. For what greater master can we find than God, the author of the universe? And what more beautiful hymn can we sing to him than one in which the witness of things themselves expresses his praise? 12 But the more one can give reasons for his love, the more one loves God. To find joy in the perfection of another - this is the essence of love. Thus the highest function of our mind is the knowledge or what is here the same thing, the love of the most perfect being, and it is from this that the maximum or the most enduring joy, that is, felicity, must arise. Nor should we think that anything is badly arranged in the universe or that God neglects those who honor
HANOVER TO THE ITALIAN JOURNEY, 1676-87 281 him. But the proper place to show this more fully is in another science. It must be mentioned, however, lest, as sometimes happens, the most important application of theoretical physics be neglected. Empirical physics is useful for human life and should be cultivated in the state The other use, which applies to our common life, is shared by theoretical and empirical physical science. For if we have a so-called specific remedy for an illness but are ignorant of its mode of action, we may nonetheless be cured by it. Most of the things however, which are required for the effective conduct of life men have derived from experience; such are the use of fire and water; the separation of metals from their ores through melting, so that they can be shaped when hot but become firm when cold; the power of the earth to put forth plants from seeds; the hunting, taming, and breeding of animals; the difference between poisonous and wholesome foods; clothing and shelter; and finally, men's communication with each other, without which this life would be wretched and bestial. Thus human societies have come into being and duties have been distributed, some administering public affairs, others using certain specific skills through which the common need is alleviated through the collection, preparation, and distribution of material things. Thus physical science has always been regarded most highly in the state, and those who taught men how to sow and to plant vines were in antiquity superstitiously placed among the gods. Today the wisest princes offer rewards to discoverers and inventors, and deservedly so, for sometimes one small observation will cause whole cities and provinces to flourish. As an example may be given the cultivation of silk, introduced a few centuries ago into Italy and more recently in France, yet from which so many thousands of men live. The first man to cook alum in Europe should also be mentioned, this skill having been brought in from Rocca in Syria; and whoever first showed that herring could be preserved with salt, a most profitable discovery for the Belgians. Surely there is scarcely any handicraft which does not rest upon some particular observation of nature. I believe too that many things are known to some people, for which, if others knew them, an application could at once be found to a variety of crafts. A catalogue ofexperiments is to be compiled Thus it is a concern of the state to publish the observations with which only a few are concerned and which very often seem to the scientists themselves to be of no use, by setting up a history of nature in which experiments will be brought together in a catalogue. One who deals with only a limited field rarely discovers anything new, since he soon exhausts his subject. But from those who investigate many different things and are gifted with a combinatorial genius we may expect many new and useful interconnections of things. If men would now undertake such an inventory of experiments, a fertile field would be prepared for new discoveries in all sciences and technologies. Men endowed with judgment and industry should thus be appointed to select, verify, order, and classify by means of various indices those experiments which are already known to mankind, whether put down in writing or merely preserved in some tradition. It seems that the emperors of Constantinople long ago undertook something of this kind in all fields of science, but though we have some collected facts and excerpts coming from their times, they are not adequate for the purpose of learning. For references see p. 289
282 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS New experiments are to be undertaken at public expense, and only men outstanding not merely in science but in virtue are to be placed in charge Yet many experiments of great importance are still quite dubious and full of errors. Also, men of genius could propose many that are still to be undertaken. It follows that laboratories must be set up at various places by public authority, along with depositories for machines and collections of exotic materials [exoticophylaciis]1\ in which the varied wonders of nature and of art can be both observed and tested. Here everyone will be free to make trial of his genius at public expense, provided only that he has secured from just judges an approval of his plan. To these are to be added zoOlogical gardens and hospitals. From physicians, hunters, workmen, and foreigners who have an opportunity to learn many things, faithful accounts must be demanded. Rewards must be set up for industrious achievement. But the main thing, the observance of which assures that great things will be achieved with small outlay, but whose neglect will make even the greatest expenditures futile, is this: men must be chosen and placed at the head of this business who not only are outstanding in ability, judgment, and learning but also are endowed with a unique goodness of mind; in whom rivalry and jealousy are wanting; who will not use despicable devices to appropriate for themselves the labors of others; who are not factious and have no wish to be regarded as the founders of sects; who labor for love of learning itself and not for ambition or sordid pay. Such men will certainly become friends and will push forward the laudable undertakings of others, thus deserving much from mankind. The great Mersenne was a man of this kind long ago, and I should prefer that these men today should fall behind him a little in science rather than in probity.14 With the experiments are to be combined accurate and thoroughly extended reasonings after the manner ofgeometry, for only in this way can causes be discovered. Yet the most outstanding experiments are in vain if men who will use them are lacking. The utility of experiments is of two kinds: one for the varied conveniences of life, which are revealed by reasoning from cause to effect; the other to bring to light true principles, by proceeding from effect to causes. Each way of reasoning may be either combinatorial or analytic. The former method, namely, the combinatorial, consists of a kind of simple reflection, and, when one has it pointed out to him by a single word, he understands it at once and wonders why the same thing had not occurred to him. Such a case is the invention of the mortar after gunpowder was already known or the invention of the chronometer after the equality of pendulum vibrations was known. The latter method is connected in a longer chain of reasons and involves a kind of geometry or calculus and cannot be understood without much thought. Such is the discovery of the curve which controls the unequal vibrations of pendulums. The former mode, as I have already said, will be ready for men of ability when once we have an inventory of experiments, because a multitude of applications to various uses and works of craftmanship will occur to those who study this inventory. But the discovery of causes, without which we cannot hope for great advances in the most urgent field of physical science, namely medicine, can be obtained not through such quick flights by glowing geniuses but only through profound and almost geometrical reasonings. For our body is a hydraulic-pneumatic machine and contains fluids which act not only by weight and in other ways manifest to the senses but also in certain
HANOVER TO THE ITALIAN JOURNEY, 1676-87 283 hidden ways, namely through solution, precipitation, evaporation, congealment, filtration, and in many other processes in which composite things are dissolved into insensible parts. Unless principles are advanced from geometry and mechanics which can be applied with equal ease to sensible and insensible things alike, nature in its subtlety wiII escape us. And reason must supply this most important lack in experiment. For a corpuscle hundreds of thousands times smaller than any bit of dust which flies through the air, together with other corpuscles of the same subtlety, can be dealt with by reason as easily as can a ball by the hand of a player. 1s The most perfect method involves the discovery of the interior constitution of bodies a priori from a contemplation of God, the author of things. But this method is a difficUlt one and not to be undertaken by anyone whatever Just as there is a twofold way of reasoning from experiments, one leading to the application, the other to the cause, so there is also a twofold way of discovering causes, the one a priori, the other a posteriori, and each of these may be either certain or conjectural. The a priori method is certain if we can demonstrate from the known nature of God that structure of the world which is in agreement with the divine reasons and from this structure, can finally arrive at the principles of sensible things. This method is of all the most excellent and hence does not seem to be entirely impossible. For our mind is endowed with the concept of perfection, and we know that God works in the most perfect way. I admit, however, that, though this way is not hopeless, it is certainly difficult and that not everyone should undertake it. Besides, it is perhaps too long to be covered by men. For sensible effects are too greatly compounded to be readily reduced to their first causes. Yet superior geniuses should enter upon this way, even without the hope of arriving at particulars by means of it, in order that we may have true concepts of the universe, the greatness of God, and the nature of the soul, through which the mind can be most perfected, for this is the most important end of contemplation. Yet we believe that the absolute use of this method is conserved for a better life. 16 Some hypotheses can satisfy so many phenomena, and so easily, that they can be taken for certain. Among other hypotheses, those are to be chosen which are the simpler; these are to be presented, in the interim, in place of the true causes The conjectural method a priori proceeds by hypotheses, assuming certain causes, perhaps, without proof, and showing that the things which now happen would follow from these assumptions. A hypothesis of this kind is like the key to a cryptograph, and the simpler it is, and the greater the number of events that can be explained by it, the the more probable it is. But just as it is possible to write a letter intentionally so that it can be understood by means of several different keys, of which only one is the true one, so the same effect can have several causes. Hence no firm demonstration can be made from the success of hypotheses. Yet I shall not deny that the number ofphenomena which are happily explained by a given hypothesis may be so great that it must be taken as morally certain. Indeed, hypotheses of these kind are sufficient for everyday use. Yet it is also useful to apply less perfect hypotheses as substitutes for truth until a better one occurs, that is, one which explains the same phenomena more happily or more phenomena with equal felicity. There is no danger in this if we carefully distinguish the certain from the probable. To offer such hypotheses which one knows to be fictitious, may not be useful to knowledge, yet may meanwhile serve the memory. Such are the For references see p. 289
284 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS fictitious etymologies by which Hebrew roots are derived from German words so that they can be more easily retained by German schoolboys. Phenomena are virtually contained in the hypothesis from which they can be deduced, so that anyone who remembers the hypothesis will more easily recall these phenomena when he wishes, even if he knows that the hypothesis is false and that certain other phenomena are known with which it conflicts. Thus the Ptolemaic hypothesis may suffice for the beginner in astronomy who is content with certain popular notions of heavenly bodies. In my opinion, however, it is better to teach the true conception when we have it. Analogies are useful in guessing at causes and in making predictions The hypothetical method a posteriori, which proceeds from experiments, rests for the most part upon analogies. For instance, seeing that many terrestrial phenomena agree with magnetic phenomena, some men teach that the earth is a great magnet, that the structure of the earth corresponds to this, and that heavy bodies are drawn to earth as a magnet draws iron. Others explain everything by fermentation, even the ebb and flow of the tides. Still others, seeing that lye fights against acids, reduce all corporeal conflicts to those of acid and alkali. We must guard against the abuse of analogies. Yet they can be of exceedingly great use in making inductions and in setting up aphorisms from inductions by means of which we can also make predictions about matters of which we as yet have little experience. This too is useful in investigating the true causes of things, for it is always easier to discover the cause of a phenomenon which several things have in common. So it is also easier to solve cryptographs when we have found a number of letters in the concealed meaning which are written according to the same key. Then too, the cause of the same phenomenon can be investigated more easily in one subject than in another, as anatomists who dissect different animals well know. The method of reasoning from experiments resolves the phenomenon into its attributes and seeks the causes and effects ofeach attribute There remains the certain method of reasoning from experiments to causes, which I hold needs to be cultivated more widely and with greater care than heretofore. Many men are content with analogies because they stimulate the imagination, even though they do not satisfy the mind. But the true method of reasoning from experiments is this - we must resolve every phenomenon into all its circumstances by considering separately color, odor, taste, heat, and cold, and other tactile qualities, and finally, the common attributes of magnitude, figure, and motion. Now if we have discovered the cause of each of these attributes in itself we will certainly have the cause of the whole phenomenon. But if by chance we do not come upon the reciprocal and permanent cause of certain attributes, but only several possible causes, we can exclude those which are not pertinent here,17 For example, assume two attributes, A and L, of the same phenomenon and assume that there are two possible causes of A, namely, band c, and two of L, namely, m and n. Now, if we establish that cause b cannot exist along with either m or n, it follows necessarily that the cause of A is c. If we can further establish that m cannot exist along with c, then the cause of L must be n. But if it is not in our power to achieve a complete enumeration of possible causes, this method of exclusion will at most be probable. If the effects rather than the causes of a pheno-
HANOVER TO THE ITALIAN JOURNEY, 1676-87 285 menon are sought, the method is the same; the effects of the separate attributes will have to be examined. Composite attributes are to be resolved into simple, and those which are simple with respect to the senses but not with respect to intellectual principles are to be reduced to their immediate cause Of the attributes which are presented to the senses, some are simple, others are compounded of simple ones. Simple attributes include heat, firmness, duration; composites are such as fusibility, which consists of a body ceasing to be firm when heated. Thus composite attributes are to be resolved into simple ones. Simple attributes, again, are simple by their own nature and for intellectual reasons, or they are simple with respect to our senses. As an example of an attribute simple in nature can be offered 'to be itself' or 'to endure'. An attribute simple with respect to the senses, on the other hand, would be heat, for the senses do not show us by what mechanism the state of a body is produced which brings about the sensation of warmth in us, yet the mind properly perceives that warmth is not something absolute which is understood in itself but that it will only then be adequately understood when we explain of what it consists or distinctly describe its proximate cause - perhaps the expansion of air, or rather some particular motion of a fluid which is thinner than air. Con/used attributes are sufficiently distinguished only by being shown It follows clearly from this, moreover, that attributes which are sensible can be divided into confused and distinct by intellectual principles. Confused attributes are those which are indeed composite in themselves or by intellectual principles but are simple to the senses and whose definition therefore cannot be explained. These attributes can be imparted not by description but only by pointing them out to the senses. Imagine a land where men do not know the sun and fire and have blood which is cold, not warm; surely they cannot be made to understand what heat is merely by describing it, for even if someone were to explain to them the innermost secrets of nature and even interpret perfectly the cause of heat, they would still not recognize heat from this description if it were presented to them, for they could not know that this peculiar sensation which they perceived in their minds is excited by this particular motion, since we cannot notice distinctly what arises in our mind and what in our organs. But if someone kindles a fire near them, they would at length learn what heat is. Similarly a man born blind could learn the whole of optics yet not acquire any idea of light. Distinct attributes are those whose resolution is known, if they have one Distinct attributes are either simple to the intellect itself or understood in themselves, as 'to be', 'to endure'; or they can be explained through a definition, that is, they can be recognized by us through certain signs, as for example, roundness or the equidistance of all points from one, and gravity or a striving toward the center of the earth. The former are conceived distinctly enough without resolution, for they are incapable of resolution; the latter should be resolved into those concepts through which they may be understood and distinguished. Although certain attributes can be resolved only into others that are confused, for example fusibility, in whose definition heat is, as we have said, an ingredient, they can nevertheless be held for distinct to the For references see p. 289
286 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS extent that they are resolved. Those attributes are more distinct, however, which are resolved into others which are distinct; for example, the figure of a circle or rectilinear motion. Attributes common to several senses are distinct above the rest, and among the distinct attributes the homogeneous ones are the more simple 18 It must be noted, however, that attributes common to several senses are to be regarded as distinct in comparison with others, for they are resolvable not into confused ones and then again into those dependent upon the senses, but into concepts attained by the intellect. Such attributes are magnitude, position, duration, and motion. We need not wonder at this, for since they are common to several senses, they do not depend upon the particular constitution of a sense organ or upon its insensible movements, the subtlety and number of which lead to our confused perception. They depend rather upon a nature common to diverse organs, that is, the nature of the body itself, and so they are freed from the confusion of particular perceptions. It is also to be noted that among the distinct attributes those are the simpler which apply equally to the whole and to the part and which are by some called similars. Thus extension is simpler than figure, for what can be ascribed to the whole but not to the parts belongs to the whole because the whole consists of these parts. Such an attribute can therefore be explained from a consideration of the parts. So such attributes can be revolved into the attributes of the parts out of which they arise; this cannot be said of attributes that are homogeneous. But by these I mean only distinct homogeneous attributes such as extension, since confused homogeneous attributes, such as whiteness, can indeed be ascribed to the whole as well as the parts, but only to the sensible parts. For it cannot safely be said that each part of a white body, however insensible, is also white; it is rather truer to assert the contrary, since we see that though foam is white, the single bubbles of foam are not white. In general, the simpler and the more homogeneous attributes are to be preferred in our thinking In the same way, homogeneous bodies (even if only to the senses), such as fluids, salts, and metals, are to be considered as simpler than organisms like plants and animals, which are composed of various parts each of which is preferred above others in our consideration, even if all are confused. Moreover, those ways of treating and examining bodies are more useful and to be preferred in our consideration which happen 'by themselves', as the chemists commonly say, that is, without the addition of anything other than the common elements of matter, fire, air, water, and earth, and these only in the highest degree of purity, without being tainted by any particular quality. And in general, if any phenomenon arises equally in simple and composite things, or if any effect can be produced from simple or composite things alike, the simple is to be preferred by which matters are altered. Thus experiments carried out with the aid of heat from the sun's rays are simpler than those carried out with fire from our cooking stoves, which gives forth an acid which affects the result. There is a way of resolving confused attributes experimentally into other attributes which is frUitful practically as well as in theory but which does not make them cease being confused
HANOVER TO THE ITALIAN JOURNEY, 1676-87 287 To investigate the causes of confused attributes, however, and to obtain their resolution or an analysis of them, we must relate them to other attributes as well as to the subjects which contain them. Subjects themselves can be known only through attributes. So the bringing-together of an attribute with a subject is nothing more than the bringing-together of the attribute with an aggregate of others which concur in the same subject. Thus a confused attribute can be related either to other confused attributes or to distinct attributes. The relating of an attribute to others, however, consists in making apparent their concurrence in the same subject, their connection with each other, their compatibility, and on the other hand, how one can be changed into another or can be produced out of several others. Thus there sometimes occurs another kind of resolution of confused attributes, which I call experimental to distinguish it from intellectual resolution. For example, the color green arises from a mixture of blue and yellow, no change taking place in the colored object but only in the eye. Furthermore, the separate ingredients can sometimes be distinguished with a microscope, each with its own color, yellow or blue. We cannot yet say with any certainty, however, that blue and yellow are prior to or simpler in nature than green, for we do not understand, but merely experience, that green arises out of yellow and blue. Therefore, neither could we have foreseen it. On the other hand, we understand though we may not experience that a square is made by two right isosceles triangles joined by a common hypotenuse and lying in the same plane or that from two odd numbers there arises an even number. For in intellectual resolution or in definition, one understands that which is described when the ingredients of the description are understood. But this is not the case in a resolution made by sense alone, and what is resolved in this way does not cease being confused. We do not grasp how the third color is given us through the confused appearance of these two colors. When we consider the subject of any confused attribute, for example, of light, its cause or the way in which it is produced or increased, or its contrary or the way it is destroyed or diminished, and finally, its effects, we do this by bringing it together with an aggregate of many other confused or distinct attributes taken together. But distinct attributes are to be preferred to the rest, namely duration, magnitude, motion, figure, angle, and other circumstances, for we can reason only to the extent that we consider distinct attributes. The application of mathematics to physical science consists in such consideration of the distinct attributes which accompany confused ones. Once we have learned that the angles of incidence and reflection of a ray of light are equal and that these angles are taken with respect to the perpendicular striking a plane tangent to the surface at the point of incidence, then we can easily establish the science of catoptrics. Similarly few experiments about refraction are needed to set up the foundations of dioptrics. Since everything confused is by its nature resolvable into the distinct, even though it may not always be in our power to do this, it follows that all qualities and mutations of bodies can, according to their nature, at length be reduced to certain distinct concepts. But in a body viewed as matter only, or as that which fills space, nothing can be conceived distinctly beyond magnitude and figure which are themselves contained intelligibly in space, and motion which is a variation of space. Thus material things can be explained through magnitude, figure, and motion. I know that some learned men disagree with this and consider qualities such as heat, light, elastic force, gravity, and magnetic force, as certain absolute entities emanating from substantial forms. Nor do For references see p. 289
288 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS I completely reject their opinion, for very often it is not necessary to seek a resolution of such qualities. Thus a mechanic does not care whether a body is heavy because of an intrinsic principle or because it is impelled to the earth from without. Hence the mechanic may be permitted to take gravity, and the optician light, as something absolute to be grasped in itself. But the truth of the matter is that one must give the reason for such qualities and explain how they arise in a body. Imagine that some angel wished to explain to us how bodies are made heavy; he could achieve nothing by speaking, however beautifully, about a substantial form, or sympathy, or other things of this kind. Rather he would only then satisfy our curious understanding when he gave us an explanation, sufficiently understood, which, when we have comprehended it, will enable us to demonstrate with geometric certainty that gravity must necessarily arise from it. This angel must therefore necessarily present only such things as we can perceive distinctly. But we perceive nothing distinctly in matter save magnitude, figure, and motion. If someone wishes in addition to ascribe to bodies a substantial form or a soul, and likewise sense and appetite, I do not contradict him, but I maintain that this contributes nothing toward explaining purely material phenomena and that it is not sufficient to say that a heavy body senses and desires the earth unless we explain at the same time how this sense and this desire arise. In this way we should finally have to come to the construction of the organs of the sensing being, that is, to the mechanical principles. For what happens with perception happens nonetheless mechanically, and to the passions of the soul there correspond bodily motions in the organs which always follow mechanical laws. I know too that there are excellent and most learned men who cannot abide having all bodily phenomena explained mechanically. For they think that this injures religion, and they believe that if it were accepted, the world mechanism would need neither God nor any other incorporeal substance. This they rightly regard as absurd and dangerous. Hence some of them make use of an immediate intervention of God everywhere, while others introduce intelligences or angels as moving forces here and there. Some set up a kind of a world soul or a hylarchic principle, through whose operations heavy bodies are made to strive toward the earth and other things happen which are needed to conserve the world system. But all these things are insufficient to explain thing~, for whether we introduce God or an angel or a soul or whatever other incorporeal operative substance, the cause and the mode of operating can always be explained in the truth which we have about the things themselves. But the way in which a body operates cannot be explained distinctly unless we explain what its parts contribute. This cannot be understood, however, unless we understand their relation to each other and to the whole in a mechanical sense, that is, their figure and position, the change of this position or motion, their magnitude, their pores, and other things of this mechanical kind, for these always vary the operation. I admit that these outstanding men have had unimpeachable grounds for shrinking back from the philosophy of certain recent thinkers, because many philosophers today resort to efficient and material causes only, completely neglecting formal and final causes. But those who are wise know that every effect has a final as well as an efficient cause - final because everything that happens is done by a perceiving being, efficient because everything that happens naturally in a body takes place through the corporeal organ and according to the laws of bodies. If those who oppose mechanical laws had known that these laws themselves are finally resolved into metaphysical reasons and that these metaphysical
HANOVER TO THE ITALIAN JOURNEY, 1676-87 289 reasons arise from the divine will or wisdom, they would not have so strongly opposed mechanistic explanations. In fact, I have contended that the reasons for physical motion cannot be found in mathematical rules alone but that metaphysical propositions must necessarily be added. This will be made clearer in its proper place. Here it will be well, however, to explain a little more distinctly how a middle way can be found, in my opinion, between the Scholastic and the mechanistic basis for philosophy; or better, in what sense there is truth on both sides. If this is understood, the internecine war will cease which has recently disturbed not only the schools and universities but from time to time also the church and the state. The mechanists condemn the Scholastics, namely, as ignorant of what is useful for living, while the Scholastics and the theologians who cultivate the Scholastic philosophy hate the mechanical philosophers as harmful to religion. 19 I must admit that both sides have exceeded proper bounds and that even the philosophers have uncautiously said things which cannot be proved. This is what I think. Everything is by nature to be understood clearly and distinctly and could be manifested to our understanding by God if he willed to do so. And the operation of a body cannot be understood adequately unless we know what its parts contribute; hence we cannot hope for the explanation of any corporeal phenomenon without taking up the arrangement of its parts. But from this it does not at all follow that nothing can be understood as true in bodies save what happens materially and mechanically, nor does it follow that only extension is to be found in matter. For even though the confused attributes of bodies can be referred back to distinct ones, we must recognize that there are two kinds of distinct attributes, one of which must be sought in mathematics, the other in metaphysics. Mathematical science provides magnitude, figure, situation, and their variations, but metaphysics provides existence, duration, action and passion, force of acting, and end of action, or the perception of the agent. Hence I believe that there is in every body a kind of sense and appetite, or a soul, and furthermore, that to ascribe a substantial form and perception, or a soul, to man alone is as ridiculous as to believe that everything has been made for man alone and that the earth is the center of the universe. But on the other hand, I think that when once we have demonstrated the general mechanical laws from the wisdom of God and the nature of the soul, then it is as improper to revert to the soul or to substantial forms everywhere in explaining the particular phenomena of nature as it is to refer everything to the absolute will of God. For the action of the soul is determined by the state of the organ of the soul and its object, and the operation of God by the conditions of the individual things, and this not by the necessity of matter but by the impulsion of the final cause or the good. REFERENCES * Elementa physicae. The connotation of the term 'physics' is much broader than at present and is often as inclusive as 'nature'. Bod. LH., XXVII, iv, 1-10. The Elementa physicae and the Elementa de mente had been companion projects of Leibniz since his pre-Paris years and were intended both for the Introduction to the Catholic Demonstrations (PA., VI, i, 494; see also No. 28) and for the universal encyclopedia (G., VII, 60, 65). 2 For an earlier account of phosphorus see Leibniz's instructions to Huygens in No. 27. Robert Boyle, inspired by hints about Brand's method, published accounts of his own experi- 1
290 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS ments with the new chemical in 1680 and 1682, using the designations The Aerial Noctiluca and The Icy Noctiluca. 3 Historia. See No.2, Sec. 32. In the definitions which summarize the present paper (sheets 7 and 8), Leibniz defines historiae as "singular truths of sense, like an account of a certain lunar eclipse". 4 Leibniz uses quality to include both sensory and nonsensory properties of bodies, as Boyle had done in The Origin of Forms and Qualities (cf. Nos. 1 and 70). Note that in Sec. II ofthe present paper, 'attribute' is used as an equivalent term. 5 Motion, size, and figure are the categories of explanation in Boyle's corpuscular philosophy. For their place in the geometry of situation see No. 27. 6 More details concerning this method of geometric definition through the intersection of loci are contained in No. 27, II, and No. 70. 7 For the tornatorial science see Couto OF., pp. 525-26, where it is included in phoronomy or the science of motion. S Reading with the manuscript vasis for pa/is (Ger.). 9 cr. No. 34, below, where Leibniz rejects the Cartesian principle of the conservation of quantity of motion, or momentum, about which he here expresses doubt and No. 46, II, where the conservation of total quantity of motion in a system is reaffirmed, on condition that directions of motion are treated algebraically. 10 See the Tentamen anagogicum, No. 50. U This is the end of Leibniz's plan. What follows on the same page differs in ink and script and was clearly added later. It is obviously the first draft of the opening sections in the Introduction which follows. 12 The figure treating science as a hymn of praise Leibniz probably owed to Boyle (cf. The Usefulness of Natural Philosophy [Birch, II, 52J). Cf. 'the hymn of Galen' (G., VII, 71, 273). 13 Cf. Couto OF., p. 224, in the list of contents oCa universal atlas. 14 In his first draft Leibniz had named as examples of the probity required of the scientist also Gassendi and Joachim Jung of Hamburg. His demand is all the more remarkable at a time when scientific jealousies were bitter and persistent. 15 Leibniz's nearest approach to the fulfilment of this remarkable prophesy is the principle of the conservation of total force and total direction of motion in a system of bodies (No. 46). 16 By 1686 Leibniz had concluded that an infinity of steps is involved in the a priori derivation of truths of fact and that this is therefore impossible for man. See also No. 29, above. 17 This is the method of establishing universal causal laws. Note that Leibniz distinguishes uncertainty in scientific conclusions which arises from the inadequacy of method (hypothesis and analogy) from uncertainty resulting from the impossibility of enumerating all the causal factors involved in a problem. Hence his frequent emphasis upon exhaustiveness in the enumeration of qualities. The experimental potency of the method of difference is here not yet apparent. 18 Leibniz here uses the term simi/aria, which is translated by his more general term homogeneous, basic for his mathematical and metaphysical analyses. The relation between similarity and homogeneity is alluded to in Part I of the present essay and treated more clearly in No. 70. 19 This frequently repeated attempt at the philosophical synthesis of mechanical and final causality (cf. No. 35, Secs. 19-23, No. 50, etc.) follows the argument of Boyle in The Origin of Forms and Qualities and elsewhere, save that Leibniz substitutes mechanical philosophy for corpuscular philosophy, Boyle's term for his own position.
33 MEDITATIONS ON KNOWLEDGE, TRUTH, AND IDEAS Acta eruditorum, November, 1684 Leibniz's first published paper on philosophical issues (in the mature period of his thought) is the result of his criticism of Descartes's incomplete conception of truth and was clearly occasioned by the appearance of Arnauld's attack on Malebranche's theory of knowledge in the Des vraies et des fausses idees, though Leibniz did not study the controversy in detail untillater.1 That he regarded this essay as definitive for his own conception ofknowledge is shown by his frequent reference to it in his later works. [G., IV, 422-26] Since distinguished men are today engaged in controversies about true and false ideas, a matter of great importance for understanding the truth and one to which even Descartes did not entirely do justice, I should like briefly to explain what I think may be established about the different kinds and the criteria of ideas and of knowledge. Knowledge is either obscure or clear; clear knowledge is either confused or distinct; distinct knowledge is either inadequate or adequate, and also either symbolic or intuitive. The most perfect knowledge is that which is both adequate and intuitive. A concept is obscure which does not suffice for recognizing the thing represented, as when I merely remember some flower or animal which I have once seen but not well enough to recognize it when it is placed before me and to distinguish it from similar ones; or when I consider some term which the Scholastics had defined poorly, such as Aristotle's entelechy, or cause as a common term for material, formal, efficient, and final cause, or other such terms of which we have no sure definition. A proposition also becomes obscure when it contains such a concept. Knowledge is clear, therefore, when it makes it possible for me to recognize the thing represented. Clear knowledge, in turn, is either confused or distinct. It is confused when I cannot enumerate one by one the marks which are sufficient to distinguish the thing from others, even though the thing may in truth have such marks and constituents into which its concept can be resolved. Thus we know colors, odors, flavors, and other particular objects of the senses clearly enough and discern them from each other but only by the simple evidence of the senses and not by marks that can be expressed. So we cannot explain to a blind man what red is, nor can we explain such a quality to others except by bringing them into the presence of the thing and making them see, smell, or taste it, or at least by reminding them of some similar perception they have had in the past. Yet it is certain that the concepts of these qualities are composite and can be resolved, for they certainly have their causes. Likewise we sometimes see painters and other artists correctly judge what has been done well or done badly; yet they are often unable to give a reason for their judgment but tell the inquirer that the work which displeases them lacks 'something, I know not what' . For references see p. 294
292 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS A distinct concept, however, is the kind of notion whichassayers have of gold; one, namely, which enables them to distinguish gold from all other bodies by sufficient marks and observations. We usually have such concepts about objects common to many senses 2, such as number, magnitude, and figure, and also about many affections of the mind such as hope and fear; in a word, about all concepts of which we have a nominal definition, which is nothing but the enumeration of sufficient marks. We may also have distinct knowledge of an indefinable concept, however, when this concept is primitive or is the mark of itself, that is, when it is irreducible and to be understood only through itself and therefore lacks requisite marks. But in composite concepts the single component marks are indeed sometimes known clearly but nevertheless confusedly, such as heaviness, color, aqua fortis, and others which are some of the marks of gold. Such knowledge of gold may therefore be distinct, but it is nonetheless inadequate. But when every ingredient that enters into a distinct concept is itself known distinctly, or when analysis is carried through to the end, knowledge is adequate. I am not sure that a perfect example of this can be given by man, but our concept of numbers approaches it closely. Yet for the most part, especially in a longer analysis, we do not intuit the entire nature of the subject matter at once but make use of signs instead of things, though we usually omit the explanation of these signs in any actually present thought for the sake of brevity, knowing or believing that we have the power to do it. Thus when I think of a chiliogon, or a polygon of a thousand equal sides, I do not always consider the nature of a side and of equality and of a thousand (or the cube of ten), but I use these words, whose meaning appears obscurely and imperfectly to the mind, in place of the ideas which I have of them, because I remember that I know the meaning of the words but that their interpretation is not necessary for the present judgment. Such thinking I usually call blind or symbolic; we use it in algebra and in arithmetic, and indeed almost everywhere. When a concept is very complex, we certainly cannot think simultaneously of all the concepts which compose it. But when this is possible, or at least insofar as it is possible, I call the knowledge intuitive. There is no other knowledge than intuitive of a distinct primitive concept, while for the most part we have only symbolic thought of composites. This already shows that we do not perceive the ideas even of those things which we know distinctly, except insofar as we use intuitive thought. It often happens that we falsely believe ourselves to have ideas of things in our mind, when we assume wrongly that we have already explained certain terms which we are using. It is not true, or at least it is ambiguous, to say, as some do, that we cannot speak of anything and understand what we say without having an idea of it. For often we understand after a fashion each single word or remember to have understood it earlier; yet because we are content with this blind thinking and do not sufficiently press the analysis of the concepts, we overlook a contradiction which the composite concept may involve. I was led to examine this point more distinctly by an argument which was famous among the Scholastics long ago and was revived by Descartes. It is an argument for the existence of God and is stated as follows. Whatever follows from the idea or definition of a thing can be predicated of the thing itself. Existence follows from the idea of God, or the most perfect being, or that than which no greater can be thought. For a most perfect being involves all perfections, among which existence is one. Therefore existence can be predicated of God. It should be noticed however, that the most you can draw out of this argument is
HANOVER TO THE ITALIAN JOURNEY, 1676-87 293 that if God is possible, it follows that he exists; for we cannot safely infer from definitions until we know that they are real or that they involve no contradiction. The reason for this is that from concepts which involve a contradiction, contradictory conclusions can be drawn simultaneously, and this is absurd. To explain this I usually make use of the example of the most rapid motion, which involves an absurdity. Suppose that a wheel turns at a most rapid rate. Then anyone can see that if a spoke of the wheel is extended beyond its rim, its extremity will move more rapidly than will a nail in the rim itself. The motion of the nail is therefore not the most rapid, contrary to hypothesis. Yet at first glance we may seem to have a idea of the most rapid motion, for we understand perfectly what we are saying. But we cannot have any idea of the impossible. Likewise it is not enough to think of a most perfect being in order to assert that we have an idea of it, and in the demonstration which I referred to above we must either prove or assume the possibility of a most perfect being in order to reason rightly. However, there is nothing truer than that we have an idea of God and that the most perfect being is possible and indeed necessary. But the above argument is not conclusive and has already been rejected by Thomas Aquinas. This gives us, too, a means of distinguishing between nominal definitions, which contain only marks for discerning one thing from others, and real definitions, through which the possibility of the thing is ascertained. In this way we can meet the view of Hobbes, who held truths to be arbitrary because they depend on nominal definitions, not considering that the reality of the definition does not depend upon our free choice and that not all concepts can be combined with each other. 3 Nominal definitions do not suffice for perfect knowledge unless it has been established by other means that the defined thing is possible. Thus the difference between a true and afalse idea also becomes clear. An idea is true when the concept is possible; it is false when it implies a contradiction. Now we know the possibility of a thing either a priori or a posteriori. We know it a priori when we resolve the concept into its necessary elements or into other concepts whose possibility is known, and we know that there is nothing incompatible in them. This happens, for instance, when we understand the method by which the thing can be produced; hence causal definitions are more useful than others. We know an idea a posteriori when we experience the actual existence of the thing, for what actually exists or has existed is in any case possible. Whenever our knowledge is adequate, we have a priori knowledge of a possibility, for if we have carried out the analysis to the end and no contradiction has appeared, the concept is obviously possible. Whether men will ever be able to carry out a perfect analysis of concepts, that is, to reduce their thoughts to the first possibles or to irreducible concepts, or (what is the same thing) to the absolute attributes of God themselves or the first causes and the final end of things, I shall not now venture to decide. 4 For the most part we are content to learn the reality of certain concepts by experience and then to compose other concepts from them after the pattern of nature. From this therefore I believe we can understand that it is not always safe to appeal to ideas and that many thinkers have abused this deceptive word to establish some of their own fancies. That we do not always at once have an idea of a thing of which we are conscious of thinking, the example of most rapid motion has shown. Nor is it less deceptive, I think, when men today advance the famous principle that whatever I perceive clearly and distinctly in some thing is true, or may be predicated of it. For what seems clear and distinct to men when they judge rashly is frequently obscure and For references see p. 294
294 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS confused. This axiom is thus useless unless the criteria of clearness and distinctness which we have proposed are applied and unless the truth of the ideas is established. For the rest, the rules of common logic, of which also the geometricians make use, are not to be despised as criteria of the truth of judgments; so, for example, the rule that nothing is to be admitted for certain unless it has been proved by careful experience or by sound demonstration. A demonstration is sound when it observes the form prescribed in logic, although it need not always follow the form of syllogisms arranged in the Scholastic manner (such as Christian Herlinus and Conrad Dasypodius applied to the first six books of Euclid) 5 ; it is merely necessary that the argument be conclusive by virtue of its form. As an example of such argumentation carried through in proper form one could also quote any valid calculation. Thus no necessary premise is to be omitted, and all premises must be proved in advance, or at least admitted to be hypotheses, in which case the conclusion, too, is hypothetical. Whoever obeys these rules carefully will easily protect himself against deceptive ideas. That brilliant genius Pascal agrees entirely with these principles when he says, in his famous dissertation on the geometrical spirit, a fragment of which is preserved in the outstanding book of the celebrated Antoine Arnauld on the Art of Thinking 6, that it is the task of the geometrician to define all terms though ever so little obscure and to prove all truths though little doubtful. I only wish that he had defined the limits beyond which any concept or judgment is no longer even a little obscure or doubtful. But the necessary conditions for this can be learned from a careful study of what we have just said; we must now strive to be brief. As to the controversy whether we see all things in God (an old opinion which, properly understood, is not entirely to be rejected) or whether we have some ideas of our own 7, it must be understood that even if we sawall things in God, it would still be necessary to have our own ideas also, not in the sense of some kind of little copies, but as affections or modifications of our mind corresponding to the very object we perceive in God. For whenever thoughts succeed each other, some change occurs in our mind. There are also ideas in our mind of things of which we are not actually thinking, as the figure of Hercules is in the rough marble. But in God there must actually be the ideas not only of absolute and infinite extension but also of every figure, since figure is nothing but a modification of absolute extension. s Moreover, when we perceive colors or odors, we are having nothing but a perception of figures and motions, but of figures and motions so complex and minute that our mind in its present state is incapable of observing each distinctly and therefore fails to notice that its perception is compounded of single perceptions of exceedingly small figures and motions. So when we mix yellow and blue powders and perceive a green color, we are in fact sensing nothing but yellow and blue thoroughly mixed; but we do not notice this and so assume some new nature instead. REFERENCES Seep.276,note13. In the New Essays, II, 5 (G., V, 116), Leibniz assigns these concepts (called by Locke simple· ideas which come from several senses) to the common sense (Aristotle De anima ii. 6) but identifies the common sense with "the mind itself, for they are ideas of the pure understanding, which relate to the external world and which we perceive through the senses". 1 2
HANOVER TO THE ITALIAN JOURNEY, 1676-87 295 See p.lS5, note 3. On Leibniz's identification of simple concepts with the perfections of God see the Introduction, Sec. V; see also Nos. 14 and 16, andp.169, note 2. 5 On this effort to reduce Euclid to syllogistic form see Cantor, op. cit., II, 553. 8 Art de penser, Part IV, chaps. IX and X. Leibniz had read Pascal's De ['esprit geometrique in Paris (Cout. OF., p. lSI). 7 This is another allusion to the Arnauld-Malebranche controversy. Arnauld had attacked Malebranche's view that we see objects by means of ideas in God's mind and had asserted that perception is esentially a modification of our own soul. See also p. 271, note S. 8 This comment refers to Malebranche's theory of an intelligible extension in God, to which Leibniz here gives qualified approval, though he insists that this does not absolve God from particular knowledge, as Malebranche had held. Cf. Leibniz's theory of the immensum during the Paris period (No. 12). 3 4
34 A BRIEF DEMONSTRATION OF A NOT ABLE ERROR OF DESCAR TES AND OTHERS CONCERNING A NATURAL LAW, According to Which God Is Said Always To Conserve the Same Quantity of Motion; a Law Which They Also Misuse in Mechanics Acta eruditorum, March, 1686 In this criticism of the Cartesian principle of the conservation of quantity of motion or of momentum, Leibniz began to fulfil his promise to refute the Cartesian physics, and particularly the laws of motion, by means ofa new principle (No. 31,111). His analysis of the relations of energy expended and work done involves the principle of equipollence as applied to physical processes. Replies were made to the paper by two outstanding Cartesians, the Abbe Catelan in 1686 and Denis Papin in 1691. Both answers involved Leibniz in a series of discussions which led to sharper formulations of his principles. The supplement is a later addition which reflects his thinking at the time of the Specimen dynamicum (No. 46). [GM., VI, 117-19] Seeing that velocity and mass compensate for each other in the five common machines, a number of mathematicians have estimated the force of motion by the quantity of motion or by the product of the body and its velocity. Or to speak rather in geometrical terms, the forces of two bodies (of the same kind) set in motion, and acting by their mass as well as by their motion, are said to be proportional jointly to their bodies or masses and to their velocities. Now since it is reasonable that the same sum of motive force should be conserved in nature and not be diminished - since we never see force lost by one body without being transferred to another - or augmented, a perpetual motion machine can never be succesful because no machine, not even the world as a whole, can increase its force without a new impulse from without. This led Descartes, who held motive force and quantity of motion to be equivalent, to assert that God conserves the same quantity of motion in the world. 1 In order to show what a great difference there is between these two concepts, I begin by' assuming, on the other hand, that a body falling from a certain altitude acquires the same force which is necessary to lift it back to its original altitude if its direction were to carry it back and if nothing external interfered with it. For example, a pendulum would return to exactly the height from which it falls except for the air resistance and other similar obstacles which absorb something of its force and which we shall now refrain from considering. I assume also, in the second place, that the same force is necessary to raise the body A (Figure 11) of 1 pound to the height CD of 4 yards as is necessary to raise the body B of 4 pounds to the height EF of 1 yard. Cartesians as well as other philosophers and mathematicians of our times admit both
HANOVER TO THE ITALIAN JOURNEY, 1676-87 297 of these assumptions. Hence it follows that the body A, in falling from the height CD, should aquire precisely the same amount of force as the body B falling from the height EF. For in falling from C and reaching D, the body A will have there the force required to rise again to C, by the first assumption; that is, it will have the force needed to raise a body of 1 pound (namely, itself) to the height of 4 yards. Similarly the body 1A @!C I I I I I I I I I 1 I 14 I I 1 I I 1 I 1 I 1 I Al /:.-=)10 c::r.·· Fig. 11. B, after faIling from E to F, will there have the force required to rise again to E, by the first assumption; that is, it will have the force sufficient to raise a body of 4 pounds (itself, namely) to a height of 1 yard. Therefore by the second assumption, the force of the body A when it arrives at D and that of the body B at Fare equal. Now let us see whether the quantities of motion are the same in both cases. Contrary to expectations, there appears a very great difference here. I shall explain it in this way. Galileo has proved that the velocity acquired in the fall CD is twice the velocity acquired in the fall EF. So, if we multiply the mass of A (which is 1) by its velocity (which is 2), the product, or the quantity of motion, is 2; on the other hand, if we multiply the body B (which is 4) by its velocity (which is 1), the product, or quantity of motion, is 4. Therefore the quantity of motion of the body A at D is half the quantity of motion of the body B at F, yet their forces are equal, as we have just seen. 2 There is thus a big difference between motive force and quantity of motion, and the one cannot be calculated by the other, as we undertook to show. It seems from this that force is rather to be estimated from the quantity of the effect which it can produce; for example, from the height to which it can elevate a heavy body of a given magnitude and kind but not from the velocity which it can impress upon the body. For not merely a double force, but one greater than this, is necessary to double the given velocity of the same body. We need not wonder that in common machines, the lever, windlass, pulley, wedge, screw, and the like, there exists an equilibrium, since the mass of one body is compensated for by the velocity of the other; the nature of the machine here makes the magnitudes of the bodies - assuming that they are of the same kind - reciprocally proportional to their velocities, so that the same quantity of motion is produced on For references see p. 301
298 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS either side. For in this special case the quantity of the effect, or the height risen or fallen, will be the same on both sides, no matter to which side of the balance the motion is applied. It is therefore merely accidental here that the force can be estimated from the quantity of motion. There are other cases, such as the one given earlier, in which they do not coincide. 3 Since nothing is simpler than our proof, it is surprising that it did not occur to Descartes or to the Cartesians, who are most learned men. But the former was led astray by too great a faith in his own genius; the latter, in the genius of others. For by a vice common to great men, Descartes finally became a little too confident, and I fear that the Cartesians are gradually beginning to imitate many of the Peripatetics at whom they have laughed; they are forming the habit, that is, of consulting the books of their master instead of right reason and the nature of things. It must be said, therefore, that forces are proportional, jointly, to bodies (of the same specific gravity or solidity) and to the heights which produce their velocity or from which their velocities can be acquired. More generally, since no velocities may actually be produced, the forces are proportional to the heights which might be produced by these velocities. They are not generally proportional to their own velocities, though this may seem plausible at first view and has in fact usually been held. Many errors have arisen from this latter view, such as can be found in the mathematico-mechanical works of Honoratius Fabri, Claude Deschales, John Alfonso Borelli, and other men who have otherwise distinguished themselves in these fields. In fact, I believe this error is also the reason why a number of scholars have recently questioned Huygens' law for the center of oscillation of a pendulum, which is completely true. 4 SUPPLEMENT It is to be shown that the power required to lift 1 pound 2 feet is the same as the power required to lift 2 pounds 1 foot. This proposition is not only admitted but explicitly applied and regarded as a principle by Descartes in his letters and the short treatise on mechanics which was edited with his letters, and separately as well. It was also accepted by Pascal in his treatise on the equilibrium of fluids; by Samuel Morland, the Englishman who invented the stentorian tubes, in the hydraulic treatise which he recently published 5; and by a certain learned Cartesian who has tried to reply to my demonstration against Descartes in the Nouvelles de la republique des lettres published in Holland with a number of evasions, though he did not adequately understand my argument. 6 I shall not mention other Cartesians or the opinions of other philosophers. So I can safely apply the principle in refuting the alleged natural law of the Cartesians. The same proposition is confirmed also by the five commonly recognized· mechanical powers - the lever, windlass, pulley, wedge, and screw; for in all the~e our proposition seems to be true. For the sake of brevity, however, it will suffice to show this in the single case of the lever, or - what amounts to the same thing - to deduce from our rule that the distances and weights of bodies in equilibrium are in reciprocal proportion. Let us assume A C (Figure 12) to be double BC, and the weight B double the weight A; then I say A and B are in equilibrium. For if we assume either one to preponderate, B, for example, and so to sink to B', and A to rise to A', and drop perpendiculars A' E and B'D from A' and B' to AB, it is clear that if DB' is 1 foot, A'E will be 2 feet, and
HANOVER TO THE ITALIAN JOURNEY, 1616-81 299 therefore that, if 2 pounds descend the distance of 1 foot, 1 pound will ascend to the height of 2 feet, and thus that, since these two are equivalent, nothing is gained and the descent becomes useless, everything remaining in equilibrium as before. 7 It can be shown in the same way that A cannot descend or predominate. So our proposition or hypothesis, so to speak, is confirmed a posteriori, for, by assuming it, one can prove that all the common mechanical propositions apply to equilibrium or to the five machines. Indeed, I might even risk affirming that there is no mechanical theorem in which our hypothesis is not confirmed or presupposed, as can be shown, for instance, by the law of the inclined plane, or by fountains, or by the acceleration of falling bodies. B Fig. 12. Even if some of these seem reconcilable with that hypothesis which estimates power by the product of mass by velocity, this is only accidentally, since the two hypotheses coincide in the case of dead forces [potentia mortuus] in which only the beginning or end of conatuses is actualized. But in living forces or those acting with an actually completed impetus, there arises a difference, just as the example shows which I have given above in the published paper. For living power is to dead power, or impetus (actual velocity) is to conatus, as a line is to a point or as a plane is to a line. Just as two circles are not proportional to their diameters, so the living forces of equal bodies are not proportional to their velocities but to the squares of their velocities. But since we cannot stop with an appeal to authority in this matter, and the mind which seeks to know will not be satisfied with mere inductions and hypotheses, we will now give a demonstration of our proposition, so that it can be placed for the future among the immutable foundations of the science of mechanics. I assume the single principle that a heavy body, falling from any height, will have exactly or precisely the power necessary for it to rise back to the same height, if it is understood to have lost no force on its way by friction or resistance by the medium or some other body. Corollary. So a body of 1 pound which descends from a height of 1 foot, acquires exactly the power of raising a body of 1 pound (equal to the first body itself) to the height of 1 foot. I postulate besides that I am permitted to assume various connections of the heavy bodies with each other, and their separation again, and to introduce any other changes which do not involve a change of force. I also make use of threads, axes, levers, and other mechanisms lacking in weight and resistance. 8 Theorem. With these assumptions, I assert that the fall of the body B (Figure 13) of 1 pound for the distance BB", a height of 2 feet, will have exactly as much force as is necessary to raise the body A of 2 pounds to the height of AA' of 1 foot. Demonstration. I assume the body A composed of two parts, E and F, each of which For references see p. 301
300 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS is 1 pound. Now the body B, of 1 pound, has exactly the power, in descending from the height BB' of 1 foot, that is necessary to raise the body E of 1 pound to the height EE' of 1 foot (by the corollary), if a connection is assumed between them (by the postulate). We assume further (by the same postulate) that the body B in the position B' is freed from its connection with body E, which remains at E', and is connected now with body F. Then the body B, continuing its descent for the distance B'B" will be able to lift the body F of 1 pound for the distance FF', a height of 1 foot (by the corollary). Therefore the whole body B of 1 pound, descending 2 feet, BB", has raised the body composed of both E and F, or A, of 2 pounds through AA', a height of 1 foot. But exactly this was to be proved possible. T )1( i I I I I I I Bt I I I I I E,i F' r-t-1 t_tJ E F A I i I I B't I I I ! I I I i B'" I Fig. 13. Scholium If the matter is carefully considered, it will easily be understood, without any appa- ratus or figures, that these two things are equivalent - to raise 1 pound to 2 feet (i.e., a pound 1 foot, and then again a pound 1 foot), and to raise 2 pounds 1 foot (i.e., a pound 1 foot and, joined to it, another pound 1 foot). In general, forces are to be calculated from their effects, not from the time; for time can be varied by external circumstances. Thus the sphere C, with a specific impetus (degree of velocity) by whose action it can raise itself to the height HG on an inclined plane LM or LN, needs more time in proportion to the increasing length of the plane (Figure 14). In either case, however, it __________________ .!"1 ____ N G I I I I I I i cO Q -------------------.! H -----------i Fig. 14.
HANOVER TO THE ITALIAN JOURNEY, 1676-87 301 will rise to the same perpendicular height if, naturally (as must be done in these problems), the resistance of air and the plane be taken as zero. The force of the sphere will remain the same, whatever may be the inclination of the line in which it lifts itself. I understand here such an effect as itself constitutes a natural force or one by whose production the impetus is diminished. Such an effect is the ascent or elevation of any heavy object, the tension of a spring, the impulsion of a body to motion or the retardation of its motion, and other operations of this kind. On the other hand, the greater or less progress of a body once put in motion in a horizontal plane is not an effect of this kind from which I calculate absolute force, for the force remains the same during the progress of the body in this case. This is worth noting explicitly for the sake of avoiding errors, since it has not been adequately explained. Of course I admit that from a given time or its reciprocal, the velocity, and from other known circumstances, a judgment is possible about the force of a given body; but I assert that not the time nor the velocity but only the effect is an absolute measure of force, for when the force remains the same, the effect remains the same, and neither the time nor other circum- ' stances can vary it. Hence it is not surprising that the forces of two equal bodies are proportional not to their velocities but to the causes or the effects of their velocity, i.e., to the heights producing them or capable of being produced by them, or to the squares of their velocities. It also follows therefore that when two bodies collide, there is conserved after the collision, not the same quantity of motion or impetus, but the same quantity of force. 9 It follows also that a string must be stretched by a fourfold weight to produce a tone twice as high, for the weight represents the force, the sound the velocity of the vibrations of the string. The ultimate reason, however, is that motion is not something absolute and real in itself. REFERENCES Principiaphilosophiae, Part II, Sees. 48ff. See also Leibniz's critical analyses in the corresponding sections of No. 42. 2 Leibniz's conclusion may be summarized as follows. According to the law of falling bodies, d = 19t 2 • But v = gt; hence v 2 = 2gd, or distances vary as the squares of velocities. More generally, then, Leibniz holds that work accomplished, measured by the motion of a body through a horizontal distance, is proportional to a quantity of force accumulating through time and is therefore an integral or summation of successive initial impulses themselves whose effects in velocity are conserved and accumulated. It is therefore proportional to v2 rather than to v. Forces in equilibrium are special cases of the more general equation between force exerted and work done, when the force remains dead (or is restricted to momentary acceleration). For the relation among force, energy, and work the student should consult such standard works in theoretical mechanics as that by Sir James Jeans. Kepler's, but particularly Galileo's, analysis of force (as inertia times acceleration, as opposed to velocity) is important in understanding the background of Leibniz's thought. But his conclusion itself is first found in Huygen's De motu corporum ex percussione (1668), where Proposition 9 affirms that in a case of colliding bodies the sums of the products of m and v2 remain constant. For these historical relations see E. Hoppe, Geschichte der Physik, Brunswick 1926, pp. 60ff. On the issue at stake between Descartes and Leibniz see Mach, The Science of Mechanics, 5th ed., pp. 364ff. See also p. 451 , notes 7 and 9. 3 In the case of static machines, equilibrium requires that the common center of gravity of the system not be effected by virtual displacements within the elements of the system. But these 1
302 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS momentary impulsions to displacement or conatuses (ds/dt) are proportional to velocity = ds/dt), and Descartes's principle thus applies. In the case of living forces, or forces operative through time, on the other hand, the distance is an integral of the velocity and thus proportional to v2 • 4 Honoratius Fabri, Physica, i.e., Scientia rerum corporearum in X tractatus distributa, Leyden 1669; Claude Francois Deschales, Cursus seu mundus mathematicus, Leyden 1674; Giovanni Alfonso Borelli, De motionibus naturalibus a gravitate pendentibus, Leyden 1686. Huygens' Hor%gium oscillatorium (1673) had, like his earlier work on impact (note 2, above), involved the new measure of motive force and was therefore opposed by Cartesian physicists. 5 The definition of energy as capacity to do work is found in Kepler and Galileo (Hoppe, op. cit., p. 63). Descartes discusses the relation with Mersenne, July 13 and September 12, 1638 (Adam and Tannery, Correspondence, II, 222, 352). Samuel Morland's Hydrostatics appeared in 1695. Thus this supplement reflects the physical work of the middle 1690's. On Pascal's hydrostatics see Mach, op. cit. pp. 66, 116-17. 6 A French translation of the Brief Demonstration appeared in this emigre journal for September, 1686, along with a reply by the Abbe Catelan. 7 Since the distance is proportional to the square of the velocity (note 2, above). 8 This methodological assumption originated in Galileo's use of the pendulum and inclined plane in deriving the law of falling bodies. But it received brilliant development in Huygens's analysis of the oscillation center of a compound pendulum into the problem of simple pendulums with varied weights and lengths, which could be combined mathematically into a rigid system or released from it (see BC., I, 253, n. 189). 9 For a detailed discussion of the laws of impact and a criticism of Descartes's laws by means of the principle of continuity see No. 42. Until the appearance of Newton's Principia in 1687, the discussion of laws of motion was dominated by the problem of the impact of two colliding bodies. In Leibniz's later studies, however (cf. No. 46), collision becomes a special case of dynamic systems in which absolute force, relative force, and progress of direction are conserved. (v
35 "DISCOURSE ON METAPHYSICS" 1686 The first mature synthesis of Leibniz's philosophical opinions is an essay without title which is described in a letter to the Landgrave Ernest of Hesse-Rheinfels on February 1/11,1686. Finding myself recently at a place with nothing to do for a few days, I wrote a little discourse on metaphysics, on which I should like to have the opinion of Mr. Arnauld. For I have treated the questions of grace, the co-operation of God with creatures, the nature of miracles, the cause of sin, the origin of evil, the immortality of the soul, ideas, etc., in a way which seems to provide new openings proper to clearing up the greatest difficulties [G., II, II]. So far as is known, however, the work itself was never sent to Arnauld, but only the 37 propositions summarizing its conclusions, which Leibniz asked the Landgrave to forward to him. Though it has been esteemed very highly as a statement of Leibniz's mature philosophy, he himself considered it inadequate on the nature and kinds of substances, on the interpretation of body, and on the various degrees ofperception. In contrast to his later philosophical summaries (Nos. 66 and 67), its emphasis is predominantly theological beginning with the argument for God rather than with the argument for individual substances, and it may have been a study for the preface to the Catholic Demonstrations. Gerhardt's text has been corrected with the comparatively collated text of Schmalenbach (Sch. I, 1-50) based on the critical edition by Lestienne. Only the more significant variations found in earlier drafts of the essay, of which G. 's text is the third, are found in the notes. [G., IV, 427-63] 1. On the divine perfection, and that God does all in the most desirable way. The most widely accepted and meaningful concept which we have of God is very well expressed in the phrase that he is an absolutely perfect being; yet the consequences of this definition have not been adequately considered. To penetrate more deeply into its meaning, it is convenient to notice that there are several entirely different perfections in nature, that God possesses them all together, and that each one belongs to him in a supreme degree. We must also know what is meant by perfection. A fairly sure test of it is this one: those forms or natures which are incapable of a highest degree are not perfections; for example, the nature of number or figure. For the greatest number of all, or the number of all numbers, and the greatest of all figures are concepts which imply contradiction, but the greatest knowledge and omnipotence involve no impossibility. Therefore power and knowledge are perfections and insofar as they belong to God, have no limits. Hence it follows that God, who possesses supreme and infinite wisdom, acts in the most perfect way and does this not only in a metaphysical but also in a moral sense. With respect to ourselves we can also express this as follows: the For references see p. 328
304 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS more enlightened and informed we are about the works of God, the more we shall be inclined to find them excellent and in entire conformity with everything which might have been desired. 2. Against those who claim that there is no goodness in the works of God; or that the rules ofgoodness and beauty are arbitrary. Thus I am far from holding to the opinion of those who maintain that there are no rules of goodness and perfection in the nature of things or in the ideas which God has of them and who say that the works of God are good only for the formal reason that God has made them. For if this were so, God, who knows that he is the author of things, would have had no reason to regard them afterward and find them good, as is reported in the Holy Scriptures, which seem to have used this anthropological conception only to make us understand that the excellence of God's works may be recognized by considering them in themselves, even without reflecting upon this empty designation which relates them to their cause. This is all the more true, since it is through a consideration of his works that we can discover the craftsman. Thus his works must carry his mark in themselves. I confess that the contrary opinion seems to me extremely dangerous and to come very near to that of the latest innovators 1 whose opinion it is that the beauty of the universe and the goodness which we ascribe to the works of God are nothing but the chimeras of men who think of him in terms of themselves. Then, too, when we say that things are not good by any rule of excellence but solely by the will of God, we unknowingly destroy, I think, all the love of God and all his glory. For why praise him for what he has done if he would be equally praiseworthy in doing exactly the opposite? Where will his justice and wisdom be found if nothing is left but a certain despotic power, if will takes the place of reason, and if, according to the definition of tyrants, that which is pleasing to the most powerful is by that very fact just? Besides it seems that every act of will implies some reason for willing and that this reason naturally precedes the act of will itself. This is why I find entirely strange, also, the expression of certain other philosophers who say that the eternal truths of metaphysics and geometry, and consequently also the rules of goodness, justice, and perfection, are merely the effects of the will of God; while it seems to me that they are rather the consequences of his understanding, which certainly does not depend upon his will any more than does his essence. 3. Against those who believe that God might have made things better. Nor am I able to approve the opinion of certain moderns who maintain boldly that what God has done is not supremely perfect but that he could have done much better. For it seems to me that the consequences of this opinion are wholly contrary to the glory of God. Uti minus malum habet rationem boni, ita minus bonum habet rationem mali. 2 To act with less perfection than one is capable of is to act imperfectly. To show that an architect could have done his work better is to find fault with his work. This opinion is also contrary to the Holy Scriptures, which assure us of the goodness of God's works. For supposing this opinion were justified, since the imperfections follow a scale descending endlessly, whatever works God might have created, they would always be good in comparison with the less perfect. But a thing is hardly praiseworthy if it can be praised only is this way. I believe also that a great many passages will be found in the divine writings and the Church Fathers which favor my opinion but scarcely any supporting that of the moderns 3, an opinion which was, I think, unknown to all antiquity and is based only on the inadequate knowledge which we have of the general harmony of the
HANOVER TO THE ITALIAN JOURNEY, 1676-87 305 universe and the hidden reasons for God's conduct. This makes us judge rashly that many things might have been made better. Besides, these moderns insist on certain untenable subtleties, for they imagine that nothing is so perfect that there is not something more perfect, which is an error.4 They believe also that thus they are safeguarding God's freedom, as though it were not the highest freedom to act in perfection according to sovereign reason. For to think that God acts in any matter without having any reason for his will, even overlooking the fact that this seems impossible, is an opinion which is hardly in accord with God's glory. Let us assume, for example, that God chooses between A and B and that he takes A without having any reason for preferring it to B. I say that such action by God is at least not praiseworthy, for all praise should be based on some reason, and there is none here, by hypothesis. I hold, instead, that God does nothing for which he does not deserve to be praised. 4. That the love of God requires our entire satisfaction with and acquiescence in that which he has done. The general knowledge of this great truth, that God always acts in the most perfect and the most desirable way possible, is in my opinion the basis of the love which we owe to God above all things, since he who loves seeks his satisfaction in the felicity or perfection of the object loved and of his actions. Idem velie et idem nolle vera amicitia est. 5 I believe that it is difficult to love God truly if, having the power to change his inclination, one is not inclined to will what he wills. In fact, those who are not satisfied with what he does seem to me like discontented subjects whose intentions are not very different from those of rebels. According to these principles, I hold therefore that, in order to act in conformity to the love of God, it is not enough to force ourselves to be patient; we must be truly satisfied with everything that has happened to us according to his will. I mean this acquiescence to apply to the past; for as to the future we ought not to be quietists and stand with folded arms ridiculously waiting to see what God will do, in conformity with the sophism which the ancients called M),ov aep)'ov, or the lazy reason. 6 We must rather act in accordance with the presumptive will of God, so far as we are able to know it, trying with all our might to contribute to the general welfare and particularly to the ornament and perfection of that which concerns us or that which is nearest us and so to speak, within our reach. For though the outcome may perhaps show us that God did not wish our good will to be effective for the present, it does not follow that he did not will us to do what we did. On the contrary, since he is the best of all masters, he never demands more than righteous intentions, and it is for him to know the proper hour and place for making our good designs successful. 5. Of what the rules of the perfection of the divine action consist; and that the simplicity of the means is in balance with the richness of the effects. It is enough, then, to have this confidence in God that he does everything for the best and that nothing can harm those who love him. But to understand the reasons in particular which have moved him to choose this order of the universe - to allow sin to be committed, to dispense his saving grace in a certain way - this surpasses the powers of a finite mind, especially if this mind has not yet attained the blessedness of the vision of God. Some general remarks can be made, however, about the ways of providence in the government of affairs. It can be said, then, that he who acts perfectly is like an excellent geometrician who knows how to find the best constructions of a problem; or a good architect who makes the most advantageous use of the space and the capital intended for a building, leaving nothing which offends or which lacks the beauty of which it is capable; or a For references see p. 328
306 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS good family head who makes such use of his holdings that there i<> nothing uncultivate d and barren; or a skilled machinist who produces his work by the easiest process that can be chosen; or a learned author who includes the greatest number of subjects in the smallest possible volume. But the most perfect of all beings, and those which occupy the smallest volume, that is to say, those which least obstruct each other, are spirits, whose perfections consists in their virtues. This is why there can be no doubt that the happiness 7 of spirits is the principal end of God and that he puts this principle into practice as far as the general harmony permits. We shall have more to say about this later. As for the simplicity of the ways of God, this is shown especially in the means which he uses, whereas the variety, opulence, and abundance appears in regard to the ends or results. The one ought thus to be in equilibrium with the other, just as the funds intended for a building should be proportional to the size and beauty one requires in it. It is true that nothing costs God anything, even less than it costs a philosopher to build the fabric of his imaginary world out of hypotheses, since God has only to make his decrees in order to create a real world. But where wisdom is concerned, decrees or hypotheses are comparable to expenditures, in the degree to which they are independent of each other, for reason demands that we avoid multiplying hypotheses or principles, somewhat as the simplest system is always preferred in astronomy.s 6. That God does nothing which is unorderly. and that it is not even possible to assume events which are not according to rule. The volitions or actions of God are commonly classified into ordinary and extraordinary acts. But it i<> well to understand that God does nothing without order. So whatever passes for extraordinary is so only in relation to some particular order established among creatures. For as concerns universal order, everything is in conformity with it. So true is this that not only does nothing happen in the world which is absolutely irregular but one cannot even imagine such an event. For let us assume that someone puts down a number of points on paper entirely at random, as do those who practice the ludicrous art of geomancy; I maintain that it is possible to find a geometric line whose law is constant and uniform and follows a certain rule which will pass through all these points and in the same order in which they were drawn. And if someone draws an uninterrupted curve which is now straight, now circular, and now of some other nature, it is possible to find a concept, a rule, or an equation common to all the points of the line, in accordance with which these very changes must take place. There is no face, for example, whose contour does not form part of a geometric curve and cannot be drawn in one stroke by a certain regular movement. But when the rule for this movement is very complex, the line which conforms to it passes for irregular. Thus we may say that no matter how God might have created the world, it would always have been regular and in a certain general order. But God has chosen that world which is the most perfect, that is to say, which is at the same time the simplest in its hypotheses and the richest in phenomena, as might be a geometric line whose construction would be easy but whose properties and effects would be very remarkable and of a wide reach. I make use of these comparisons merely to portray an imperfect semblance of the divine wisdom and to say that which can at least lift our spirit to some conception of what cannot well be expressed. But I do not at all claim to explain by means of it the great mystery upon which the entire universe depends. 7. That miracles conform to the general order although they may be contrary to the
HANOVER TO THE ITALIAN JOURNEY, 1676-87 307 subordinate regulations; on what God wills or what he permits, and on his general or particular will. Now since nothing can happen which is not according to order, it can be said that miracles are as much subject to order as are natural operations and that the latter are called natural because they conform to certain subordinate maxims which we call the nature of things. For we may say that this nature is merely acustom of God's with which he can dispense for any reason stronger than that which moved him to use these maxims. As for general or particular volitions, we may say, depending upon how the matter is understood, that God does everything according to his most general will which conforms with the most perfect order which he has chosen. But we can also say that he has particular volitions which are exceptions to these subordinate maxims. 9 For the most general of God's laws, which rules the whole sequence of the universe, is without exception. It can also be said that God wills everything which is an object of his particular volition; but as for the objectives of his general will, such as the actions of creatures, especially of those which are reasonable and with whom God wishes to co-operate, we must make a distinction. If the action is good in itself, we can say that God wishes it and sometimes commands it, even though it does not take place. But if the action is evil in itself, and becomes good only by accident because the course of events, particularly punishment and satisfaction, corrects its malignity and repays the evil with interest in such a way that more perfection is found in the whole sequence than if the evil had not occurred - then we must say that God perInits it but not that he wills it, although he has concurred init through the natural laws which he has established and because he knows how to draw a greater good from it. 8. To distinguish the actions of God from those of creatures we must explain what the concept of an individual substance is. It is rather difficult to distinguish the actions of God from those of creatures 10, for there are those who believe that God does everything, while others imagine that he does nothing but conserve the force which he has given to creatures. We shall see in what follows the sense in which we can say the one or the other. Now since activity and passivity pertain distinctively to individual substances (actiones sunt suppositorum) 11, it will be necessary to explain what such a substance is. It is of course true that when a number of predicates are attributed to a single subject while this subject is not attributed to any other, it is called an individual substance. But this is not enough, and such a definition is merely nominal. We must consider, then, what it means to be truly attributed to a certain subject. Now it is certain that every true predication has some basis in the nature of things, and when a proposition is not an identity, that is to say, when the predicate is not expressly contained in the subject, it must be included in it virtually. This is what the philosophers call in-esse, when they say that the predicate is in the subject. So the subject term must always include the predicate term in such a way that anyone who understands perfectly the concept of the subject will also know that the predicate pertains to it. This being preInised, we can say it is the nature of an individual substance or complete being to have a concept so complete that it is sufficient to make us understand and deduce from it all the predicates of the subject to which the concept is attributed. An accident, on the other hand, is a being whose concept does not include everything that can be attributed to the subject to which the concept is attributed. Thus the quality of king which belonged to Alexander the Great, if we abstract it from its subject, is not determined enough to define an individual, for it does not include the other qualities of the same subject or everything which the concept of this prince includes. For references see p. 328
308 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS God, on the contrary, in seeing the individual notion or 'haecceity' of Alexander, sees in it at the same time the basis and the reason for all the predicates which can truly be affirmed of him - for example, that he wiII conquer Darius and Porus - even knowing a priori (and not by experience) what we can know only through history - whether he died a natural death or by poison. Thus when we well consider the connection of things, it can be said that there are at all times in the soul of Alexander traces of all that has happened to him and marks of all that will happen to him and even traces of all that happens in the universe, though it belongs only to God to know them all. 9. That each singular substance expresses the whole universe in its own way, and that in its concept are included all of the experiences belonging to it together with all of their circumstances and the entire sequence of exterior events. From these considerations there follow a number of important paradoxes; among others that it is not true that two substances can resemble each other completely and differ only in number and that what St. Thomas says on this point about angels or intelligences (quod ibi omne individuum sit species infima) 12 is true of all substances, provided that we take the specific difference as geometricians understand it in their figures. It follows also that a substance cannot come into being except by creation, or perish except by annihilation; that a substance cannot be divided in two, or one substance made out of two, so that the number of substances does not increase or diminish naturally, though they are often transformed. Moreover, every substance is like an entire world, and like a mirror of God or of the whole universe which it expresses, each in its own manner, about as the same city is represented differently depending on the different positions from which it is regarded. Thus the universe is in a certain sense multiplied as many times as there are substances, and the glory of God is likewise redoubled by as many wholly different representations of his work. It can even be said that every substance in some way bears the character of God's infinite wisdom and omnipotence and imitates him as much as it is capable. For it expresses, however confusedly, everything that takes place in the universe, past, present, or future; this resembles somewhat an infinite perception or an infinite knowledge. And since all other substances in their tum express this one in their own way, and adapt themselves to it, it can be said that each extends its power over all the rest in imitation of the omnipotence of the creator. 10. That there is something sound in the belief in substantial forms, but that these forms change nothing in the phenomena and must not be used to explain particular effects. Not only the ancients but also many able men given to deep meditation who taught theology and philosophy some centuries ago, some of whom are to be respected also for their saintliness, seem to have had some knowledge of what we have just said; this is why they have introduced and maintained the substantial forms which are so widely discredited today. But they are not so far from the truth, or so ridiculous, as our modem philosophers commonly imagine. I agree that the consideration of these forms serves no purpose in the details of physics and that they ought not to be used to explain particular phenomena. In this the Scholastics failed, as did the physicists of the past who imitated them, thinking that they could account for the properties of bodies by mentioning forms and qualities, without taking pains to examine the manner of their operation. This is as if one were content to say that a clock has a time-indicating property proceeding13 from it~ form, without inquiring wherein this property consists. This is of course enough for the man who buys it, if he turns over its care to someone
HANOVER TO THE ITALIAN JOURNEY, 1676-87 309 else. But this inadequate understanding and abuse of the forms ought not to make us reject something whose knowledge is so necessary in metaphysics that without it, I hold, we cannot well understand the first principles or raise the spirit to the knowledge of incorporeal natures and the wonders of God. A geometrician does not need to encumber his mind with the famous labyrinth of the composition of the continuum, and no moral philosopher, and still less a jurisconsult or politician, needs to trouble himself with the great difficulties involved in reconciling free will with the providence of God, since the geometrician can carry through his demonstrations, and the politician finish his deliberations, without entering these discussions; yet these problems are nonetheless necessary and important in philosophy and theology. Just so a physicist can give an explanation of his experiments, making use, now of simpler experiences already past, now of geometric and mechanical demonstrations, without needing the general considerations which belong to another sphere. If he does make use of the co-operation of God or of some soul or Archeus 14 or of something else of this nature, he is raving, just as much as a man who would enter into the great discussion concerning the nature of destiny and of our liberty, in deciding an important practical problem. Men in fact often commit this fault without thinking of it when they encumber their mind by the consideration of fatalism and are even sometimes diverted by it from some good resolve or from some necessary concern. II. That the thoughts of the theologians and philosophers who are called scholastics are not to be entirely disdained. I know that I am advancing a great paradox in seeking to restore the old philosophy in some respects and to restore these almost-banished substantial forms. But perhaps I shall not be condemned so lightly when it is known that I have given much thought to the modern philosophy and that I have spent much time in physical experiments and geometric demonstrations and was for a long time convinced of the emptiness of these beings to which I am at last compelled to return in spite of myself and as by force. This is after I have myself carried out studies which convinced me that our moderns do not do enough justice to St. Thomas and other great men of his time and that the opinions of the Scholastic philosophers and theologians are much sounder than has been imagined, provided that they are used appropriately and in their proper place. I am even convinced that if some exact and thoughtful mind were to take the pains to clarify and to assimilate their thoughts after the manner of the analytic method of geometricians, he would find a great treasure of very important and strictly demonstrative truths. 12. That the concepts which are involved in extension include something imaginary and cannot constitute the substance of the body. But to take up the thread of my considerations again, I believe that anyone who will meditate about the nature of substance as I have explained it above will find 15 that the entire nature of the body does not consist merely in extension, that is to say, in size, figure, and motion, but that there must necessarily be recognized in it something related to souls, which is commonly called a substantial form, although this form makes no change in the phenomena, any more than does the soul of beasts if they have one. It can even be demonstrated that the concepts of size, figure, and motion are not so distinct as has been imagined and that they include something imaginary and relative to our perceptions, as do also (though to a greater extent) color, heat, and other similar qualities which one may doubt truly are found in the nature of things outside of ourselves. 16 This is why qualities of this kind cannot constitute any substance. And if there is no other principle of identity in For references see p. 328
310 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS body than those we have just mentioned, no body can ever subsist longer than a moment. 17 Meanwhile the souls and the substantial forms of the other bodies are very different from intelligent souls, who alone know their actions and who not only never perish naturally but even preserve always the fundamental knowledge of what they are. This makes them alone susceptible of punishment and reward and citizens of the commonwealth of the universe of which God is the monarch. It follows also that all the other creatures should serve them; a matter which we shall discuss more fully later. 13. Since the individual concept of each person includes once and for all everything which can ever happen to him, one sees in it a priori proofs or reasons for the truths ofeach event and why one has happened rather than another, but these truths, however certain, are nevertheless contingent, being based on the free will of God and of creatures. It is true that their choice a/ways has its reasons, but these incline without necessitating. But before we go further we must try to meet a great difficulty which may grow out of the foundations which we have laid above. We have said that the concept of an individual substance once and for all includes everything which can ever happen to it and that in considering that concept, one can see everything which can truly be predicated of it, just as we can see in the essence of the circle all the properties which can be deduced from it. But it seems that this will destroy the distinction between contingent and necessary truths, that it will leave no place for human liberty, and that an absolute fatalism will rule over all our actions as well as over the other events of the world. To this I reply that we must distinguish between what is certain and what is necessary. It is universally agreed that future contingents ate certain, since God foresees them, but this does not make us say that they are necessary. But someone may object that if a certain conclusion can be deduced infallibly from a given definition or concept, that conclusion will be necessary. And we are now maintaining that everything that happens to some person is already contained virtually in his nature or concept, just as the properties of the circle are contained in its definition. Thus the difficulty still subsists. To answer it squarely, I say that there are two kinds of connection or sequence. One is absolutely necessary, for its contrary implies a contradiction, and this deductive connection occurs in eternal truths like those of geometry. The other is necessary only ex hypothesi, and by accident, so to speak, and this connection is contingent in itself when its contrary implies no contradiction. A connection of this kind is not based on pure ideas and on the simple understanding of God but also on his free decrees and on the sequence of events in the universe. Let us take an example. Since Julius Caesar is to become perpetual dictator and master of the republic and will destroy the liberty of the Romans, this action is contained in his concept, for we have assumed that it is the nature of such a perfect concept of a subject to include everything, so that the predicate is included in it - ut possit inesse subjecto. One could say that it is not by virtue of this concept or idea that he must commit this act, since the concept fits him only because God knows everything. But, someone will insist, his nature or form corresponds to this concept, and since God imposed this personality upon him, it is henceforth necessary for him to fulfil it. I could reply by pointing out the case of future contingents, which as yet have reality only in the understanding and the will of God; but since God has given them this form in advance, it is all the same necessary for them to respond to it. But I prefer to meet difficulties rather than to extenuate them by pointing out certain other similar difficulties, and what I am about
HANOVER TO THE ITALIAN JOURNEY, 1676-87 311 to say will serve to clear up the one as well as the other. It is here, then, tl;tat we must apply the distinction we have made between the classes of connections, arid I say that whatever happens in conformity to these divine anticipations is assured but not necessary anq that if anyone were to do the contrary, he would not do anything impossible in itself, though it would be impossible ex hypothesi for it to happen. For if some man were able to carry out the complete demonstration by virtue of which he could prove this connection between the subject, who is Caesar, and the predicate, which is his successful undertaking, he would actually show that the future dictatorship of Caesar is based in his concept or nature and that there is a reason in that concept why he has resolved to cross the Rubicon rather than stop there, and why he has won rather than lost the day at Pharsalus, and why it was reasonable and consequently assured that this should happen. But this man could not show that these events are necessary in themselves or that their contrary implies a contradiction. In the same way it is reasonable and assured that God will always do what is best, even though what is less perfect implies no contradiction. For it will be found that this demonstration of the predicate of Caesar is not as absolute as that of numbers or of geometry but that it supposes the sequence of things which God has freely chosen and which is founded on the first free decree of God, which leads him always to do what is most perfect, and on the decree which God has made about human nature (following the primary one), which is that man shall always do, though freely, that which appears to him to be best. But every truth which is based on this kind of a decree is contingent, even though it is certain, for these decrees do not change the possibility of things. And as I have already said, though God assuredly always chooses the best, this does not prevent something less perfect from being and remaining possible in itself, even though it will never happen, for it is not its impossibility but its imperfection which causes God to reject it. Now nothing is necessary whose opposite is possible. So we are in a position to meet difficulties of this kind, no matter how great they may seem (and in fact they are no less pressing for all the other thinkers who have taken up this matter), provided that we consider carefully that all contingent propositions have reasons for being as they are and not otherwise or what amounts to the same thing, that they have a priori proofs of their truth which make them certain and which show that the relation between subject and predicate of these propositions has its basis in the nature of both. But we must consider too that these proofs are not demonstrations of necessity, since these reasons are based only on the principle of contingency or of the existence of things, that is to say, on what'is or appears to be the best among several equally possible things. Necessary truths, by contrast, are based on the principle of contradiction and on the possibility or impossibility of essences themselves, without considering in this relation the free will of God or of the creatures. 1S 14. God produces diverse substances according to the different views he has of the world, and through the intervention of God the nature proper to each substance involves that what happens to one corresponds to what happens to all the others, without their acting upon one another directly. After having to some extent seen in what the nature of substances consists, we must try to explain the dependence they have on each other and their actions and their passions. Now it is clear, first of all, that the created substances depend on God, who preserves them and indeed even produces them continually by a kind of emanation, as we produce our thoughts. For as God turns the universal system of phenomena which he has seen fit to produce in order to manifest For references see p. 328
312 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS his glory, on all sides and in all ways, so to speak, and examines every aspect of the world in every possible manner, there is no relation which escapes his omniscience, and there thus results from each perspective of the universe, as it is seen from a certain position, a substance which expresses the universe in conformity to that perspective, if God sees fit to render his thought effective and to produce that substance. And since God's perspective is always true, our perceptions are also always true; it is our judgments, which come from ourselves, which deceive US. 19 But we have already said, and it follows from what we have just said, that each substance is as a world apart, independent of everything outside of itself except God. Thus all our phenomena, that is to say, all the things that can ever happen to us, are only the results of our own being. And since these phenomena maintain a certain order which conforms to our nature or, so to speak, to the world which is within us, so that we are able to make observations that are useful for controlling our own conduct and justified by the success of future phenomena, with the result that we can often judge the future by the past without deceiving ourselves, this would be sufficient to enable us to say that these phenomena are true, without being put to the task of inquiring whether they are outside of us and whether others perceive them also. Nevertheless it is true that the perceptions or expressions of all substances intercorrespond, so that each one, following with care the established reasons or laws which it has observed, meets with others who have done this also. When a number of people have agreed to meet together in some place on a previously determined day, they can do this successfully if they wish. But although all express the same phenomena, it does not follow from this that their expressions are exactly alike; it suffices that they are proportional. So a number of spectators believe that they see the same thing and are in fact in agreement about it, although each one sees and speaks of it according to the measure of his own point of view. It is only God (from whom all individuals emanate continually and who sees the universe not only as they see it but also entirely differently from all of them), who is the cause of this correspondence between their phenomena and who makes public to all that which is peculiar to one; otherwise there would be no interconnection. 20 We might say, then, in a way, and with good meaning, though not in accordance with common usage, that one particular substance never acts upon another particular substance, nor is it acted upon by it, if we keep in mind that what happens to each is solely the result of its own complete idea or concept, since this idea already includes all the predicates or events and expresses the whole universe. Nothing can in fact happen to us except thoughts and perceptions, and all our future thoughts and perceptions are only the consequences, however contingent they may be, of our preceding ones, so that if I were capable of considering distinctly everything that is happening to me or appearing to me at this hour, I could see in it everything which will ever happen or appear to me. And this,would not fail to happen to me, even if all that there is outside of me were to be destroyed, provided there remained only God and myself. But since we do attribute to other things as causes acting upon ourselves that which we perceive in a certain way, we must consider the basis of this judgment and the element of truth which it has in it. 15. The action of one finite substance upon another consists in nothing but the increase of degree of its expression together with the diminution of the expression of the other, insofar as God hasformed them in advance in such a way that they are adapted to each other. To reconcile the language of metaphysics with that of practice, it will suffice for the
HANOVER TO THE ITALIAN JOURNEY, 1676-87 313 present, without entering into a long discussion, to remark that we ascribe to ourselves, primarily and with reason, those phenomena which we express more perfectly and that we attribute to other substances those phenomena which each expresses best. Thus a substance which has an infinite extension, insofar as it expresses everything, becomes limited through the more or less perfect way in which it expresses each thing. It is in this sense, then, that we can think of substances as impeding and limiting each other, and consequently it is in this sense that we can say that they act upon each other and are obliged, so to speak, to adapt themselves to each other. For it can happen that a single change which increases the expression of one will diminish that of another. Now it is the virtue of a particular substance to express well the glory of God, and the better it expresses it, the less limited it is. And whenever anything exercises its virtue or power, that is to say when it acts, it improves and enlarges itself in proportion to its action. Therefore when a change takes place by which a number of substances are affected (as a matter offact, every change affects them all), I believe it can be said that any substance which thereby passes immediately to a greater degree of perfection or to a more perfect expression exercises its power and acts, while any substance which passes to a lesser degree of perfection shows its weakness and suffers. I hold too that every action of a substance which has perfection involves some pleasure, and every passion some pain, and vice versa. Yet it may well happen that a present advantage may be destroyed by a greater evil in the future, so that one can sin in acting or in exercising his power and in finding pleasure. 16. The extraordinary concourse of God is included in that which our essence expresses, for this expression includes everything. But this concourse surpasses the power of our nature or of our distinct expression, which is finite and follows certain subalternate maxims. For the present it remains for me only to explain how God can sometimes influence men and other substances through an extraordinary and miraculous intervention, since it seems that nothing can happen to them which is extraordinary or supernatural, inasmuch as all events are only consequences of their own nature. But we must remember what we have said above concerning miracles occurring in the universe - that they always conform to the universal law of general order, even though they may be above the subordinate rules. Since every person or substance is like a little world which expresses the great one, we can say equally that this extraordinary action of God upon this substance is always miraculous, though it is included in the general order of the universe insofar as that order is expressed by the essence or individual concept of this substance. Therefore there is nothing supernatural in us if we include in our nature everything which it expresses, for it extends to everything, since an effect always expresses its cause and since God is the true cause of the substances. But that which our nature expresses more perfectly belongs to it in a particular way, because it is in this expression that its power consists; yet this power is limited, as I have just explained. There are therefore many things which surpass the powers of our nature and even the powers of all limited natures. To speak more clearly, therefore, I say that the miracles and extraordinary interventions of God have this peculiarity that they cannot be foreseen by the reasoning of any created spirit, no matter how enlightened, because the distinct understanding of the general order is beyond all such spirits. Everything which is called natural, on the other hand, depends on less general maxims which creatures can understand. In order, then, that my words as well as my meaning may be beyond criticism, it is convenient to adapt certain ways of speech to For references see p. 328
314 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS certain thoughts. We can therefore define our essence or idea as that which includes everything which we express. And since our substance expresses our union with God himself, it has no limits and nothing is beyond it. But whatever is limited in us could be called our nature or our power, and in this seme, whatever surpasses the natures of all created substances is supernatural. 17. An example of a subalternate maxim in a law of nature; where it is shown that God always conserves by rule the same force but not the same quantity of motion, against the Cartesians and many others. I have already made frequent mention of subordinate rules or of the laws of nature, and it seems desirable to give an example of these. Our new philosophers commonly make use of the famous rule that God always conserves the same quantity of motion in the world. This rule is indeed most plausible, and I have in the past regarded it as beyond doubt. But more recently I have di~covered wherein it is in error. This is that Descartes and many other able mathematicians believed that the quantity of motion, that is, the velocity multiplied by the magnitude of the moving body, coincides exactly with the moving force; or to speak geometrically, that the forces are proportional to the product of velocities and masses. 21 Now it is reasonable that the same force should always be conserved in the universe. Also, when we attentively observe the phenomena, it is clear that perpetual mechanical motion cannot occur, because then the force of a machine, which is always diminished a little by friction and must therefore soon come to an end, would restore itself and consequently increase itself without any new impulsion from without. We observe also that the force of a body is only diminished in proportion as it imparts force to some bodies contiguous to it or to its own part!! insofar as they have a separate movement. So these mathematician!! have thought that what can be said of force can also be said of the quantity of motion. But to show that there is a difference, I make the assumption that a body falling from a certain height acquires the force to rise again to the same height if its direction carries it that way and if it meets with no obstructions. For example, a pendulum would rise again exactly to the height from which it has descended if air resistance and other small obstacles did not ~lightly diminish its acquired force. I make the further assumption that it takes as much force to lift a body A of 1 pound to the height CD of 4 fathoms as it takes to lift a body B of 4 pounds to the height of 1 fathom. All this is admitted by our new philosophers. It is clear, then, that having fallen from the height of CD, the body A has acquired exactly as much force as the body B when it has fallen from the height EF (see No. 34, Figure 11, p. 297). For the body B, having fallen to F and possessing at this point the force to rise again to E (by my first assumption) has therefore enough force to lift a body of 4 pounds, that is to say, itself, to the height EFof 1 fathom; and similarly, the body A, having fallen to D and having at this point enough force to rise to C, has the power to lift a body of 1 pound, that is, itself, to the height CD of 4 fathoms. Then (by the second assumption) the force of these two bodies is equal. Let us see now if the quantity of motion is also equal in the two bodies; here we shall be surprised to find a very great difference. For as Galileo has demonstrated, the velocity acquired by the fall CD is twice the velocity acquired by the fall EF, though the height is four times as big. Then if we multiply the body A (equal to 1) by its velocity (equal to 2), the product or the quantity of motion will be equal to 2; on the other hand, if we multiply the body B (equal to 4) by its velocity (which is equal to 1), the product or quantity of motion will be equal to 4. So the quantity of motion of the body A at the point D is half the quantity of motion of the body B at the point F;
HANOVER TO THE ITALIAN JOURNEY, 1676-87 315 yet their forces are equal. Thus there is a great difference between quantity of motion and force, which was to be proved. We may see from this that force must be estimated by the quantity of the effect which it can produce, for example, by the height to which a heavy body of a certain size and kind can be lifted; and thi .. is quite different from the velocity which can be imparted to it. To give it double its velocity, more than double the force is necessary. Nothing is simpler than this proof, and Descartes has fallen into error here only because he had too much confidence in his thoughts even when they were not yet sufficiently mature. But I am surprised that his disciples have not since discovered this error. I fear that they are beginning little by little to imitate certain of the Peripatetics whom they ridicule, like them gradually acquiring the habit of consulting the books of their master rather than reason and nature. 18. The distinction between force and quantity of motion is important among other reasons in order to show that we mllst have recourse to metaphysical considerations apart from extension in order to explain the phenomena of bodies. This consideration, in which force is distinguished from quantity of motion, is of importance not only in physics and mechanics in finding the true laws of nature and the rules of motion, and even in correcting many errors in practice which have slipped into the writings of a number of able mathematicians, but also in metaphysics for the better understanding of the principles. For considering only what it mean~ narrowly and formally, that is, a change of place, motion is not something entirely real; when a number of bodies change their position with respect to each other, it is impossible, merely from a consideration of these changes, to determine to which bodies motion ought to be ascribed and which should be regarded as at rest, as I could show geometrically if I wished to stop now to do it. But the force or the immediate cause of these changes is something more real, and there is a sufficient basis for ascribing it to one body rather than to another. This, therefore, is also the way to leam to which body the motion preferably belongs. Now this force is something different from size, figure, and motion, and from this we can conclude that not everything which is conceived in a body consists solely in extension and its modifications, as our modems have persuaded themselves. Thus we are compelled to restore also certain beings or forms which they have banished. And although all particular phemomena of nature can be explained mathematically or mechanically by those who understand them, it becomes more and more apparent that the general principles of corporeal nature and of mechanics themselves are nevertheless metaphY3ical rather than geometrical and pertain to certain forms or indivisible natures as the causes of what appears rather than to the corporeal or extended mas'l. This reflection is capable of reconciling the mechanical philosophy of the modems with the caution of certain intelligent persons of good will who fear, with some reason, that we may withdraw too far from immaterial beings and thereby put piety at a disadvantage. 19. The utility affinal causes in physics. Since I do not like to accuse people wrongly, I make no charge against our new philosophers who claim to banish final causes from physics, but I am nonetheless obliged to confess that the consequences of this opinion seem to me to be dangerous, expecially if I combine it with the view which I refuted at the beginning of this discourse, which seems to go the length of denying final causes entirely, as if God in acting had proposed no end or good whatever, or as if the good were not the object of his will. I hold on the contrary, that it is exactly in this that the principle of all existences and of the laws of nature is to be sought, for God always For references see p. 328
316 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS aims at the best and the most perfect. I willingly admit that we are liable to deceive ourselves when we try to determine the ends or design~ of God, but this is only when we seek to limit them to some particular design, thinking that he has had in view only one particular thing, when in fact he at the same time takes into consideration the whole. Thu~ it i~ a great abuse to believe that God made the world only for us, although it is very true that he made it in its entirety for us and that there is nothing in the universe which does not affect us and which does not also comply with the regard which he has for us, in accordance with the principles set forth above. Therefore when we see any good effect or some perfection which occurs or which ensue~ from the works of God, we can say with certainty that God has purposed it, for he does nothing by chance and is not comparable to us, who sometimes fail to do what is good. Therefore, while overzealous politicians may deceive themselves by imagining too much subtlety in the designs of their princes, or while commentators may err in seeking more erudition in their author than he has, we cannot be mistaken in this or attribute too much reflection to thi~ infinite wi~dom, and there is no subject in which we need less to fear error provided we limit ourselves to affirmations and avoid negative statements which limit the designs of God. Anyone who sees the wonderful structure of animals will find himself forced to recognize the wisdom of the Author of all things. And I advise tho~e who have any feeling of piety, and indeed of true philosophy, to keep away from the phrases of certain would-be freethinkers who say that we see because we happen to have eyes but that eyes were not made for the purpose of seeing. If one seriously accepts these opinions which ascribe everything to the necessity of matter or to a certain chance (though both of these views should seem ridiculous to anyone who understands what we have explained above), it is difficult to acknowledge an intelligent Author of nature. For the effect must correspond to its cause and is even known best through a knowledge of its cause. It is unreasonable to introduce a sovereign intelligence as the orderer of things, and then, instead of making use of his wisdom, to employ only the properties of matter in explaining phenomena. This is as if a historian should try to explain the conquest of some important place by a great prince, by saying that it occurred because the small particles of gunpowder, set free by the contact of a spark, escaped with a velocity capable of pushing a hard and heavy body against the walls of the place, while the little particles which composed the bronze of the cannon were so firmly interlaced that this velocity did not force them apart; instead of showing how the foresight of the conqueror led him to choose suitable time and means, and how his power overcame all obstacles. 20. A noteworthy passage by Socrates in Plato's Phaedo against the philosophers who are too materialistic. This reminds me of a beautiful passage by Socrates in Plato's Phaedo which agrees most remarkably with my opinions on this point and seems to be directed expressly against our too materialistic philosophers. Hence I have been tempted to translate this account, although it is a little long. Perhaps this little sample will lead someone to select for us many of the other beautiful and sound thoughts which are found in the writings of this famous author. 22 21. Ifmechanicallaws depended upon geometry alone without metaphysics, phenomena would be entirely different. Now since the wisdom of God has always been recognized in the detail of the mechanical structure of certain particular bodies, it must also be shown in the general economy of the world and in the constitution of the laws of
HANOVER TO THE ITALIAN JOURNEY, 1676-87 317 nature. This i~ so true that one can observe the designs of this wisdom in the general laws of motion. For if there were nothing in bodies but extended mass, and nothing in motion but change of place, and if everything should and could be deduced solely from the definitions of these by geometric necessity, it would follow, as I have elsewhere shown, that the smallest body, in colliding with the greatest body at rest, would impart to it its own velocity, without losing any of this velocity itself; and it would be necessary to accept a number of other such rules which are entirely contrary to the formation of a system. 23 But the decree of the divine wisdom to conserve always the same total force and the same total direction has provided for this. I find even that several effects of nature can be doubly demonstrated; once, by the consideration of their efficient cause, and again, independently, by the consideration of the final cause, making use for example, of the decree of God always to produce his effect by the easiest and most determined ways, as I have shown elsewhere in accounting for the rules of catoptrics and dioptrics; I shall have more to say about this soon. 24 22. A reconciliation of two methods of explanation, one of which proceeds by final causes, the other by efficient causes; to satisfy both those who explain nature mechanically as well as those who have recourse to incorporeal natures. It is convenient to make this comment in order to reconcile those who hope to explain mechanically the formation of the primary texture of an animal and the whole machinery of its parts, with those who account for this same structure through final causes. Both methods are good, both can be useful not only for admiring the skill of the great workman but also for making usefuJ discoveries in physics and in medicine. Authors who take these different routes ought not to abuse each other. For those who are intent on explaining the beauty of the divine anatomy, I observe, laugh at those who imagine that what seems to be a chance flow of certain liquids could have produced so beautiful a variety of part~ and denounce them as rash and irreverent. And these latter, I observe also, treat the former in their turn as simple and superstitious, comparing them to the ancients who regarded the physicists as impious when they maintained that it is not Jupiter who thunders but some matter found in the clouds. 25 The best would be to combine the two points of view, for if I be permitted to use a lowly comparison, I acknowledge and praise the skill of a workman, not only in showing the plans which he had in making the pieces of his machine, but also in explaining the tools which he has used in making each piece, especially when these tools are simple and cleverly contrived. And God i~ an artisan skilful enough to produce a machine a thousand times more ingenious than that of our bodies, by using nothing but certain rather simple fluids formed expressly in such a way that only the ordinary laws of nature are needed to give them the organization necessary to produce so admirable an effect. But it is true also that this would not happen If God were not the Author of nature. Yet I find that the way of efficient causes, which is in fact the profounder and in some ways the more immediate and a priori, is on the other hand, rather difficult when one comes to details, and I believe that for the most part our philosophers are still far from mastering it. The way of final causes, however, is easier and is often useful for understanding important and useful truths, which one would be a long time seeking by the other more physical route; of this fact, anatomy can provide significant examples. I believe, too, that Snell, who first discovered the rules of refraction, would have waited a long time to find them if he had sought first to discover how light is formed. But apparently he followed the method which the ancients used in catoptrics, which is in fact that of final causes. For seeking For references see p. 328
318 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS the easiest way in which to direct a ray from one given point to another through reflection by a given plane (assuming that the easiest way is the plan of nature), they discovered the equality of the angles of incidence and reflection, as one can see in a little treatise by Heliodorus of Larissa and elsewhere. This method, I believe, Snell, and later though independently of him Fermat, applied most ingeniously to refraction. For when rays in the same media observe a ratio between the sines which is equal to the ratio of the resistances of the media, this happens to be the easiest, or at least the most determined way to pass from a given point in one medium to a given point in another. The demonstration which Descartes sought to give of this same theorem by the method of efficient causes is not nearly so good. At least we have grounds to suspect that he would never have found it by this method if he had not learned anything of Snell's discovery in Holland. 26 23. To return to immaterial substances, it is explained how God acts on the understanding of spirits; and whether one always has the idea of that which he thinks. I have found it proper to stress these considerations about final causes, incorporeal natures, and an intelligent cause m connection with bodies in order to show their usefulness even in physics and mathematics and thus to purge the mechanical philosophy, on the one hand, of the impiety with which it is charged and, on the other hand, to raise the spirit of our philosophers from exclusively material considerations to nobler meditations. Now it will be fitting to return from bodie~ to immaterial natures, and particularly to spirits, and to say something about the way God takes to enlighten them and to act upon them. We must not doubt that there are certain laws of nature here also, about which I could speak more fully elsewhere. At present it will suffice to say something about the doctrine of ideas, and whether we see all things in God, and the sense in which God is our light. 27 It may be observed appropriately that a wrong use of the ideas gives occasion for several errors. For when one reasons about ~omething, one imagines himself to have an idea ofthat thing, and this is the basis on which certain philosophers, ancient and modern, have built one of the demonstrations of God which is most imperfect. For I must have an idea of God, they say, or of a perfect being, since I think of him, and one cannot think without an idea; now the idea of this being includes all perfections, and existence is one of these; therefore he exists. But since we often think of impossible chimeras, for example, of the highest degree of speed, or the largest number, or the intersection of the conchoid with its base or asymptote, this reasoning is insufficient. In this sense, then, we can say that there are true and false ideas, according to whether the thing concerned is possible or not. So one can boast of having an idea of a thing only when one is assured of its possibility. Thus the argument given above at least proves that God exists necessarily, if he is possible. It is indeed an excellent privilege of the divine nature that it needs only its possibility or essence in order actually to exist, and this is precisely what we mean by an ens a se. 24. On what constitutes clear or obscure, distinct or confused, adequate or inadequate, intuitive or suppositive, knowledge; nominal, real, causal, and essential definition. In order better to understand the nature of ideas, we must to some extent touch upon the various kinds of knowledge. 28 When I can recognize one thing among others but cannot say in what its differences or properties consist, my knowledge is confused. In this way we sometimes know clearly, and without having a doubt of any kind, if a poem or a picture is well done or badly, because it has a certain 'something, I know not
HANOVER TO THE ITALIAN JOURNEY, 1676-87 319 what' which either satisfies or repels us. But when I can explain the criteria I use, my knowledge is called distinct. Of this kind is the knowledge of an assayer who distinguishes the true gold from the false by means of certain tests and marks which make up the definition of gold. But distinct knowledge has degrees, for usually the concepts which enter into the definition would themselves need definition and are known only confusedly. But when everything which enters into a definition or distinct knowledge is known distinctly, down to the primitive concepts, I call such knowledge adequate. And when my mind grasps all the primitive ingredients of a concept at once and distinctly, it possesses an intuitive knowledge. This is very rare, since for the most part human knowledge is merely either confused or suppositive. It is well also to distinguish nominal and real definitions. I call a definition nominal when it can stilI be doubted that the defined concept is possible. So for example, if I say that an endless screw is a line in three dimensions whose parts are congruent or can be brought to coincide with each other, anyone who does not know from another source what an endless screw is could doubt whether such a line is possible, even though this is in fact one of the reciprocal properties of the endles,> screw, for the other lines whose parts are congruent to each other (there are only two, the circumference of a circle and the straight line) are plane figures, that is to say, they can be drawn in a plane. This shows us that every reciprocal property can serve as a nominal definition but that when the property makes us understand the possibility of a thing, it establishes a real definition. As long as we have only a nominal definition, we cannot be sure of the consequences drawn from it, for if it concealed some contradiction or impossibility, we could draw conflicting conclusions. This is why truths do not depend on names and are not arbitrary, as some modem philosophers have thought. Nevertheless, there is still a great difference between the kinds of real definitions, for when possibility is proved only through experience, the definition is only real and nothing more; as in the definition of quicksilver, the possibility of which we recognize because we know that such a body, extremely heavy and yet rather volatile, is actualIy found. But when the proof of possibility is presented a priori, the definition is both real and causal, as when it contains the possible production of the thing. And when the definition pushes its analysis back to the primitive concepts without assuming anything which needs an a priori proof of its possibility, it is perfect or essential. 25. In what case our knowledge is combined with the comtemplation 0/ the idea. Now it is obvious that we have no idea of a concept when it is impossible. And in the case of merely suppo,itive knowledge, even if we may have an idea, we do not grasp that idea, for such a concept is known only in the same way as are those concepts which involve a hidden impossibility; even if it is possible, we cannot learn of its possibility by this way of knowing. For example, when I think of the number 1,000, or ofa regular polygon of a thousand sides, I frequently do it without grasping the idea; just as I do when I say that a thousand is 10 times 100, without taking the trouble to think of what 10 and 100 are, because I suppose that I know it and do not think it necessary to stop just at present to conceive them. So it may very well happen - as it does in fact often happen that I am in error about a concept which I suppose or believe I understand, although it is in fact impossible, or at least incompatible with other concepts with which I combine it. And whether I am in error or not, this suppositive way of forming concepts remains the same. It is therefore only when our knowledge of confused concepts is clear, and our knowledge of distinct concepts is intuitive, that we see their whole ideas. For references see p. 328
320 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 26. That we have within us all of the ideas. Plato's doctrine of reminiscence. In order properly to conceive correctly what an idea is, we must forestall an ambiguity, for several thinkers take the idea for the form or the differential of our thoughts, and thus we have an idea in our mind only insofar as we are thinking of it, and every time we think of it anew we have another idea of the same thing, though it is similar to the preceding ones. But others, it seems, take the idea to be an immediate object ofthought or for some permanent 29 form which remains even when we no longer contemplate it. As a matter of fact, our soul always does have within it the disposition to represent to itself any nature or form whatever, when an occasion arises for thinking of it. I believe that this disposition of our soul, insofar as it expresses some nature, form, or essence, is properly the idea of the thing, which is in us and is always in us whether we think of it or not. For our soul expresses God and the universe, and all the essences as well as all the existences. This is in accord with my principle~, for nothing enters naturally into our minds from without, and it is a bad habit we have of thinking as if our soul received certain 'species' as messengers and as if it had doors and windows. 30 We have all these forms in our own minds, and even from eternity, for at every moment the mind expresses all its future thought and already thinks confusedly of everything of which it will ever think distinctly. Nothing can be taught us the idea of which is not already in our minds, as the matter out of which our thought is formed. This Plato has excellently recognized in proposing his doctrine of reminiscence, a well-founded doctrine provided it is taken rightly and purged of the error of pre-existence and provided that we do not imagine that the soul must already have known and thought distinctly at some past time about what it learns and thinks now. Plato has also confirmed his opinion by a beautiful test, introducing a small boy, whom he gradually guides toward the most difficult geometric truths about incommensurables without teaching him anything, but merely asking the appropriate questions in good order. 31 This shows that our soul knows all these things virtually and needs only to turn its attention to them to recognize truth, and therefore that it at least has the ideas upon which these truths depend. One may even say that it already possesses these truths, if we consider them as the relations between the ideas. 27. How our soul can be compared to empty tablets, and how our notions come from sense. Aristotle preferred to compare our soul~ to tablets that are still blank but upon which there is a place for writing and maintained that there is nothing in our understanding which does not come from the senses. This conforms more with popular notions, as Aristotle usually does, while Plato goes deeper. Yet these kinds offormulas or practical commonplaces are allowed in ordinary usage, in about the same way as Copernicam continue to say that the sun rises and sets. I even find that such usages can often be given a good meaning, according to which they involve no falseness, in the same way that I have already shown in what sense we may truly say that particular substances act upon each other. In this same sense we can also say that we receive our knowledge from without through the ministry of the senses, because certain exterior things contain or express more particularly the reasons which determine our sou to certain thoughts. But when the exactness of metaphysical truths is involved, it is important to recognize the compass and independence of our soul, which reaches infinitely further than is popularly thought, even though we ascribe to it, in the language of ordinary life, only what is most manifestly perceived and what pertains to us more particularly, since under these conditions it serves no purpose to go further. It would
HANOVER TO THE ITALIAN JOURNEY, 1676-87 321 be appropriate, nevertheless, to choose fitting terms for the two meanings, in order to avoid equivocation. So the expressions which are in the soul, whether conceived or not, can be called ideas, but those which are conceived or formed can be called notions or concepts. But in whatever sense they are taken, it is always false to say that all of our notions come from the senses which are called external; for the notions which I have of myself and of my thoughts, and, consequently of being, of substance, of action, of identity, and of many others, come from an internal experience. 28. God is the only immediate object of our perceptions which exists outside of us, and he only is our light. In the rigorous sense of metaphysical truth there is no external cause which acts upon us except God alone, and he alone communicate~ himself to us immediately by virtue of our continual dependence upon him. Whence it follows that there is no other external object which affects our soul and immediately excites our perception. It is also only by virtue of the continual action of God upon us that we have in our soul the ideas of all things; that is to say, since every effect expresses its cause, the essence of our soul is a certain expression, imitation, or image of the divine essence, thought, and wiII and of all the ideas which are comprised in God. So it can be said that God alone is our immediate object outside of us and that we see all things through him; for example, when we see the sun and the stars, it is God who has given us and preserves in us the ideas of them and who determines us, through his ordinary concourse, actually to think of them at the moment when our senses are set in a certain manner, in conformity with the laws which he has established. God is the sun and the light of souls - lumen illuminans omnem hominem venientem in hunc mundum 32 ; and this opinion has not been invented only today. In addition to the Holy Scriptures and the Fathers, who were always more Platonists than Aristotelians, I recall having observed long ago that at the time of the Scholastics, several believed that God is the light of the soul and as they put it, the intellectus agens animae rationalis. 33 The Averroists gave this a bad turn of meaning, but others, among them William of Saint Amour, I believe, and several mystical Theologians, understood it in a way worthy of God and capable of elevating the soul to a knowledge of its true good. 29. Nevertheless we think immediately through our own ideas and not through those of God. I am not of the opinion of certain able philosophers, however, who seem to hold that our ideas themselves are in God and not at all in us. In my opinion this results from their failure adequately to consider the nature of substances as we have here explained it, and the full compass and independence of the soul, which includes all that happens to it and expresses God and with him all actual and possible beings as an effect expresses its cause. It is also inconceivable that I should think by means of the ideas of someone else. The soul, too, must actually be affected in a certain way when it is thinking of something, and must therefore have within it, in advance, not merely a passive power of being thus affected, a power already entirely determined, but also an active power by virtue of which it has always had, within its own nature, marks of the future production of this thought and the disposition to produce it at the proper time. All this already enfolds the idea embraced in this thought. 34 30. How God inclines our soul without necessitating it; that there is no reason whatever for complaint; that we must not ask why Judas sinned since this free action is contained in his concept, but we must ask only why Judas the sinner, is admitted to existence in preference to other possible persons. As for the action of God upon the human will, this involves many rather difficult problems which it would take too long to pursue here. For references see p. 328
322 LEI'BNIZ: PHILOSOPHICAL PAPERS AND LETTERS Yet these rough indications may be given. In concurring ordinarily with our actions, God follows only the laws which he has established, that is to say, he continually preserves and produces our being in such a way that our thoughts come to us spontaneously or freely in the order which the concept of our individual substance implies. In this concept it was possible to foresee them frpm all eternity. Furthermore, by virtue ofthe decree which he has made that the will ~hall always strive toward the apparent good, by expressing or imitating God's will pnder certain particular conditions (with respect to which this apparent good always fS to some extent a true good), God determines our will to choose what seems to be the best, but without constraining it. For in an absolute sense the will is in a state of indifference, insofar as this is the opposite of necessity, and it has the power to act otherwise or also to suspend its action ent,irely, since both alternatives are and remain possible. It rests with the soul, therefore, to guard itself against surprises coming from appearances by means of a firm will, to reflect, and not to' act or judge in certain circumstances until after careful and mature deliberation. It is nonetheless true and, indeed, even assured from all eternity that a certain soul will not make use of this power in such circumstances. But whose fault is that? Can the soul complain of anyone but itself? For all such complaints made after the deed are unjust, if they would have been unjust before the deed as well. Could this soul, just before sinning, in good faith complain of God as if he determined it to sin? Since the determinations of God in such matters cannot be foreseen, how can the soul know that it is determined to sin unless it is already sinning in fact? It is merely a question of not willing, and God could not grant an easier and juster condition. So, too, all judges consider only the question of how evil a man's will is, without seeking the reasons which have disposed him to have an evil will. But can it be that it is assured from all eternity that I shall sin? Answer this for yourselves; perhaps it is not. So instead of musing on what you cannot know and what cannot give you any light, act according to the duty which you know. But someone else may say, how does it come that this man will certainly commit this sin? The reply is easy; it is that otherwise he would not be this man. For God foresees from all time that there wiII be a certain Judas, whose idea or concept which God has contains this future free act. There remains then only this question: Why does such a Judas, a traitor, who is merely possible in the idea of God, actually exist? But to this question no answer can be expected here on earth, except the general one that since God has found it good that he should exist in spite of the sin which God foresaw, this evil must be compensated for with interest in the universe and that God wiII draw a greater good from it and that it wiII tum out finally that this sequence of events, including the existence of this sinner, is the most perfect among all other possible kinds. But as long as we are sojourners in this world, it will be impossible always to explain the admirable economy of this choice; it is enough to know it without understanding it. Here it is time to acknowledge the height of the riches, the depth and the abyss, of the divine wisdom, without seeking a detail which involves infinite considerations. It is well understood, however, that God is not the cause of evil. For it is not only after man 's fall from innocence that originalsin has got hold of the soul; even before, there was an original limitation or imperfection connatural to all creatures, which makes them capable of sin or failure. There is therefore no greater difficulty in supralapsarianism than in other views. And to this, I believe, the opinion of St. Augustine and other authors should be reduced who hold that the root of evil lies in nothingness,
HANOVER TO THE ITALIAN JOURNEY, 1676-87 323 that is, in the privation or limitation of creatures, which God graciously corrects by that degree of perfection which it pleases him to give. This grace of God, whether ordinary or extraordinary, has its degrees and measures; in itself it is always efficacious in producing a definite proportional effect, and furthermore, it is always sufficient not only to protect us from sin but even to accomplish salvation, provided that man meets it with his own powers. But it is not always sufficient to surmount the inclinations of man, for otherwise he would have nothing more to strive for, and this is reserved solely for the absolutely efficacious grace which is always victorious, whether through itself or through the congruity of circumstances. 31. On the motives ofelection, on faith foreseen, on the middle science, on the absolute decree, and that every thing reduces itself to the reason why God has chosen and resolved to admit to existence a particular possible person whose concept includes just such a sequence of graces and of free actions. This brings to an end at once all the difficulties. Finally, God's acts of grace are those of an entirely pure grace, and creatures have no claim upon them. Yet in accounting for the choices which God makes in dispensing his grace, it is not enough to have recourse to his absolute or conditional foresight into the future actions of men. Just so it is also a mistake to imagine absolute decrees without any reasonable motive. As for God's foreknowledge of faith and good works, it is most true that God has elected only those whose faith and charity he has foreseen, quos se fide donaturum praescivit. 3s But the same question once more arises: Why will God give the grace of faith and good works to some rather than to others? As for this knowledge of God, which is the foresight not of man's faith and good deeds but of the material and predisposition for them, or that which man on his part would contribute, it seems to some that one might say that God, seeing what man would do without grace or extraordinary help, or at least what man would contribute on his side apart from grace, might resolve to bestow his grace upon those who have the best natural dispositions or at any rate, the least imperfect and evil dispositions. For there are diversities on the side of man as truly as on the side of grace; man needs, indeed, to be aroused to the good and converted, but he must also act afterward in this direction. But if this be so, it could still be said that these natural dispositions, insofar as they are good, are still the effect of a grace, though of ordinary grace, God having favored some more than others. And since he very well knows that these natural advantages which he gives will serve as motives of his extraordinary grace or assistance, is it not ture according to this doctrine that eventually everything is reduced entirely to his mercy? I think therefore that since we do not know how much and in what way God takens into consideration the natural dispositions in dispensing his grace, it will be most exact and certain to say, in accordance with our principles and as I have already said, that among the possible beings there must be that person Peter or John whose concept or idea contains the entire sequence of grace, ordinary and extraordinary, along with all the other events and their circumstances, and that it has pleased God to choose this one person for actual existence among an infinity of other equally possible persons. With this it seems to me that all questions are answered and all difficulties have vanished. As for the one great question of why it has pleased God to choose one out of so many other possible persons, it would be very unreasonable not to be content with the general reasons which we have given, since the details lie beyond us. So instead of having recourse to an absolute decree which is unreasonable since it has no reason, For references see p. 328
324 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS or to reasons which do not solve the difficulty completely and need further reasons themselves, it will be best to say, with St. Paul, that in this God has obeyed certain great counsels of wisdom or of congruity unknown to mortals and based on the general order whose end is the greatest perfection of the universe. It is to this that are reduced the motives of the glory of God, ofthe manifestation of his justice as well as his mercy and of his perfections in general, and finally, that immense depth of his riches with which the soul of St. Paul himself was so transported. 36 32. Usefulness of these principles for matters of piety and of religion. For the rest, it seems that far from harming religion, the thoughts which we have just presented particularly the great principle of the perfection of God's works and that of the concept of substance which include~ all its experiences along with the circumstances under which they occur - serve rather to confirm it, to dissipate very great difficulties, to inflame souls with a divine love, and to elevate spirits to the knowledge of the incorporeal substances much better than do the hypotheses which we have seen until now. For it appears most clearly that all the other substances depend on God as our thoughts emanate from our substance, that God is all in all, that he is closely united with all his creatures, yet in proportion to their perfection, and that it is he alone who determines them from without through his influence. If to act means to determine immediately, then it can be said in this sense, in the language of metaphysics, that only God acts upon me and only he can do good or evil to me, all other substances contributing only in proportion to these determinations, since God, who takes them all into consideration, distributes his goodness and compels all substances to adjust themselves to each other. So only God, also, constitutes the link or communication between the substances, and it is through him that the phenomena of the one meet with and agree with those of the others and that consequently there is reality in our perceptions. In practice, however, action is attributed to particular reasons in the sense which I have explained above, because it is not necessary always to mention the universal cause in particular cases. We see also that every substance has a perfect spontaneity, which becomes freedom in the intelligent substances, that everything which happens to it is the result of its idea or its being, and that nothing determines it save God alone. It is for this reason that a person of exalted spirit, revered for her saintliness, was wont to say that the soul should often think as if only God and itself were in the world. Nothing can give us a stronger understanding of immortality than this independence and compass of the soul, which protects it absolutely from all external things, since it alone makes up its own world and is self-sufficient with God. And it is as impossible for the soul to perish, except by annihilation, as it is for the world (of which it is a living, perpetual expression) to destroy itself. It is therefore impo~sible that the changes in this extended mass which is called our body could affect the soul in any way, or that the decomposition of the body could destroy that which is indivisible. 33. Explication of the relation of the soul to the body, a matter which has been regarded as inexplicable or as miraculous; and on the origin of confused perceptions. We are thus unexpectedly brought to a clear insight into the great mystery of the union of body and soul, that is to say, how it happens that the passions and actions of the one are accompanied by the actions and passions, or their corresponding phenomena, in the other. For there is no way in which we can conceive of an influence 37 of the one on the other, and it is unreasonable simply to have recourse to the extraordinary operation of the universal cause in so ordinary and particular a thing. But the true principle is this: We
HANOVER TO THE ITALIAN JOURNEY, 1676-87 325 have said that everything which happens to the soul and to each substance follows from its concept; hence the idea itself, or the essence of the soul, carries with it that all its appearances or perceptions must arise spontaneously out of its own nature and in just such a way that they correspond, by themselves, to what happens in the entire universe but more particularly and more perfectly to what happens in the body which is assigned to it. For the soul expresses the state of the universe only in a particular way and at a definite time, according to the relation of other bodies to its own. This shows us also how our body belongs to us without being attached to our essence. 38 I believe that those who have the gift of meditation will judge favorably of our principles for the single reason that they will be able to realize easily in what consists the connection between the soul and the body, which seems inexplicable in any other way. We see also that our sense perceptions, even when they are clear, must necessarily contain a certain confused feeling, for, since all the bodies of the universe are in sympathy with each other, ours receives impressions from all the rest, and though our senses are in response to all of them, it is impossible for our soul to pay attention to every particular impression. This is why our confused sensations result from a really infinite variety of perceptions. This is somewhat like the confused murmur heard by those who approach the seashore, which comes from the accumulation of innumerable breaking waves. For if out of several perceptions which do not harmonize so as to make one, there is no single one which surpasses the others, and if these perceptions make impressions that are about equally strong and equally capable of holding the attention of the soul, it can perceive them only confusedly. 34. 39 On the difference between spirits and other substances, souls or substantial forms; that the immortality which is required includes memory. Assuming that the bodies which make up a unum per se, for example man, are substances and that they have substantial forms, and assuming that beasts have souls, we must admit that these souls and substantial forms cannot entirely perish any more than can atoms or the ultimate parts of matter in the opinions of other philosophers. For no substance perishes, although it may become entirely different. Those substances, too, express the whole universe, although more imperfectly than do the spirits. But the chief difference is that they do not know what they are or what they do, and since, consequently, they cannot reflect, they are unable to discover necessary and universal truths. It is also because they lack reflection about themselves that they have no moral quality.40 Hence, though animals may pass through a thousand transformations like that which we see when a caterpillar changes into a butterfly, yet from the moral or practical point of view the result is just as if they had perished; indeed, one may even say that they have perished in a physical sense, that is, in the sense in which we say that bodies perish through their corruption. But the intelligent soul, knowing what it is and being able to say this little word 'I' which means so much, not merely remains and subsists metaphysically (which it does in a fuller sense than the others) but also remains the same morally and constitutes the same character. For it is memory or the knowledge of this 'I' which makes it capable of punishment and reward. Likewise, the immortality which is demanded in morals and religion does not consist merely in this perpetual subsistence which is common to all substances, for without a memory of what one has been, there would be nothing desirable about it. Suppose some private man should suddenly become king of China, but only on condition that he forget what he had been, just as if he were being born anew; would it not be the same practically, or so far as discernible For references see p. 328
326 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS effects are concerned, if he were annihilated and a king of China created at the same instant in his place? This particular man has no reason whatever to desire this. 35. The excellence of spirits; that God considers them preferable to other creatures; that spirits express God rather than the world, while the other simple substances express the world rather than God. But in order to support by natural reasons the view that God will preserve for all time not merely our substance but also our person, that is to say, the memory and knowledge of what we are (though the distinct knowledge is sometimes suspended in sleep and in fainting fits), we must add morals to metaphysics. That is to say, we must consider God, not only as the principle and cause of all substances and all beings, but also' as the head of all persons or intelligent substances and as the absolute monarch of the most perfect city or state, such as is the universe composed of all the spirits together, God himself being the most perfect of all spirits, as well as the greatest of all beings. For certainly spirits are the most perfect of beings and those which best express the divine being. And since the whole nature, end, power, and function of substance is merely t,o express God and the universe, as we have explained at length, there is no reason to doubt that those substances which express him with a knowledge of what they are doing, and which are capable of knowing the great truths about God and the universe, express him better beyond all comparison than do those natures which are either brutish or incapable of knowing truth or entirely destitute of feeling and knowledge. Moreover, the difference between the intelligent substances and those which have no intelligence at all is just as great as that between a mirror and one who sees. And since God himself is the greatest and wisest of spirits, it is easy to understand that the beings with whom he can enter into conversation, so to speak, and even into a society, communicating his opinions and his will to them in a particular manner and in such a way that they can recognize and love their benefactor, must be infinitely nearer to him than all other things which can pass only for the instruments of spirits. So we see that all wise persons value man infinitely more highly than any other thing, no matter how precious, and it seems that the greatest satisfaction that a soul can have, which is content in other respects, is to see itself loved of others. However there is this difference with respect to God - the glory and the worship which we offer cannot add to his satisfaction, since the knowledge of creatures is only a result of his sovereign and perfect happiness, far from contributing to it or being a partial cause of it. However, whatever ;s good and re,\sonable in finite spirits is found preeminently in him. And just as we would praise ~ king who prefers to save the life of one man above that of his rarest and most preci~us animal, so we cannot doubt that the most enlightened and most just of all monarchs is of the same opinion. 36. God is the monarch of the most perfect Republic consisting of all spirits, and the happiness 0/ this City 0/ God is his principal design. Spirits are indeed the most perfectible of substances, and their perfections have the particular advantage of interfering with each other in the least possible degree, or rather of supporting each other, for only the most virtuous can be the most perfect friends. Hence it obviously follows that God, who always aims at the greatest general perfection, will have the greatest concern for spirits and will give to them, not only in general but to each one in particular, the greatest degree of perfection which the universal harmony can permit. It can even be said that God, insofar as he is a spirit, is the origin of existences, for otherwise, if he had lacked the will to choose the best, there would be no reason why one possible being should exist in preference to others. So this property of God's being himself a spirit
HANOVER TO THE ITALIAN JOURNEY, 1676-87 327 comes before all other considerations which he may have with regard to the creatures. Only spirits are made in his image and are, as it were, of his blood or like the children of his household, for only they can serve him freely and act with knowledge in imitation of the divine nature. One single spirit is worth a whole world, because it not only expresses the world but also knows it and conducts its life there after the manner of God. So it seems that though every substance expresses the whole universe, yet the other substances express the world rather than God, while the spirits express God rather than the world. This nature of spirits, so noble that they approach divinity as closely as is possible for simple creatures, brings it about that God derives infinitely more glory from theIl1 than from all the other beings or rather that the other beings merely provide spirits with matter for glorifying him. This is why this moral nature of God, which makes him the lord and monarch of spirits, is of a quite singular concern to God personally, if we may say so. It is in this relation that he humanizes himself, that he is willing to tolerate anthropomorphisms, and that he enters into a society with us, as a prince with his subjects. So dear is this consideration to him that the happy and flourishing state of his Empire, which consists in the greatest possible felicity of its inhabitants, becomes his highest law.41 For happiness is to persons what perfection is to beings. And if the highest principle ruling the existence of the physical world is the decree which gives it the greatest perfection possible, the highest purpose in the moral world, or the city of God which is the noblest part of the universe, should be to spread in it the greatest possible happiness. It must not be doubted, therefore, that God has ordered everything in such a way not only that spirits can live forever, which is inescapable but also that they shall forever preserve their moral status, in order that no person may be lost to the city, just as no substance is lost to the world. As a result they will always know what they are, otherwise they would be incapable of reward and punishment, botl\. of which are essential in a republic and especially in the most perfect one where nothing can be overlooked. Finally, since God is at the same time the most just and the most.benevolent of monarchs and demands only a good will, provided it be sincere and serious, his subjects cannot desire a better state. To make them perfectly happy, he asks only that they love him. 37. Jesus Christ has revealed to men the mystery and the admirable laws of the Kingdom of,Heaven and the grandeur of the supreme happiness which God prepares for those who ltve him. The ancient philosophers knew very little about these important truths. Only Jesus Christ has expressed them divinely well and in a manner so clear and simple that the dullest spirits have grasped them. His gospel has thus entirely changed the aspect of human affairs; it has revealed to us the kingdom of heaven or that perfect republic of spirits which deserves the title of the city of God, the admirable laws of which he has revealed to us. He alone has made us see how much God loves us and with what exactness he has provided for all that concerns us; how God who cares for the sparrows will not neglect the reasonable creatures who are infinitely more dear to him; how all the hairs on our head are counted; how heaven and earth may pass away, but the word of God and all that pertains to the economy of our salvation shall endure; how God has more concern for the least of these intelligent souls than for the whole world-mechanism; how we ought not to fear those who can destroy bodies but cannot do any harm to the souls, since only God can make the souls happy or wretched; and how the souls of the righteous are protected by his hand against all the revolutions of the world, since nothing can act upon them save God alone; how none of For references see p. 328
328 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS our acts is forgotten but everything is placed on account, even idle words and a wellused spoonful of water; finally, how everything work<; for the greatest good of those who are good, and the righteous shall be as suns, so that neither our sense nor our spirit has ever tasted anything approaching the happiness which God has prepared for those who love him. REFERENCES Leibniz had been more specific in the original draft, writing 'les Spinozistes'. On Leibniz's grounds for connecting Descartes's voluntarism and mechanism with Spinoza see No. 31, land II. 2 "As a lesser evil is relatively good, so a lesser good is relatively evil." 8 In the original draft, "ofthe new Scholastics". 4 In the illustration originally added here, Leibniz used a geometrical example of the principle ofthe best possible or of maximal determination: "For example, there is an infinity of regular figures, but only one is the most perfect, the circle. If a triangle is to be made without any specification of the kind, God would certainly make an equilateral triangle, because it is the most perfect, absolutely speaking." 5 "To will the same thing and to dislike the same thing is true friendship." 6 Quietism is that extreme mystical doctrine according to which the soul, in surrendering itself to God, is emptied of its own desires and purposes and achieves a state of passive contemplation. The 17th-century movement was stimulated by the Guida spirituafe (1675) of Miguel de Molinos, who died in the prison of the Inquisition in 1696. Among the leaders were Mme Guyon and Fenelon, whose Explication des maximes des saints sur fa vie interieure was a classic of the movement and a center of controversy, notably his own controversy with Bossuet. 7 Originally "the greatest perfection"; since pleasure is the perception of harmony or perfection, the two terms are psychologically and metaphysically analogical to each other. 8 Thus the principle of parsimony is equivalent to the principle of the best possible or of maximal determination. 9 In his Treatise on Nature and Grace Malebranche had restricted God's role in nature to the willing of general principles. See p. 295, note 8. 10 Originally Leibniz had added: "as well as the actions and passions of these creatures themselves". 11 See Introduction, Sec. V, and p. 119, note II. Note that individual substance and logical subject are united by Leibniz in the concept of suppositum. 12 "That here every individual is an infima species" (see p. 271, note 7). 13 Readingprovenante, in accordance with the first draft, rather thanprevenante, as in G., IV, 434. 14 Paracelsus' doctrine of an Archeus was popularized by the elder Van Helmont (Jean Baptiste, 1577-1644), whom Leibniz seems to have associated with it (G., IV, 217). For Leibniz's earlier sources for similar doctrines see No.3 and p. 104, note 20. 15 The phrase that followed in the first draft was: "that bodies are not substances in strict metaphysics (this was indeed the opinion of the Platonists), and ... ". 16 For the arguments for the relativity of space and time see the letters to Clarke (No. 71). They are phenomenal but not subjective in the sense of Berkeley and Hume, for they rest upon the well-ordered relationship of representational systems within existence which derive from the harmonious laws of the individual monads. 17 Identity of past, present, and future is thus assured by the continuity involved in the individual concepts of the monads. Reality which transcends the moment must be analogous to mind. 18 The question arises of the relation of this contingency in man's choices to the subordinate 1
HANOVER TO THE ITALIAN JOURNEY, 1676-87 329 regulations of nature discussed in Sees. 7 and 17. These regulations are abstractions from harmoniously serial laws possessing the same kind of contingency (or self-determination) as man's, though sometimes much simpler. The question may well be raised whether these subordinate regulations, therefore, have the ontological status which Leibniz has assigned to them or are not rather phenomenal. 19 How our judgments can be exempt from the determination of our acts by the law of our nature, Leibniz does not say. 20 Solipsism and even a pluralism of island minds with private experiences are thus avoided, since it is a universal and common realm of meaning which we represent when we think. This Leibniz has shown in his earlier refutations of the arbitrariness of definitions and propositions (No. 17, etc.). This passage also shows the difference between Leibniz's a priorism and Kant's. Both find a region of universality and necessity as the basis for phenomena, and both derive intellectual activity from it, but Leibniz's conception is metaphysical from the beginning, in contrast to Kant's transcendentalism; the realm of universal and necessary truths is an absolute which serves as regulative of our experience rather than constitutive of it. 21 On Leibniz's notion of mass see p. 103, note 8. His concept of mass is clearer than in his early writings, however, being a quantitative measure of passive derivative force or inertia. 22 Leibniz here left a space in the manuscript to insert his paraphrase. His version may be found in G., VII, 335, or more briefly, in No. 37. See also p. 276, note 3. 23 The reference is to the Theory 0/ Abstract Motion, Sec. 20 (No.8, I). 24 See the Tentamen anagogicum (No. 49). The argument was first published in 'Unicum opticae, catoptricae et dioptricae principium', Acta eruditorum (1682). 25 To the old argument between Aristotelians and the moderns as to the nature of life, the discoveries made possible by the microscope in the 17th century added new arguments for both sides. Descartes, influenced by Bacon and Harvey, was of course the chief philosophical authority for mechanism, which was confirmed by the analysis of various organic systems and their functions, such as the lymphatic and other glands, the lungs, and the pyramid cells in the brain. Leibniz's opinion mediates between this mechanism and the extreme vitalism of those like Cudworth and More, and later even Stahl, who introduced animistic principles (see E. Nordenskiold, The History 0/ Biology, New York 1929, chap. 11). 26 On the problem of the relation of Descartes's optics to Snell's, see Mach, The Principles 0/ Physical Optics (trans. Anderson and Young) (1925), pp. 32-33. 27 See Nos. 21 and 33 on the nature of ideas; also p. 271, notes 8, p. 295, notes 7 and 8. 28 Deleted in the first draft: "When I know the possibility of a thing merely through experience, because everything that exists is possible, my knowledge is confused. It is thus that we know bodies and their qualities. But when I can prove the possibility a priori, this knowledge is distinct. " 29 Originally 'subsistent'. The two theories conform to Arnauld's conception of idea as the internal meaning of a perception and Malebranche's conception of an eternal object of our intellect. 30 The Scholastic interpretation of impressed species as mediating between the object and the intellect had led to a material interpretation of them supported by Suarez (De anima, Book iii, chap. 1; Book iv, chap. 2) and others. The view had been critized by Descartes and Hobbes and was discussed by Malebranche in the Recherche, III, Part II, chap. ii. 31 Meno 82c-f 32 "The light which lightens every man that cometh into this world" (John 1 :9). 33 "The active intellect of the rational soul." 34 Malebranche had restricted the activity of the soul to willing. 35 "Whom, he foresaw, he would endow with faith. 36 Cf. Rom. 8:28-30, 9:14-29, etc. 37 See p. 83, note 6.
330 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 38 Thus Leibniz does not regard the soul as the form or activating principle of the body but views their relation as external and determined by the universal harmony. This view is often confused, however, by statements that every composite body (sometimes every living body only) has a uniting and reifying soul. 39 Originally Sec. 34 opened as follows: "I do not yet undertake to determine whether bodies are substances, speaking with metaphysical rigor, or wl).ether they are only true phenomena like the rainbow; nor, as a result, whether there are substances, souls, or substantial forms which are not intelligent." 40 Originally, "no character [personnagej". 41 Originally, "the highest ofthe subalternate laws of his conduct".
36 CORRESPONDENCE WITH ARNAULD 1686-87 (Selections) In February, 1686, Leibniz sent to Count Ernest of Hesse-Rheinfels a summary of his 'petit discours de metaphysique , in 37 propositions, to be transmitted to Antoine Arnauld for his criticism. The latter entered into correspondence with Leibniz reluctantlY, seizing upon one proposition, No. 13, only,for his criticism: Since the individual concept of each person contains once for all everything that will ever happen to him. one may see in it a priori the proofs or reasons for the truth of every event, or why one thing happens rather than another. But however certain they may be, these truths are nonetheless contingent, being founded on the free will of God and of creatures. It is true that there are always reasons for their choice, but these reasons incline without necessitating. In his letter to Ernest of March 13,1686, Arnauldfound this view frightening and without utility, since it implied a 'llecessity more than fatal'. Beginning with the problem ofindividual freedom, the correspondence roughly falls into two parts. In the first Leibniz at length wins a qualified assent to his proposition; in the second the discussion is extended to the more general issues such as the nature of 'concomitance' or harmony, the role of expression in sustaining it, and the interpretation of substance, particularly material substance. The important concluding letters from each part - those of July 14, 1686, and of October 9, 1687 - are here translated. Arnauld's criticisms are sufficiently clear from Leibniz's carefully stated replies. The latter's Italianjourney closed the correspondence in 1687, though he tried without success to renew it in 1690 (No. 38). [G., II, 47-59] July 14, 1686 1 Since I have great deference for your judgment, I was happy to see that you have moderated your criticism after seeing my explanation of the proposition which I regard as important but which you found strange: that "the individual concept of each person contains once and for all everything that will ever happen to him". From it you at first concluded that from the single assumption that God resolved to create Adam, all the remaining human events which happened to Adam and to his posterity followed by a fatal necessity, so that God would no longer have the freedom to control them any more than he could have failed to create a creature capable of thought after he had made the decision to create me. To this I replied that since the designs of God which concern this whole universe are all interrelated in conformity with his sovereign wisdom, he made no decision For references see p. 348
332 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS about Adam without taking into consideration everything which has any connection with him. It is therefore not because of the decision made about Adam but because of the decision made at the same time about everything else (to which the decision made about Adam involves a perfect relation) that God makes up his mind about all human events. There seems to me no fatal necessity in this, or anything contrary to God's freedom, any more than in the generally accepted hypothetical necessity to which God himself is subject, of carrying out what he has resolved. In your reply, Sir, you agree with this relationship which I have proposed between the divine decisions, and you even admit sincerely that at first you understood my proposition in an entirely different sense, because it is not customary, for example (these are your words), to consider the specific concept of a sphere by its relation to that which it is represented to be in the divine mind but by the relation to what it is in itself, and you believed (l admit with good reason) that this is also true in the case of the individual concept of each person. I, for my part, have thought that the full and comprehensive concepts are represented in the divine mind as they are in themselves. 2 But now that you know that this is my opinion, this will suffice for you to accept it as such and to examine whether it removes the difficulty. You seem then to recognize, Sir, that explained in this way, my opinion about full and comprehensive concepts such as are found in the divine mind is not only free from offense but even right. For these are your words: 1 agree that the knowledge which God had of Adam when he resolved to create him includes a knowledge of everything that has happened to him and everything that has happened or will happen to his posterity, and that taking the individual concept of Adam in this sense, what you say is most certain. 3 We shall soon see in what the difficulty which you still find here consists. Meanwhile I shall say a word about the reason for the difference that exists here between the concepts of species and those of individual substances with respect to the divine will rather than to simple understanding. This difference is that the most abstract concepts of species contain only necessary or eternal truths which do not at all depend on the decrees of God (although the Cartesians say they do, you yourself do not seem to be concerned about this point). But the concepts of individual substances, which are complete and suffice to distinguish their subjects completely, and which consequently enclose contingent truths or truths of fact, and individual circumstances of time, place, etc., must also enclose in their concept taken as possible, the free decrees of God, also viewed as possible, because these free decrees are the principal sources of existences or facts. Essences, on the other hand, are in the divine understanding prior to any comideration of the will. This will help us better to understand everything else and to satisfy the difficulties which seem still to remain in my explanation. For you continue as follows: But it seems to me that it still remains to ask - and it is here that my difficulty lies - whether the connection between these objects (I mean Adam and human events) is such in itself independently of all the free decrees of God, or whether it is dependent upon them. In other words, whether it is only as a result of these free decrees by which God has ordained everything that will happen to Adam and to his posterity that God knows everything t hat will happen to them, or whether there is an intrinsic and necessary connection between Adam,
HANOVER TO THE ITALIAN JOURNEY, 1676-87 333 on the one hand, and all that has happened and will happen to him and his posterity on the other, independently of these decrees. It seems to you that I choose the second alternative, because I have said that "God has found, among the possible ones, an Adam with such individual circumstances and who has among his other predicates also that of having such a posterity in the course of time". You assume, now, that I will agree that possibilities are possible before all the free decrees of God. Assuming then that this explanation of my meaning follows the second alternative, you conclude that it contains insurmountable difficulties. For (as you say quite rightly) there is an infinity of human events which happen through particular ordinances of God, such for example, as the Jewish and the Christian religions, and especially the incarnation of the divine Word. And I do not see how one can say that all this (which has happened by the very free decrees of God) was included in the individual notion of the possible Adam. He who is considered as possible must have everything which he is conceived to have according to this concept, independently of the divine decrees. I have tried to report your difficulty exactly, Sir, and now hope to meet it completely even to your satisfaction. For it must have a solution, since we cannot deny that there is truly such a full notion of Adam, accompanied by all his predicates and conceived as possible, and that God knows this before he decides to create him, as you have agreed. But I believe that the dilemma of the twofold explanation which you propose is not exhaustive and that the connection which I conceive between Adam and human events is intrinsic, indeed but not necessary independently of the free decrees of God, because the free decrees of God taken as possible, enter into the concept of a possible Adam, while it is these same decrees of God become actual that are the cause of the actual Adam. I agree with you as against the Cartesians that possibilities are possible before all of God's actual decrees, but sometimes not without assuming these same decrees considered as possibilities. For the possibilities of individuals or of contingent truths include within their concepts the possibility of their causes, namely, the free decrees of God. It is in this that they differ from the possibilities of species or of eternal truths, which depend on God's understanding alone without involving his will, as I have already explained above. 4 This may suffice. But in order to make myself better understood, I will add that I think there is an infinity of possible ways in which to create the world, according to the different designs which God could form, and that each possible world depends on certain principal designs or purposes of God which are distinctive of it, that is, certain primary free decrees (conceived sub ratione possibilitatis) or certain laws of the general order of this possible universe with which they are in accord and whose concept they determine, as they do also the concepts of all the individual substances which must enter into this same universe. Everything belongs to an order, even miracles, though they may be contrary to certain subordinate maxims or laws of nature. Hence, assuming the choice of Adam as made, all human events must have happened as they have happened in fact, but not so much because of the individual concept of Adam, though this incloses them, as because of the designs of God which also enter into this individual concept of Adam and which determine the concept of the whole universe, and therefore the concept of Adam as well as those of all other individual substances in this universe. Each individual substance expresses the whole universe of which it is a For references see p. 348
334 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS part according to a certain relationship, through the connection which it has to all things by virtue of the coherence of the decisions or purposes of God. I find that you raise still another objection, Sir, which is not concerned with consequences which seem to be contrary to freedom, as was the case in the objection which I have just answered, but with the thing itself and with the idea which we have of an individual substance. For since I have the idea of an individual substance, namely, the idea of myself, you say: It seems to be in this that we must seek what should be said about the concept of an individ ual and not in the way in which God conceives individuals. I need only to consult the specific concept of a sphere to conclude that the length of its diameter is not determined by its concept; in the same way (you say) I can discover clearly in this individual concept which I have of myself that I shall remain myself whether I make a journey which I ha're planned, or do not makeit. 5 To reply distinctly to this, I agree that the connection of events, though certain, is not necessary, and that I am free to make or not to make this journey. For although it is included in the concept of me that I shall make this journey, it is also included that I shall make it freely. And there is nothing whatever in me that can be conceived sub ratione generalitatis seu essentiae seu notionis specificae sive incompletae 6 , from which one can draw the conclusion that I shall make it necessarily, while on the contrary one can conclude from the fact that I am a man that I am able to think and as a consequence that if I do not make this journey, it will not conflict with any eternal or necessary truth. Yet, since it is certain that I shall make it, there must be some connection between me, who am the subject, and the execution of the journey, which is the predicate, for in a true proposition the notion of the predicate is in the notion of the subject. If I did not make the journey, there would therefore be a falsehood which would destroy my individual or complete concept, or what God conceives of me or did conceive of me before he resolved to create me. For considered as possible, this concept includes existences or truths of fact or the decrees of God upon which facts depend. I agree also that in order to judge the concept of an individual substance, it is well to consult the concept which I have of myself, just as we must consult the specific concept of a sphere to judge its properties. But there is a great difference between the two, for the concept of myself In particular and of every other individual substance is infinitely more inclusive and more difficult to grasp than is a specific concept such as that of a sphere, which is incomplete and does not incl~de all the circumstances necessary practically to arrive at a particular sphere. To t.\nderstand what this I is, it is not enough that I sense myself as a substance that th~nks; I must also distinctly conceive that which distinguishes me from all other possible spirits. 7 But of this I have only a confused experience. Although it is easy, therefore, to judge that the length of its diameter is not included in the concept of a sphere in general, it is not so easy to judge with certainty - though it can be judged with enough probability - whether the voyage which I plan to make is included in the concept of me. Otherwise it would be as easy to.be a prophet as to be a geometrician. Yet experience cannot show me the infinity of insensible things in my body of which the general consideration of the nature of body and of motion can convince me. So likeWise, although experience cannot let me sense everything that is included in my individual concept, I can know, in general,
HANOVER TO THE ITALIAN JOURNEY, 1676-87 335 through a general consideration of the individual concept, that everything which pertains to me is included in it. Surely, since God can form and does in fact form this complete concept which includes enough to explain all the phenomena that come to me, such a concept is possible and is the true complete concept of what I call myself, in virtue of which all my predicates pertain to me as their subject. This could be proved just the same, then, without mentioning God 8, except insofar as it is necessary to indicate my dependence. But a stronger expression is given to this truth by deriving the concept which we are examining from the divine knowledge as its source. I admit that there are many things in the divine wisdom which we cannot understand, but it,seems to me that we do not need to penetrate into them in order to answer our question. If in the life of some person, moreover, or even in the universe as a whole, some event were to occur in a different way than it actually does, there would still be nothing to prevent us from saying that this would be another person or another possible universe which God has chosen. And it would in that case be truly another individual. There must thus also be a reason a priori, independent of my experience, which justifies us in saying truly that it is I who was in Paris and that it is also I and not someone else who am now in Germany and that consequently the concept of myself must combine or include these different conditions. Otherwise it could be said that this is not the same individual, even though it might seem to be. 9 Some philosophers, who have failed adequately to understand the nature of substances or of indivisible beings, or beings per se, have in fact thought that nothing remains truly the same. It is for this reason, among others, that I conclude that bodies would not be substances if there were only extension in them. I believe, Sir, that I have now satisfied your difficulties regarding the principal proposition. But since you also make some important comments on certain incidental expressions which I have used, I shall try to explain these as well. I said that the supposition from which all human events can be deduced is not the creation of some vague Adam but the creation of an Adam such that he is determined in all his circumstances and chosen from an infinity of possible Adams. To this you make two important remarks, one in opposition to a plurality of Adams, and the other in opposition to the reality of merely possible substances. On the first point, you say with very good reason, that it is no more possible to conceive of several possible Adams, if Adam be taken as a singular nature, than it is to conceive of several 'myselves'. I agree. But when I speak of several Adams, I do not take Adam for a determined individual but for some person conceived in a relation of generality (sub ratione generalitatis), under circumstances which s~m to us to determine Adam to be an individual but which do not truly do so sufficitfu.tly; as for instance, when we mean by Adam the first man, whom God puts in a pleasure garden, which he leaves through sin, and from whose ~ide God makes a woman. But all this does not sufficiently determine him, and so there might be several other disjunctively possible Adams, or several individuals whom these conditions fit. This is true no matter what finite number of predicates incapable of determining all the rest one takes. But that concept which determines a certain Adam must include, absolutely, all his predicates, and it is this complete concept which determines the relation of generality in such a way as to reach an individual (rationem generalitatis ad individuum). For the rest, so far removed am I from holding that a single individual is a plurality that I am even deeply convinced of the teaching of St. Thomas about intelligences but hold that it is valid generally, For references see p. 348
336 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS namely, that there cannot be two individuals entirely similar or differing only in number.10 As for the reality of 'purely possible substances', or 'those which God will never create', you say, Sir, that you are "strongly inclined to believe that they are chimeras", an opinion to which I am not opposed, if as I think, you mean that they have no other reality than that which they have in the divine understanding and the active power of God. Yet you see by this, Sir, that in order to explain them satisfactorily, we are forced to have recourse to the divine knowledge and power. Your next observation I also find sound: that we never conceive of any purely possible substance except in terms of 'some one' - or in terms of the ideas included in 'some one' - of those which God has created. We imagine (you add) that before God created the world he envisaged an infinity of possible things, from which he chose some and rejected others; several possible Adams or first men, each accompanied by a great train of persons with whom he is intrinsically connected. And we assume that the connection of all these other things with one of these possible Adams (or first men) is exactly like that which relates the created Adam with his whole posterity. So we are led to believe that God has chosen this particular one out of all the possible Adams, and that he did not will any of the rest. In this you seem to recognize that these thoughts, which I admit are mine, provided the plurality of Adams and their possibility be understood in the sense which I have explained and provided that this is all regarded in terms of the way I conceive of a definite order in the thoughts and acts which I ascribe to God - you seem, I say, to recognize that they occur quite naturally to the mind when we think a little about the matter and even that they cannot be avoided. Perhaps they have displeased you only because you assumed that the intrinsic connection between these concepts cannot be reconciled with the free decrees of God. Everything that is actual can be conceived as possible, and if the actual Adam will have a certain posterity in the course of time, one cannot deny this same predicate to this Adam thought of as possible, especially since you agree that God envisages in him all his attributes when he decides to create him. So these attributes pertain to him, and I do not see that what you say about the reality of possibilities is contrary to this. In order to call something possible, it is enough merely to be able to form a concept of it when it is only in the divine understanding, which is, so to speak, the realm of possible realities. As concerns possibles, I am thus content that one can form true propositions from them; thus one can judge, for example, that a perfect square implies no contradiction, even if there has never been a perfect square in the world. If we wished absolutely to reject such pure possibles, we should destroy contingency and freedom, for if nothing is possible except what God has actually created, whatever God has created would be necessary, and in willing to create something, God could create only that thing alone, without any freedom of choice. This leads me to hope that after the explanations I have given, to which I have always attached reasons in order to convince you that they are not subterfuges contrived to evade your objections, your thoughts will in the end be found to be not so far removed from mine as at first they seemed. You approve the interconnection of God's decisions; you accept as certain my principal proposition in the sense in which I explained it in my reply; you still question only whether I made this interconnection
HANOVER TO THE ITALIAN JOURNEY, 1676-87 337 independent of the free decrees of God, and this quite rightly has given you difficulty. But I have shown that in my opinion it does depend upon his decrees and that though it is intrinsic, it is not necessaryP You have insisted upon the difficulty there would be in saying that if I do not take the journey which I should take, I am no longer myself, and I have explained the sense in which this can be said or not. Finally, I have given a decisive reason, which I believe has the force of a demonstration. It is that always, in every true affirmative proposition, whether necessary or contingent, universal or particular, the notion of the predicate is in some way included in that of the subject. Praedicatum inest subjecto; otherwise I do not know what truth is. Now I do not demand any further connection here than what is really found [a parte rei] between the terms of a true proposition, and it is only in this sense that I say that the concept of an individual substance includes all its events and all its denominations, even those which are commonly called extrinsic 12 , that is, those which pertain to it only by virtue of the general connection of things and from the fact that it expresses the whole universe in its own way. For there must always be some foundation for the connection between the terms of a proposition, and this must be found in their concepts. This is my great principle, with which I believe all philosophers should agree, and one of whose corollaries is the commonly held axiom that nothing happens without a reason, which can always be given, why the thing has happened as it did rather than in another way, even though this reason often inclines without necessitating. A perfect indifference is a deceptive or incomplete assumption. It will be seen that I draw surprising conclusions from this stated principle, but this is only because we have not customarily carried our clearest knowledge far enough. The proposition which has occasioned this discussion is, I may add, very important and deserves to be firmly established, for it follows from it that every individual substance expresses the entire universe in its own way and in a certain relationship, or from that point of view, so to speak, from which it regards it. It follows also that its subsequent state is the result, though free or contingent, of its preceding state, as if there were only God and itself in the world. Thus each individual substance or complete being is as a world apart, independent of every other thing but God. There is no stronger demonstration, not only that our soul is indestructible, but also that it preserves always within its nature the traces of all its preceding conditions with a virtual memory which can always be awakened because the soul has consciousness of, or knows within itself, that which each one calls 'myself'. It is this that makes it capable of moral qualities and of punishment and reward, even after this life. For without memory immortality would be worthless. Yet this independence does not prevent the intercourse of substances with each other, for since all created substances are a continual production of the same sovereign being, by the same designs, and expressing the same universe or the same phenomena, they correspond exactly with each other. This leads us to say that one acts upon the other, because one expresses more distinctly than does the other the cause or reason of their changes. This is very much like our ascribing motion to a ship rather than to the whole sea, and with good reason, even though, speaking abstractly, another hypothesis about motion could be set up, since motion in itself, abstracted from its cause, is always something relative. It is thus, I believe, that the intercourse between created substances must be understood and not as a real physical influence or dependence; such an influence can never be conceived distinctly. It is for this reason that some thinkers have been comFor references see p. 348
338 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS pelled to admit that as concerns the union of soul and body, or the action and passion of a spirit in relation to some other created being, their immediate interaction is inconceivable. Yet the hypothesis of occasional causes will not satisfy a philosopher, it seems to me, because it introduces a kind of continuous miracle, as if God were at every mo~ent changing the laws of bodies on the occasion of the spirits' thoughts or were changing the regular course of the thoughts of spirits by arousing other thoughts in them on the occasion of bodily motions; or in general, as if God as a rule interfered in some other way than by preserving each substance in its course and in the laws established for it. Thus only the hypothesis 0/ concomitance or of the correspondence of substances with each other explains everything in a way that is understandable and worthy of God and is even demonstrative and in my opinion inevitable on the basis of the proposition which we have established. It seems to me also that it agrees better with the freedom of reasonable creatures than does the hypothesis of impressions or that of occasional causes. God created the soul in the first place in such a way that ordinarily it has no need of these alterations. Whatever happens to the soul arises out of its own depths without any need of its adapting itself to the body in successive events, any more than the body needs to adapt itself to the soul. Each following its own laws, the one acting freely, the other without any choice, each agrees with the other in the same phenomena. In spite of all this, the soul is still the form of its body, because it expresses the phenomena of all other bodies in accordance with their relation to its own body. It may be more surprising, perhaps, that I deny the action of one corporeal substance upon another, which nevertheless seems so clear. But aside from the fact that others have already done so, we must keep in mind that such action is a play of the imagination rather than a distinct conception. If the body is a substance, and not a simple phenomenon like the rainbow, or a being united by accident or by aggregation, like a pile of stones, it cannot consist in being extended, and we must of necessity conceive of something which we may call its substantial form and which corresponds in some way to the soul. After having long held otherwise, I have finally been convinced of this, almost in spite of myself,13 Yet however much I may support the Scholastics in this general and so to speak, this metaphysical explanation of corporeal principles, I agree also as closely as anyone can with the corpuscular theory in the explanation of particular phenomena, for to introduce forms or qualities here is to explain nothing. 14 We must always explain nature mathematically and mechanically, provided we keep in mind that the principles themselves, or the laws of mechanics or of force, do not depend on mere mathematical extension but on certain metaphysical reasons. After all this, I believe that the propositions contained in the summary which was sent to you, Sir, will now seem not only more understandable but perhaps also more sound and more important than could have been thought at first. II [G., 11,111-29] October 9, 1687 15 Since I shall always place great weight upon your judgment when you can be brought to see the point at issue, I shall make an effort this time to make the positions which I consider to be important and all but certain seem at least tenable, if not certain, to
HANOVER TO THE ITALIAN JOURNEY, 1676-87 339 you. For it does not seem to me difficult to reply to the doubts which you still have; these come, in my opinion, only from the fact that however able a person may be, if he has preconceptions and his mind is distracted by other matters, he finds it very difficult at first to enter into a new line of thought, especially of a kind where figures, models, and sense perception are of no help. I have said that the soul, which naturally expresses the entire universe in a certain sense and according to the relationship which other bodies have to its own, and which as a consequence expresses more immediately the properties of the parts of its body, must therefore, by virtue of the laws of relationship which are essential to it, particularly express certain unusual motions of the parts of its body. This happens when it feels pain. To this you reply that you have no clear idea of what I mean by the word express. If I understand by it a thought, you do not agree that the soul has more thought and more knowledge of the motion of the lymph in the lymphatic ducts than it has of the satellites of Saturn. But if I mean something else (you say), you do not know what it is. Therefore (assuming that I cannot explain it distinctly) this term will in no way help us to understand how the soul can give itself a feeling of pain, since to do this it would already have to know (in your opinion) that I had been pricked, instead of which it arrives at this knowledge only through the pain which it felt. In reply to this criticism, I shall explain the term which you judge to be obscure, and I shall apply it to the difficulty which you have raised. One thing expresses another, in my usage, when there is a constant and regular relation between what can be said about one and about the other. It is in this way that a projection in perspective expresses a geometric figure. Expression is common to all the forms and is a genus of which natural perception, animal feeling, and intellectual knowledge are species. In natural perception and feeling it suffices that what is divisible and material and is found dispersed among several beings should be expressed or represented in a single indivisible being or in a substance which is endowed with a true unity. The possibility of such 16 a representation of several things in one cannot be doubted, since our soul provides us with an example of it. But in the reasonable soul this representation is accompanied by consciousness, and it is then that it is called thought. Now this expression takes place everywhere, because every substance sympathizes with all the others and receives a proportional change corresponding to the slightest change which occurs in the whole world, although this change will be more or less noticeable as other bodies or their actions have more or Jess relationship with ours. With this I believe Descartes would himself have agreed, for he would undoubtedly grant that, because of the continuity and divisibility of all matter, the slightest movement exerts its effect upon near-by bodies, and so from body to body to infinity, but in diminishing proportion. So our body must be affected in some way by the changes of all the rest. Now to all the motions of our body there correspond certain perceptions or thoughts of our soul, more or less confused; thus the soul will also have some thought of all the motions of the universe, and in my opinion every other soul or substance will have some perception or expression of it. It is true that we do not perceive all the motions of our body distinctly, as for example, that of the lymph. But to make use of an example which I have already used, I must have some perception of the motion of each individual wave on the shore, in order to be able to perceive what results from the whole, namely, the great noise which is heard near the sea. So we also sense some confused result of all the motions taking place within us, but being accustomed to this internal For references see p. 348
340 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS motion, we do not perceive it clearly and with reflection except when there is an important change, as in the beginning of illnesses. It would be desirable for physicians to work at the task of making a more exact distinction among the kinds of confused feelings which we have of our body. Now, since we perceive other bodies only through the relation which they have to ours, I was right in saying that our soul expresses best what pertains to our own body. Also, we should not know the satellites of Saturn and Jupiter except as the result of a motion taking place in our eyes. In all this, I believe, a Cartesian would agree with me, except that I assume that there are surrounding us souls other than ours, to whom I ascribe an expression or perception inferior to thought, while the Cartesians, instead, deny that beasts feel and admit no substantial forms outside of man. But this does not affect the question which we are discussing at present, namely, the cause of pain. We are now concerned with knowing how the soul perceives the motions of its body, since we do not see any means of explaining through what channels the action of an extended mass is transmitted to an indivisible being. The common run of Cartesians admit that they cannot give a reason for this union; the author~ of the hypothesis of occasional causes consider it a nodus vindice dignus, cui Deus ex machina inter venire debeatP I myself explain it in a natural way. By the concept of substance or of a completed being in general, which implies that its present state is always a natural result of its preceding state, it follows that it is the nature of each individual substance, and consequently of each soul, to express the universe. It has been created from the beginning in such a way that by virtue of the laws of its own nature it must come to agree with all that takes place in bodies. and particularly in its own. So we need not be surprised at the fact that it is its nature to represent the prick to itself at the moment that this happens to its body. To complete my explanation of this matter,let there be: The state of the body at moment A The state of the body at the following moment B (prick) The state of the soul at moment A The state of the soul at the following moment B (pain) Just as the state of the body at moment B follows the state of the body at moment A, so the state of the soul at B follows from the preceding state of the same soul at A, in accordance with the concept of substance in general. But the states of the soul are naturally and essentially expressions of the corresponding states of the world and particularly of the bodies which then belong to them. Since, therefore, the prick is a part of the state of the body at moment B, the representation or expression of this prick, which is pain, will also be a part of the state of the soul at moment B. For as one movement follows another, one representation similarly follows another in a substance whose nature it is to be representative. So the soul must perceive the prick, since the laws of correspondence require that it should express more distinctly any more noticeable change in the parts of its body. It is true that the soul does not always perceive the causes of the prick and of its future pain distinctly, when these are still concealed in the representation of state A, as i~ the case when one is asleep or for some other reason does not see the pin approaching. But this is because the pin then makes too small an impression upon us, and although we are already affected in some way by all the motions and their representations in our soul, and so have within us the representation or expression of the causes of the prick, and therefore the cause of the representation of this same prick, that is, the cause of the pain, we cannot untangle
HANOVER TO THE ITALIAN JOURNEY, 1676-87 341 them from so many other thoughts and motions until they become noticeably strong. Our soul reflects only on more unusual phenomena which are singled out from the rest; it does not think distinctly of any when it thinks equally of all. After all this I cannot guess where one can still find the slightest shadow of difficulty, unless we are to deny that God can create substances so constituted from the beginning that by virtue of their own nature they thereafter agree with the phenomena of all the others. But there is no apparent ground whatever for denying this possibility. For we see that mathematicians represent the motions of the heavens in a mechanism, as when Jura poli rerumque fidem legesque deorum Cuncta Syracusius transtulit arte senex 18 - a thing which we can do much better today than could Archimedes in his day. Why should not God, then, who infinitely surpasses the mathematicians, be able to create representative substances in the beginning in such a way that by their own laws and following the natural change of their thoughts or representations, they express everything which must happen to every body? It seems to me that this is not only easy to conceive but also worthy of God and of the beauty of the universe and in some sense necessary. For all substances should be in mutual harmony and interrelation, and all should express within themselves the same universe and its universal cause, which is the will oftheir Creator, and the decrees or laws which he has set up so that they may adjust themselves to each other in the best way possible. This mutual correspondence of different substances (which cannot act upon each other, speaking with metaphysical rigor, and which nevertheless agree as though they were acting upon each other) is also one of the strongest proofs of the existence of God or of a common cause which each effect must always express according to its point of view and its capacity. Otherwise the phenomena of different spirits would not at all accord with each other, and there would be as many systems as there are substances; or better, it would be pure chance if they were sometimes to agree. The whole concept which we have of time and space is based on this agreement; but I should never finish if I had to explain everything exhaustively that is involved in our subject. Yet I should prefer to be lengthy rather than to fail in expressing myself adequately. To go on to your other doubts, I think, Sir, that you will now see what I mean when I say that a corporeal substance gives itself its motion, or rather what is real in motion at each moment, namely, the derivative force from which motion follows. For every present 19 state of a substance is the result of its preceding state. It is true that a body which has no motion cannot impart motion to itself, but I hold that there is no such body.20 You will say that God can reduce a body to the state of perfect rest, but I reply that God can also reduce it to nothing and that this body, deprived of action and passion, cannot in any sense comprise a substance. At least it suffices to say that if God should ever reduce any body to perfect rest, a thing which can happen only through a miracle, a new miracle would be needed to give it some motion. You will see, also, that my opinion confirms rather than destroys the proof of a prime mover. A reason must always be given for the beginning of motion, for its laws, and for the agreement of motions with each other, and this cannot be done without having recourse to God. Furthermore, my hand does not move because I will it, for I might well will a mountain to move, but unless I have a most miraculous faith it will not happen; my hand moves because I could not successfully will its motion except at the exact moment when For references see p. 348
342 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS the muscles of the hand make the contractions necessary to that end. All the more true is it that the passions of my soul agree with the motions of my body. The two always accompany each other by virtue of the correspondence which I have established above, but the immediate cause of each is within itself. I come to the matter of the forms or souls, which I hold to be indivisible and indestructible. I am not the first to hold this opinion. Parmenides, of whom Plato speaks with veneration, as well as Melissus, maintained that there is only apparent generation and corruption, as Aristotle testifies in the De caelo, Book 3, chapter 2. And the author of the first book De diaeta, which is ascribed to Hippocrates, says explicitly that an animal cannot be engendered entirely anew or entirely destroyed. Albertus Magnus and John Bacon seem to have believed that substantial forms already lie concealed in matter from eternity; Fernel has them descend from heaven; not to mention those who take them from the world soul. These men have all seen a part of the truth but have not developed it. 21 Many of them believed in transmigration, others in the traduction 22 of souls, instead of noticing the transmigration that also transforms an animal already formed. Others, unable to explain the origin of forms in any other way, agreed that they originate by a true creation. And whereas I admit this creation in temporal succession only in the case of reasoning souls, and hold that all forms which do not think were created with the world itself, they believe, by contrast, that it takes place every day in the generation of the smallest worm. Philoponus, an ancient interpreter of Aristotle, in his book against Proclus, and Gabriel Biel seem to have been of this opinion. St. Thomas seems to me to consider the soul of beasts to be indivisible. Our Cartesians go even further, for they maintain that every true soul and substantial form must be indestructible and without generation. This is why they deny souls to beasts, although Descartes says in a letter to Henry More 23 that he cannot be sure that they have none. Since no offense is taken at those who introduce atoms which subsist permanently, why should it be found strange when the same thing is said about souls, to which indivisibility belongs by their very nature, especially since this becomes necessary when we combine the Cartesian conception of substance and the soul with that which everyone holds about the soul of beasts? It will be difficult to rid mankind of this opinion which has been held always and everywhere and which is universal if any opinion deserves that term, namely, that beasts have feelings. Now assuming that it is true, my view about these souls is not only necessary on Cartesian principles; it is also important for morality and religion, in order to destroy a dangerous opinion to which many intelligent persons are inclined and which the Italian philosophers who follow Averroes have spread abroad, namely, that particular souls return to the world soul when animals die. This is in conflict with my demonstrations of the nature of individual substance and cannot be conceived of distinctly, since every individual substance must forever subsist separately, once it has begun to exist. This is why the truths I advance are very important. All who recognize that beasts have souls should approve them, while others ought at least not to find them strange. Now to come to your doubts about this indestructibility. 1. I maintained that we must acknowledge something in bodies which is a truly single being, since the matter or extended mass itself can never be other than many beings [plura entia], as St. Augu~tine, following Plato, very well observed. Now I infer that where there is not even one thing that is a true being, there cannot be many beings and that every multitude presupposes a unity. To this you make various answers, but
HANOVER TO THE ITALIAN JOURNEY, 1676-87 343 without touching the argument itself. This you do not threaten, since you use only ad hominem arguments and point out weaknesses, trying to show that what I say is inadequate to meet the difficulty. First of all, you are surprised that I can make use of a reason which would be appropriate for Mr. Cordemoi, who explains everything by atoms, but which must necessarily be false for my position (as you judge it), since leaving aside animated bodies, which make up less than the hundred-millionth part of the rest, all other beings must necessarily be plura entia, so that the difficulty returns. But I see from this, Sir, that I have not explained myself well enough for you to understand my hypothesis. For aside from the fact that I do not remember having said that there is no substantial form outside of souls, I am far from holding the opinion that animated bodies are only a very small part of the rest. For I believe rather that everything is filled with animated bodies. And in my opinion there are incomparably more souls than there are atoms according to Mr. Cordemoi 24 , who makes their number finite, while I hold the number of souls, or at least of forms, to be infinite. And since matter is infinitely divisible, no portion can be designated so small that it does not contain animated bodies, or at least bodies endowed with a primitive entelechy or, if you permit me to use the concept of life so generally, with a vital principle; in short, corporeal substances, of all of which one can say in general that they are living. 2. As for the other difficulty which you made, Sir, namely, that the soul joined to matter is not truly one being, since matter is not truly one in itself and the soul gives it, as you think, only an extrinsic denomination; I reply that it is the animated substance to which this matter belongs which is truly a being and that matter, taken for the mass in itself, is only a phenomenon or a well-founded appearance, as are space and time also. It does not even have the exact and fixed qualities which could make it pass for a determined being, as I have already implied in my last letter, because in nature even the figure which is the essence of an extended and bounded mass is never exact or rigorously fixed on account of the actual division of the parts of matter to the infinite. There is never a globe without irregularities, or a straight line without intermingled curves, or a curve of finite nature without being mixed with some other, and this in its small parts as in its large; so that far from being constitutive of the body, figure is not even an entirely real and determinate quality outside of thought. One can never assign a definite and precise surface to any body, as could be done if there were atoms. 2S I can say the same thing about magnitude and motion, namely, that these qualities or predicates are of the nature of phenomena, like colors and sounds, and though they involve more distinct knowledge, they can no more sustain a final analysis. As a consequence, extended mass considered without entelechies and consisting only in these qualities is not the corporeal substance but a mere phenomenon like the rainbow. Philosophers have also recognized that it is the form that gives detenninate being to matter, and those who have not taken this into consideration will never escape from the labyrinth of the composition of the continuum once they enter it. It is only indivisible substances and their different states which are absolutely real. Parmenides, Plato, and other ancient thinkers have rightly seen this. For the rest, I agree that the name one can be given to an aggregate of inanimate bodies even if no form unites them; thus I can say, 'This is one rainbow or one herd.' But this is merely a phenomenal unity or a unity in thought, which is insufficient for the reality within the phenomena. 26 3. You object that I ascribe substantial forms only to animate bodies - a view. For references see p. 348
344 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS however, which I do not remember having taken. 27 But since all organized bodies are plura entia (you continue), it follows that the forms or souls, far from making them one being, rather require several beings in order that the body can be animated. I reply that, assuming there is a soul or entelechy in beasts or in other corporeal substances, we must reason in this matter just as we all reason in regard to man. Man is a being endowed with a true unity given him by his soul, in spite of the fact that the mass of his body is divided into organs, ducts, humors, and spirits and that these parts are undoubtedly filled with an infinity of other corporeal substances endowed with their own entelechies. Since this third objection substantially merges with the preceding one, the solution given there will also apply here. 4. You conclude that there is no basis for giving a soul to beasts and that if they had one, it would have to be a spirit, that is, a substance which thinks, since we know only bodies and spirits and have no idea whatever of any other substance; but that it is difficult to believe that an oyster thinks or a worm thinks. This objection applies equally to all who are not Cartesians. But aside from the fact that we must believe that what the whole human race has always held to be true about the feeling of beasts cannot be entirely without reason, I believe that I have shown that every substance is indivisible and thattherefore every corporeal substance must have a soul or at least an entelechy which is analogous to the soul, since otherwise bodies would be only phenomena. To hold that every substance which is indivisible - this would, in my opinion, be every substance in general- is a spirit and must think seems to me incomparably more rash and unfounded than is the conservation of forms. We know only five senses and a limited number of metals; must we conclude that there are no others in the world? It is far more probable that nature, which loves variety, has produced forms other than those which think. If I can prove that there are no other figures of the second degree than the conic sections, this is because I have a distinct idea of these lines which gives me a method for arriving at their exact classification. But since we have no distinct idea of thought, and cannot demonstrate that the concept of an indivisible substance is the same as that of a substance which thinks, we have no basis for this assertion. I agree that the idea which we have of thought is clear, but not everything that is clear is also distinct. We know thought only through an internal sense, as Father Malebranche has already remarked. 28 But through sense we can know only the things we have experienced, and since we have not experienced the functions of other forms, we need not be surprised that we have no clear idea of them, for we could not have one even if we were agreed that there are such forms. It is wrong to try to use confused ideas, no matter how clear they may be, to prove that something is impossible. And when I consider only distinct ideas, it seems to me conceivable that divisible phenomena or a plurality of beings can be expressed or represented in a single indivisible being; and this is sufficient for the concept of a perception, without the necessity of adding thought or reflection to this representation. I should like to be able to explain the differences or degrees of the other immaterial expressions which are without thought, in order to distinguish corporeal or living substances from the animals so far as they can be distinguished. But I have not yet meditated enough about this and have not sufficiently observed nature to be able to distinguish the forms by the comparison of their organs and activities. On the basis of very important analogies in anatomy, Mr. Malpighi is strongly inclined to believe that plants can be included in the same genus with animals and that they are imperfect animals. 29
HANOVER TO THE ITALIAN JOURNEY, 1676-87 345 5. It now remains for me merely to reply to the difficulties which you allege against the indestructibility of substantial forms. First of all, I am surprised that you find this strange and untenable, because according to your own opinions, everyone who ascribes a soul and feeling to beasts must maintain this indestructibility. These supposed difficulties are only prejudices of the imagination which may stop the popular mind but which can have no effect upon mind" capable of meditation. I think, too, that it will be easy to satisfy you in regard to them. Those who conceive that there is as it were an infinity of small animals in the least drop of water, as Mr. Leeuwenhoek has shown, and who do not find it strange that matter should be filled everywhere with animated substances, will not find it any more strange that there is something animated even in ashes, so that fire can transform an animal and reduce it to small size, instead of destroying it entirely. What can be said of one caterpillar or silkworm can be said of a hundred or a thousand animals. It does not follow that we should see the silkworm arise again from the ashes, for perhaps this is not the order of nature. I know that several people have affirmed that the seminal powers remain in the ashes in such a way that plants can arise from them again, but I do not want to make use of any doubtful experiences. I am unable to determine whether these small organized bodies, which are inclosed by a kind of contraction in a greater body which has just been corrupted, stand entirely out of the line of generation, as seems to be true, or whether they can return to the stage in their time. These are the decrees of nature, about which men should acknowledge their ignorance. 6. It is only apparently and in terms of the imagination that the difficulty is greater in the case of larger animals which are seen to arise only from the union of two sexes. This seems to be no less true of the smallest insects. I learned some time ago that Mr. Leeuwenhoek holds opinions very close to mine, in that he believes that even the largest animals arise through a kind of transformation. I do not venture either to approve or to reject the details of his opinion, but I hold this to be true in general, and Mr. Swammerdam, another great investigator and anatomist, gives enough evidence of also inclining toward it. The opinions of these men in such matters are worth as much as those of many other men. It is true that so far as I have seen, they do not extend this opinion so far as to say that corruption and death itself is also a transformation in the case of living beings devoid of a reasonable soul, as I hold it to be. But I believe that if they were informed about this opinion, they would not find it absurd, and there is nothing more natural than to think that whatever has no beginning will also never perish. When one recognizes that all generation is but the increase and development of an animal which is already formed, it is easy to be persuaded that corruption or death is nothing but the diminution and involution of an animal which does not cease to subsist and to remain alive and organized. It is not as easy, it is true, to make this credible by means of particular observations as is the case in generation, but the reason is obvious; it is because generation proceeds in a natural manner, little by little, so that we have leisure to observe it, but death is a sudden reverse by a leap [per saltum] a return all at once to parts which are too small for us, because death ordinarily occurs in too violent a way to permit us to observe the details of the retrogression. Nevertheless, sleep, which is an image of death; and ecstasy; and the envelopment of a silkworm in its cocoon, which can pass for death; the resuscitation of drowned flies by covering them with a certain dry powder (instead of which they would have died completely if left alone); the reviving ofswallows which make their winter quarters in the For references see p. 348
346 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS reeds and are found without an appearance of life; and finally, the experiences of men frozen to death, drowned, or strangled, who have been brought back to life, about which a man of discernment has recently written a book in German, giving examples from his own experience and urging people who are confronted with such cases to make greater efforts to reviye them than is usually done and describing methods - all these things serve to confirm my opinion that these different states differ only in degree. If we do not have the means for bringing about resuscitation in other kinds of death, this is only because we do not known what must be done, or knowing it, our hands, our instruments, and our other remedies are inadequate, especially when the dissolution proceeds at once to the very small parts. Therefore we must not stop with the common conceptions of death or life, since we have both analogies and, what is more, firm arguments which prove the contrary. For I believe I have shown sufficiently that there must be entelechies if there are corporeal substances and that if we grant these entelechies or these souls, we must recognize that they are incapable of generation and destruction. It is incomparably more reasonable,' accordingly, to conceive of transformations of animated bodies than to imagine the passage of souls from one body to another, an ancient conviction which apparently comes only from transformation poorly understood. To say that the souls of beasts remain without a body or that they remain hidden in an unorganized body - all this seems less natural. Whether the animal resulting from the contraction of the body of the ram which Abraham sacrificed in place of Isaac should be called a ram is a question of terms, somewhat like the question of whether a butterfly can be called a silkworm. Your difficulty with this ram reduced to ashes, Sir, arises only because I did not explain myself sufficiently. For you assume that there remains no organized body in the ashes, and this gives you a right to say that such an infinity of bodiless souls would be a monstrosity, while I assume that there is no soul in the natural order without an animated body and no animated body without organs. Neither ashes nor other masses seem to me incapable of containing organized bodies. As for spirits, that is substances which think and are capable of knowing God and discovering eternal truths, I hold that God governs them according to laws which differ from those by which he governs the other substances. For while all the forms of substances express the whole universe, it can be said that the substances of beasts express the world rather than God, but that spirits express God rather than the world. Also, God governs the substances of beasts according to the material laws of force or of the transmission of motion. But he governs spirits according to the spiritual laws of justice, of which the others are incapable. It is for this reason that the substances of beasts can be called material, because the economy which God follows with respect to them is that of a worker or a mechanic; but with respect to spirits God fulfils the function of a prince or a legislator, which is infinitely higher. With regard to material substances God is only what he is in relation to everything - the universal Author of beings. He assumes another role with regard to spirits, in which we are led to conceive him as endowed with will and moral qualities, since he is himself a spirit, and as one among us, he even enters with us into the relationship of a society, of which he is the head. And it is this society or universal republic of spirits under this sovereign monarch which is the noblest part of the universe, being composed of so many little god~ under this supreme God. For one may say that created spirits differ from God only in degree, or as finite to infinite. It can truly be said that the whole universe was not made ex-
HANOVER TO THE ITALIAN JOURNEY, 1676-87 347 cept to contribute to the ornament and happiness of this City of God. This is why everything is arranged in such a way that the laws of force or purely material laws work together everywhere to carry out the laws of justice or of love, so that nothing can harm the souls which are in the hand of God, and everything must work for the greatest good of those who love him. It is for this reason that spirits must preserve their personalities and their moral qualities, so that the City of God will lose no person; they must particularly preserve some kind of reminiscence or consciousness, or the power to know what they are, upon which all their morality, sufferings, and punishments depend. As a result they must be exempt from those upheavals of the universe which would make them entirely unknowable to themselves, so that in the moral sense, they would be another person. For the substances of beasts, on the other hand, it is enough if they merely remain the same individual in a metaphysical sense, though they may be subject to all imaginable changes, since they are also without consciousness or reflection. As for the details of this state of the human soul after death, and the way in which it is exempt from the upheavals of the world, only revelation can instruct us in the particulars; the jurisdiction of reason does not reach so far. An objection will perhaps be made to my holding that God has given souls to all natural machines which are capable of them. Because souls do not interfere with each other and occupy no space, it is possible to give these machines souls in proportion to the perfection that they have, God doing everything in the most perfect way possible, and a vacuum of forms existing no more than a vacuum of bodies. One could say, then, that for the same reason God ought to give reasonable souls or souls capable of reflection to all living substances as well as to spirits. But I reply that laws superior to those of material nature, namely, the laws of justice, would oppose this. Since the order of the universe has not permitted justice to be observed in regard to all things, it had to be so arranged that at least no injustice should be done to them. This is why they were made incapable of reflection or consciousness and therefore not susceptible of happiness and unhappiness. Finally, to summarize my thoughts in a few words, I hold that every substance contains, in its present state, all its past and future states and even expresses the whole universe according to its point of view, nothing being so remote from anything else that there is no intercourse between them. This is particularly so in its relation to the parts of its own body, which it expresses more immediately. Consequently, nothing happens to it except from its own depths and by virtue of its own laws, provided we join to it the concourse of God. But every substance perceives other things because it expresse~ them naturally, having been created in the first place in such a way that it can do this thereafter and can adapt itself as it should. It is in this obligation imposed from the beginning that what is called the action of one substance on another consists. As for corporeal substances, I hold that when we consider only that which is divisible, mass is a pure phenomenon; that every substance has in metaphysical rigor a true unity; that it is indivisible, incapable of generation and corruption; that all matter must be filled with animated, or at least living substances; that generation and corruption are nothing but transformations from small to great or the reverse; and that there is no particle of matter which does not contain a world of innumerable creatures, organized as well as massed together. Above all, I hold that the works of God are infinitely greater, more beautiful, more numerous, and better ordered than is commonly thought and that the mechanism 0r organization - in other words, the order For references see p. 348
348 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS is essential to them even to their smallest parts. Thus no hypothesis can give us a better knowledge of the wisdom of God than can mine, according to which there are substances everywhere which show forth his perfection, being so many mirrors, all different, of the beauty of the universe, nothing remaining empty, barren, uncultivated, and without perception. We cannot even doubt that the laws of motion and of the revolutions of bodies serve the very laws of justice and of public order which are undoubtedly observed as well as possible in the government of spirits, that is, of intelligent souls which enter into society with God and with him constitute a kind of perfect City of which he is the monarch. Now I believe, Sir, that I have omitted none of the difficulties which you have propounded or at least indicated or any which I thought you might have in addition. This has made my letter long, it is true, but it would have been more difficult to put the same meaning in fewer words, and could perhaps not have been done without obscurity. I believe now that you will find my beliefs consistent enough within themselves, as well as with accepted opinions. I do not in any way repudiate established beliefs but explain them and push them further. If you could find leisure sometime to re-examine what we finally agreed upon as to the concept of an individual substance, you would perhaps find that by granting me these beginnings, you are compelled to agree with all the rest. I have tried nevertheless to write this letter in such a way that it contains its own explanation and defense. The questions could still be separated, for those who are unwilling to recognize souls in beasts and substantial forms elsewhere could still give approval to my method of explaining the union of mind and body and all that I say about true substance. But they would have to save the reality of matter and of corporeal substances as well as they can without such forms and without anything which has a true unity, either by means of points or of atoms, as they find best. Or they might leave this undecided, for one can place limits on one's investigations wherever it seems fitting. But we must not linger along so beautiful a way if we desire true ideas of the universe and of the perfection of God's works, which still provide us with the soundest arguments with respect to God and our soul. It is strange how entirely the Abbe Catelan missed my meaning, and you were right in suspecting this.30 He advances three propositions and says that I find contradictions in them. But I do not; in fact, I have used these very propositions to prove the absurdity of the Cartesian principle. This is the result of dealing with people who consider matters only superficially. If this happens in a question of mathematics, what can we expect in metaphysics and ethics? This is why I consider myself fortunate in having found in you a critic who is as exact as he is just. I wish you many more years, for the public interest and for my own. REFERENCES On his draft of the letter Leibniz noted, "Was sent in this form, June 1686"; in the edition of Arnauld's works it is dated July 14. 2 Leibniz's marginal note: "A/ull concept includes all the predicates ofthe thing; for example, of heat. A complete concept includes all the predicates of a subject; for example, of this heat. In individual substances they coincide". 3 See Arnauld's letter of May 13, 1686 (G., II, 28). 4 Thus there is a pure possibility which involves no decisions of God's creative will and 1
HANOVER TO THE ITALIAN JOURNEY, 1676-87 349 includes the eternal truths of logic and mathematics. But these possibilities do not involve complete concepts and are therefore not determinative of existence. The class of existing substances, regarded as possible existences, involves God's choice or determination by the principleofthe best possible. 6 G.,II,32-33. 6 "Under the principle of generality or essence, or of a specific or incomplete concept"; that is, a partial, abstract, and therefore not entirely determined concept. A warning may be needed that in the discussion which follows, 'specific' means 'referring to a species'. Man's knowledge of himself is, like his knowledge of other existence, limited to this incomplete kind, though his experience of himself is immediate. cr. notes 7 and 9 below. 7 The real self is therefore more than the object of reflection or inner awareness; self-knowledge involves the construction, so far as this is possible, of the law of the individual. 8 To do this was the task which Leibniz undertook in this metaphysical logic. The Generales Inquisitiones, the most extensive discussion (though far from complete) of his logical theory, was written in the same year as the Discourse and this letter, 1686. It undertakes the logical synthesis of his metaphysics (Cout. OF., pp. 356---99). 9 Personal identity is therefore not given in self-experience alone but only in the law of the individual nature. Moral responsibility, on the other hand, depends more directly on the memory and enduring purposes which the inner sense makes possible. See the Discourse, Sec. 12. 10 See p. 271, note 7. The reference is to Thomas' doctrine that all pure intelligences are infimae species. 11 Leibniz seems to say that it is intrinsic only to the complete idea in God's willed thought. But this would entail that only God's idea of the entire creation is a complete concept and that the individual concept is a completely determined concept only as it is contained in this. 12 Seenotesp.271, notes 4 and 8; note 11 above. 13 This is the point which Arnauld selects for further discussion in the later correspondence. In moving from the problem of colliding bodies to that of the relation of the mind to its body, the paragraph leaves it unclear whether Leibniz is assigning a soul only to living bodies or to inorganic ones as well (cf. p. 330, note 38). This ambiguity appears in some of Leibniz's later work. Compare the various discussions with Des Bosses (No. 62) with that in the two metaphysical summaries of 1714 (Nos. 66 and 67). 14 The corpuscular philosophy (as Robert Boyle called his system) must, insofar as Leibniz approves it, be understood, not as atomism, which he rejects except as a fiction, but as any philosophy which explains physical events mechanistically or in terms of magnitude, figure, and motion. 16 This is again the date in Arnauld's works; Leibniz marked his copy September, 1687. This is the last letter in the controversy, since Arnauld did not answer it, and Leibniz left shortly afterward for his journey of historical research. From its limited beginning in Arnauld's attack on the thirteenth proposition of the Discourse, the content of the correspondence had widened and its analyses had deepened. This letter is concerned primarily with two problems: (i) the theory of concomitance, with its explanation in the theory of representation or expression, and (ii) the nature of corporeal substance. Biological interests are prominent, and there are clear statements on the nature of the affections and of substance in general. 16 G. has belle for telle. 17 "A knot worthy for God to intervene ex machina." Loosely quoted from Horace (see p. 119, note 4). 18 "The just order of the heavens, the trustworthy ways of things, and the laws of the gods" all this together the old man of Syracuse represented by his art. 19 Readingpresent for precedent (G., 11,115). 20 In the original draft the following note was put in brackets, to be omitted in the copy sent to Arnauld: "Strictly speaking, bodies are not impelled by others when a collision takes place
350 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS but by their own motion or by their elasticity, which is also a motion of their parts. Every corporeal mass, great or small, already has within it as much force as it is able to acquire, but the directed impact of other bodies merely gives it direction, or better, this determination of direction occurs only at the time of impact." 21 John Bacon is Baconthorpe, a 14th-century Scholastic with Averroistic leanings. Jean Fernel was a French physician of the 16th century; Philoponus or Johannes Grammaticus a Christian Aristotelian of the 6th century. Gabriel Biel was the German Occamist whose writings influenced Luther. Note that Leibniz has a different group of documentations for the theory of substantial forms than in his youth (Nos. 3, 7, etc.). 22 That is, the transmission of the soul from parents to offspring. 23 Correspondence (Adam and Tannery), V, 267ff. 24 See p. 271, note 12. 26 cr. the concluding sections of No. 30 and p. 271, note 6. 26 Bracketed by Leibniz for omission in the sent letter: "If we take as the matter of corporeal substance, not its mass without forms, but a secondary matter which is the multitude of substances whose mass is that of the whole body, it can be said that these substances are parts of this matter, as those which enter into our body are parts of it. For as our body is the matter and the soul is the form of our substance, it is the same in this respect with other corporeal substances. I do not find any more difficulty here than in the case of man, where everyone agrees with this whole point. The difficulties which arise in these matters come, among other things, from the fact that we do not commonly have a sufficiently distinct concept of the whole and the part. In the last analysis, the part is nothing but an immediate component ofthe whole and is in some way homogeneous to it. Thus parts can constitute a whole, whether it has or has not a true unity. It is true that a whole which is a true unity can remain the same individual in a rigorous sense even when it loses or gains parts, as we experience in ourselves. Thus the parts are its immediate requisites only pro tempore. But if by the term matter we understand something which is always essential to the same substance, one can mean by it, in the sense of certain Scholastics, the primitive passive power of a substance. Matter in this sense will not be extended or divisible, though it will be the principle of divisibility or that which corresponds to it in the substance. But I do not want to argue about the use of terms." 27 Arnauld's misunderstanding seems to have good grounds (see note 13, above). 28 Recherche de la verite, Part III, chap. VII. 29 Marcello Malpighi (1628-94) was, after Leeuwenhoek, the founder of microscopic anatomy, and his studies of respiration, cell development, and other functions did much to strengthen the conviction that all life contains common principles. Together with Jan Swammerdam (1637-80) he established the theory of preformation which confirmed Leibniz in his conviction that every individual develops out of the law of its own nature. 80 See Nos. 34 and 37, and p. 302, note 6.
37 LETTER OF MR. LEIBNIZ ON A GENERAL PRINCIPLE USEFUL IN EXPLAINING THE LAWS OF NATURE THROUGH A CONSIDERATION OF THE DIVINE WISDOM; TO SERVE AS A REPL Y TO THE RESPONSE OF THE REV. FATHER MALEBRANCHE Nouvelles de la republique des lettres, July, 1687 This paper is Leibniz's second reply in a controversy begun by the Abbe Catelan in Bayle's journal, on the criticism 0/ Descartes's physics in the 'Brie/ Demonstration' (No. 34). In it Leibniz extends his criticism to Malebranche's laws o/motion in Book VI 0/ the Recherche de la verite, charging that he as well as Descartes has violated the principle 0/ continuity. The paper contains a clear statement 0/ this principle and its importance in physical analysis. There exists also a Latin version (GM., VI, 129-35). [G., III, 51-55] I have seen in the Nouvelles de la republique des fettres the reply of the Rev. Father Malebranche to the comment which I made on certain laws of nature which he had set up in the Recherche de la verite. 1 He seems somewhat inclined to abandon these laws himself, and this frankness is most commendable. But he offers reasons and restrictions which would lead us back into the obscurity from which I have tried to free this subject and which violate a principle 0/ general order which I have observed. I hope, therefore, that he will have the kindness to permit me to use this opportunity to explain this principle, which is of great value in reasoning and which I find is not used enough or sufficiently understood in its entire scope. This principle has its origin in the infinite and is absolutely necessary in geometry, but it is effective in physics as· well, because the sovereign wisdom, the source of all things, acts as a perfect geometrician, observing a harmony to which nothing can be added. This is why the principle serves me as a test or criterion by which to reveal the error of an ill-conceived opinion at once and from the outside, even before a penetrating internal examination is begun. It can be formulated as follows. When the difference between two instances in a given series or that which is presupposed can be diminished until it becomes smaller than any given quantity whatever, the corresponding difference in what is sought or in their results must o/necessity also be diminished or become less than any given quantity whatever. Or to put it more commonly, when two instances or data approach each other continuously, so that one at last passes over into the other, it is necessary for their consequences or results (or the unknown) to do so also. This depends on a more general principle: that, as the data are ordered, so the unknowns are ordered also. [Datis ordinatis etiam quaesita sunt ordinata.F But examples are needed in order to For references see p. 354
352 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS understand this. We know that a given ellipse approaches a parabola as much as is wished, so that the difference between ellipse and parabola becomes less than any given difference, when the second focus of the ellipse is withdrawn far enough from the first focus, for then the radii from that distant focus differ from parallel lines by an amount as small as can be desired. And, as a result, all the geometric theorems which are proved for the ellipse in general can be applied to the parabola by considering it as an ellipse one of whose foci is infinitely far removed from the other, or (to avoid the term 'infinite') as a figure which differs from some ellipse by less than any given difference. The same principle is found in physics. For example, rest can be considered as an infinitely small velocity or as an infinite slowness. Therefore whatever is true of velocity or slowness in in general should be verifiable also of rest taken in this sense, so that the rule for resting bodies must be considered as a special case of the rule for motion. If this does not work, on the other hand, this will be a certain sign that the laws are wrongly formulated. Likewise equality can be considered as an infinitely small inequality, and inequality can be made to approach equality as closely as we wish. It is through his neglect of this consideration, among other things, that Descartes, able man that he was, failed in more ways than one in his proposed laws of nature. I shall not repeat here what I have said before about the other source of his errors, in taking the quantity of motion for the force. But his first and second rules, for example, do not agree with each other. 3 The second says that if two bodies Band C collide in a straight line and with equal velocities, but B is but the least amount greater than C, C will be reflected with its former velocity, but B will continue its motion. But according to his first rule, if Band C are equal and collide in a straight line, both will be reflected and return at a velocity equal to that of their approach. This difference in the outcome in these two cases is unreasonable, however, for the inequality of the two bodies can be made as small as you wish, and the difference between the assumptions in the two cases, that is, the difference between such inequality and a perfect equality, becomes less than any given difference; therefore, according to our principle, the difference between the effects or consequences ought also to become less than any given difference. Yet, if the second rule were true as well as the first, the result would be the contrary, for according to this second rule, any increase, however small, of the body B, formerly equal to C, will make the greatest difference in the effects, in that it will change an absolute regression into an absolute continuation of motion. And this is an enormous leap from one extreme to another, whereas the body B should be reflected only a little less in this case, and the body C a little more, than in the case of their equality, from which this one can hardly be distinguished. There are many other inconsistencies like this which result from the Cartesian rules and which an attentive observer using our principle will easily detect. That which I have found in the rules of the Recherche de fa verite comes from the same source. The Rev. Father Malebranche admits in a way that there is some difficulty in them, but he continues to believe that since the laws of motion depend on the good pleasure of God, God could therefore have established laws as irregular as these. But the good pleasure of God is ruled by his wisdom, and geometricians would be nearly as surprised to see irregularities of this kind occur in nature as to see a parabola to which the properties of an ellipse with an infinitely remote focus could not be applied. Nor do
HANOVER TO THE ITALIAN JOURNEY, 1676-87 353 I believe that any example of such inconsistency can be met with in nature; the more one knows her, the more geometric one finds her. It is easy also to see from this that these irregularities do not properly arise from the cause to which Malebranche ascribes them, namely, the false hypothesis of the perfect hardness of bodies; I agree that this is not found in nature. For if we were to assume this hardness, conceiving of it as an infinitely prompt elasticity, nothing would follow here from this assumption which could not be adjusted perfectly to the true laws of nature that apply to elastic bodies in general, and we should never arrive at rules as invalid as those with which I have been finding fault. It is true that in composite things a small change can sometimes bring about a great effect. So a small spark, for example, which falls into a large mass of gunpowder can demolish an entire city. But this is not contrary to our principle, for it can be explained by these same general principles. Nothing like this can happen in primary or simple things, however, for otherwise nature would not be the effect of infinite wisdom. By this we see, a little better than by what is commonly said about it, how the true physics should in fact be derived from the source of the divine perfections. It i~ God who is the ultimate reason of things, and the knowledge of God is no less the beginning of science than his essence and his will are the beginning of beings The most reasonable philosophers agree with this, but few of them can use it to discover any truths of importance. Perhaps these little samples will arouse some of them to go much further. It sanctifies philosophy to make its streams arise from the fount of God's attributes. Far from excluding final causes and the consideration of a being who acts with wisdom, it is from these that everything must be derived in physics. It is this that Socrates has already said most admirably in Plato's Phaedo, in arguing against Anaxagoras and other philosphers who are too materialistic and who, having first recognized an intelligent principle beneath matter, make no use whatever of it when they come to philosophize about the universe and instead of showing that this intelligence does everything for the best and is the reason for the world which it has found good to produce in conformity with its ends, try to explain everything solely by the concourse of crude particles, thus confusing conditions and instruments with the true cause. This, says Socrates, is like trying to explain the fact that I am sitting in prison awaiting the fatal cup and am not rather on my flight to the Boeotians or some other people, where we know I could have saved myself, by saying that I have bones, tendons, and muscles that could be flexed in such a way as necessary in order to sit down. Truly, he says, these bones and these muscles would not be here, nor would you see me in this posture, if my mind had not judged that it is more worthy for Socrates to submit to what the laws of his country command. This passage of Plato deserves to be read as a whole, for it contains some very beautiful and very profound thoughts. However, I agree that the particular effects of nature can and ought to be explained mechanically, though without forgetting their admirable ends and uses, which providence has known how to contrive. But the general principles of physics and mechanics themselves depend upon the action of a sovereign intelligence and cannot be explained without taking it into consideration. It is in this way that we must reconcile piety and reason and that we can satisfy those good people who fear the results of the mechanistic or corpuscular philosophy\ as if it could alienate us from God and from immaterial substances, whereas in truth, with the necessary corrections and rightly understood, it ought rather to lead us to them. For references see p. 354
354 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS REFERENCES For Leibniz's criticism of Malebranche's laws see G., III, 46-49. s In brief, the law of continuity holds that if y=/(x), and there are two values Xl and X2 such tha,t xs-xl<d, where d is any assignable difference, however small, then the corresponding values ya - Yl < any assignable difference as well. 3 Principia philosophiae, Part II, Arts. 46-47. Leibniz's more detailed use of the principle in analyzing the errors in Descartes's laws is found in No. 42, II, on Arts. 45-53. 4 See above, p. 349, note 14. 1
INTRODUCTION TO PARTS III AND IV To judge from his own willingness to publish his opinions, and the works which he later mentIOns with approval, the mature period of Leibniz's thought begins with the Meditations on Knowledge, Truth, and Ideas (No. 32). It is only after his return from Italy in 1690, however, that such fundamental concepts as those of individuality, force, the intercourse between monads, and the gradations of substance are analyzed in detail. The year 1690 may therefore be regarded as the line of demarcation between Leibniz's early period of eclecticism and discovery and his mature system. Yet his thought cannot be regarded as either complete or stable, even in this last period of about twenty-five years. Indeed, as old age sets in, his complaints increase for the lack of time and peace of mind to complete and to perfect; and he never abandons his cautious eagerness to test his new ideas by submitting them, first of all, to his friends and critics. The first decade of this period, roughly coextensive with the 1690's, itself involves a fundamental shift in his philosophical interests. Newton's Principia, reaching him in Italy, arouses his zeal to complete his own dynamics, with the result that his thinking is permanently shifted from an emphasis upon the universal harmony to a concern for the individual. The logical foundations are neglected for an explicit dynamism, the theory of causality developed earlier is applied in more detail to the mind-body problem, a priorism recedes into the background and an a posteriori argument for God is perfected, and the claim to demonstrate gives way to the recognition that his philosophy is hypothetical. The climax of this change is 1695, when the Specimen dynamicum and the New System are published; and the controversies which these works arouse continue until Leibniz's death and, indeed, far beyond, metaphysical issues crystallizing first, and scientific ones taking form more slowly but becoming the more bitter as they grow. The death of the Elector Ernest August on January 23, 1698, weakened Leibniz's position at the court at Hanover at the very time when his European reputation and influence were highest and his scientific and diplomatic successes had been felt in all the great centers - London, Berlin, Vienna, Paris, and St. Petersburg. The history of the House of Brunswick, in which his third Hanoverian master, George Louis (after 1714, George I of England), set such stock, began increasingly to confine his intellectual activities. Yet the intensity of his other studies did not diminish; his journeys grew more frequent; projects for inventions, societies, alliances, settlements, and unifications continued to be formulated, some of them to be carried out; and intrigues ensnared him to the extent that prolonged philosophical work became less possible than ever. Leibniz's achievements in this field are remarkable, however, even in this period. The great efforts at synthesis, however incomplete, are behind him. Most of his philosophical writing belongs in the areas, first of popularization, and then of contro-
356 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS versy. The queen of Prussia, his illustrious and capable pupil and friend, called forth some of his better expositions, and the Theodicy, published in 1710, 5 years after her death, was a monument to her intellectual and religious interests. Even the controversy in which he was engaged at his death with Clarke and Newton was continued with another royal reader in mind, Caroline of Anspach, the princess of Wales, who mediated the letters. Meanwhile he sought to establish his ideas, and perhaps himself, in England through correspondence with Lady Masham, Gilbert and Thomas Burnet, and Pierre Coste (the translator of Locke, Shaftesbury, and other English authors), while such works as the Principles of Nature and of Grace, apparently written for Eugene of Savoy in Vienna but sent to a Parisian group as well, and the Monadology were designed to persuade or enlighten a popular following on the Continent. Leibniz was still in earnest about the intellectual unity of Europe and about the noble support upon which he believed this unity depended. Popularization did not exclude controversy, however, or more critical efforts to perfect his system, particularly the concept of individual substance. Indeed, Leibniz seemed no longer able to do protracted philosophical writing except when continuity was provided by the works he was refuting; the two great monuments of the period were running commentaries and refutations of others: Locke in the New Essays and Bayle in the Theodicy. The two series of letters, one to the Scholastic Cartesian De Voider, the other to the Scholastic Jesuit Des Bosses, span the last period of Leibniz's thought and together constitute a prolonged effort to attain clarity on the nature of individual substance and to formulate it convincingly for others. Leibniz's style achieves its height only in this period. The ponderous erudition of his earlier writings is left behind, at least sometimes, and a more perfect harmony or 'consent' appears between meaning and expression. The Monadology is by no means an adequate statement of his philosophy, but it is nonetheless the layman's best outline of his metaphysics.
PART III HANOVER TO THE DEATH OF ERNEST AUGUST 1690-98
38 LETTER TO ARNAULD Venice, March 23,1690 At the end of his long jQurney to Austria and Italy in, quest of materials for the history of the House of Brunswick, Leibniz once more tried to resume his philosophical correspondence with Antoine Arnauld. Though the Italian stay had been filled with historical and practical interests, more theoretical work had not entirely lagged. The most important fruit of the period was the preparation of a work on physics, the Dynamica de potentia et legibus naturae corporeae, which he left with his friend Baron Bodenhausen in Florence. In March, 1690, he prepared a summary of his philosophical opinions for the Cartesian Platonist, Michelangelo Fardella, editor of St. Augustine's works. To Arnauld he sent essentially the same summary in this letter. Arnauld did not answer, and the correspondence ended. [G., II, 134--38] I am now about to return home after a long journey undertaken by order of my prince for the pllrpose of historical investigations. In its course I have found patents, titles, and indubitable proofs adequate to confirm tIie common origin of the noble houses of Brunswick and Este, upon which Justel, Du Cange, and others were right in casting doubts, because there were contradictions and errors on the matter in the historians of Este, together with a complete confusi<;m of times and persons. At present I plan to return and once more take up myoId routine. Having written to you two years ago, shortly before my departure 1, I am taking that same liberty in order to inquire after your health and to let you know that the thought of your outstanding merit is always in my mind. While in Rome I saw a new letter denounced which was attributed to you or to your friends. And I have since seen the letter of the Reverend Father Mabillon to one of my friends, in which he says that the Reverend Father Le Tellier's defense of the missionaries against the practical morality of the Jesuits has given several people a favorable impression( of this order but that he had heard that you have replied to it and that it is said thM YOll have annihilated the reasons of this father geometrically. All this has convinced me that YOll are still in a position to render the public a service 2, and I pray God that this may be so for a long time. It is true that I have an interest in this, but it is a laudable one, for it will provide me with a means of instruction, whether in common with all the others who will read your works, or when your criticisms instruct me in particular - if the limited leisure which you have permits me still to hope for this privilege occasionally. Since this journey has enabled me in part to dismiss from my mind ordinary occupations, I have had the satisfaction of conversing with many able men of science and learning, and I have communicated my particular ideas, with which you are acquainted, to some of them in order to profit by their doubts and difficulties. There were some among them who, dissatisfied with the usual doctrines, found an unusual satisfaction in For references see p. 361
360 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS certain opinions of mine. This has led me to put them in writing so that they can be communicated more easily, and some day, perhaps, I shall have some copies printed without my name, solely in order to send them to my friends for the purpose of receiving their criticism. I wish that you could examine them first, and it is for this that I have made the following summary of them. A body is an aggregate of substances; it is not, properly speaking, one substance. Consequently, there must be found throughout the body indivisible substances incapable of generation and corruption, corresponding somewhat to souls. All these substances have always been, and will always be, united to organic bodies capable of diverse transformations. Each of these substances contains in its nature a law of the continuation of the series of its own operations 3 and everything that has happened and will happen to it. Except for its dependence upon God, all its actions come from its own depths. Each substance expresses the universe as a whole, but one does it more distinctly than another, each one pre-eminently with regard to certain things and according to its point of view. The union of the soul with the body, and even the operation of one substance on another, consists only in this perfect mutual accord, explicitly established by the order of the original creation, in virtue of which each substance, following its own laws, agrees with the demands of the others, and the operations of the one thus follow or accompany the activity or change of the others. Intelligences or souls capable of reflection and of knowing the eternal truths and God have many privileges which exempt them from the upheavals of bodies. For them moral laws must be joined with the physical. All things have been made principally for them. Together they form the commonwealth of the universe, whose monarch is God. There is a perfect justice and order observed in this city of God, and there is no evil action without punishment or good action without a proportional reward. The more thoroughly one understands things, the more beautiful one finds them, and the more conformable with the wishes which a wise man could make. One must always be content with the order of the past, since it is in absolute conformity with the will of God, which we known from its outcome. But we must try to make the future, as much as depend~ on us, conform to the presumptive will of God or to his commandments to adorn our Sparta, and to labor in welldoing, yet without being cast down when success escapes us, in the firm faith that God will know how to find the most proper time for changes for the good. Those who are not content with the order of things cannot claim to love God as they ought. Justice is nothing but the charity of the wise man. Charity is a benevolence that is universal, which the wise man carries into execution in conformity with the measures of reason, to the end of obtaining the greatest good. And wisdom is the science of happiness of or the means of arriving at a lasting contentment, which consists of a continuous progression toward a greater perfection or at least in the variation of a same degree of perfection. As concerns physics, we must understand the nature of force; that it is entirely different from motion, which is something more relative. This force must be measured by the quantity of the effect. There is an absolute force, a force of direction, and a relative force. 4 Each of these forces is conserved in the same quantity, in the universe or in each machine which has no communication with others, and the two last forces taken together compose the first, or absolute force. But the same quantity of motion is not conserved, for I show that otherwise perpetual motion would be discovered, and the effect would be more powerful than its cause.
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 361 Some time ago I published in the Leipzig Acts an essay in physics in which I seek the physical causes of the motions of stars. As a basis I propose that all motion of a solid in the fluid, which takes place in a curved path or whose velocity is varied continuously, comes from the motion of the fluid itself. From this I conclude that the stars have orbits that are deferent but fluid. 5 I have demonstrated an important general theorem: that every body which moves in harmonic revolution (that is, in such a way that as the distances from the center vary in arithmetic progression, the velocities are in harmonic progression or reciprocal to the distances) and which, moreover, has a paracentric motion, that is, one determined by gravity or levity with reference to the same center (whatever the law of this attraction or repulsion may be), moves with areas necessarily proportional to the times, in the way which Kepler observed in planets. Then, taking into consideration,/rom observations, that the motion is elliptical, I find that the law of paracentric motion combined with the harmonic revolution described in ellipses must be such that gravitation is reciprocally proportional to the squares of the distances, like the radiations/rom the sun. 6 I shall say nothing to you about my calculus of increments or differences, by which I find tangents without removing irrational numbers and fractions, even when the unknown is involved in them, and by which I subject quadratures and transcendental problems to analysis. Nor shall I speak of an entirely new analysis, belonging to geometry and entirely different from algebra 7, and still less of some other matters on which I have not yet had time to present essays. I should have hoped to be able to explain these all to you in a few words in order to have your opinion, which would be of incalculable value to me, if you had as much leisure as I have deference for your judgment. But your time is precious, and my letter is already long enough. Therefore I end it here and am with zeal, etc. REFERENCES After the last philosophical letter of 1687 (No. 36,10, Leibniz had sent a more personal one from Niirnberg in 1688 (G., II, 132-34). He had also drafted one on religious questions which was not sent (G., 11,129-30). 2 Michel Ie Tellier (1643-1719) was a Jesuit and confessor of Louis XlV. His Defense des nouveau chretiens et des missionaires de fa Chine, du Japon, et des Indes (1687) had been attacked by Arnauld and referred to Rome for a judgment. In view of the close relations between Leibniz and the Jesuits in Rome at this time, his remark is discreetly ambiguous and diplomatic. 3 Two advances from the earlier correspondence are here noteworthy; Leibniz has partly cleared up the ambiguity about the nature of corporeal beings, and he has interpreted the 'individual concept' as a law governing a continuous series. 4 Leibniz's discussion here is restricted to physical force, or as he later calls it, derivative force. His analysis of the three aspects of force and the formulas for their conservation is developed in the account of living force in the Specimen dynamicum, Part I (No. 46). See below, p. 451, note 9. 5 A deferent circle, in the Ptolemaic system, was the path of a body, or of the center of an epicycle, about the earth. At this point the text follows the letter as sent to Arnauld. Montgomery gives the version of the first draft, which involved more details on the cosmological position (cf. G., 11,137,138 n.). 6 Thus Leibniz seeks an a priori verification of Newton's law of inverse squares and an interpretation reconciling it with the vortices of Descartes and Huygens. For more details see 1
362 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS No. 43. Leibniz had received a copy of Newton's Principia mathematica philosophiae natura/is (1687) while on his journey and had sent a review of it to the Acta eruditorum which appeared in June, 1688. The effort to secure credit for some of his own conclusions which he now found in Newton must have moved him to work so intensively in this period at physical studies which he had begun long before at Mainz. Leibniz's reasoning, though it strives for a broader application of the law of inverse squares than to gravity alone, is less general than Newton's (Principia, Book I, Propositions I, 2, 14), since it presupposes harmonic motion. 7 SeeNo.27.
39 ON THE METHOD OF DISTINGUISHING REAL FROM IMAGINARY PHENOMENA Date Unknown Though the date of this study on the criterion for testing truths of facts is unknown, it presupposes the viewpoint of the Meditations on Knowledge, Truth, and Ideas and the Discourse on Metaphysics (Nos. 33 and 35) but supplements the former by discussing the tests for the validity of phenomena. At the end, however, it moves toward clearer notions of body and of force, such as were developed in the 1690's. As a statement of Leibniz's phenomenalism it may be compared with the letter to Foucher in 1675 and the Paris notes relating to it (Nos. 11 and 13) and to the Dialogue of 1677 (No. 17). But the argument for a real, harmonious order and particularly the argument for the existence of other minds, are much more fully developed. [G., VII, 319-22] A being is that whose concept involves something positive or that which can be conceived by us provided what we conceive is possible and involves no contradiction. We know this, first, if the concept is explained perfectly and involves nothing confused, but then in a shorter way, if the thing actually exists, since what exists must certainly be a being or be possible. Just as being is revealed through a distinct concept, however, so existence is revealed through a distinct perception. To understand this better, we must see by what means exixtence may be proved. In the first place, I judge without proof, from a simple perception or experience, that those things exist of which I am conscious within me. These are, first, myself who am thinking ora variety of things and then, the varied phenomena or appearances which exist in my mind. Since both of these namely are perceived immediately by the mind without the intervention of anything else, they can be accepted without question, and it is exactly as certain that there exists in my mind the appearance of a golden mountain or of a centaur when I dream of these, as it is that I who am dreaming exist, for both are included in the one fact that it is certain that a centaur appears to me. Let us now see by what criteria we may know which phenomena are real. We may judge this both from the phenomenon itself and from the phenomena which are antecedent and consequent to it as well. We conclude it from the phenomenon itself if it is vivid, complex, and internally coherent [congruum]. It will be vivid if its qualities, such as light, color, and warmth, appear intense enough. It will be complex if these qualities are varied and support us in undertaking many experiments and new observations; for example, if we experience in a phenomenon not merely colors but also sounds, odors, and qualities of taste and touch, and this both in the phenomenon as a whole and in its various parts which we can further treat according to causes. Such a For references see p. 366
364 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS long chain of observations is usually begun by design and selectively and usually occurs neither in dreams nor in those imaginings which memory or fantasy present, in which the image is mostly vague and disappears while we are examining it. A phenomenon will be coherent when it consists of many phenomena, for which a reason can be given either within themselves or by some sufficiently simple hypothesis common to them; next, it is coherent if it conforms to the customary nature of other phenomena which have repeatedly occurred to us, so that its parts have the same position, order, and outcome in relation to the phenomenon which similar phenomena have had. Otherwise phenomena will be suspect, for if we were to see men moving through the air astride the hippogryphs of Ariostus, it would, I believe, make us uncertain whether we were dreaming or awake. But this criterion can be referred back to another general class of tests drawn from preceding phenomena. The present phenomenon must be coherent with these if, namely, it preserves the same consistency or if a reason can be supplied for it from preceding phenomena or if all together are coherent with the same hypothesis, as if with a common cause. But certainly a most valid criterion is a consensus with the whole sequence of life, especially if many others affirm the same thing to be coherent with their phenomena also, for it is not only probable but certain, as I will show directly, that other substances exist which are similar to us. Yet the most powerful criterion of the reality of phenomena, sufficient even by itself, is success in predicting future phenomena from past and present ones, whether that prediction is based upon a reason, upon a hypothesis that was previously successful, or upon the customary consistency of things as observed previously.1 Indeed, even if this whole life were said to be only a dream, and the visible world only a phantasm, I should call this dream or this phantasm real enough if we were never deceived by it when we make good use of reason. But just as we know from these marks which phenomena should be seen as real, so we also conclude, on the contrary, that any phenomena which conflict with those that we judge to be real, and likewise those whose fallacy we can understand from their causes, are merely apparent. We must admit it to be true that the criteria for real phenomena thus far offered, even when taken together, are not demonstrative, even though they have the greatest probability; or to speak popularly, that they provide a moral certainty but do not establish a metaphysical certainty, so that to affirm the contrary would involve a contradiction. Thus by no argument can it be demonstrated absolutely that bodies exist, nor is there anything to prevent certain well-ordered dreams from being the objects of our mind, which we judge to be true and which, because of their accord with each other, are equivalent to truth so far as practice is concerned. Nor is the argument which is popularly offered, that this makes God a deceiver, of great importance. At least no one will fail to see how far it is from a demonstration having metaphysical certainty, for we are deceived not by God but by our judgment, asserting something without accurate proof. And though a great probability may be involved, nevertheless God, in offering us this probability, is not therefore a deceiver. For what if our nature happened to be incapable of real phenomena? Then indeed God ought not so much to be blamed as to be thanked, for since these phenomena could not be real, God would, by causing them at least to be in agreement, be providing us with something equally as valuable in all the practice of life as would be real phenomena. What if this whole short life, indeed, were only some long dream and we should awake at death, as the
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 365 Platonists seem to think? Since we are destined for eternity, and this whole life, even if it were to contain many thousands of years, would be like a point with respect to eternity, how trifling a thing is this small dream, to be interposed upon such fulness of truth, to which its relation is less than that of a dream to a lifetime. Yet no reasonable person calls God a deceiver if some short dream which is completely distinct and coherent is experienced in the mind. So far I have spoken of appearances; now we must examine those things which do not appear but which nevertheless can be inferred from appearances. It is indeed certain that every phenomenon has some cause. But if anyone says that the cause of phenomena is in the nature of our mind which contains the phenomena, he will affirm nothing false, but nevertheless he will not be telling the whole truth. For in the first place, there must necessarily be a reason why we ourselves exist rather than not. And even if we are assumed to have existed from eternity, we should still have to find a reason for eternal existence, and this reason must be sought either within the essence of our mind or outside of it. And certainly there is nothing to prevent innumerable other minds from existing as well as ours, although not all possible minds exist. This I demonstrate from the fact that all existing things are interrelated (inter se habent commercium). However, minds of another nature than ours can be conceived which also are 2 interrelated with ours here. That all existing things have this intercourse with each other can be proved, moreover, both from the fact that otherwise no one could say whether anything is taking place in existence now or not, so that there would be no truth or falsehood for such a proposition, which is absurd; but also because there are no 3 extrinsic denominations, and no one becomes a widower in India by the death of his wife in Europe unless a real change occurs in him. For every predicate is in fact contained in the nature of a subject. Now, if some possible minds exist, the question is: Why not all? Furthermore, since all existents must be interrelated, there must be a cause of their interrelations; indeed, everything must necessarily express the same nature but in a different way. But the cause which leads all minds to have intercourse with each other or to express the same nature, and therefore to exist, is that cause which perfectly expresses the universe, namely God. This cause does not have a cause and is unique. Hence it is at once clear that there exist many minds besides ours, and, since it is easy to think that men who converse with us can have exactly the same reason to doubt our existence as we have to doubt theirs; and since no reason operates more strongly for us than for them, they will also exist and have minds. Thus both sacred and profane history, and indeed whatever pertains to the status of minds or rational substances, may be considered confirmed. Concerning bodies I can demonstrate that not merely light, heat, color, and similar qualities are apparent but also motion, figure, and extension. And that if anything is real, it is solely the force of acting and suffering, and hence that the substance of a body consists in this (as if in matter and form). Those bodies, however, which have no substantial form, are merely phenomena or at least only aggregates of the true ones. Substances have metaphysical matter or passive power insofar as they express something confusedly; active, insofar as they express it distinctly. 4 For references see p. 366
366 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS REFERENCES Correspondence with fact, conformity with past experience, agreement with the experiences of others, and fruitfulness in prediction through hypotheses at~thus the criteria for empirical truth for Leibniz. One of the marks of a genuine idea was for him its operation, and mere combinations of symbols or qualities which lack this practical applicability do not express an idea. 2 BC., n, 127, here inserts a non which is not in G. and which alters the sense unjustifiably. 3 G., vn, 321, omits the negative, reading: "there are many extrinsic denominations." We read nullae for multae. 4 Note that here metaphysical matter, or materia prima, is an aspect of the monad or individual substance rather than of the composite bodies, as in the physical treatises which follow. The relation betw~n primary matter in the monad (its static, qualitative aspect) and primary matter in bodies (extension and inertia) is one of the controversial issues which played a part in the correspondence with Des Bosses (No. 62). See p. 451, note 5. 1
40 ON THE TRUE THEOLOGIA MYST{CA Ca. 1690 (?) This religious interpretation of Leibniz's thought is written in German and reveals his skill in finding a popular terminology for his metaphysical concepts (so, for example, Selbstbestandfor 'substance', Unwesenfor 'matter', etc.), a practice he had urged in the Preface to Nizolius many years earlier and for which he had pointed out the advantages of German. Though Guhrauer, who printed it in his collection of Leibniz's German writings, may have claimed too much by calling it a confession, no work serves better to reveal the Platonic pattern of Leibniz's religious thinking, and nowhere is the intellectualistic quality of what has been called his mysticism more apparent. Guhrauer dates it in the last 10 or 15 years of the 17th century. [Guh. DS., I, 410-13] Every perfection flows immediately from God, as essence, power, existence, spirit, knowledge, wilP Only the inner light which God himself kiJ;ldles in us has the power to give us a right knowledge of God. The divine penections are concealed in all things, but very few know how to discover them there. Z Hence there are many who are learned without being illumined, because they believe not God or the light but only their earthly teachers or their external senses and so remain in the contemplation of imperfections. This light does not come from without, although external teaching can, and sometimes must, give us an opportunity to get a glimpse ofit. Among these external teachers there are two which best awaken the inner light 3 : the Holy Scriptures and the experience of nature. But neither of these helps us if the inner light does not work with them. (The knowledge of God is the beginning of wisdom, and the divine attributes are the primary truths for the right order of knowledge.) The essential light is the eternal Word of God, in which is all wisdom, all light, indeed the original of all beings and the origin of all truth. Without the radiation of this light no one achieves true faith, and without true faith no one attains blessedness. God is the easiest and the hardest being to know; the first and easiest in the way of light; the hardest and last in the way of shadows. Most knowledge and invention [Tichten] belongs to the shadow way, such as history, languages, the customs of man and of nature. There is also some light in these shadows, but few can separate the light from the darkness. This light fills the mind [Gemuth] with clarity and assurance but not with images and vain motions. There are some who imagine a world of light in their brains and think that they behold the brilliance and splendor and are surrounded by many thousands of little lights. But this is not the light but only a heating of their blood. 4 For references see p. 369
368 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS When anyone sees the true light, he is convinced that it is of God and not of the flesh or devil. Just as the sun bears witness of itself, so also does this light. All creatures derive from God and from nothingness [Nichts]. Their self·being [Selbstwesen] is of God, their nonbeing [Unwesen] is of nothing. (Numbers too show this in a wonderful way, and the essences of things are like numbers. 5 No creature can be without nonbeing; otherwise it would be God. Angels and saints must have it. The only self·knowledge is to distinguish well between our self·being and our non· being (and so to prevent our straying from the way of light. But one must make use of sensual things [Ergetzlichkeiten] and must view the shadow pictures only as an aid or a tool and not rest in them). Within our self·being there lies an infinity, a footprint or reflection of the omnisci· ence and omnipresence of God. Every single self·state [Selbststand], such as I or you, is a unified, indivisible, in· destructible thing and does not consist of three parts: soul, spirit, and body. Yet there is a diversity of things which belong directly to the one being and are, as it were, embodied in it. Although every single self·state is without parts, yet other things are impressed in it without thereby taking up any space in it. In each and every being there is everythingbut with a certain degree of clearness. Bodies are the mere work of God; spirits are essentially the kingdom of God. God belongs to me more intimately than my body. (Bodies in themselves are no self·states but shadows which flow away.) Corporeal things are but shadows which flow away, glimpses, shapes, truly dreams. Essential truth is in the spirit alone. But inexperienced men take the spiritual for a dream and what is tangible for the truth. Sin is not from God, but original sin has arisen in some creatures from their non· being and hence out of nothingness. God has permitted sin because he knows how to bring a greater good out of evil. Only the evil themselves have suffered any loss through sin; the whole creation of God has not lost but gained through it. (God does not have an unconditioned will to power [Machtwille] but wills everything with a cause and for the best. Election by his grace [Gnadenwahl] has its origin in his foreknowledge of the worth of men and therefore not in his foreknowledge of their faith or their works but from much higher causes. For if a man believes, or says, or thinks, or does anything good, this is a result of God's foreseen election of him in Christ.) For one unimportant thing added to another can often produce something better than can two things added together which are in themselves more precious than either of the others. It is here that the secret of the election of grace lies hidden and that its knot is to be untied. Duo irregularia possunt aliquando facere aliquid regulare. 6 God wills the salvation of all creatures and their best. The denial of self is the hatred of the non being which is in us and the love of the origin of our self· being, or God. 'Crucifying the old Adam', drawing near to Christ, dying to Adam and living in Christ - all these consist in this: that we deny non being and cling to self-being. Whoever understands how to prefer the inner light to its images, or self-being to non being, loves God above all things. He who merely fears God loves himself and his non being more than God.
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 369 Faith without knowledge comes not of the spirit of God but of the dead letter or the empty echo. Faith without light awakens no love but only fear or hope and is not living. He who does not act according to his faith has no faith, even though he may boast of it. It is deplorable that so few people know what light and faith, love and life, Christ and blessedness, are. Christ's teaching is spirit and truth, but many make of it flesh and shadow. Most men have no earnestness. They have never tasted truth and are bogged down in a secret unbelief. Let each examine himself whether he has faith and life. If he finds any other joy and pleasure greater than that in the love of God and the glorification of his will, he does not sufficiently know Christ and does not yet feel the prompting of the Holy Spirit. Scripture gives us a beautiful test to determine whether a man loves God, namely, if he loves his brother and strives to serve others as far as he can. Whoever does not do this boasts falsely of his illumination or of Christ and the Holy Spirit. REFERENCES 1 The analogy of Leibniz's mystico-theological terminology with his logical and metaphysical terms may be suggested in the following equivalents. perfections degree of perfection imperfections (plural) attributes of God essential light radiation finding God's perfections inner light shadows nonbeing self-being simple primary concepts which make possible all definition and determination 'quantity of essence' or oflogical determination finiteness and plurality, confused and inadequate representation of many in one primary concepts and truths the region of ideas or possibilities operation of ideas through the law of the best possible using the method of analysis and synthesis discovery of the law of one's individuality through the internal sense or reflection external senses, confused and indistinct knowledge passivity, materiaprima activity according to the law of the individual Thus self-denial involves clear and distinct representation of universal harmony, whether in science or in ethical and social relations. 2 Leibniz, while in Rome, developed the plan of transforming the monasteries into research institutions or, perhaps, of forming a religious order for developing the universal encyclopedia (Guh. L., 11,92-93; Couto OF., pp. 3, 5-6). 3 Leibniz's notes on William Penn's journal contain the following comment: "The true sign of the spirit and the grace of God is to enlighten and make better; everything else is freakishness and fancy" (Baruzi, Leibniz, p. 335; Bod. HS., I, v, 3). 4 Leibniz was aware of the psychological causes of some so-called 'mystical phenomena'. His letter to the Electress Sophia in 1691, about the dreams and visions of Fraulein Rosamunde von Asseburg, which were then being widely discussed, is an example. "I marvel at the nature of the human spirit, all of whose powers and capacities we do not know. When we meet such persons, we must, far from condemning and trying to change them, try rather to conserve them in this beautiful frame of mind, just as one preserves a curiosity or a cabinet-piece." After
370 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS repeating the criteria by which true perceptions are to be distinguished (No. 39), and pointing out that visions are related to the natural constitutions of those who have them, he adds the following: "I sometimes think: that Ezekiel must have studied architecture or been a court engineer, for he had magnificent visions of beautiful buildings. But a prophet from the country, like Hosea or Amos, sees only landscapes and rural pictures, while Daniel, who was a statesman, rules the kingdoms of the world" (Guh. L., II, 40-40. 6 An allusion to the binary number system, 'the image of creation', in which all numbers are derived from unity and zero. e "Two irregularities can sometimes make something regular."
41 A STUDY IN THE LOGICAL CALCULUS Early 1690's This paper is one of several which mark the most advanced stage reached by Leibniz in his efforts to establish the rules for a logical calculus. They are certainly later than August, 1690, when he wrote the logical studies given in Couto OF., pages 232-37 and 421-23. The fundamental logical relations are still identity or coincidence, inclusion or containment, and combination - still expressed as logical addition, as in the earlier paper given in No. 26, I, from 1679. Leibniz's own title for a companion study, less complete than this one, but introducing also the relation of subtraction, which is missing here (cf. p. 381, note I), was 'An Example, Not Inelegant, of Demonstrating in Abstract Terms' (G., VII,228). [G., VII, 236-47] Definition 1. Same or coincident terms are those which can be substituted for each other anywhere without affecting truth. For example, 'triangle' and 'trilateral', for in all the propositions demonstrated by Euclid about a triangle, trilateral can be substituted, and the converse, without affecting their truth. A 00 B signifies that A and B are the same; thus we may say of the straight lines XY and YX: YX 00 XY, or the shortest distance of motion from X to Yand from Y to X coincides (Figure 15). A " ... - ... ------ --"--.. - ........ ... x(:' ............... _-----_ ... -_ ... - .... ...'" . :~y . B Fig. 15. Definition 2. Diverse terms are those which are not the same or in which substitution sometimes does not work. Such are the circle and the triangle, also the square (that is, the perfect square, as geometricians always understand it) and the equilateral quadrangle, for the latter can be said of the rhombus, which cannot however be called a square. A non 00 B signifies that A and B are diverse, as are the lines XYand RS (Figure 16). R s. . y . x Fig. 16. Proposition 1. If A 00 B, then also Boo A. If anything is the same as another thing, that other will be the same as it. For since A 00 B (by hypothesis) (by Def. 1), B can be substituted for A, and A for B in the statement A 00 B (true by hypothesis); therefore, it follows that Boo A. For references see p. 381
372 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Proposition 2. If A non 00 B, B is also non 00 A. If one thing is diverse from another, the other will be diverse from the first. Otherwise B would be 00 A. Then, however (by the preceding theorem), A would be 00 B, which is contrary to hypothesis. Proposition 3. If A 00 Band B 00 C, A will be 00 C. Terms which are the same as a third term are the same as each other. For if in the statement A 00 B (true by hypothesis) C is substituted in place of B (by Def. 1, since Boo C), it follows that the proposition is true. Corollary. If AooBand Boo C,and CooD, A will be 00 D, and so forth. For A 00 Boo C, therefore A 00 C (by this proposition). Further A 00 Coo D, therefore (by this proposition) A 00 D. Hence, since equals are the same in magnitude, the consequence is that terms equal to a third term are equal to each other. Euclid, to make an equilateral triangle, makes both sides equal to the base, with the result that they are equal to each other. If something is moved in a circle, it needs only to be shown that the paths of any two successive periods or rotations to the same point coincide with each other to conclude that the paths of any periods whatever coincide. Proposition 4. If A 00 Band B non 00 C, A non 00 C. If one of two terms which are the same as each other is diverse from a third, the other is also diverse from the third. For if in the proposition B non 00 C (true by hypothesis) A is substituted in place of B, the true proposition results that A non 00 C. Definition 3. A is in L or L contains A is the same, and L can be substituted for a plurality of terms taken together which includes A. Definition 4. All things which contain whatever is in L are said together to be components with respect to L, and L is the composed or constituted. Bffi NooL denotes that B is in L or that L contains B; but Band N together constitute or compose L. The same applies in the case of many terms. Definition 5. Subalternates I call terms of which one is in the other; as A and B, if B is in A, or A is in B. Definition 6. Disparates are terms of which neither is in the other. Axiom 1. BffiN 00 NffiB, or transposition makes no difference here. Postulate 1. Given any term whatever, something can be assumed to be diverse from it, and, if desired, disparate, or so that one is not in the other. Postulate 2. Any number of terms whatever, such as A and B, can be added together into one, composing A ffi B or L. Axiom 2. A ffi A 00 A. If nothing new is added, nothing new results, or repetition changes nothing. (For though four coins and another four coins are obviously eight coins, this is not true of four coins and the same four coins counted again.) Proposition 5. If A is in B, and A 00 C, C is also in B. Whatever coincides with an inexistent is also inexistent. For if we substitute C for A (by Def. 1, since A 00 C by hypothesis) in the proposition A is in B (true by hypothesis) the result is that C is in B. Proposition 6. IfC is in B, and A 00 B, C is also in A. Whatever is in one of two coincident terms is also in the other. For substituting A for C (since A 00 C), in the proposition C is in B, A is in B. (This is the converse of the preceding proposition.) Proposition 7. A is in A. Any term whatever is in itself For A is in A ffi A (by definition of inexistence or by Def. 3) and A ffi A 00 A (by Axiom 2). Therefore (by Prop. 6) A is inA. Proposition 8. If A 00 B, A is in B. One of two coincidents is in the other. This is
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 373 clear from the preceding proposition, for according to it, A is in A, that is (by hypothesis),inB. Proposition 9. If AeoB, AEElCeoBEElC. If coincident terms are added to the same term, the results coincide. For if you substitute for A its coincident B (by Def. 1) in the proposition A EEl Ceo A EEl C (true in itself), the result is that A EEl CeoBEEl C (Figure 17). A triangle B trilateral i ~ coincide; A + C equilateral triangle B + C equilateral trilateral ~ coincide. Scholium. This proposition cannot be converted, much less the following two. In the problem of Proposition 25 below, a way will be taught to show this at once. B(f)C Fig. 17. Proposition 10. If A eo Land B eo M, A EEl B eo L EEl M. If coincidents are added to coincidents, the results are coincident. For since Beo M, A EEl B will be eo A EEl M by the preceding theorem; and substituting L for the second A (since A eo L by hypothesis), AEElBeoLEElM. A, a triangle, and L, a trilateral, coincide. B, regular, and M, the largest area with the same perimeter and same number of sides, coincide. A regular triangle and a trilateral making the largest area of any three-sided figure with the same perimeter coincide (Figure 18). A(f)B L(f)M Fig. 18. For references see p. 381
374 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Scholium. This proposition cannot be converted, for if A EB Boo L EB M and A 00 L it does not follow that Boo M. And much less can the following proposition be converted.! Proposition 11. If AooL and BooM 'and CooN, AEBBEBCooLEBMEBN, and so forth. If there is any number whatever of terms and some of them coincide with an equal number of others, term for term, any term composed of the former will coincide with a term composed of the latter. For (by the preceding proposition, since A 00 L and Boo M) it will follow that A EB B 00 L EB M. Hence, since CooN, it follows further by the preceding that A EB B EB CooL EB M EB N. Proposition 12. IfB is in L, AEBB will be in AEBL. If the same term be added to the contained and the container, the former result will be contained in the latter. For let LooBEBN (by definition of inexistence); then AEBB is in BEBN®A (by the same definition), that is, in LEBA. Let B be equilateral, L regular, A quadrilateral. Equilateral is in or is a part of regular. Therefore quadrilateral equilateral is in quadrilateral regular or perfect square. YS is in RS. Therefore RT® YS or RS is in RTEBRX, or in RX (Figure 19). AEBL L Fig. 19. Scholium. This proposition cannot be converted, for if A EB B is in A EB L, it does not follow that B is in L. Proposition 13. IfL EB B 00 L, B will be in L. If any term with another added to it does not become another term, the thing added is in it. For B is in LEBB (by definition of inexistence) and L®Boo L (by hypothesis). Therefore (by Prop. 6) Bis in L. RYEB RX 00 RX; therefore, RYis in RX. RYis in RX; therefore, RY® RX 00 RX. Let L be a parallelogram (whose opposite sides are parallel) and B a quadrilateral. A quadrilateral parallelogram is the same as parallelogram; therefore, quadrilateral is in parallelogram. On the other hand, quadrilateral is in parallelogram; therefore, quadrilateral parallelogram is the same as a parallelogram (Figure 20). Proposition 14. IfB is in L, L®BooL. Subalternates compose nothing new, or if what is in another term is added to it, it makes nothing more than the term itself This is the converse of the preceding. If B is in L, LooBEBP (by definition of inexistence). Therefore (by Prop. 9), LEBBooB®PEBB, that is (by Axiom 2) ooBEBP, which is (by hypothesis) 00 L. Proposition 15. If A is in Band B is in C, A is also in C. A term contained in a contained term is contained in its container. For A is in B (by hypothesis); therefore A EB L
HANOVER TO THE DEATH OF ERNEST AUGUST, " " ,/ R\ /~,. #''',..,..---c--.. . , . . . . '" \\ • ) ~,~ '.... ............ 375 " y " ......... _-_ ....."",., , , B '... 1690-98 _---_.--.." ,'" ~ / !X : " Bel Fig. 20. ooB (by definition of inexistence). Similarly since B is in C, BffiM will be 00 C. Substituting A Ee L (which we showed to coincide with it) for B in this assertion, it follows that A EeL Ee Moo C. Therefore (by definition of inexistence), A is in C (Figure 21). R T 5 X Fig. 21. RT is in RS and RS is in RX. Therefore, RT is in RX. Let A be quadrilateral, B a parallelogram, and C a rectangle. To be a quadrilateral is in parallelogram, and to be a parallelogram is in rectangle (that is, a figure all of whose angles are right). Therefore, to be a quadrilateral is in rectangle. These can be inverted, if in place of the notions considered in themselves we consider the individuals comprehended in the notion, and let A be rectangle, B parallelogram, and C quadrilateral. For all rectangles are comprehended in the number of parallelograms, and all parallelograms in the number of quadrilaterals. Hence all rectangles are contained in quadrilaterals. In the same way all men are contained in all animals, and all animals in all corporeal substances; therefore all men are contained in all corporeal substances. But on the contrary, the notion of corporeal substance is in the notion of animal, and the notion of animal is in the notion of man. For to be a man contains to be an animal. Scholium. This proposition cannot be converted, and the following even less so. Corollary. If A Ee N is in B, N also is in B. For N is in A Ee N (by definition of inexistence). Proposition 16. If A is in B, and B is in C, and C is in D, A is also in D, and so forth. A term contained in one contained is contained in the container. For if A is in Band B is in C, A is in C (by the preceding proposition). Proposition 17. If A is in Band B is in A, AooB. Terms which contain each other coincide. For if A is inB, A EeNooB (by definition of inexistence) (Figure 22). Now Bis in A (by hypothesis); hence A ffi N is in A (by Prop. 5). Therefore (by corollary or For references see p. 381
376 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS B ...... ' ........ -', "\ , Fig. 22. Prop. 15), Nis in A. Therefore (by Prop. 14), AooAEBN or AooB. Let RTbe N; RS, A; RS EB RT, B. To be trilateral is in triangle, and to be triangle is in trilateral. Therefore triangle and trilateral coincide. Similarly to be omniscient is to be omnipotent. Proposition 18. If A is in L, and B is in L, A EB B is also in L. What is composed of two inexistents in the same term is in that same term. For since A is in L (by hypothesis), it can be understood that A EBM 00 L (by definition of inexistence). Similarly, since B is in L, it can be understood that BEB N 00 L. Combining these, it follows (by Prop. 10) that A EBMEBBEBNooLEBL (Figure 23). Therefore (by Axiom 2), A EB MEB BEBNoo L. Therefore (by definition of inexistence), A EBB is in L. Thus RYS is in RX. YSTis in RX. Therefore, RTis in RX. L A®S Fig. 23. Let A be equiangular; B equilateral; A EB B equiangular equilateral, or regular; L square. Equiangular is in square; equilateral is in square. Therefore, regular is in square. Proposition 19. If A is in Land B is in Land C is in L, A EB B EB C will be in L, and so forth. Or in general, if terms taken separately are in a term, their composite is also in it For A EB B is in L (by the preceding proposition). Now C is also in L (by hypothesis); therefore (also by the preceding proposition), A EB B EB C is in L. Scholium. It is clear that these propositions and similar ones can be converted. For if A EB B 00 L, it is clear from the definition of inexistents that A is in Land B is in L. Likewise if A EB B EB CooL, it is clear that A is in L, and B is in L, and C is in L. Likewise A EB B is in L, and A EB C is in L, and B EB C is in L, and so forth.
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 377 Proposition 20. If A is in M and B is in N, A EB B will be in M EB N. If one of two terms is in a third term, and the other is in another fourth term, the composite of the antecedent terms is in the composite of the two other terms. For A is in M (by hypothesis) and M is in MEBN (by definition of inexistence). Therefore (by Prop. 15), A is in MEBN. Similarly, since B is in N, and N is in MEBN, B is in MEBN. But if A is in M EB Nand B is in M EB N, then (by Prop. 18) A EB B is in M EB N (Figure 24). M(ilN AG>S Fig. 24. RTisin RYandSy in SX; therefore,RTEBSYor RYisin RYEBSXor RX. Let A be quadrilateral, B equiangular; then AEBB will be rectangular. Let M be a parallelogram, and N, regular, then MEBN is a square. Now a quadrilateral is in parallelogram, and equiangular is in regular; therefore, rectangular (or equiangular quadrilateral) is in regular parallelogram or square. Scholium. This proposition cannot be converted. Though A be in M, and also A EB B in M EB N, it does not always follow that B is in N, for it may happen that A as well as B is in M, or that some things which are in B are also in M and others in N. Hence the following proposition similar to it even less convertible. Proposition 21. If A is in M andB is in N, andC is in P, AEBBEBC is in MEBNEBP, and so forth. A composite of contained terms is in a composite of containing terms. For since A is in M and B is N, A EB B is in M EB N (by the preceding proposition). Further, since Cis in P(again by the preceding proposition), A EBBEB Cis in MEBN(f)P. Proposition 22. Given two disparate terms A and B, to find a third term C diverse from them which with them will form the subalternates A (f) C and B (f) C; that is, so that, though A and Bare not in each other, A (f) CandBEB Cwill be in each other. Solution. If we wish A EB C to be in B(f) C, though A is not in B, this can be done as follows: Assume something D (by Postulate 1) such that it is not in A, but making (by Postulate 2) A + D Cf) C, then what we seek has been accomplished (Figure 25). For A (f) CCf) A (f)A (f)D 3 (by construction) Cf) A EBD (by Axiom 2). Similarly, BEB C Cf) BEBA (f)D (by construction). But A (f)D is in BEBA (f)D (by Def. 3). Therefore, A (f) C is in B(f)C. Which was to be done. SYand YX are disparate. Let RSEBSYCf) YR; then SY(f) YR will be in XY(f) YR. Let A be equilateral, B parallelogram, D equiangular, C equilateral equiangular or regular. Then it is clear that though equilateral and parallelogram are disparate so that neither is in the other, yet a regular equilateral is in a regular parallelogram or square. But, you say, this prescribed construction does not succeed in all cases of the problem. For example, let A be a trilateral, B a quadrilateral. Then no notion 2 For references see p. 381
378 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 8@C Fig. 25. can be found such that A and B are both in it and that A EB C is also in a given B(fj C, since A and B are incompatibles. I reply that our general construction depends upon the second postulate, according to which something can be composed of anything whatever. Thus God, soul, body, point, and heat together constitute an aggregate of these five things. And so a quadrilateral and a trilateral can be compounded, and the problem solved. Assume D as anything which is not contained in a trilateral; let us say, a circle. Then A EB D is a trilateral and a circle, which may be called C. Then C EB A is nothing again, but a trilateral and a circle. For in any case it is in CEBB, that is, in a trilateral, a circle, and a quadrilateral. But if anyone seeks to apply this general calculus of compounds of any kind whatsoever to some special type of compounding, for example, if someone wishes the trilateral and circle and quadrilateral not merely to compose an aggregate, but each as a concept to be in the same subject,' he must see whether they are compatible. Thus immovable scattered straight lines may indeed be taken to compose one aggregate but not to compose a continuum. 4 Proposition 23. Given two disparate terms A and B, to find a third, C, diverse from them. Solution. Assume (by Postulate 2) that Coo A (fj B, and the problem is solved. For since A and B are disparate (by hypothesis), that is, neither is in the other (by Def. 6), it follows that C cannot be 00 A, nor CooB (by Prop. 13). Therefore, these three terms are diverse, just as the problem presupposes. Furthermore, A EB Coo A (fj A EB B (by construction); that is, 00 A EB B (by Axiom 2). Therefore, A EB Coo A EB B, which was to be done. Proposition 24. To find any desired number of terms, each diverse from the others, and related to each other in such a way that no new term can be composed from them, nor a term diverse from any ofthem whatsoever. Solution. Assume A, B, C, and D to be ahy terms whatever diverse from each other (by Postulate 1). From them (by Postulate 2), let A (fjBoo M; M(fj Coo N; and N(fjDoo P. Then A, B, M, N, and P are the desired terms. For by construction, M is made from A and B, and furthermore, A or B is in M, and M is in N, N in P. Therefore, by Proposition 16, any of the prior terms is in anyone of the posterior. Now, if you compound any two terms with each other, no new term is constituted. For if you compound the same terms with itself, there is no new term. LEBLooL, by Axiom 2. But if you compound one with another, you compound an earlier with a later, and therefore an inexistent term with its container, as L EB N. But L EB NooN (by Prop. 14). Now, if you compound three term together, as L EBN EBP, you compound a binary, L EBN, with one, P. But the binary L (fj N in itself compounds nothing new but only one of its own
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 379 terms, namely, the latter one, N, as I have already shown. Therefore to compound the binary L (f) N with the one term P is the same as to compound the one term N with P, and as I have just shown, compounds nothing new. Therefore, a binary together with one, or a ternary, compounds nothing new. And so on for many terms. Q.E.D. Scholium. It would have sufficed to add terms continuously inexistent in themselves, as M, N, P, and this will indeed result if in our construction we set A OC) nothing, and let BOC) M. But the given solution seems a little more inclusive. Undoubtedly all the problems so far could be soved in other ways. But to show all these possible solutions, that is, to prove that there are no other possible methods, would require that many more propositions should previously be proved. For example, five terms, A, B, C, D, and E, can have only the following methods of arrangement, so that no new term can be compounded from them: first, if A is in B, Bin C, C in D, and D in E; second, if A (f)BOC) C, and Cis in D, and D in E; third, if A EBBOC) C, and A is in D, and B(f)DOC) E. In this third or last mode, moreover, there are these five notions: equiangular A, equilateral B, regular C, rectangular D, square E. From these no new term can be compounded which does not already coincide with them, because equiangular and equilateral coincides with regular, and equiangular is in rectangular, and equilateral rectangular coincides with square. Hence equiangular regular is the same as regular and equilateral regular is also, and equiangular rectangular is rectangular, and regular rectangular is square. Scholium to Definitions 3, 4, 5, and 6. We say that the notion of a genus is in the notion of a species but that the individuals of the species are in the individuals of the genus. The part is in the whole, and the indivisible is also in the continuum, as a point is in a line, even though a point is not a part of a line. Thus the notion of a modification or a predicate is in the notion of the subject. This consideration has in general the very widest application. We say too that inexistents are contained in the terms in which they are. In this connection it makes no difference to this general notion how the terms are in each other or in a container. s Thus our demonstrations also apply to those things which compose something distributively, as all species together compose a genus. Hence all the inexistents sufficient to constitute a container, or which contain all the terms which are in the container, are said to compose the container itself. For example, A EEl B is said to compose L, if A, B, and L signify straight lines RS, YX, RX, since RS EEl YX OC) RX. Similarly RS EEl SX OC) RX. Such parts which exhaust a whole, I usually call 'cointegrants', especially if they have no part in common, in which case they may be called 'comembers', as RS and RX. Hence it is clear that the same term can be composed in many ways, if the terms of which it is composed are further composite. Indeed, if they can be resolved into the infinite, the variations of composition are infinite. Thus analysis and synthesis together depend upon the foundations constructed here. Furthermore, if the terms which are contained are homogeneous with that in which they are contained, they are called 'parts', and the container is called the 'whole'. If any two parts whatever are so related that a third can be found having a part of each in common, that which is composed of the three is a continuum. Thus it is clear how one consideration gradually arises out of another. Furthermore, I call terms of which one is in the other 'subalternates'; for example species in a genus, and the straight line RS in the straight line RX. I call them 'disparates' when this is not true; for example, the straight lines RS and YX, two species ofthe same genus, a perfect and an imperfect metal. This applies especially to members of diverse divisions of the same For references see p. 381
380 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS whole which have something in common; for example, if we divide metals into perfect and imperfect, and further into those which are soluble in aqua fortis and those insoluble in it, it is clear that a metal insoluble in aqua fortis and a perfect metal are two disparates and that there is a perfect metal, or one that fulminates, which remains in the retort which is yet soluble in aqua fortis, namely, silver, and that on the other hand, there is an imperfect metal insoluble in aqua fortis, namely tin. Scholium to Axioms 1 and 2. Since the art of characteristics [speciosa generalis] 6 is nothing but the representation and treatment of combinations by signs, and there are various conceivable laws of combination, the result is that various methods of compounding arise. Here, however, we take no account of variations which consist in merely changing the order of terms; AB is the same as BA for us. Furthermore, we also take no account here of repetition; AA is the same as A for us. Thus, wherever these laws are observed, the present calculus can be applied. But this calculus is clearly observed in the compounding of absolute concepts, where there is no ground for arrangement or for repetition; thus it is the same to say 'warm and bright' as to say 'bright and warm', and to say a 'warm fire' or 'white milk', as the poets do, is redundant, for white milk is nothing but milk and rational man merely rational animal, since rational is nothing but rational animal. The same holds when certain determinate things are said to exist in things. It is vain to add the same real more than once. When two and two are said to make four, the latter two must be diverse from the former two. If they were the same, they would produce nothing new. This would be like trying, in jest, to make six eggs out of three, by counting first the three eggs, then taking away one and counting the remaining two, and again taking away one and counting the remaining one. But in the calculus of numbers and magnitudes, A or B or any other signs do not signify a definite thing, but any cases whatever of the same number of congruent parts; for any two feet whatever are signified by 2 if the foot is the unit of measure. Hence 2 + 2 make a new term 4, and 3 times 3 a new term 9; for it is always presupposed that diverse terms, though of the same magnitude, are involved. But the case is different in certain matters, for example, lines. Assume that a movable point draws a straight line, RYEB YXoo RYX, or PEBBoo L, extending from R to Y (Figure 26). Let us assume then that the same point returns from X toward Yand stops there. sEBc A\t)C Fig. 26.
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 381 Then, although it has twice described YX or B, it has produced nothing more than if it had once described YX. LEBB is the same as L, or P EBB EBB or RYEB YXEBXYis the same as RYEB YX. This warning is of great importance in estimating the magnitude of those things which are generated by the magnitude and motion of things generating or describing them. For here one must be careful not to have one part retrace another or to have one part of the describing line take the place of another; or we must subtract it in this case, so that the same term is not added more than once. It is also clear that according to the notion used here, the magnitudes of components added together can constitute a magnitude greater than that of the thing which they compose. Thus the composition of terms and of magnitudes differs greatly. For example, if the whole line L, or RX, has two parts A or RS, and B or YX, of which each is greater than half of RX itself (for instance, if RX is 5 feet, RS is 4 feet, and YX is 3 feet), obviously the magnitudes of the parts will compose the magnitude of 7 feet, which is greater than that of the whole line, yet the lines RS and YX themselves compose only RX, or RS EB YX 00 RX. It is for this reason that I designate real addition by EB, while I designate the addition of magnitudes by +. Finally, it makes a big difference in real addition what the order is when we are dealing with the actual generation of things, for the foundation must be laid before the house is built. But in the mental formation of terms the result is the same, whatever ingredient we consider first, even though one method of consideration may be more useful than another. Hence order does not affect the development of the theory of this calculus. We shall have to consider order at the proper time. But now R Y EB YS EB SX is the same as YS EB R Y EB SX. Scholium to Proposition 24. RS and YX are diverse, and also disparate, so that neither is in the other. Let RSEB YXoo RX; then RSEBRXwill be the same as YXEBRX. For the straight line RX is always compounded in its notions. Let A be a parallelogram, B equiangular, term~ which are disparate. Let C be A EBB, that is, rectangular. Then rectangular parallelogram will be the same as equiangular rectangle, for neither is anything but rectangular. In general, let Maevius be A, Titius B, the pair of men composing C. Then Maevius will be one of this pair just as Titius will be one, and nothing will result but this pair on both sides. Another solution can be given to this which is more elegant and specialized, when A and B have something given in common and also have something that is distinctive of each. Thus let M be distinctive of A and N distinctive of B; make MEBNooD; and let P be what is common to both. I say A EBD will be 00 BEBD. For since A ooPEBM, and BooPEBN, A EBD will be 00 PEBMEB N, and BEBD also will be 00 PEBMEBN. REFERENCES At this point the companion study, the 'Not Inelegant Example', included the following proposition on subtraction: "If coincident terms are subtracted from coincident terms, the remainders will coincide. If A 00 L,andB 00 M, thenA-Boo L-M. For A-B 00 A-B(this is true in itself), and, by substituting L for A and M for B on either side (by the definition of co incidents), the result is that A-B 00 L-M. Q.E.D." This theorem was accompanied by the following marginal note: "Subtraction of concepts is one thing, negation another. For example, nonrational man is absurd or impossible. But it is permissible to say that an ape is a man except that it is not rational. [They are] men except in the respect in which man differs from a beast, as in the Jumbo of Grotius. Man -rational is 1
382 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS different from nonrational man. For man -rational 0Ci beast. But nonrational man is impossible. Man -rational-animal is nothing. Hence subtraction can result in nothing or in simple nonexistence; in fact, in less than nothing. But negation gives impossibility" (G., VII, 232"C"33 and note). 2 ReadingSYfor ST(G., VII, 242) and, below,SXfor SYand RXfor RY. 3 G.hasL. 4 The parallel to the distinction between nominal and real definitions, so frequently discussed by Leibniz, at once suggests itself. 5 That is, the rules will be the same, whether the proposition is interpreted intensionally or extensionally. 6 One of Leibniz's many names for his new science, derived from the more particular 'specious analysis' of Descartes, or algebra (cf. No. 13 and p. 166, note 2).
42 CRITICAL THOUGHTS ON THE GENERAL PART OF THE PRINCIPLES OF DESCARTES 1692 The critical notes which Leibniz wrote to the first two parts of the Principia philosophiae were intended to be the nucleus for a definitive judgment on Descartes's entire system from Leibniz's point of view and therefore summarized and united all the special criticisms of particular points which he had been making for the previous twenty years. In 1692 Leibniz sent the manuscript to Basnage de Beauval in Holland, with instructions to find a publisher (an assignment which Basnage was unable to carry out) and at the same time to submit the notes to Huygens, Bayle, and other scholars for their criticism. Basnage kept the document until 1697, when he sent it to John Bernoulli at Groningen. In the Principia philosophiae, Part I, Descartes had restated the general metaphysical position of the Meditations more exactlyJollowing them in Part 1/ with his conception of the nature of body and of motion. Thus Leibniz's notes on Part I are valuable for their sharp formulation of his own views on knowledge and truth and for his careful analysis of the psychological and epistemological nature of error. Part 1/ is one of the best statements available of the methodological use which Leibniz makes of the principle of continuity in physics. The text is that of Leibniz's revision. Several readings from his first draft are printed in the notes. [G., IV, 354-92] ON PART I On Article 1. Descartes's dictum that everything in which there is the least uncertainty is to be doubted might have been better and more exactly formulated in the precept that we must consider the degree of assent or dissent which a matter deserves or, more simply, that we must look into the reasons for every doctrine. This would end all the caviling about Cartesian doubt. But perhaps the author preferred to use paradoxes, in order to stimulate the sluggish reader through novelty. I wish, however, that he had remembered his own precept or rather, that he had understood its true force. We can best explain this matter and its application by the example of geometricians. They are agreed upon axioms and postulates, upon whose truth the rest depends. We accept these, both because they satisfy the mind immediately and because they are proved by countless experiences; nevertheless, it would be an aid to the perfection of science to prove them. This was attempted of old for certain axioms by Apollonius and Proclus and recently by Roberval. Euclid tried to prove that two sides of a triangle taken together are greater than the third (a fact which, as a certain old writer jokingly said, even a jackass knows when he goes to his feed in a straight line rather than a roundabout way), because it was his purpose to base geometric truths not on sensory images but on reason. In the same manner he might also have demonstrated that two straight For references see p. 410
384 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS lines (which do not coincide when extended) can have only one point in common if he had only had a good definition of a straight line. 1 I am convinced that the demonstration of the axioms is of great assistance to true analysis or the art of discovery. So if Descartes had wished to carry out what is best in his rule, he should have worked at the demonstration of scientific principles and thus achieved in philosophy what Proclus tried to do in geometry, where it is less necessary. But our author seems sometimes to have preferred applause rather than certainty. I should not blame him for being satisfied so often with verisimilitude, if he himself had not aroused expectations with so strong a profession of exactness. I blame Euclid much less for assuming certain things without proof, for he at least established the fact that if we assume a few hypotheses, we can be sure that what follows is equal in certainty, at least, to the hypotheses themselves. If Descartes or other philosophers had done something similar to this, we should not be in difficulty. Moreover, the skeptics, who despise the sciences on the pretext that they sometimes use undemonstrated principles, ought to regard this as said also to them. I hold, in contrast, that the geometricians should be praised because they have pinned down science with such pegs, as it were, and have discovered an art of advancing and of deriving so many things from a few. If they had tried to put off the discovery of theorems and problems until all the axioms and postulates had been proved, we should perhaps have no geometry today. On Article 2. Furthermore, I do not see what good it does to consider what is doubtful as false. This would be not to lay aside prejudices but to change them. But if this is understood merely as a fiction, it should not have been abused, as for instance, in the fa:Ilacy which will be seen, below in Article 8, to arise where the difference between mind and body is discussed. On Article 4. About sensible things we can know nothing more, nor ought we to desire to know more, than that they are consistent with each other as well as with rational principles that cannot be doubted, and hence that future events can to some extent be foreseen from past. To seek any other truth or reality than what this contains is vain, and skeptics ought not to demand any other, nor dogmatists promise it. 2 On Article 5. There can be no doubt in mathematical demonstrations except insofar as we need to guard against error in our arithmetical calculations. For this there is no remedy except to re-examine the calculation frequently or to have it tested by others and also to add confirmatory proofs. This weakness of the human mind arises from a lack of attention and memory and cannot be completely overcome, and Descartes's mention of it, as if he knew a remedy, is in vain. It would be enough if the state of affairs in other fields were the same as that in mathematics; indeed, all reasoning, even the Cartesian, however convincing and accurate, is subject to this doubt, whatever may be said about some powerful deceiving spirit or about the distinction between dreams and waking. On Article 6. We have a free wiII not in perceiving but in acting. Whether honey will seem sweet or bitter to me does not lie with my will, but neither does it lie with my will whether a proposed theorem will seem true or false to me; it is the business of consciousness merely to examine what appears to it. Whoever makes an affirmation of anything is conscious either of a present perception or reason or at least of a present memory bringing back a past perception or the perception of a past reason, although we are often deceived in this through unreliable memory or faulty attention. But consciousness of the present or past is in no way dependent on our will. This one thing we
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 385 recognize to be within the power of will- to command attention and exertion. And so the will, though it does not bring about any opinion in us, can nevertheless contribute to it obliquely. Thus it happens that men often finally come to believe what they will to be true, after having accustomed the mind to attend most strongly to the things which they favor. In this way they finally succeed in making it satisfy not merely their will but also their consciousness. 3 See on Article 31. On Article 7. I think, therefore I am. Descartes has well noted that this belongs to the first truths. But it would have been equitable not to neglect others of equal significance. In general, therefore, this can be expressed as follows. Truths are either offact or of reason. The primary truth of reason is the principle of contradiction or, what amounts to the same thing, that of identity, as Aristotle has rightly observed. There are as many primary truths of fact as there are immediate perceptions or if I may say so, consciousnesses. However, I am conscious not only of myself thinking but also of my thoughts, and it is no more true and certain that I think than that this or that is thought by me. Hence the primary truths of fact can conveniently be reduced to these two: 'I think' and 'Various things are thought by me'. Whence it follows not only that I am, but that I am affected in various ways. On Article 8. It is not valid to reason: 'I can assume or imagine that no corporeal body exists, but I cannot imagine that I do not exist or do not think. Therefore I am not corporeal, nor is thought a modification of the body,' I am amazed that so able a man could have based so much on so flimsy a sophism. Certainly he adds nothing more in this article; what he has added to it in the Meditations I shall examine in its proper place. No one who thinks that the soul is corporeal will admit that we can assume that nothing corporeal exists, but he will admit that we can doubt (as long as we are ignorant of the nature of the soul) whether anything corporeal exists or does not exist. And since we nevertheless see clearly that our soul exists, he will admit that only one thing follows from this: that we can still doubt that the soul is corporeal. And no amount of torture can extort anything more from this argument. But Descartes provided an opening for this fallacy above in Article 2 by taking the license of rejecting what is doubtful as false, so that it becomes possible to assume that there are no corporeal beings because we can doubt that they exist, a point which cannot be granted him. It would be different if we understood the nature of the soul as perfectly as we do its existence, for then it would be established that whatever does not appear in it is not in it. On Article 13. I have already observed, on Article 5, that the errors which can arise from defective memory or attention and which can also occur in arithmetical calculations even after a perfect method has been found, as in numbers, have been mentioned here to no purpose, since no method can be devised in which such errors are not to be feared, especially when the reasoning is long drawn out. So one must resort to criteria. For the rest, God seems to be called in here merely as a kind of display or showpiece\ not to mention that strange fiction or doubt as to whether we are not led to err even in the most evident things, which should convince no one because the nature of evidence prevents it and the experiences and successes of the whole of life witness against it. And if this doubt could once be justly raised, it would be straightway insuperable; it would always confront Descartes himself and anyone else, however evident the assertions presented by them. Aside from this, we must recognize that this doubt cannot be established by denying God or removed by introducing him. For references see p. 410
386 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS For even if there were no God, we should nonetheless be capable of truth, if only it remained possible for us to exist. And even if it be granted that God exists, it does not thence follow that there exists no created being that is entirely fallible and imperfect, especially ~ce it is possible~hat its imperfection may not be native but superinduced, perhaps· by some great sin, as the Christian theologians teach concerning original sin, so that this evil could not be imputed to God. But even though it does not seem ~pproprJate to have introduced God here, I nevertheless think that the true knowledge of God is the principle of higher wisdom, though for other reasons. For God is the first cause no less than the ultimate reason of things, and there is no better knowledge of things than through their causes and reasons. On Article 14. The argument for the existence of God taken from the concept of God was first discovered and stated, so far as is known, by Anselm, archbishop of Canterbury, in his book Contra insipientem, which still exists. s It was frequently examined by various authors of the Scholastic theology and by Thomas Aquinas himself, from whom Descartes, who was no stranger to this knowledge, having studied with the Jesuits of La Fleche, seems to have borrowed it. This reasoning contains something beautiful but is nevertheless imperfect. The argument reduces to this. Whatever can be demonstrated from the concept of a thing can be ascribed to that thing. Now from the concept of a most perfect or greatest being, its existence can be demonstrated. Therefore existence can be attributed to the most perfect being (God), or God exists. The minor premise is proved thus: The most perfect or greatest being contains all perfections, and therefore existence, which is undoubtedly one of the perfections, since it is more or greater to exist than not to exist. So much for the argument. But, by omitting perfection and greatness, the argument could have been formulated more fittingly and strictly in this way. A necessary being exists (that is, a being whose essence is existence or a being which exists of itself), as is clear from the terms. Now God is such a being, by definition of God. Therefore God exists. These arguments are valid, if only it is granted that a most perfect being or a necessary being is possible and implies no contradiction or, what amounts to the same thing, that an essence is possible from which existence follows. But as long as this possibility is not demonstrated, the existence of God can by no means be considered as perfectly demonstrated by such an argument. In general, we must recognize, as I have long since pointed out, that nothing can safely be inferred about a definite thing out of any given definition, as long as the definition is not known to express something possible. For if it should happen to imply some hidden contradiction, it would be possible for something absurd to be deduced from it. 6 Meanwhile we do learn from this argument the admirable advantage of the divine nature, that if it is merely possible, by this fact itself it exists, an argement which does not suffice to prove the existence of other things. Therefore to have a geometric demonstration of the divine existence it remains only to demonstrate the possibility of God with an exactness adequate for geometric rigor. Meanwhile the existence of a thing which merely needs possibility thus acquires great credibility; and besides, that there is some necessary thing is established in another way, from the fact that contingent things exist. 7 On Article 18. That we have an idea of a perfect being and that a cause of that idea therefore exists - that is, a perfect being exists (this is Descartes's second argument)is more doubtful than the possibility of God and is denied by many of those who
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 387 profess with the highest zeal not merely the possibility but also the existence of God. Nor is the remark valid which, as I recall, Descartes made somewhere to the effect that when we speak of something with an understanding of what we say, we have an idea of the thing. 8 For it often happens that we combine things that are incompatible, as when we think of a most rapid motion, which is certainly impossible, and hence not an idea; and yet we may speak of it, understanding what we mean. For I have elsewhere explained that we often think only confusedly of what we are talking about, and we are not conscious of the existence of an idea in our mind unless we understand the thing and analyze it sufficiently. 9 On Article 20. The third argument suffers, among other things, from the same vice, namely, when it assumes that there is in us an idea of the highest perfection, God, and concludes from this that God exists because we who have this idea exist. On Article 21. From the fact that we now are, it follows that we will be in the next moment, unless there exists a reason for change. And so, unless it were established in some other way that we cannot even exist without the beneficence of God, nothing is established about the existence of God from our own duration; as if one part of this duration were entirely independent of another, which we cannot admit. 1 0 On Article 26. Even though we are finite, we can yet know many things about the infinite: for example, about asymptotic lines, or lines which approach each other continuously when infinitely produced but never meet; about spaces which are infinite in length but not greater in area than a given finite space; and about the sums of infinite series. Otherwise we should also know nothing with certainty about God. However, it is one thing to know something about a matter and another to comprehend the matter, that is, to have within our power all that is hidden in the matter. On Article 28. As for the ends which God has proposed to himself, I am fully convinced both that they can be known and that it is of the highest value to investigate them; and that to disdain this inquiry is not without danger or suspicion. In general, whenever we see that anything is particularly useful, we may safely assert that one, among others, of the ends which God has proposed to himself in creating this thing is precisely that it render these services, since he both knew and planned this use of it. I have elsewhere pointed out, and shown by examples, that certain concealed physical truths of great importance can be discovered by considering final causes, which could not have been discovered as easily by efficient causes. 1 1 On Article 30. Even if we admit that the perfect substance exists and that it is in no way the cause of imperfections, we shall not thereby remove the true or fictitious reasons for doubt which Descartes introduced, as I have already pointed out in Article 13. On Articles 31, 35. I do not admit that errors are more dependent upon the will than upon the intellect. To give credence to what is true or to what is false - the former being to know, the latter to err - is nothing but the consciousness or memory of certain perceptions or reasons and so does not depend upon will except insofar as we may be brought by some oblique device to the point where we seem to see what we wish to see, even when we are actually ignorant. See Article 6. Hence we make judgments not because we will but because something appears. And when it is said that will reaches further than intellect, this is more ingenious than true; to put it bluntly, it is a bit of popular ornamentation. We will only what appears to the intellect. The source of all errors is precisely the same in its own way as the reason for errors which is observed For references see p. 410
388 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS in arithmetical calculation. For through a lack of attention or memory it often happens that we do what we ought not, or fail to do what we ought, or that we think that we have done what we did not do, or have not done what we have. So it happens in calculations (to which reasoning corresponds in the mind) that necessary figures are not put down but unnecessary ones are, or that something is skipped in the combination, or that the method is not duly observed. For when our mind is tired or distraught, it does not adequately attend to its present operations, or it assumes by an error of memory that something was long since proved which has become more firmly fixed in us only because it was more frequently impressed, or more fixedly considered, or more eagerly desired. The remedy for our errors is the same as that for errors in calculation - to pay attention to the matter and form, to proceed slowly, to repeat and vary our operations, to introduce tests and checks, to divide longer chains of reasoning into parts so that the mind gets a breathing spell, and to confirm each part in turn through special proofs. And since we are sometimes in a hurry to act. it is an important matter to have acquired presence of mind through practice, as do those who are still able, in the midst of noise and without written calculations, to compute very large numbers. Thus the mind will not be easily distracted, whether by the external senses or by its own images and affections, but will rise above what it is doing and retain the power of criticism or as it is commonly called, of reflecting upon itself, so that it can constantly say to itself, as would an external monitor, 'Watch what you are doing. Why are you doing it? Time is passing.' The Germans use the excellent term: sich begreifen; the French, the equally happy one: s'aviser, as if to warn one's self, to suggest to one's self, as the Roman nomenclators pointed out to Roman candidates the names and merits of influential citizens, or as the prompter gives out cues for the remaining lines to a comedian, or as a certain youth called out to Philip of Macedon: 'Remember that yOll are morta!.' But this very criticism, this s'aviser, is not in our power or the choice of our will; it must first of all occur to our intellect, and it depends upon the present degree of our perfection. It is the business of the will to strive beforehand with all zeal, to prepare the mind well in advance. This can be done usefully, partly through a contemplation of the experiences of others, their injuries and dangers; partly by the use of our own experiences, which should if possible be free of danger, or at least involve only slight and negligible harm; and partly also by training the mind to follow a definite series and method when thinking, so that later the required attitude offers itself spontaneously, as it were. However, there are matters which escape us or do not occur to us through no fault of ours; in these we suffer from a defect, not of judgment, but of memory or of mental capacity, and so are not so much in error as in ignorance, since it is beyond Ollr power to know or to remember all that we will. This is not a matter to be discussed here. That sort of critical reflection by which we fight against a lack of attention will suffice. Whenever memory reports to us past proofs which may not have been valid, we should hold the confused recollection for suspect, and either repeat our inquiry if possible and if the matter is important or trust past proofs only if sufficient care has been given them. On Article 37. The highest perfection of man consists not merely in that he acts freely but still more in that he acts with reason. Better, these are both the same thing, for the less anyone's use of reason is disturbed by the impulsion of the affections, the freer one is. On Article 39. To ask whether our will is endowed with freedom is the same as to
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 389 ask whether our will is endowed with will. Free and voluntary signify the same thing. For freedom is the same as spontaneity with reason, and to will is to be brought to act through a reason perceived by the intellect. But the purer this reason is, and the less mixed up it is with the impact of base and confused perceptions, the freer is the act. To refrain from judgment is not the business of our will but of the intellect imposing upon itself some critical reflection, as I have already said on Article 35. On Article 40. Anyone who is convinced that God preordains all things but that he himself is free, and who is shown the conflict between these views but replies only what Descartes recommends, namely, that his mind is finite and cannot grasp such matters, seems to me to be answering the conclusion rather than the argument and to be cutting rather than untying the knot. The question is not whether we grasp the matter itself but rather whether we grasp our own absurdity when it is pointed out. There should surely be no contradiction even in the mysteries of faith; much less so in the mysteries of nature. So if we wish to stand out as philosophers, we must once more take up the argument, which with some semblance of truth implies contradictory conclusions from your own assertions, and uncover the fallacy in it, a thing which is certainly always possible unless we have made a mistake. On Articles 43, 45, 46. I have elsewhere called attention to the fact that there is not much use in the celebrated rule that only what is clear and distinct shall be approved, unless better marks of clearness and distinctness are offered than those of Descartes. Preferable are the rules of Aristotle and the geometricians, namely, that with the exception of principles, that is, of first truths or hypotheses, we are to admit nothing unless proved by a valid argument. By valid, I mean one that is suffering from neither a formal nor a material fallacy. There is a material fallacy when anything is assumed besides principles and what has been further proved from principles by a valid argument. Also, by right form I understand not only the common syllogistic form but also any other form demonstrated beforehand which is conclusive by virtue of its structure. The forms of arithmetical and algebraic operations also meet this requirement, as do the forms of the bookkeepers, and indeed to some extent the forms of judicial processes, for sometimes we are content to act upon a certain degree of probability. However until now the part of logic, of great practical value, which deals with the calculation of degrees of probability, remains to be treated; I myself have set down a number of things about it. On form, compare further what is said on Article 75. On Articles 47, 48. Someone, I do not know who (Comenius, I believe), rightly pointed out long ago that though Descartes promises in Article 47 summarily to enumerate all the simple concepts, he deserts us at once in Article 48, and, having named some, he adds 'and so forth'. Besides, several of those which he names are not simple. This is an inquiry of greater importance than is thought. On Article 50. It is most desirable to demonstrate truths which are relatively simple but which the prejudiced opinions of men keep them from admitting, by means of simpler ones. On Article 51. I do know whether the definition of substance as that which needs for its existence only the concurrence of God fits any created substance known to us, unless we interpret it in some unusual sense. For not only do we need other substances; we need our own accidents even much more. Therefore, since substance and accident depend upon each other, other marks are necessary for distinguishing a substance from an accident. Among them may be this one: That a substance needs some accident For references see p. 410
390 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS but often does not need a determinate one but is content, when this accident is removed, with the substitution of another. An accident, however, needs not only some substance in general but that very one in which it inheres, so that it cannot change it. But there are other things of greater importance and worthy of a profounder discussion, which remain to be said elsewhere about the nature of substance. On Article 52. I admit that there is one principal attribute of every substance which expresses its essence, but if we mean an individual substance, I doubt whether this can be explained in words and especially in a few words, in the way the other genera of substances may be explained by definitions.u That extension constitutes the common nature of corporeal substance I find asserted by many, with much confidence, but never proved. Certainly neither motion or action nor resistance or passion can be derived from it. Nor do the natural laws which are observed in the motion and collision of bodies arise from the concept of extension alone, as I have shown elsewhere. Indeed, the notion of extension i'l not a primitive one but is resolvable. For an extended being implies the idea of a continuous whole in which there is a plurality of things existing simultaneously. To speak of this more fully, there is required in extension, the notion of which is relative, a something which is extended or continued as whiteness is in milk, and that very thing in a body which constitutes its essence; the repetition of this, whatever it may be, is extension. I fully agree with Huygens, whose opinion in natural and mathematical matters I value highly, that the concept of an empty place and of extension alone is the same. In my judgment mobility or antitypy themselves cannot be understood from extension alone but from the subject of extension, by which place is not merely constituted but filled. On Article 54. I do not recall that it has ever been perfectly demonstrated either by our author or by his followers that the thinking substance lacks extension or the extended substance lacks thought, so that we can be certain that the one attribute is not demanded for the other in the same subject and, indeed, cannot ever subsist along with it. Nor is this strange, for the author of the Recherche de ta verite (who has made some excellent critical remarks) has rightly pointed out that the Cartesians have given no distinct concept ofthought; so it is not strange that they do not exactly know what is involved in itP On Articles 60, 61. To deny a real distinction between modes is an unnecessary change in the accepted use of words. For until now modes have been\considered as things and have been held to differ in reality, as a spherical figure of wjlx differs from a square one. Cerainly the transformation of one figure into the other is a true change, and it has therefore a real foundation. On Article 63. To think of thought and extension as the thinking or extended substance itself seems to me neither correct nor possible. Such an expedient is suspect and is similar to that which enjoins us to hold the doubtful for false. Such distortions of things prepare minds for stubbornness and fallacies. On Articles 65-68. Descartes, following the ancients, rendered a useful service in eradicating the prejudice that makes heat, colors, and other phenomena seem to be things outside of us, since it is evident that the same hand on which water seemed very hot soon finds it tepid; and a man who observes a green color in a powdered mixture no longer sees it as green when his eye is aided by an instrument but as a mixture of yellow and blue and can grasp the causes of these two colors with the use of better instruments and other observations or reasons. From these considerations it seems
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 391 that no such thing exists outside of us, the phantasm of which appears to our imagination. We are commonly like boys who have been convinced that there is a pot of gold at the very end of the rainbow where it touches the earth and who run toward it in a vain effort to find it. 14 On Articles 71-74. In my comments on Articles 31 and 35, I have already made some remarks about the causes of error. These also provide reasons for the errors discussed here, for the prejudices of infancy belong to the class of unproved assumptions. Moreover, fatigue diminishes attention, and the ambiguity of words belongs with the abuse of signs and involves a formal fallacy. This is as if we put X in place of V in our calculation, to use a German proverb, or as if a druggist were to put sandarac into his prescription i~ place of dragon's blood [sanguis draconis]. On Article 75. It seems to me only fair to give the ancients their due and not to conceal their merits by a silence that is malignant and injurious to ourselves. The things which Aristotle set down in his logic, though not sufficient for discovering, are nonetheless generally sufficient for judging, at least where necessary consequences are concerned. It is an important thing for the conclusions of the human mind to be stabilized as if by certain mathematical rules. And I have pointed out that the fallacies which are introduced into serious matters are more often sins against logical form than is commonly believed. So to avoid all errors, nothing more is necessary than to make use of the most common rules of logic with great constancy and rigor. But because the complexity of matters often prevents this persistence, we provide certain special logical forms in the sciences and in fields of action, which should be demonstrated in advance by these general rules but with the peculiar nature of the subject taken into consideration. Just so Euclid has a certain logic of his own concerning the conversion, composition, and division of proportions, which are first proved in a particular book of the Elements and then are applied throughout the whole geometry.1S Thus both brevity and confidence are assured, and the more of rules of this kind we have the more we improve science. Add to this what I have observed on Articles 43ft'. on socalled 'formal argumentations' which should be more widely extended than is commonly believed. ON PART II On Article 1. The argument by which Descartes tries to prove that material things exist is weak; it would have been better not to try. The gist of the argument is this: the reason why we perceive material things lies outside of us; therefore it is either in God or in someone else or in the material things themselves. It is not in God, for if no material things existed, he would be a deceiver; it is not in someone else - this he has forgotten to prove; therefore it is in the things themselves, and they therefore exist. To this we can reply that a sensation may come from some other being than God, who permits other evils for certain important reasons and who can also permit us to be deceived without having himself the character of a deceiver, especially since this involves no injury, since it would rather be disadvantageous for us to be undeceived. Besides, there is a further fallacy in that the argument neglects another possibility that while our sensations may indeed be from God or from someone else, the judgment (as to whether the cause of the sensation lies in a real object outside of us), and hence the deception itself, may originate in us. A similar thing happens when colors and other things of this sort are held to be real objects. Through previous sins, moreFor references see p. 410
392 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS over, souls may have deserved their condemnation to such a life full of deception, in which they snatch at shadows instead of things. The Platonists do not seem to have shrunk back from such an opinion, since this life seemed to them like a dream in the cave of Morpheus, the mind having lost its reason through the lethal drink before it came here, as the poets used to say.16 On Article 4. Descartes tries to prove that body consists in extension alone by enumerating the other attributes and eliminating them. But he should have shown that his enumeration is complete. Also, not all the attributes are correctly eliminated; in fact, those who hold to atoms, that is, to bodies of maximum hardness, will hold, not that hardness consists in a body not yielding to the pressure of the hands, but in it conserving its shape. And those who find the essence of body in antitypy or impenetrability derive the concept of it, not from our hands or from any senses, but from the fact that a body does not give place to another body homogeneous to it unless it can move elsewhere. Thus if we imagine a cube having six other cubes exactly similar to it converging upon it simultaneously and with equal velocities, so that a face of each one of them exactly coincides with one face of the confined cube, then it will be impossible for either the confined cube or any part of it to be moved from its position, whether it be thought of as flexible or rigid. But if this middle cube be thought of as penetrable extension or mere space, then the six concurrent cubes will oppose one another with their edges; but if they are flexible, nothing will prevent their middle parts from breaking into the confined cubical space. From this we may also understand what the difference is between hardness, which is a property of some bodies only, and impenetrability, which belongs to all. Descartes should have considered the latter as well as hardness. On Articles 5, 6, and 7. Descartes has admirably explained that the rarefaction and condensation which we perceive by sense can occur without our having to admit either the existence of vacua interspersed within matter or a change of dimensions in the same part of matter. On Articles 8-19. Many of those who defend a vacuum hold space to be a substance and hence cannot be refuted by Descartes's arguments. Other principles are needed to end this dispute. They will admit that quantity and number have no being outside the things to which they are attributed, but they will deny that space or place is the quantity of a body; they will assume rather that space has a quantity or capacity equal to that of the body contained in this space. Descartes should have shown that the space or internal place of a body is not different from its substance. 17 Those who hold the contrary will defend their view with the popular conception of mortals, according to which one body, in succeeding another, passes into the same place and the same space which the former body has deserted - a thing which cannot possibly be said if space coincides with the very substance of the body. Though it may be accidental to a body, however, to have a certain position or to be in a given place, these opponents will no more admit that place is itself an accident of the body than they will that since contact is an accident, the body contacted is also one. Indeed, it seems to me that Descartes does not so much offer sound reasons for his own opinions as he replies to opposing arguments, which he does very skilfully at this point. And he often uses this device instead of demonstration. But we expected something more, and if I am not mistaken, we were invited to expect it. It must be admitted that nothingness has no extension, and this is a fit retort to all who assume some imaginary - I know not
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 393 what - sort of space. But those who consider space a substance are not touched by this argument; they would certainly be affected if Descartes had proved above what he assumes here, namely, that every extended substance is a body.1s On Article 20. The author's attack on atoms does not seem to be satisfactory. Those who defend them will admit that they can be divided in our thinking as well as by divine power. But the question which (to my amazement) Descartes does not even touch on here is whether bodies which have a firmness which natural forces cannot overcome (this is, according to them, the true concept of atoms) can exist naturally at all. Yet he declares here that he has destroyed the atoms and assumes it in the whole further course of his work. We shall say more about atoms below, on Article 54. 19 On Articles 21, 22, and 23. That the world has no limits in extension and hence can be only one and that the whole of matter is everywhere homogeneous and therefore can be differentiated only through its motions and shapes - these are opinions which are here built upon the proposition that the extended and body are the same, though this is neither universally admitted nor demonstrated by the author. 20 On Article 25. If motion is nothing but the change of contact or of immediate vicinity, it follows that we can never define which thing is moved. For just as the same phenomena may be interpreted by different hypotheses in astronomy, so it will always be possible to attribute the real motion to either one or the other of the two bodies which change their mutual vicinity or position. Hence, since one of them is arbitrarily chosen to be at rest or moving at a given rate in a given line, we may define geometrically what motion or rest is to be ascribed to the other, so as to produce the given phenomena. Hence if there is nothing more in motion than this reciprocal change, it follows that there is no reason in nature to ascribe motion to one thing rather than to others. The consequence of this will be that there is no real motion. Thus, in order to say that something is moving, we will require not only that it change its position with respect to other things but also that there be within itself a cause of change, a force, an action. 21 On Article 26. From what has been said in the preceding paragraph it follows that Descartes's assertion that no more action is required in a body for motion than for rest cannot be sustained. I admit that force is necessary for a body at rest to maintain its rest against colliding bodies. But this force is not in the body itself which is at rest, for the surrounding bodies themselves, opposing each other by their force of motion, cause the body at rest to preserve its given position. 22 On Article 32. Archimedes was the first author transmitted to us who worked on the composition of motion, in his treatise on spirals. Kepler, in his Optical paralimpomena, was the first to apply this to an explanation of the equality of the angles of incidence and reflection, by dividing an oblique motion into a perpendicular and a parallel motion. In this Descartes followed him, as he did also in his Dioptrics. GaIiIeo was the first to show the fullest use of the composition of motion in physics and mechanic~.23 On Articles 33, 34, 35. What Descartes says here is most beautiful and worthy of his genius, namely, that every motion in filled space involves circulation and that matter must somewhere be actually divided into parts smaller than any given quantity. Yet he does not seem to have weighed sufficiently the importance of this last conclusion. On Article 36. The most famous proposition of the Cartesians is that the same quantity of motion is conserved in things. They have given no demonstration of this, however, for no one can fail to see the weakness of their argument derived from the For references see p. 410
394 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS constancy of God. For although the constancy of God may be supreme, and he may change nothing except in accordance with the laws of the series already laid down, we must still ask what it is, after all, that he has decreed should be conserved in the series whether the quantity of motion or something different, such as the quantity of force. I have proved that it is rather this latter which is conserved, that this is distinct from the quantity of motion, and that it often happens that the quantity of motion changes while the quantity of force remains permanent. The arguments by which I have shown this and defended it against objections may be read elsewhere. 24 But since the matter is of great importance, I shall give the heart of my conception in a brief example. Assume two bodies: A with a mass of 4 and a velocity of 1, and B with a mass of 1 and a velocity of 0, that is, at rest. Now imagine that the entire force of A is transferred to B, that is, that A is reduced to rest and B alone moves in its place. We ask what velocity B must assume. According to the Cartesians, the answer is that B should have a velocity of 4, since the original quantity of motion and the present quantity would then be equal, since mass 4 multiplied by velocity 1 is equal to mass 1 multiplied by velocity 4. Thus the increase in velocity is proportional to the decrease of the quantity of the body. But in my opinion the answer should be that B, whose mass is 1, wiII receive the velocity 2, in order to have only as much quantity of power as A, whose mass is 4 and whose velocity is 1. I shall explain my reason for this as briefly as possible, lest I appear to have proposed it without any reason. I say, then, that B will have only as much force as A had previously or that the present and the former force are equal, a thing which is worth proving. To go deeper, namely, and explain the true method of computation - which is the duty of any really universal mathematics, though it has not yet been carried out - it is clear, first of all, that force is doubled, tripled, or quadrupled when its simple quantity is repeated twice, three times, or four times, respectively. So two bodies of equal mass and velocity will have twice as much force as one of them. It does not follow, however, that one body with twice the velocity must have only twice the force of a body with simple velocity, for even though the degree of velocity may be doubled, the subject of this velocity is not itself duplicated, as it is when a body twice as great, or two bodies of the same velocity, are taken in place of one, so that they completely repeat the one in magnitude as well as motion. Similarly 2 pounds elevated to the height of 1 foot are exactly double in essence and power to one elevated the same distance, and two elastic bodies stretched equally are double one of them. But when the two bodies possessing this power are not fully homogeneous and cannot be compared with each other in this way, or reduced to a common measure of matter and force. an indirect comparison must be attempted by comparing their homogeneous effects or causes. Every cause whatever has a force equal to its total effect, or to the effect which it produces in using up its own force. Therefore, since the two bodies mentioned above, A with mass 4 and velocity 1, and B with mass 1 and velocity 2, are not exactly comparable, and no one quantity possessing force can be designated whose simple repetition will produce both, we must examine their effects. Let us assume, namely, that these two bodies are heavy and that A can change its direction and rise; then by virtue of its velocity of 1 it will rise to the height of 1 foot, while B, by virtue of its velocity of 2, will rise 4 feet, as Galileo and others have demonstrated. In each case the effect will entirely consume the force and so be equal to the cause which produces it. But these two effect~ are equal to each other in force or power, namely, the elevation of body A, 4 pounds, to 1 foot, and the elevation of body
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 395 B, 1 pound, to 4 feet. Therefore the causes, too, are equal; that is, the body A of 4 pounds with velocity of 1 is equal in force or power to the body B of 1 pound with velocity 4, as was asserted. But if someone denies that the same power is needed to raise 4 pounds 1 foot and 1 pound 4 feet, or that these two effects are equivalent (though, unless I am mistaken, almost everyone will admit this), he can be convinced by the same principle. If we take a balance with unequal arms, 4 pounds can be raised exactly 1 foot by the descent of 1 pound for 4 feet, and no further work can be done; thus the effect exactly exhausts the power of the cause and is equal to it in force. Let me summarize, therefore. If the whole power of body A, 4, with a velocity of 1, is transferred to B, 1, B must receive a velocity of 2; or, what amounts to the same thing, if B is first at rest and A in motion, but A is then at rest and B has been placed in motion, other things remaining equal, the velocity of B must be double, since the mass of A was quadruple. If, as is popularly held, B should receive four times the velocity of A because it has one-fourth of its mass, we should have perpetual motion or an effect more powerful than its cause. For when A was moving, it could raise 4 pounds only 1 foot, or 1 pound 4 feet; but later, when B moved, it would be able to lift 1 pound 16 feet, for altitudes are as the square of the velocities by force of which bodies are lifted, and four times the velocity will raise a body sixteen times the altitude. With the aid of B not only could we thus once more raise A for 1 foot, after its descent had given it its original velocity, but we could do many other things besides and thus exhibit perpetual motion, since the original force is restored but there is still more left. Moreover, even though the assumption that the whole force of A is transmitted to B cannot actually be realized, this does not affect the matter, since we are here concerned with the true calculation, or with the question of how much force B would necessarily take on according to this hypothesis. Even if a part of the force is retained and only a part transmitted, the same absurdities would still arise, for if the quantity of motion is to be conserved, the quantity of forces can obviously not always be conserved, since the quantity of motion is known to be the product of mass and velocity, while the quantity of force is, as we have shown, the product of mass and the altitude to which it can be raised by force of its power, altitudes being proportional to the square of the velocities of ascent. Meanwhile this rule can be set up: The same quantity of force as well as of motion is conserved when bodies tend in the same directions both before and after their collision, as well as when the colliding bodies are equal. 2' On Articles 37, 38. It is a very true and indubitable law of nature that the same thing, so far as in it lies, always persists in the same state - a law which both Galileo and Gassendi, and several others as well, have long held. It is surprising therefore that it has occurred to some men that a projectile owes the continuation of its motion to the air but that it has not occurred to them that by this same reasoning we should with equal right have to look for some new reason for the continued motion of the air itself. For air could not, as they hold, impel the stone forward unless it itself had the power to continue its received motion and found itself impeded in this by the resistance of the stone. On Article 39. Not only did Kepler observe the very beautiful law of nature according to which bodies describing a circular or curved path strive to leave it in the line of the tangent straight line (others may have preceded him in this), but he already made that application of this law which I consider essential in making clear the cause of gravity. This is apparent from his Epitome of the Copernican Astronomy.26 For references see p. 410
396 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Descartes has rightly affirmed this law and brilliantly expounded it, but he has not demon~trated it, as one would have expected of him. On Articles 40-44. In Articles 37 and 39 Descartes has presented two very true laws of nature which are clear in their own light. But the third seems to me to be so far, not merely from truth, but even from probability, that I wonder how it ever occurred to the mind of such a man. Yet he at once builds his laws of motion and of impact upon it and says that it contains all the causes of particular changes in bodies. He conceives it as follows: one body colliding with another stronger one lo~es none of its motion but merely changes its direction; however, it can receive some additional motion from the stronger body. But in colliding with a weaker body, it loses only as much motion as it transfers to the weaker body. In actual fact, however, it is only in the case ofa collision of bodies moving in opposite directions that a body colliding with a stronger one loses no motion but either retains or increases its velocity. When a weaker but swifter body overtakes one that is stronger but slower, then the contrary occurs, and it is generally true, and can be observed in nature, that the velocity of the pursuing body is diminished by the impact. For if it continued its motion after the collision, it could not in any case proceed at its earlier velocity without giving this velocity to the body ahead as well, in which case the total power in the whole would be increased. If it came to rest after the collision, it would be clear in itself that its velocity had been diminished, and indeed destroyed, by the blow. This coming to rest, moreover occurs in hard 27 bodies (which are here always to be understood) when the ratio of the excess of mass in the first body over that of the one overtaking it to the mass of the body overtaken 28 is double the ratio of the velocity of the first body to the one overtaking it. 29 Finally, if the body is thrown back after the collision, it is again clear that the motion of the repelled body is less than before. For otherwise the velocity of the forward body would necessarily be increased by the added impulsion of the body overtaking it, and whether we think of it as increasing its velocity after its rebound or merely retaining its earlier velocity, the aggregate of power would be increased, which is absurd. If anyone were to defend Descartes by holding that this third law of his on the collision of bodies must be understood to deal only with the collision of bodies from opposite directions, I readily agree with it. But then it must be admitted that he has not provided for the collision of bodies moving in the same direction, though, as we have already seen, he himself claims that this law covers all particular cases. Also, if the demonstration which he attempts in Article 41 is correct, it includes all cases of colliding bodies, whether they move in the same or in opposite directions. But it does not seem to me to have even the semblance of a proof. I admit that it is correct to distinguish quantity and direction of motion and that one of these sometimes changes while the other remains constant. But it is also true that frequently both change together. In fact, both work together to preserve each other, and a body tends to preserve its determination or direction with its whole force and its whole quantity of motion. Whatever is taken away from the velocity when the direction remains constant is also lost from the determination, since a body proceeding more slowly in the same direction is less determined to conserve it. Besides, if a body A collides with a smaller body B at rest, it will continue in the same direction but with diminished motion; if it collides with a body B, at rest but equal to itself, it stops, so that, while it itself remains completely at rest, its motion is transferred to B; and finally, if it collides
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 397 with B, which is at rest but greater than it, or is equal to it with an opposite movement, then A will simply be turned back.30 Hence we can understand that a greater opposing force is necessary for A to be reflected in a direction opposite its original direction than for it merely to be brought to rest, a fact which directly contradicts Descartes's pronouncements. For the opposition must be greater, since the thing opposed is greater, or since the tendency opposing it is greater. But I hold his proposition that motion perseveres as a simple state until it is destroyed by an external cause, to be true not only for the quantity of motion but for its determination also. This determination of a moving body, or its tendency to advance, itself has its own quantity which is more easily diminished than reduced to nothing or to rest and can furthermore be more easily destroyed or reduced to rest than changed into a contrary or regressive motion, as we have just pointed out. Thus, even though one motion is not opposed to another in kind, the present motion opposes the present motion of a body which collides with it, and one advance opposes another contrary advance, since a smaller change and a smaller opposition are necessary, as we have shown, to diminish an advance than to destroy it entirely or to transform it into a retreat. So it seems to me that Descartes's reasoning is like trying to argue that when two bodies oppose each other, they ought never to break or fall apart but to bend each other so that their shapes are molded to each other, on the ground that matter is distinct from shape and that in this case matter is not opposed to matter, but shape to shape, and the quantity of matter can be conserved in the body while its shape is changed. Whence it would follow that the magnitude of a body can never change and that only the shape of the body can change. If Descartes had taken into consideration that every body which collides with another must, before it is repelled, first reduce its advance, then come to a stop, and only then be turned back, and must thus pass from one direction to the opposite, not by a leap but by degrees, he would have set up other rules of motion for us. We must recognize that, no matter how hard, every body is nevertheless flexible and elastic to some degree; like a ball inflated with air which gives way a little when it falls to the floor or is struck with a stone, until the impetus or advance of what strikes it is gradually broken and at last completely stopped, after which the ball resumes its shape and repels the stone, which now no longer resists, or until it rebounds by itself from the floor to which it had fallen. Experiments have taught us convincingly that something similar to this takes place in every rebound, even if the bending and restoration are not visible. But being too confident of posterity, Descartes in his letters very superciliously condemned this explanation of reflection by elastic force, which was first noted by Hobbes. 31 We do not need to examine anew the reasoning by which he tries, in Article 42, to demonstrate the last part of this law of nature which he wants to promulgate - the part, namely, which holds that whatever quantity of motion is lost to one colliding body is added to the other. For this assumes that the quantity of motion must remain constant, and we have already shown in Article 36 how great an error this is. On Article 45. Before I turn to an examination of the special rules of motion given by the author, I shall set up a general criterion or touchstone, as it were, by which they can be examined. I usually call this the law of continuity. I have already explained this principle elsewhere, but it must be repeated and amplified here. 32 When two hypothetical conditions or two different data continuously approach each other until the one at last passes into the other, then the results sought for must also approach each For references see p. 410
398 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS other continuously until one at last passes over into the other, and vice versa. For example, if one focus of an ellipse remains fixed and the other recedes farther and farther away from it, while the latus rectum remains constant, the new ellipses which thus come into being continuously approach a parabola and finally pass over into it completely, namely, when the distance of the receding focus becomes immense. Therefore the properties of these ellipses must also approach more and more the properties of a parabola until at last they pass over into them, and the parabola can be considered as an ellipse whose second focus is infinitely distant. All the properties of an ellipse in general will thus be found in the parabola considered as such an ellipse. Geometry is full of examples of this kind, but nature, whose most wise Author uses the most perfect geometry, observes the same rule; otherwise it could not follow any orderly progress. Thus gradually decreasing motion finally disappears in rest, and gradually diminishing inequality passes into exact equality, so that rest can be considered as infinitely small motion or as infinite slowness, and equality as infinitely small inequality. Whatever is demonstrated about motion in general, or about inequality in general, must for this reason also be verifiable about rest or equality, if this interpretation is right. So the rules for rest or equality can in a sense be considered as special cases of the rules for motion or inequality. If this cannot be done, we may be certain that the proposed rules are inconsistent or wrongly conceived. Hence we shall also show, in Article 53, that to the continuous curve which represents the variations of the hypothetical conditions there must correspond a continuous curve representing the variations of the results but that the Cartesian rules of motion present these results by a figure which is absurd and incoherent. On Article 46. Let us now examine the Cartesian rules of motion. We must understand the bodies involved to be hard and unimpeded by other conditions. Rule 1. If two equal bodies Band C, with equal velocities, collide directly, both will be deflected with the velocities of their approach. This first rule is the only one of Descartes that is entirely true. It can be demonstrated in this way: since the properties of both bodies are equal, either both will continue in their motion and so penetrate each other, which is absurd; or both will come to rest, in which case power will be lost; or both wiIl be repelled, and with their original velocity, because, if the velocity\ of one is diminished, the velocity of the other mu~t also be diminished, because of the equality of their properties. But if the velocity 9f both is diminished, the whole will be diminished, which is impossible. On Article 47. Rule 2. If Band C collide with equal velocities, but B is the greater, then only C is deflected, and B continues; both with their earlier velocities, and so both moving in the original direction of B. This rule is false and conflicts with the preceding one, as is clear from the criterion we have just set up. For if the inequality, or the excess of B over C, is gradually diminished until it passes into full equality, the effects of inequality should also pass over continuously into the effects of equality. So if we assume that B, striking C, overcomes it with so excessive a force that it continues to advance after the collision, it wiIl be necessary, if B is gradually diminished, for its advance also to diminish continuously until, when a certain ratio is reached between Band C, B will at length come to rest and then, by a continuous diminution, be turned into con trary motion; this will
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 399 gradually increase until finally, when all inequality between Band C is removed, the motions end in the rule for equality, in which the regressive motion of each body after collision is equal to its progressive motion before collision, as the first rule states. So this second rule of Descartes cannot stand, for however much we diminish B so that it approaches the magnitude of C, even to the point at which the difference between the two becomes inexplicably small, the consequences which correspond to these two cases of inequality and equality will still remain very' great, if we may believe him, and will not gradually approach each other, since B will always continue in the same direction at the same velocity, no matter how small the difference between it and C may become. The result is that this irregularity must finally be corrected all at once, so to speak, ~nd a great gap must be introduced in the results to correspond with a very small change in the conditions. At the point, that is, where the excess of B over C finally disappears completely, and the very small differenCe between them is further decreased, the motion must pass over from a definite progression to a definite regression, with all the intervening degrees omitted in a single leap, as it were. The result will be that two instances which have an infinitely small variation in the hypotheses or given conditions (that is, a difference smaller than any given amount) will nevertheless have the greatest and mdst noticeable difference in their results, so that it must be in the very last moment only that the two bodies both begin and end their mutual approach and that they both approach each other and break apart in the moment that they coincide, which is absurd. It would follow that the rule for equal bodies or for bodies with infinitely small inequality could not be subsumed under the general rule for inequality. So since two bodies Band C, equal and with equal velocities, are both reflected with their precious velocity when they collide with each other (by Rule 1), it follows necessarily that in the case when B is somewhat increased or, B remaining constant, C is diminished, some change must occur in the consequences and something must be added to the t;esult which would still be present when C is diminished as much as possible, that is, removed entirely. But when C is decreased and becomes less than B, we can move from the case of complete equality, or of the total reflection of B, to the case of the greatest inequality, or the complete removal of C and the unimpeded progress of B, only by gradually diminishing the reflection of B itself. Then as we gradually increase the difference between Band C, there will be a point at which B will not be reflected at all but will be caught halfway between regression and advance, as it were. If the difference is further increased, B will continue to advance in its former direction, though its magnitude can never be increased continuously to such a point that its velocity of advance will not be retarded by collision with a body moving in the opposite direction, until its ratio to C becomes infinite, that is, until C completely disappears or is removed. This is the true manner of motion of bodies which are unequal but collide with equal velocities; it is in every respect consistent with reason and with itself. This is not the place, however, to determine the quantity of the resulting velocities; that is a matter needing further examination, to which I have given special treatment elsewhere. On Article 48. Rule 3. If Band C are equal and collide with unequal and opposite motions, then the more rapid body B carries with itself the slower body C, and half of the difference of their velocities subtracted from the velocity of B is added to the velocity of C, so that they move together with equal velocities. For references see p. 410
400 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS This rule is no less false than the preceding one and conflicts with reason no less than with experience. For to apply our criterion, let the more rapid body B carry the slower one with it in the way described, by hypothesis, and let the velocity of B decrease continuously until the two become equal or what amounts to the same thing, until the excess of B's velocity over C's becomes incomparably small. Then both are carried along at the velocity of B itself, diminished by no assignable quantity. But this is absurd and contrary to the first rule, which asserts, correctly, that in the case of perfect equality, both of magnitude and of velocity, both are reflected at their own velocity or at least at velocities differing from them by no assignable quantity. And it is impossible for the result of a disappearing inequality not to vanish into the result of equality. On Article 49. Rule 4. If B is less than C, and B moves while C is at rest, B will be reflected with the velocity of its approach, but C will remain at rest. This rule is true to this extent - that a smaller body is always deflected by a greater one at rest, though not with the velocity of its approach. For the more the excess of C 33 is decreased, the more the repulsion is decreased, until we reach the case of equality dealt with in Rule 6. It is absurd for the given conditions gradually to approach the case of the equality of the two bodies while the results do not approach this case but remain constant until at last they pass over into the case of equal bodies at one blow, as it were, or by a leap. One can easily understand, too, that it is far from reasonable for the given conditions to vary continuously while the results vary not at all, since the result ought rather to vary in all things in the same way as do the conditions, except in determinate cases where several distinct variables compensate for each other. On Article 50. Rule 5. If B is greater than C, and B moves but C remains at rest, then B continues, and both are carried along at the same velocity and with the previous quantity of motion. This rule too is erroneous, for it errs in fixing the true quantity of the velocity of each body, since it assumes that both advance together after the collision; but this can never happen in the collision of hard bodies. The rule is right in asserting that every larger body which strikes one at rest continues after the collision. But that the two bodies cannot move together in this case is also clear from our criterion. For the case in which B is very little larger than C, and the case in which C is very little larger than B, can be considered to approach each other by an incomparably small difference. So it is impossible that their results should differ so greatly that in the former case they should move together in the direction of B. but in the latter case B should be repelled in the contrary direction with its whole velocity. On Article 51. Rule 6. If Band C are equal but B moves and C remains at rest, then B is reflected at three-fourths of its velocity of approach, and C will move in the former direction of B at the remaining one-fourth of the velocity. Thus our author; I am not sure that anything more foreign to reason could have been thought up in this matter. It is beyond understanding how such a thing could have occurred to the mind of this distinguished man. But we shall let the Cartesians look for the reason for their master's remarks; it will suffice for us to show the inconsistency of his rules. If Band C are equal and collide with equal velocities, then both are reflected at the velocity of their approach, by Rule 1. Now if the velocity of C be diminished
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 401 continuously, while that of B remains constant, B will have to be reflected less and C more than before, since the quantity taken from the velocity of one equal body is added to the other. Now let the velocity of C disappear, or let it come to rest; we ask how much velocity is to be subtracted from the deflected B. This rule of Descartes affirms that only a fourth is to be subtracted. But let us continue by diminishing the magnitude of C at rest a little; then, by the preceding rule, B will continue its motion. Through a very small change in the conditions, therefore, there results a huge change in the consequences, or a leap occurs. For when C is at rest and equal to B, the velocity of reflection of B is great, namely, three-fourths of its original velocity, but when Cis diminished a very little, the reflection of B is suddenly destroyed entirely; indeed, it is further converted into its contrary, that is, into advance. All the intervening cases are passed over in a leap, which is absurd. We must therefore say that when Band Care equal and C is at rest prior to collision, B is at rest after the collision, and its entire velocity is transferred to C. This can also be inferred from what is true in Rules 4 and 5. For by Rule 4, B is reflected when it collides with a greater body C, which is at rest. Further, by Rule 5, B continues in its course when it collides with a smaller body C, which is at rest. Therefore when B coJIides with a body C at rest which is equal to itself, it neither continues nor is reflected but (what is between these two) comes to rest, and its whole force is transferred to C. On Article 52. Rule 7. If Band C move in the same direction, with B in the rear moving the more rapidly, and C ahead but more slowly, and C is the greater, but the ratio of C to B is less than the ratio of the velocity of B to that of C, then both will advance together in their earlier direction after collision and with a velocity which will make the quantity of motion the same as it was before collision. But if C remains the greater but the ratio of C to B is greater than that of the velocity of B to that of C, B will be reflected with its velocity of approach, and C will continue with its former velocity. Thus our author. But it is easily seen that these rules are inconsistent, for we have observed, not far back, that rigid bodies such as are assumed here never proceed together after collision, as is held to occur in the earlier part of this rule. Nothing is more unreasonable than what is claimed in the latter part - that the body B, in acting on C, changes nothing in C and yet itself suffers many things from the collision. If I am not mistaken, these views conflict with the natural metaphysics (if I may caJI it so) which the light of reason gives us. There are also other contradictions with earlier rules, for when C is greater by an infinitely small amount, that is, when it is equal to B, and precedes it by an infinitely small velocity, that is, when it remains at rest, the former part of this seventh rule applies, which holds that they would move together; yet, according to the sixth rule, B is reduced to rest and its whole force is transferred to C, which was formerly at rest and equal to it. In the interest of brevity I shall pass over other points no less inconsistent. But I must warn, finally, that the author has disregarded the intermediate case when the ratio of the two bodies is the reciprocal of the ratio of their velocities, and it is not clear what should be said by virtue of his rule in this case. There must indeed be some consequence in this middle case, which should certainly fall within the limits of one or the other earlier case. But though the former and latter cases have a common limit in terms ofthe hypotheses, they have none in terms of the consequences, and this again conflicts with our criterion. The case in which B is greater than C is also disregarded. Rule 8 should then have followed, in which the For references see p. 410
402 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS author should have explained what happens when two unequal bodies with unequal velocities moving in opposite directions collide. A distinction would also have to be made between centric and eccentric collisions and between perpendicular and oblique collisions. But we must put an end to this investigation and no longer expatiate upon this discredited and deplorable doctrine. On Article 53. Descartes acknowledges that it is difficult to use his rules, because, namely, he sees that they completely conflict with experience. But in the true rules of motion there is a remarkable agreement between reason and experience, nor do discrepancies impede the success of the true rules as much as he seems to fear, since he had exceptions already prepared to escape these discrepancies. The greater bodies are in hardness and size, on the contrary, the more accurately the rules are supported by observation. We shall see shortly what the hardness or liquidity of bodies involves; here it seems desirable to show by means of a figure, for easier comprehension, how, by means of our criterion, the truth in these matters can be outlined in advance, as it were, or as a kind of prelude, even before we have succeeded in a perfect delineation of it. This is most useful, both in detecting errors and in approximating the truth. 34 Let us assume, therefore, that Band C are equal in mass, and let the velocity and direction of B be represented by the straight line BW, so that it moves from B to W with a velocity proportional to BW. Let the velocity and direction of C, which will vary for different cases, be AH, so that in the case of AHI or AHz (below A) the direction of C will be the same as that of B, and in the case of AHI (which is equal to BW) the velocities of both are equal and their directions the same. But when H is taken nearer to A, as in H2, the direction of C from A to H2 will still be the same as that of B (from B to W), but its true velocity will be less than that of B, because AH2 is less than BW; so, if C precedes, it will be struck by B following it. When H coincides with A (or H 3), the direction and velocity of C are nothing, and C is at rest. But when His taken above A, as in H 4 , H" and H 6 , the direction of C is contrary to that of B. Now let the lines PP and QQ be drawn so that HP is always the velocity and direction of B, and HQ the direction and velocity of C, after the collision, observing that the direction of either one after the blow, which is the same as that of B before the blow, is represented toward the left, and a resulting direction contrary to this is represented toward the right. Now let us determine a certain point on the lines PP and QQ. The direction and velocity or in a word, the motion of B before collision, are always BW; now if the motion of C before collision is equal to it and in the same direction, namely, AHI (which equals BW), then if no contact hinders, it is certainly true that both Band C will retain their earlier velocities and directions. So the straight lines HlPl and HI QI representing the motion of Band C after collision will be equal to AHI and BWand to the left. But if the motion of C before collision is nothing, or AH3 (the point H3 falling on A), or if C is at rest, then what happens is also clear; namely, the body B will be at rest after collision, and the point P3 will also fall on A, but C will take on the velocity and direction which B had; therefore, H3Q3 will be equal to BW and to the left, so that the points P 3 and Q3 will be occupied. Finally, if the motion of C is equal to the motion of B but in a contrary direction, or is represented by AHs, equal to BW but with Hs taken above A (that is, if the two bodies, equal by hypothesis, are assumed to strike with equal velocities from opposite directions), then the outcome is also clear, for each will be reflected with the velocity of its approach, so that the points Ps and Qs will be given; HsPs will be equal to BW but to the right,
IANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 403 since B is reflected or moved in a direction contrary to its original one, and HsQs will be equal to the same thing but to the left, because C assumes the direction which B had taken. So we have as many points PI, P3, Ps, falling in a straight line (this is noteworthy) as there are points QI, Q3, Qs, falling in another straight line parallel to the line AH: the remaining points, such as Pz, P4, P 6, etc., and Qz, Q4, Q6, etc., cannot be determined by our criterion alone, of course, or from the law of continuity, for these alone do not establish what the lines PP and QQ will be. It is enough that all of them are connected in one continuous line which is their locus by our criterion. Thus all these incoherent rules are already excluded in advance of a full understanding of the matter or of the discovery of the kind of line involved. Meanwhile we actually know, from another source, that the lines PP and QQ are truly straight and that, because of the permutation of velocity and direction in equal bodies, HP is always equal to AH, and HQ to LM, so that HQ as well as LM can be thought of as signifying motion together in the same direction. For the rest, I do not extend HI, PI, and Ql further down, because then B moves more slowly than C and so does not reach it, and no collision occurs. In the case in which bodies are assumed to have equal velocities, but one body is kept constant in magnitude while the other varies, a figure can be made in the same way to show the consequences of collision upon both bodies in two lines; indeed, a similar figure can be sketched for any hypothesis whatever, providing that the terms are kept constant except for one variable. But it will suffice to have given a sample for one case, especially since everything which we have merely outlined can be understood perfectly by another method - though we can show that this procedure nonetheless has its use in refuting errors. Even if the entire doctrine were not yet discovered, this would lead to a kind of outline of it. From the Cartesian rules no continuous line whatever can be derived for the results which correspond to the continuous line representing the variable data; on the contrary, a figure is produced which is most erratic and contrary to our criterion in Article 45, or to the law of continuity. If our line is compared with the Cartesian one in the figure, the inconsistency, or rather the impossibility, of his rules will be apparent to the eye. On Articles 54, 55. I do not believe it to be entirely true, though there is some truth in it, that bodies are flUid if their particles are agitated by various motions in all directions; that they are hard if their adjacent parts are mutually at rest in relation to each other; and that matter is not held together by any other glue than the quiescence of one part in relation to another. Descartes infers therefore that hardness, or as I prefer to call it more generally, firmness (some of which there is even in soft bodies), arises from rest alone, because the glue or the cause of cohesion cannot be a body (for then the problem would repeat itself), and so it must be a mode of a body. But, he reasons further, rest is the only mode of a body which is fitting to explain this matter. Why so? Because rest is most contrary to motion. I marvel that so important a matter should be decided with so trifling and perfunctory, indeed, so sophistic a reason. The syllogism would be: Rest is that mode of body which is most contrary to motion. But that mode of body which is most contrary to motion is the cause of firmness. Therefore rest is the cause of firmness. But both premises are false, though each makes some tenuous display of truth. It For references see p. 410
404 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS happens too often in Descartes that by assuming the most uncertain matters to be certain, he dismisses the careless reader by his dictatorial brevity; as when he concludes that extension constitutes matter, that thought is independent of matter, and that the same quantity of motion is conserved in nature - pronouncements based on authority rather than arguments. I am of the opinion that motion in the opposite direction is more contrary to motion than is rest and that a greater opposing force is required to reflect a body than merely to bring it to rest, as I have shown in Article 47. But the other premise would also have to be proved, namely, that what is most opposed to motion is the cause of firmness. Did the author by chance have in mind the following prosyllogism? Firmness is most opposed to motion. The cause of whatever is most opposed to motion is itself most opposed to motion. Therefore the cause of firmness is most opposed to motion. But the premises of this pro syllogism are again both defective. Thus I deny that firmness is most opposed to motion; I admit that it is most opposed to the motion of one part without another, and it is the cause of this that he should have sought. Nor do I have any confidence in the axiom that the cause of whatever is opposed to a thing is itself also opposed to that thing. What is more opposed to death than life, but who would deny that death very often comes to an animal from a living being. No demonstration can be based upon such philosophical rules, which are entirely vague and not yet reduced to their proper limits. There will be some who read this who will be offended at us for reducing such great philosophers to the limitations of Scholasticism by putting them in syllogisms; there will perhaps also be those who will condemn this as too trivial. But we have learned that these great philosophers, and indeed, often other men too, stumble on the most serious matters through neglect of this childish logic; in fact, they scarcely ever make mistakes in any other way. For what else does this logic contain than the most general dictates of supreme reason, expressed in rules that are easy to understand? It has seemed desirable to use this example, to show, for once, how useful such rules are for putting an argument into the prescribed form, so that the force of the argument may become apparent, especially in problems where the imagination does not come to the aid of reason as it does in mathematics, and where we are dealing with an author who puts great matters into precipitate arguments. Since Descartes does not help us with reasons in this problem, therefore, we must return to a consideration of the matters themselves. In firmness, then, we must consider not so much rest as the force by which one part draws another along with it. Let two perfect cubes, A and B, be joined together and at rest with respect to each other, with their surfaces perfectly polished, and let cube B be placed to the left of cube A, with a surface of one congruent to a surface of the other, without any intervening space. Now let a small ball C strike the middle of cube A, in a direction parallel to the two congruent surfaces (Figure 27). Then the direction of the blow will not reach cube B unless it is assumed to adhere to cube A. Of course A resists the colliding body C by its rest and cannot be moved by it without diminishing the force of C, and so it is also true that in this case A by its rest resists being separated from B. But this is per aCCidens, not because it is unconnected with B, but because it
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 405 has to absorb the force of the blow itself, just as it would if B were entirely absent. So, once it has received this force, it will begin its own path, abandoning B just as if B were entirely absent from its vicinity. It is therefore a sophism to try to conclude that because each thing perseveres in its own state as much as possible, it follows that two bodies at rest in relation to each other will mutually adhere and will have firmness from their mere state of rest. You might conclude with as much right that two bodies 10 feet apart are connected together and will strive to act so that they will always be 10 feet apart. A cause must therefore be found why two cubes A and B cohere sometimes and form a firm parallelopiped AB which moves as a whole when only the part A B A Fig. 27. is impelled; or a cause must be found why the cube A, when moved, draws the cube B with it. Thus we seek the cause of traction in nature. There are, it is true, learned men who affirm that perfect unity is itself the cause of firmness, and it seems that this opinion satisfies some advocates of atoms. For if the parallelopiped is taken as an atom which is conceptually divisible into two cubes A and B, but is not really so divisible, they say that the parallelopiped is also actually indivisible and will remain firm always. Many objections may be made to this; first of all, they offer no demonstration of their position. Let us assume that two atoms, D and E, which correspond to the cubes A and B with their anterior surfaces, strike simultaneously against the parallelopiped AB in directions parallel to the common surface of A and B, but with D coming from the back, from the direction of F, with its whole surface striking the entire congruent surface of A, and with E similarly coming from in front, in the direction from G, and striking B (Figure 28). We seek a cause for A not leaving B and being propelled toward G, and for B not leaving A and being propelled toward F. I find no reason for this in the atomists' doctrine. For what else is there in the statement that a unity is composed of the two cubes A and B than that they are not actually divided? But if you hold, as do certain thinkers, that there are no parts in the continuum before actual For references see p. 410
406 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS E B A D Fig. 28. division, it follows either that this does not prevent separation, namely, when a further reason is added which tends to produce an actual division, and so determines and distinguishes the parts as it were (the reason being the impact of the bodies D and E), or that no continuum can ever be broken into parts. Suppose then that two cubical atoms A and B, formerly distinct, approach each other so that two of their surfaces coincide; will there, at the moment of contact, be no difference at all between them and the atomic parallelopiped described above? Then two atoms would be held by each other through simple contact as if by some kind of glue, and the same thing would happen even if only parts of their surfaces touched. By a natural progression it would further follow from this that atoms would continuously increase like snowballs rolled through the snow, and the outcome, finally, would be that everything would coalesce into a more than adamantine hardness, and congeal into eternal ice, since the cause of coalescence would subsist, but not that of dissolution. For those who hold these views there remains one escape - to say that there are no plane surfaces in nature, or that if there are any, they disappear in coalescence, but that all atoms terminate in curved surfaces, and these with the smallest possible areas of contact, as the case would be, for example, if all atoms were spherical, so that there would be no contact of any entire surfaces. But aside from the point that no adequate reason is given for excluding
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 407 bodies with plane surfaces, or with other congruent surfaces, we again ,ask them to give us a reason why a continuum cannot be resolved into parts. We have other strong arguments against atoms but do not propose to exhaust that matter here. There are those who explain the hardness of bodies by the same cause by which we see that two polished boards cannot be broken apart except with great force, the surrounding matter finding it impossible to penetrate so suddenly into the place to be relinquished by a separation ofthe boards. So they say that hardness arises from compression, which is right in most cases, but cannot be understood as a universal cause of hardness, because it again presupposes some hardness or firmness already to exist that of the boards themselves. It is likewise irrelevant to say that the two cubes A and B are connected by some kind of glue, for some firmness is necessary in the glue itself by which its parts adhere both to each other and to the two bodies which they connect. But if anyone thinks that some kind of little projections pass over into B from A, penetrating into its small cavities, and also to A from B, and that this is the reason why the one cannot be moved without the other unless these points are broken, a new question arises: Whence the firmness of these points? To pass over these theories, therefore, which either do not advance or do not solve the problem, I believe that the primary cause of cohesion is movement, namely, concurrent movement. (Evidently one must add impenetrability itself, when there is no place into which to give way, or when there is no reason for one body to give way rather than another; thus a perfect sphere which rotates in a uniform plenum at rest is prevented from throwing anything off by centrifugal force.) I believe that matter itself, which is homogeneous and equally divisible throughout, is differentiated. by motion alone. We see that even fluids acquire a certain firmness when in motion. Thus a vigorous jet of water will prevent anything from breaking into its own path from without with more force than the same water at rest. For the irruption of new matter necessarily creates a strong disturbance in the co-ordinated motion, and force is necessary to produce this disturbance or to change the motion so greatly. If you touch a jet of water with your finger, you will see the little drops scatter in all directions with some violence, and you will also feel your finger repelled on entering the jet. We learn from the magnet, in an elegant experiment, that things which in themselves are separate and, so to speak, sand without lime, can acquire some firmness by motion alone. When iron filings are placed near a magnet, they suddenly become connected like a rope and form filaments, and the matter arranges itself in rows. It is no doubt also by some kind of magnetism, that is, by an internal co-ordinated motion, that other parts of certain bodies are linked together. This primary cause of consistency or cohesion therefore satisfies reason no less than the senses. On Articles 56, 57. It is unnecessary to investigate the cause of fluidity, for matter is itself fluid except insofar as there are motions within it which are disturbed by the separation of certain parts. So it is not necessary for a fluid to be agitated by the varied motions of its particles. But since it is established on other grounds, by a general law of nature, that all bodies are agitated by internal motions, the conclusion is that bodies are firm insofar as these motions are concurrent, but remain fluid insofar as the motions are perturbed and not connected by any system. The result is that every body contains some degree of fluidity and some of firmness alike and that no body is so hard as not to have some flexibility, and the converse. Furthermore, this internal motion is insensible, since the parts which succeed each other continuously are not For references see p. 410
408 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS discernible by sense because of their smallness and similarity; moving rapidly, like a jet of water or the spokes of a wheel, they simulate one continuous solid. The internal motion of fluids is also confirmed by solutions of salt in water and by the corrosions which are made by acids and, indeed, also by heat in general. For when heat is great, it causes liquids to boil, when it is only moderate it produces only an agitation, but when the agitation arising from heat is weakened, as it is in winter, then the permanent internal motion of the parts of matter acting in harmony alone predominates in most liquids; hence they harden and sometimes freeze solid. Another crude example of this strangely perturbed agitation of fluids is offered in the dust particles revealed by the sun's rays in an otherwise dark place. Moreover, since the fluids which seem according to our sense perception to be at rest are really in equally unhindered motion everywhere, and in all directions, it follows that their perturbed motion is so equally distributed and compensated for within them, as it were, that when a solid is placed in such a fluid, it is assailed so equally on all sides by the blows and surges of the fluid that it is neither aided nor hindered in its own motion. On Article 59. When a body is impelled by an external force in a fluid, the author thinks that this force, though in itself not enough to move the body, nevertheless does move it by concurring with particles of the fluid which support this motion and determines the remaining particles also to support it by retaining their own motion but changing its detennination or direction. Add to this what the author says at the end of Article 56, and in his demonstration in Article 57. Hence he asserts that a hard body moving in a fluid does not obtain its whole motion from the hard body which impels it but also partly from the surrounding fluid. But soon he himself seems to demolish this in Article 60. In general, I believe that his remarks are to no purpose, because they rest upon a false principle (since he again speaks here as if rest were contrary to motion) and because they seem to have been thought up only to save the contradiction which phenomena show to the fourth rule of motion, in which our author has wrongly denied that a body at rest can be set in motion by a smaller one acting with any amount of velocity whatever (see the end of Article 61), whereas he himself was nevertheless forced to admit, in Article 56, that a hard body in a fluid is moved by the smallest force. So he makes use of this amazing comment to escape the difficulty and calls upon the particles of the fluid to help, but in vain, for since their motions from contrary directions compensate each other, they are of no avail. For if they had any effect, it would be too great and would give the movable object a motion greater than it can receive from the impelling force. It is evident, however, that such a greater motion does not arise, and hence the movable body receives no more motion than if the fluid had not acted at all. Indeed, we must rather affirm the contrary - that far from motion being added by the fluid, some is rather subtracted by it, and the velocity of the moving body is diminished, partly because of the effect of a certain resistance but partly also from the mere fact that when a hard body enters into a fluid, a part of the fluid equal to the volume of the body must continually be displaced and excited to new motion, and a certain part of the moving power must be expended to do this. I have elsewhere reduced the quantity of both kinds of resistance to calculation; one part of it is absolute and always the same in the same fluid, the other is relative and increases with the velocity of motion. 3S On Article 63. Amazing are the considerations introduced here about the reason why our hands cannot break an iron nail. He finds a difficulty where there is none, and
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 409 his answer is well adapted to hi~ twisted objection. Certainly, if a resting body can be moved by a greater one, we may well ask why the hand cannot move a part of an iron nail much smaller than itself and admittedly at rest, and why it cannot tear it away from the rest of the nail. He attributes the cause to the softness of the hand, which therefore does not act upon the nail as a whole, but only with a part - and a part of the hand which is always smaller than the part of the nail to be broken off. Surely this is not a question of motion, for the hand easily moves not merely a part of the nail but the whole nail. It must rather be asked why a part of the nail draws the rest with it, and one part does not easily allow itself to be moved without the rest. Furthermore, it is useless to fall back on the softness of the hand, for even if we assume a blow by a piece of iron or stone, however large, in place of the hand, the parts of the nail will still cling together. Granted that a hard body is broken more easily by another hard one than by a soft one, we must nevertheless ask, not why or by what force the cohesion of two parts of a nail will be overcome, but why it exists. We must ask, not why one of them is moved by some greater body (for this is false), but why it is not easily moved alone. On Article 64. The author closes his second part, which is a general part dealing with the principles of material things, with an observation which seems to me to need some restriction. He says, namely, that no other principles are necessary for the explanation of natural phenomena than those taken from abstract mathematics, or from the doctrine of size, figure, and motion, and that he recognizes no other matter than that which is the subject of geometry. I fully agree that all the particular phenomena of nature can be explained mechanically if we explore them enough and that we cannot understand the causes of material things on any other basis. But I hold, nevertheless, that we must also consider how these mechanical principles and general laws of nature themselves arise from higher principles and cannot be explained by quantitative and geometrical considerations alone; that there is rather something metaphysical in them, which is independent of the concepts which imagination offers, and which is to be referred to a substance devoid of extension. For in addition to extension and its variations, there is in matter a force or a power of action by which the transition is made from metaphysics to nature 36 and from material to immaterial things. This force has its own laws, which are derived from the principles not merely of absolute and, so to speak, brute necessity, as in mathematics, but from those of perfect reason. Once these matters have been established in a general treatment, we may afterward, in accounting for natural phenomena, explain everything mechanistically, and it is as vain here to introduce the perceptions and appetites of an Archeus, operative ideas, substantial forms, and even minds, as it is to call upon a universal cause of ail things, a deus ex machina, to move individual natural things by his simple will, as I recall the author of the Philosophia mosaica does by means of a fallacious interpretation of the words of Sacred Scripture. 37 Whoever considers these matters honestly will hold to the middle way in philosophy and do justice to theology as well as to physics. He will understand that the Scholastics sinned of old, not so much in holding to indivisible forms, as in applying them where they ought rather to have sought the modifications and instrumentalities of substance and its mode of action, that is, mechanism. Nature has, as it were, an empire within an empire, a double kingdom, so to speak, of reason and necessity, or of forms and of the particles of matter, for just as all things are full of souls, they are also full of organic bodies. These kingdoms are governed, each by its own law, with no confusion between them, and the cause of perception and appetite For references see p. 410
410 LEIBNIZ: PHILOSOPHICAL LETTERS AND PAPERS is no more to be sought in the modes of extension than is the cause of nutrition and of the other organic functions to be sought in the forms or souls. But that highest substance which is the universal cause of all brings it about, by its infinite wisdom and power, that two very different series in the same corporeal substance respond to each other and perfectly harmonize with each other, just as if one were ruled by the influence of the other. And if you observe the necessity of matter and the order of efficient causality, you will notice that nothing happens without a cause which satisfies our imagination, nothing which lies beyond the mathematical laws of mechanism; but if you contemplate the golden chain of ends and the circle offorms as an intelligible world, you will find that since the apex of metaphysics and that of ethics are united in one by reason of the perfections of their supreme author, nothing hapPl1ns without the highest reason. For the same God is the supreme form and the first efficient cause and the end or ultimate reason of the universe. But it is our part to revere his traces in nature and to meditate not merely upon his instruments in operating and the mechanical efficiency of material things but also upon the more sublime uses of his admirable craftsmanship; to know God, not merely as the architect of bodies, but above all as the king of minds, whose intelligence orders all things for the best and constitutes the universe as the most perfect state under the dominion of the most powerful and most wise Monarch. By thus combining both types of interpretation, we shall serve, in the consideration of the individual phenomena of nature, both our welfare in life and our perfection of mind, and wisdom no less than piety. REFERENCES Euclid's definition of a straight line is given on p. 247, note 5. For Leibniz's criticism of Euclid and his own definition see No. 27, II, p. 258, notes 8 and 10. See also the New Essays, Book IV, 12,4. 2 This passage, somewhat anticipatory of Kant, involves the criteria for the reality of phenomena stated in No. 39. It can be reconciled with the monadology only when it is remembered that the rational principles upon which phenomena are well founded are themselves the metaphysical basis for God's creation of individuals. 3 Conscientia. The term is obviously used here in the sense of intellect or understanding. 4 The allusion is to Descartes's vicious circle in validating our general principles by a reference to God's moral nature. 5 See p. 234, note 5. 6 The first draft contained an example which was later deleted. "For example, assume a definitum A whose definition is 'an absolutely necessary beast.' A is shown to exist in this way: whatever is absolutely necessary exists, by an indubitable axiom. A is absolutely necessary, by definition. Therefore A exists. But this is absurd. The reply to it must be that definition or concept is impossible and hence cannot be admitted as an assumption." Cf. p. 205, note 7. Leibniz here is so confident of the basic principle that possible concepts strive for existence that he uses it to infer the contradictory nature of terms which do not exist. This, however, once more threatens his distinction, worked out against Descartes and Spinoza, between possible notions and compossible ones which, ifthe best possible, will exist. 7 See Nos. 51 and 67, Sees. 37-39. 8 To Mersenne, July 1, 1641 (Correspondence, ed. Adam and Tannery, m, 392). Leibniz had repeatedly refuted this view of ideas from the Paris periods on (see Nos. 21, 25, and 33 and New Essays, Book IV, 10,7). 9 The first draft added: "Meanwhile it is very true that there is the idea of God in us, because it is most true that God is possible and hence existent and in both senses known by us. In a 1
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 411 certain way all ideas are innate in us, nor can the senses do anything else but to turn the mind to them, as is shown elsewhere." 10. The comment is directed at Descartes's tendency to atomize the contents of consciousness (cf. Meditations, Part III; Principles, Part I, Art. 21), which led his school to interpret each state as a distinct divine creation. See also the beginnings of the correspondence with De VoIder (No. 55). Leibniz's conception of force provides an internal continuity and selfdetermination to the temporal processes of the mind. 11 See No. 50, below. 12 On the doctrine of attribute see No. 35, Sec. 8, and p. 205, notes 2 and 4. Applied to individual substances, the concept of attribute can mean only the law of the individual series, and Leibniz points out that this is incapable of a complete generic definition by us. For the essence of a particular creation is beyond finite analysis, and generic definitions are possible only of partial concepts. 13 The original version adds: "Meanwhile it is very true that matter and mind are entirely different, as we will sometime show better." 14 The original version adds: "Meanwhile we are right in saying that colors and heat are in things, when we mean by this the foundations of these phenomena." 15 The allusion is to Euclid's Elements, Book v, where the principles of proportion are developed. 16 Leibniz had originally added: "I have elsewhere discussed wherein the reality of material things consists. See also Part I, Article 4." 17 Internal place is for Descartes the volume of a body; external space, the position of this volume within a larger whole. He then defines motion as change of this external position in relation to near-by bodies. 18 Addition in the first draft: "For the rest, I shall sometime make clear that a material mass is itself not a substance but an aggregate resulting from substances, and that space is nothing but the common order of all coexistents, as time is that of things which do not coexist." 19 Addition in the first draft: "We conclude that there are none on other grounds." 20 Addition in the first draft: "These opinions may be true, however, on other grounds." 21 The problem of the relativity of observed motion is thus, at this point in Leibniz's thought, an argument for an internal force in bodies. The point is further discussed in the correspondence with Huygens (No. 43) and in the Specimen dynamicum (No. 46). 22 Original addition: "although a perfectly quiescent body is in fact never found." 23 Leibniz's historical notes on the origins of the resolution of motions (and later, forces) are in general sound. Kepler's work is Ad Vitellionem paralimpomena, quibus astronomiae pars optica traditur (1604). 24 See No. 34. His argunlent will be often restated (cf. Nos. 46 and 55). 25 Leibniz's acknowledgment that the quantity of motion is conserved in the case of bodies which do not reverse their direction anticipates his own more general principle of the conservation of quantity of progress, which differs from Descartes's principle in considering the algebraic, not the arithmetic, sum of motions (see No. 46 and p. 451, note 9). 26 Kepler, Epitome astronomiae Copernicanae (1620), Book IV. 27 Durus. More exactly, Leibniz must mean bodies with perfect elasticity. Compare the discussion of Articles 56 and 57 below. See on the laws of impact, p. 302, note 9. 28 As Be. points out (I, 316), G's text is in error in reading assequens for praecedens. 29 In other words, if m is the mass and v the velocity of the first body before impact, and V its velocity after impact; and ml the mass and VI and VI the velocities before and after impact of the second body, which overtakes the first, then Vl=O when (m-ml)/m=2v/vl. Leibniz's formula can be derived from the principle of the conservation of vis viva and of momentum (or quantity of progress), both of which are true only in the case of perfectly elastic bodies: (1)
412 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS and (2) by dividing (1) by (2), solving for V in the quotient, substituting for V in (2), and then resolving the resulting equation for the case VI =0. 30 These conclusions follow from the general formula for VI in note 29, for the cases, respectively, of m<m1, m=m1, and m>m1, with v=O. 31 See Descartes to Mersenne, January 21, February 7, and March 4, 1641 (Correspondence, ed. Adam and Tannery, III, 287ff., 300ff., 318ff.). 3Z See No. 37. 38 G. has B, an obvious error. 34 To this article Leibniz offers the following long note (here somewhat abridged) giving a graphical representation of the discontinuities in Descartes's laws and the continuity in his own: Representation 0/ the rules o/motion in the case when the colliding bodies are equal. According to the truth an orderly figure: According to Descartes a monstrous figure: ~+,A:::l..-_ _ ~3 Explanation ofthe figure for Article 53. Before collision the motion of body B is BW, that of C is AH1, AHz, etc. After collision the motion of B is Hr/>l, H</>2, etc., according to Descartes; and HP1, HPz, etc., according to me. After collision the motion of C is H'l, H'2, etc., according to Descartes; and HQ1, HQ2, etc., according to me. H below or above A, and P, </>, Q, and to the right or to the left of AH, signify the same or the contrary direction, respectively, as that taken by B before collision. </>1, </>2, </>a, 'I, '2, 'a, are from Descartes's Rule 7; </>a, </>4, </>5, '3, '4, '6, are from his Rule 3; </>a, '3, are from his Rule 6; and </>5 '5, from his Rule 6. My lines and Descartes's have only two out of an infinity of cases in common: HI and H5. 35 'Schediasma de resistentia medii et motu projectorum gravium in medio resistante', Acta eruditorum, January, 1689. 36 So G., IV, 391. Be. suggests reading "transitum a mathematica ad naturam". But G.'s reading is defensible in view of the narrower meaning of naturalis just below. The concept of force is metaphysical in Leibniz but appears in science in the form of derivative force. 37 Paracelsus was the source both of Van Helmont's archeus (see p. 328, note 14) and of the animistic views of Robert Fludd (1574-1637) in his Philosophia mosaica (1638). These views are more fully criticized in Nos. 53 and 61. e
43 CORRESPONDENCE WITH HUYGENS 1692-94 (Selections) It was the Dutch mathematician and physicist Christian Huygens who helped Leibniz, in his Paris years, to master the literature of modern mathematics. It was also his discoveries in mechanics, in particular his early formulation of the laws of impact, and his later analysis of the compound pendulum, which provided the foundation for Leibniz's theories in dynamics. The correspondence between the two began in the Paris period (cf, above, No. 27) and continued until Huygens' death in 1695. In the period in which the following letters were written, the correspondence dealt with the foundations ofphysical and cosmological theory, particularly in relation to the views of Descartes, whom both had already criticized, and of Newton. After his reading of the Critical Thoughts on the General Part ofthe Principles of Descartes (No. 42), Huygens selected for comment particularly those sections in which Leibniz reduced motion on the one hand, and firmness, mass, and impenetrability on the other, to force (Part II, Arts. 25 and 54-59). The correspondence movedfrom the problem ofgravity and celestial motion to that of atoms and cohesion and eventually to the relativity of time, space, and motion. Leibniz's comments on Newton, many years before the charges of plagiarism became serious, are ofhistorical interest. [GM., 11,133-36] Hanover, Aprilljll, 1692 I hope that you have perfectly recovered from the indisposition of which you spoke in your last latter, and I wish for you good health that you may be able to finish the important meditations in which you are engaged. I will continue always to urge you to tum your thoughts to physics. I think I have shown more than once that your last treatises have pleased me infinitely. The explanation of Iceland spar is as it were a proof of the accuracy of your reasoning about light. There is in it only one circumstance about which you are not yet satisfied, but perhaps this will be cleared up later. It appears very probable that gravity comes from the same cause which has made the earth round and which rounds off drops, namely, the circular movement of the ambient in every direction. And apparently this is also the reason for the attraction of the planets to the sun; entirely as if the planets preserve a certain magnetic direction like that which we see on earth. If we conceive of the attraction of heavy bodies as due to rays emanating from a center, we can explain why the weights of the planets are inversely proportional to the square of their distance to the sun, which is confirmed by phenomena. This law of weight, combined with the trajection of Mr. Newton, or with For references see p. 419
414 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS my theory of harmonic revolution, gives the ellipses of Kepler, also confirmed by phenomena. Now it is obvious that bodies are illumined by a luminous source in inverse proportion to the squares of their distances. I believe, further, that according to this way of explaining gravity by the centrifugal force of a very subtle fluid, one can think of it as rays of attraction, these efforts of the fluid being no other thing in fact than such rays which force those bodies to descend whose circular motion is least rapid. It seems that in addition to this a kind of vortex is necessary in the heavens to explain the parallelism of axes. The spherical movement in all directions is not sufficient to do this; poles and meridians are needed. Finally, the correspondence which exists among the planets or satellites of the same system favors a common deferent liquid matter.... ... In rereading your explanation of gravity recently, I noticed that you are in favor of a vacuum and of atoms. I admit that I find it difficult to understand the reason for such infrangibility, and I believe that one must have recourse to a kind of perpetual miracle to explain this effect. Also, I do not see the necessity which compels you to return to such extraordinary entities. However, since you are inclined to accept them, you must have an important reason for it. II [GM., II, 141-46] 1 Hanover, September 16/26, 1692 I have been very busy this summer, which prevented me from replying earlier to your letter of July 11, for you touch on many important matters, which require a kind of retreat and meditation for their answer. For this reason I am not yet in a state to satisfy you entirely, but in the meantime I give you what I can. I still cannot see why the many opinions about the roundness of drops, the weight of bodies on earth, and the attraction of planets toward the sun which seem to differ cannot be reconciled. I believe one can say in general that matter is somehow agitated in an infinity of ways from all sides, and with a uniform difformity, such that perhaps pressure is exerted equally in every direction. This motion should serve as well to form bodies as to determine their place. For bodies take that position in which their motions are least interfered with and adjust themselves to each other in some way. This can make them join together when they are separated and make it hard to separate them when they are joined. One can also consider, more particularly, that if a body is surrounded by another which is more fluid and more agitated, to which it does not permit a sufficiently free passage into its interior, it will be struck from without by an infinity of waves which will help to harden and to press its parts together. A spherical body is less exposed to the blows of this surrounding fluid, because its surface is the smallest possible and because the uniform diversity of its internal motion as well as the external motions contributes to this roundness. One can arrive at much greater detail in the case of the terrestrial globe and consider that the agitations of a confined fluid will be turned into rotations, for it is in this way that they continue with the least interference; and that these rotations take place in every direction, since the agitations which produce them do also. And the rotations which are adjacent to the earth are adjusted to each other and act harmoniously to have a common center, which will be that of the terrestrial globe, doubtless because through the formation of this globe,
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 415 which was apparently similar to the formation of a drop, this center was distinguished from its other points; this rotating matter strives to draw away from the center and as a result, will force less agitated bodies to approach it. And the centrifugal pull of matter can be considered as rays of attraction leaving the center as compared with the bodies which they make approach that center. The analogy of nature may lead us to believe that there is something approaching this in the nature of the solar system - that the planets tend toward the sun for a similar reason and that their attractions are in the ratio of the inverse squares of their distances, as in illumination. And since there is a great analogy between the earth and a magnet, and since there is not only attraction but also direction in the magnet, there is ground for believing that among all the rotations around the center of the earth, to which an infinity of poles can be assigned, there are two principal poles with respect to which the matter of the earth is adjusted to a certain course of the matter in the great solar system, as magnets adapt themselves to the course of the matter of the terrestrial system. It seems, Sir, that you do not approve of these efforts at generalization, but you do not point out any particular fault which you find in them. You also do not say, for instance, why you ascribe the roundness of water drops, more particularly, to a rapid motion within them. Nor do you say why the centrifugal efforts of matter cannot be considered as rays of attraction. Yet I have noticed something which could have been said in reply, namely, that there is the same quantity oflight in all concentric spherical surfaces, but it can be doubted that there is the same quantity of attraction. It is true that this attempt of mine also seems plausible enough when we consider the speed of rotation. We must examine which explanation is the better or if they can be reconciled. The same thing can be said in regard to Mr. Newton's explanation of ellipses. Planets move as if there were only one motion of trajection or of proper direction, combined with gravity, as he has observed. Yet they also move as if they were carried along smoothly by a matter whose circulation is harmonic, and it seems that this circulation works in harmony with the proper direction of the planet. The reason why I cannot abandon this deferent matter, even after learning Mr. Newton's explanation, is among other things, that I find that all the planets move somewhat in the same direction and in a single region, a thing which applies even to the satellites of Jupiter and Saturn. Without this deferent matter, on the other hand, nothing would prevent the planets from going in every direction. There are many things to be said about all this, which I hope to clear up more definitely some day. 2 ••• ... I come to our difference on the void and the atoms, which it will be difficult to avoid. 3 You assume, Sir, that there is a certain primitive firmness in bodies, and because this is so, you conclude that this must be infinite, since there is no reason whatever to assume it of a definite degree. I agree that it would be absurd to ascribe a certain degree of firmness to all bodies, for there is nothing to determine one degree of this kind rather than another. But it is not absurd to ascribe different degrees of firmness to different bodies; otherwise one could prove by the same reason that bodies must have either a zero velocity or an infinite velocity. If it be assumed that nature must vary, reason demands that there be no atoms or bodies of an infinite firmness at all; otherwise they would all be infinitely firm, which is not at all necessary. It seems also that you have not satisfactorily answered the difficulty involved in atoms which touch each other by some surface, thereby remaining caught and inseparably attached to each other. For to deny that atoms have flat surfaces or surfaces which otherwise For references see p. 419
416 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS fit each other, even if only in their smallest parts, is a questionable assumption. But even if we admit this, I believe that in reasonings of this kind we should consider not only what is but also what is possible. Let us assume the possibility, therefore, that all atoms have only plane surfaces; then it is clear that this difficulty about their cohesion arises and that consequently the hypothesis of perfect hardness is unreasonable. 4 There are still other difficulties in the atoms. For example, they cannot obey the laws of motion, for the force of two equal atoms which collide directly and with an equal velocity must be lost, since it would seem that it is only elasticity which makes bodies rebound. But even if there were no difficulty, it seems that we ought not to admit a quality such as primitive firmness without a reason. There is nothing to be seen which attaches two masses together, and I do not see how you, Sir, can conceive that the contact alone can serve as a kind of cement. 5 Now since there is no natural connection whatever between contact and attachment, it must follow that if contact is followed by adhesion, this happens by a perpetual miracle. But if firmness is to be an explicable quality, it must come from motion, since it is only motion which distinguishes bodies. If this is assumed, everything which I can say of the original connection of bodies reduces to this - that force is necessary to detach one part of matter from another, since this detachment changes the motion and the present course of bodies. In a mass the motion of all its parts acts in harmony insofar as there is some rule or law to compare the moving parts with each other, and the mass is disturbed in the measure in which this rule becomes more composite. One can also say that every body has a certain degree of firmness and of flexibility. Yet when some iron bar or other large body is considered, it is unnecessary to have recourse at once to the primitive origin of firmness, any more than to atoms; it suffices to make use of little bodies, each of which already possesses firmness within it, but each of which remains attached to the others, a little like two boards which touch each other with their flat surfaces and which the surrounding pressure prevents from suddenly parting. I am not at all eager to publish my remarks on the general part of Descartes's philosophy. Mr. de Beauval seems to offer to take them to Holland with him. Since you have taken the trouble to examine them, I wish that you had noted the passages with which you do not agree, beyond those which con~ider the void and firmness. I wish that some able Cartesian who has retained his capacity to reason could also examine them, so that I might learn what he would say in opposition. I have written this to Mr. de Beauval. I hope some day to see what you will say about motion. I have examined the Principles of Descartes with the aid of a general principle of fitness which has no defects, in my opinion, and which seems useful for refuting errors while preparing for the pure truth. By means of this principle, it was easy to show how the Cartesian rules of motion refute themselves. My design in these comments was only to make critical observations on Descartes, without claiming to give the true philosophy... III [GM. II, 179-85] Hanover, June 12/22, 1694 6 I am greatly pleased to receive the honor of your letter after so long an absence. But I am careful not to complain, for I well know how precious your time is. And besides, I shall always be ardent in exhorting you to guard your health, especially since I learn
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 417 from your letter that it has been a little irregular. Would to God that our studies might serve to make considerable advances in medicine. But until now this science is almost entirely empirical. It is true that even empiricism would be of great use if men were interested in observing well, or even in making good use of all the observations already made. But since medicine has become a business, those who make it their profession do so only by way of gain and as far as is necessary to save appearances, knowing well that few people are capable of passing judgment upon what they are doing. I wish that some religious order such as the Capuchins, for example, would devote itself to medicine on the principle of charity. Well administered, such an order could carry it far. But enough of these useless wishes; let us come to the points in your letter. I wish the public might soon learn the particulars of your clock, for they cannot fail to be of great importance. As for your treatment of a philosophical matter, I should be pleased sometime to learn what it can be. 7 You have been too reserved until now in wishing to publish nothing but demonstrations, whereas men of your power ought not to withhold even their conjectures. This is why you will do only good by expressing your opinions on all kinds of matters, even philosophical and problematical. Your exhortation confirms me in the purpose I have of producing a treatise explaining the foundations and applications of the calculus of sums and differences and some related matters. As an appendix I shall add the beautiful insights and discoveries of certain geometricians who have made good use of my method, if they will be so kind as to send them to me. I hope that the Marquis de l'Hospital will do me this favor if you judge it fitting to suggest it to him. The Bernoulli brothers could also do it. If I find something in the works of Mr. Newton which Mr. Wallis has inserted in his algebra which will help get us forward, I shall make use of it and give him credit. 8 But I venture to ask that you yourself will favor me with what you judge appropriate, as for example, your analysis of Mr. Bernoulli's problem by means of this kind of calculus.... ... I do not know ifI have told you that Mr. Fati0 9 has communicated to me some of his thoughts about a mechanical explanation of Mr. Newton's opinions. It is true that he has done this only reservedly and in riddles. He believes that matter fills only a very small part of space and that bodies are open structures like skeletons to permit easy passage. He believes too that if space were filled with an inert fluid matter in every direction, this would greatly interfere with the motion of bodies. He speaks of the objection which you have made, namely, that matter should then grow thick around the earth and so stop it, but says that this objection vanishes when it is examined carefully and that Mr. Huygens (so he adds) is now convinced of this. In this, he says, something admirable transpires which must be commented on before one can see that your objection has no substance. It seems in this case that a circulation or reciprocal motion occurs in nature, such that a subtle but dense or compressed matter, as it moves away from the bodies which attract others, forces the larger matter to approach these bodies. But when this gross matter arrives, it is ground up and made subtle and so sent back directly to the circumference, where it is again dispersed and serves as food for other gross bodies. There may be many reasons for attraction, such as centrifugal force arising from a circular motion, which you have used, but also the straight motion of corpuscles in about the sense in which I once saw them described by an author who tried to explain For references see p. 419
418 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS on this basis the firmness of bodies and phenomena commonly ascribed to the weight of air, but which you have observed in a vacuum. Since it seems that the mass of the earth must act in such a way that more corpuscles tend to strive toward it than can arrive, one could say that this would push the body toward the earth, according to the opinion of earlier men whom you have noted. To these factors can also be added explosion, like that of an infinity of air guns [arquebuses a vent]. For could it not be said that the bodies which produce light, weight, and magnetism are still coarse in comparison with those which produce only their own force and that the latter thus inclose a compressed matter, but that when they arrive at the sun or toward the center of other bodies which make an emission (whose interior would thus be like the sun), the great movement which this body exerts breaks and unbinds them and frees the matter compressed in them? It seems in fact that it is from this matter that fire comes. There may also be many factors combined to cause weight, since nature works in such a way that everything is in as much agreement as is possible. However this may be, it will always be difficult for us to determine these things. If anyone could succeed in our time, it would be you. It is true that all ethereal matter which tends toward the earth or toward some other body without penetrating it could not return from it. For that which does not penetrate will rebound and strike some other matter arriving behind it. Thus matter must be mixed together and pack itself around the body. But perhaps the mass thus formed is at once dissipated, a little like the sunspots. As for the difference between absolute and relative motion, I believe that if motion, or better, the motive force of bodies, is something real, as it seems we must acknowledge, it is necessary for it to have a subject. For if a and b approach each other, I assert that all the phenomena involved will happen in the same way, regardless of which one the motion or rest is assigned to. Even if there were a thousand bodies, I still hold that the phenomena could not provide us (or angels) with an infallible basis for determining the subject or the degree of motion and that each body could be conceived separately as being at rest. And I believe that this is all that you ask. But you will not deny, I think, that each body does truly have a certain degree of motion, or if you wish, of force, in spite of the equivalence of these hypotheses about their motion. It is true that from this I draw the conclusion that there is something more in nature than what geometry can determine about it. This is not the least important of the many arguments which I use to prove that besides extension and its variations, which are purely geometrical things, we must recognize something higher, namely, force. Mr. Newton recognizes the equivalence of hypotheses in the case of rectilinear motions but believes that in the case of circular motions the efforts which the bodies exert to depart from the center or the axis of rotation compel us to recognize their motion as absolute. But there are reasons which make me believe that nothing breaks the general law of equivalence. It seems to me, however, that you yourself, Sir, were once of Newton's opinion in regard to circular motion .... P.S. I do not know when I shall see the work which Mr. Wallis has just published. Would you do me the favor, Sir, of having the passages in which Mr. Newton gives his new discoveries copied for me? I do not ask directly for his method of finding series, but whether he gives the methods for converse tangents or something similar. In writing me earlier, he concealed his method in transposed letters. He indicated that he had two methods, one more general, the other more elegant. I do not know if he has spoken of them here.
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 419 IV [GM., II, 193-99] Hanover, September 4/14, 169410 I begin by thanking you for communicating to me the extract from Mr. Wallis' work which concerns Mr. Newton. I see that his calculus agrees with mine, but I think that the consideration of differences and sums is more fitted for enlightening the mind, since it occurs also in the ordinary series of numbers and in a way corresponds to powers and roots. It seems to me that Mr. Wallis speaks rather coolly of Mr. Newton and implies that it would be easy to derive these methods from Barrow's lectures. When things are done, it is easy to say, "Et nos hoc poteramus."l1 Complex matters cannot so easily be disentangled by the human mind without the use of characters. I am also pleased to see, at last, the deciphering of the enigmas contained in Mr. Newton's letter to the late Mr. Oldenburg. But I am sorry not to find the new lights which I had promised myself on inverse tangents. For this is nothing but a method for expressing the value of the ordinate of a sought curve through infinite series, the basis for which I already knew in those early days, as I then testified to Mr. Oldenburg. Some time ago I published this method in the Leipzig Acts, in an easy and very general form .... . .. When I told you in Paris that it is difficult to know the true subject of motion, you replied that this could be done by means of circular motion. This interested me, and I remembered it when I read almost the same thing in Mr. Newton's book. But this was after I had already seen that circular motion has no advantages in this respect. I see that you are now of the same opinion. I hold, then, that all hypotheses are equivalent and that when I assign certain motions to certain bodies, I do not have, and cannot have, any other reason but the simplicity of the hypothesis which I choose, for I believe that one can hold the simplest hypothesis (other things being equal) for the true one. Since I have no other criterion, therefore, I believe that the difference between us is only in our manner of speech, which I try to accommodate as far as I can to popular usage, salva veritate. I am not far from your opinion, and I have adapted myself to it in a small paper which I have sent to Mr. Viviani, and which seems to me appropriate to persuade the gentlemen at Rome to allow Copernicus' hypothesis. 12 But if you hold these views about the reality of motion, I imagine your views about the nature of body should also be different from those customarily held. My views are rather unusual but seem to me to be demonstrated. I hope some day to learn your opinions about my Critical Thoughts against Descartes, which you have given me hope of receiving, and also about what I have sent you in opposition to atoms and the void .... REFERENCES In his letter of July 11, 1692 (GM., II, 139ft'.), Huygens postulated an infinite hardness in the parts of matter, in direct opposition to Descartes's theory that all the properties of bodies arise from motion and that firmness in particular comes from the grinding-off of comers and parts, which leaves spherical bodies with rapidly moving splinters between them (Principies, Part III, 49-52, 87-88). Huygens himself proposed an explanation of cohesion based upon leveral factors, among them external pressure. 2 Leibniz is driven by his search for generalized explanations to explain gravity in terms of a plenum and vertical motion and to carry out the analogy to light, magnetism, and fimmess. 1
420 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS This effort is continued until the correspondence with Clarke at the end of his life (No. 71). 8 The pun is Leibniz's. 4 See No. 42, Part II, Arts. 54 and 55. 5 Leibniz's basic objection is that atoms violate the principles of sufficient reason and of continuity, since the transition from aggregated bodies to simple atoms carries over materialistic properties such as extension and firmness but involves a leap from one set of laws of motion and cohesion to another. 6 In his letter of May 29,1694, Huygens selected another remark in the Critical Thoughts on the General Part of the Principles of Descartes for comment. Leibniz had implied (Part II, on Art. 25) that Descartes's theory involved the relativity of motion and that to determine the subject of motion, one must go beyond it to force. Huygens erroneously ascribed to Leibniz the view that it is absurd to regard motion as relative and asserted that he himself held to such a relativity and believed that Newton would change his opinion in the second edition of the Principia. 7 In his last letter, Huygens had mentioned working on "un petit traite en matiere philosophique". This was probably the Cosmotheoros, published posthumously in 1698. 8 Leibniz's plan to write a differential and integral calculus was not carried out, though he worked on the manuscript and hoped to have it published at the Louvre in Paris (No. 49). The first standard text was by the Marquis de l'Hospital himself, the Analyse des injiniment petits pour I'inte/ligence des lignes courbes (1696). The Opera mothematica (Oxford 1693) of John Wallis contained two letters of Newton with an account of his own methods. This paragraph, the postcript, and the following letter are significant for Leibniz's opinion on the value and independence of the two methods ten years before Newton's pupil, John Keill, actually pushed the charges of plagiarism. 9 Fatio de Duillier, a Swiss mathematician living in London, was the first to imply (in 1699) that Leibniz's calculus was not original with him. He had been incensed by Leibniz's failure to mention him in an article on the solutions to the brachistochrone problem in 1697. The charge of plagiarism became serious, however, only when John Keill renewed it in 1705. 10 In his reply on August 21, 1694, Huygens supplied the notes on Wallis' works and said that he had held to the absoluteness of motion until the last two or three years but that he could not agree with Leibniz that each body nevertheless has its own definite degree of motion. 11 "We too could have done this." 12 This paper was printed by Gerhardt (GM., VI, 144-47) as a note to the Tentamen de motuum coelestium causis. Leibniz's appeal to Rome was grounded upon the relativity of motion.
44 FROM THE ETHICAL AND LEGAL WRITINGS 1693-1700 Of the four studies given here, only the first two, selected from the prefaces of Leibniz's two published collections of medieval state documents, can be dated. The third, however, is also probably from the last decade of the 17th century, though its theme occurs much earlier in Leibniz's thought. The fourth selection, Leibniz's notes on Felden, is earlier. One of the fruits of the journey of historical research in 1687-90 was the collection which Leibniz made of historical documents of importance for European history and law. Impressed by the materials available through his own work and in the library at Wo/fenbiittel, and invited by the Vienna librarian, Nesse, to supplement the catalogue of state documents there, he decided to publish his own collection in competition with a similar plan pushed forward in Paris by Leonard. The Codex juris gentium diplomaticus appeared in 1693, the Mantissa codicis juris gentium in 1700. His concern for European peace was conspicuous in the Preface of the earlier work, which discussed also the importance of accurate and reliable sources for the understanding of historical causes, and as a basis for "the law of nature and of nations", in contrast with the "voluntary law" based on contracts between sovereigns and assuring only armistices rather than enduring peace., I. FROM THE PREFACE OF THE 'CODEX JURIS GENTIUM DIPLOMATICUS' 1693 (Selection) [G., III, 386-89] Even after the efforts of so many famous authors, I am not sure that the notions of Right 1 and justice have been made sufficiently clear. Right is a kind of moral power, and obligation is moral necessity. By moral, however, I mean something equivalent to natural for a good man, for as a Roman jurisconsult has well said, we should believe that we are incapable of doing things which are contrary to good morals. A good man is one who loves all men, so far as reason permits. Therefore, if I am not mistaken, we may most fittingly define justice, which is the virtue governing that affection which the Greeks call philanthropy, as the charity of the wise man, that is, as charity which follows the dictates of wisdom. So the assertion attributed to Carneades, that justice is the highest folly because it bids us consider the interests of others while neglecting our own, is based on ignorance of its definition. 2 Charity is universal benevolence, and benevolence is the habit of loving or of cherishing. But to love or to cherish is to find pleasure in the happiness of another, or what amounts to the same thing, to accept the happiness of another as one's own. Thus the knotty question of how there can be a disinterested love which is free from hope and fear, and from every consideration of utility, is solved, and in a way that is also of great importance in theology.3 For the For references see p. 430
422 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS happiness ef these whese happiness pleases us is ebvieusly built into. eur ewn, since things which please us are desired fer their ewn sake. Thus the centemplatien ef beautiful things is itself pleasant, and a painting ef Raphael affects him who. understands it, even if it effers no. material gains, so. that he keeps it in his sight and takes delight in it, in a kind ef image ef leve. But when the beautiful object is at the same time itself capable ef happiness, this affectien passes ever into. true leve. The divine love mereever, excels ever ether leves because Ged can be leved with the happiest result, since nething is happier than Ged, and at the same time no.thing can be co.nceived mere beautiful and mere wo.rthy ef happiness. And since he po.ssesses supreme po.wer and supreme wisdem, his happiness is net enly built into. eurs, (if we are wise; that is, if we lo.ve him), but it also. co.nstitutes o.urs. But since wisdo.m sheuld guide charity, we also. need a definitio.n o.f wisdo.m. I believe, ho.wever, that we will best satisfy the cencept men have ef it if we say that wisdom is no.thing but the science o.f happiness itself. So. we ceme back again to. the no.tio.n o.f happiness, which this is net the place to. explain. New from this seurce is derived natural right, o.f which there are three degrees: strict right [jus strictus) in cemmutative justice; equity (o.r charity in the narrewer sense ef the term) in distributive justice; and finally, piety (o.r prebity) in universal justice. Hence the three mo.st general and co.mmo.nly accepted precepts o.f right: to. injure no. ene, to. give to. each his due, and to. live heno.rably (o.r better, pio.usly), as I o.nce suggested as a yo.uth in a bo.ek en the methed o.f the law. 4 The precept o.f mere right o.r strict right is that no one is to be injured, lest he be given gro.und fer legal actien if a member o.f the state, er the right ef war if he is eutside the state. Frem this arises the justice which philo.so.phers call commutative, and the right which Gro.tius calls a legal claim [facultas). 5 The higher degree I call equity, o.r, if yo.u prefer, charity (that is, in the narro.wer sense). This I extend beyo.nd the rigo.r o.f strict right, to. include these o.bligatio.ns which give to. these whem they affect no. gro.und fer actien in co.mpelling us to. fulfil them, such as the ebligatien o.f gratitude and o.f almsgiving. Upen these, Grotius says, we have a moral claim [aptitudo), net a legal claim [facultas). And as the lewest degree o.f right is to. harm no. ene, so. the middle degree is to. de geed to. all men, but o.nly so. far as befits each o.ne o.r as much as each deserves, since we canno.t befriend all men equally. It is therefo.re here that distributive justice belo.ngs and the precept o.f the law that co.mmands us to. give each one his due. And it is here that the peliticallaws in a state beleng, which assure the happiness efits subjects and which usually bring it abeut that these who. had merely a meral claim acquire a legal claim, that is, that they beceme able to. demand what it is equitable fer ethers to. perferm. In the lewest degree o.f right, the differences ameng men are net co.nsidered, with the exceptio.n of these which arise frem each particular case, but all men are ceunted as equals. New, hewever, en this higher level, merits are weighed, and so. privileges, rewards, and punishments have their place. Xenephen has nicely suggested this difference between the degrees o.f right, in his example ef the bey Cyrus, who. was chesen to. act as judge between two. beys, the stro.nger ef whem had fo.rcibly exchanged garments with the ether because he fo.und that the ether's ceat fitted him and his ewn fitted the ether better. Cyrus pro.neunced in faver o.f the rebber. But his instructo.r reminded him that the questien at this po.int was net whem the ceat might fit, but o.nly to. whem it belenged, and that he might mere pro.perly use this ether ferm ef judgment o.nly
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 423 when he himself had coats to distribute. For equity itself recommends strict right, or the equality of men, to us in our dealings, except when an important consideration of greater good commands us to depart from it. What is called respect of persons, however, has its place, not in exchanging goods with others but in distributing our own or the public goods. The highest degree of right I have named probity, or rather piety. What I have said thus far can be so interpreted as to be limited to the relations within mortal life. Mere right or strict right, indeed, arises from the principle of preserving peace; equity or charity strives for something more - that while each benefits the other as much as he can, he may increase his own happiness in that of the other. In a word, strict right avoids misery whereas the higher right tends toward happiness, but only such as falls within this mortality. But that we ought to hold this life itself, and all that makes it desirable, second to the great advantage of others, so that it behooves us to bear the greatest pains for the sake of others - this is beautifully taught by philosophers rather than firmly demonstrated. For the dignity and glory, and the joyous sense by virtue of one's own mind, to which they appeal under the name of honor [honestas], are certainly goods of thought or of the mind, and indeed, great ones. But they are not such as prevail over all men, or over all the bitterness of evils, since not all men are equally moved by the imagination, especially those who have not grown used to the weighing of virtue or the cherishing of goods of the mind, whether through a liberal education or the habit of living as free men, or the discipline of life or of sect. In order really to establish by a universal demonstration that everything honorable is beneficial and that everything base is harmful, we must assume the immortality of the soul and the ruler of the universe, God. Thus it is that we may think of all men as living in the most perfect state, under a monarch who can neither be deceived in his wisdom nor eluded in his power, but who is also so lovable that it is happiness to serve such a lord. Hence whoever expends his soul for him, as Christ teaches, shall gain it. His power and providence bring it to pass that every right passes over into fact, that no one is injured except by himself, and that no right deed is without its reward, no sin without its punishment. As we are divinely taught by Christ, all our hairs are numbered, and not even a drink of water is given to the thirsty in vain; thus nothing is neglected in the commonwealth of the universe. It is on this ground that justice is called universal, and includes all other virtues, for duties that do not otherwise seem to concern others, as for example, not to abuse our own bodies or property, though they lie beyond human laws, are yet prohibited by the law [jus] of nature, that is, by the eternal laws of the divine monarchy, since we owe ourselves and our all to God. For if it is of interest to the state that no one should make bad use of his property, how much more to the interest of the universe! And so it is from this that the highest precept of the law receives its force, which commands us to live honorably (that is, piously). It is in this sense that learned men have rightly set down, among things to be desired, that the law of nature and the law of nations should follow the teachings of Christianity, that is, TU uvoJTspa, the sublime matters, the divine things of the wise, after the pattern of Christ. In this way I believe that I have interpreted the three precepts of the law, or the three degrees of justice, in the most fitting way and have pointed out the sources of natural law. Besides 6 the eternal right of a rational nature, which flows from this divine source, there is also held to be a voluntary right, which is derived from custom or established For references see p. 430
424 LEIBNI Z: PHILOSOPHICAL PAPERS AND LETTERS by a superior. And within the state, civil law does indeed receive its force from him who has the supreme power; outside of the state, or among those who take part in the supreme power (of whom there may also be several within the same state), is the sphere of the voluntary law of nations, which is derived from the silent consensus of the peoples. It is not necessary for this to be the consensus of all peoples or of all times, for there have been many cases in which one thing was judged right in India and another in Europe, and even among ourselves it has changed with the course of centuries, as this work itself will show.... But Christians have still another bond, the positive divine law contained in the sacred writings. To these are to be added the sacred canons accepted by the whole church and later, in the West, the papal law, to which kings and peoples make submission. In general, before the schism of the past century, it seems to have been accepted for a long time, and not without reason, that we must think of a kind of commonwealth of Christian nations, the heads of which are the pope in sacred matters, and the Holy Roman emperor in temporal affairs. These seem to have retained as much of the old Roman law as was needed for the common good of Christendom, without prejudice to the right of kings and the liberty of princes .... II. FROM THE PREFACE TO THE MANTISSA CODICIS JURIS GENTIUM 7 1700 ... It seems desirable, however, to reply to one objection which has been made to me, on an issue upon which I touched there [in the Preface of the Codex] before it was openly discussed, and which recently excited much argument in France, until it was suppressed by authority of the king and the supreme pontiff. 8 This is the controversy about whether love which is disinterested, and seeks the well-being of the beloved, nevertheless depends upon the impulsion toward one's own well-being. Somewhat the same question, namely, had occurred to me when I prefaced the Codex juris gentium with some remarks on the foundation of law, which I tried to find in charity, since justice is nothing but the charity of a wise man. For how can love be bestowed upon others? Who seeks the well-being of the beloved for its own sake, since we will nothing except for the sake of our own good? I should answer that whatever is pleasant is sought for itself, as opposed, that is, to what is useful to the good ends of producing the well-being of another. I observed that such is the object of true love, since to love or to cherish is to be delighted by the happiness of the beloved and his perfections. I understood the following objection to have been made against this - that it is more perfect so to submit to God that you are moved by his will alone and not by your own delight. But we must recognize that this conflicts with the nature of things, for the impulse to action arises from a striving toward perfection, the sense of which is pleasure, and there is no action or will on any other basis. Even in our evil purposes 'file are moved by a certain perceived appearance of good or perfection, even though we miss the mark, or rather pay for a lesser good, iII sought, by throwing away a greater. Nor can anyone renounce (except merely verbally) being impelled by his own good, without renouncing his own nature. And so it is to be feared that the negation of self which certain false mystics teach, and the suspension of action and thought by which they assume that we find supreme union
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 425 with God, may end at length in a doctrine of the mortality of the soul such as is taught by the Averroists and other old philosophers as well, to whom it seemed that minds do not persist after man's death, except in that ocean of divinity from which the drops had once come forth. I seem to observe the seeds of this doctrine in Valentine Weigel, in the so-called Angelus Silesius, and in Molinos, though perhaps these authors do not themselves adequately recognize it. 9 So we rightly reject the lazy reason [a8p)'o~ lo)'o~] of men, the philosophic opinion of those who locate perfection in quietude, that is, in cessation, and who thus withdraw far from true tranquillity and charity and far, too, from Telemachus himself.lO III. ON WISDOM ll [Guh. DS., I, 420-26; G., VII, 86-87) Wisdom is merely the science of happiness or that science which teaches us to achieve happiness. Happiness is a state of permanent joy. The happy man does not, it is true, feel this joy at every instant, for he sometimes rests from his contemplation, and usually also turns his thoughts to practical affairs. But it is enough that he is in a state to feel joy whenever he wishes to think of it and that at other times there is a joyousness in his actions and his nature which arises from this. Present joy does not make happy of it has no permanence; indeed, he is rather unhappy who falls into a long wretchedness for the sake of a brief joy. Joy is a pleasure which the soul feels in itself. Pleasure is the feeling of a perfection or an excellence, whether in ourselves or in something else. For the perfection of other beings also is agreeable, such as understanding, courage, and especially beauty in another human being, or in an animal or even in a lifeless creation, a painting or a work of craftsmanship, as well. For the image of such perfection in others, impressed upon us, causes some of this perfection to be implanted and aroused within ourselves. Thus there is no doubt that he who consorts much with excellent people or things becomes himself more excellent. Although the perfections of others sometimes displease us - as for example, the understanding or the courage of any enemy, the beauty of a rival, or the luster of another's virtue which overshadows or shames us - this is not because of the perfection itself but because of the circumstance which makes it inopportune for us, so that the sweetness of our first perception of this perfection in someone else is exceeded and spoiled by the consequent bitterness of our afterthoughts. We do not always observe wherein the perfection of pleasing things consists, or what kind of perfection within ourselves they serve, yet our feelings [Gemiith] perceive it, even though our understanding does not. We commonly say, 'There is something, I know not what, that pleases me in the matter.' This we call 'sympathy'. But those who seek the causes of things will usually find a ground for this and understand that there is something at the bottom of the matter which, though unnoticed, really appeals to us. Music is a beautiful example of this. Everything that emits a sound contains a vibration or a transverse motion such as we see in strings; thus everything that emits sounds gives off invisible impulses. When these are not confused, but proceed together in order but with a certain variation, they are pleasing; in the same way, we also notice certain changes from long to short syllables, and a coincidence of rhymes in For references see p. 430
426 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS poetry, which contain a silent music, as it were, and when correctly constructed are pleasant even without being sung. Drum beats, the beat and cadence of the dance, and other motions of this kind in measure and rule derive their pleasurableness from their order, for all order is an aid to the emotions. And a regular though invisible order is found also in the artfully created beats and motions of vibrating strings, pipes, bells, and indeed, even of the air itself, which these bring into uniform motion. Through our hearing, this creates a sympathetic echo in us, to which our animal spirits respond. This is why music is so well adapted to move our minds, even though this main purpose is not usually sufficiently noticed or sought after. There can be no doubt that even in touch, taste, and smell, sweetness consists in a definite though insensible order and perfection or a fitness, which nature has put there to stimulate us and the animals to that which is otherwise needed, so that the right use of all pleasurable things is really brought about in us, even though these things may give rise to a far greater harm through abuse and intemperance. I call any elevation of being a perfection. Just as illness is a debasement, as it were, and a decline from health, so perfection is something which rises above health. But health itself stands balanced in the middle and lays the foundation for perfection. Now illness comes from an injury to action, as medical men rightly observe. Just so perfection shows itself in great freedom and power of action, since all being consists in a kind of power; and the greater the power, the higher and freer the being. The greater any power is, moreover, the more there is found in it the many revealed through the one and in the one, in that the one rules many outside of itself and represents them in itself. Now unity in plurality is nothing but harmony [tJbereinstimmung], and since any particular being agrees with one rather than another being, there flows from this harmony the order from which beauty arises, and beauty awakens love. Thus we see that happiness, pleasure, love, perfection, being, power, freedom, harmony, order, and beauty are all tied to each other, a truth which is rightly perceived by few. Now when the soul feels within itself a great harmony, order, freedom, power, or perfection, and hence feels pleasure in this, the result is joy, as these explanations show. Such joy is permanent and cannot deceive, nor can it cause a future unhappiness if it arises from knowledge and is accompanied by a light which kindles an inclination to the good in the will, that is, virtue. But when pleasure and joy are directed toward satisfying the senses rather than the understanding, they can as easily lead us to unhappiness as to bliss, just as a food which tastes good can be unwholesome. So the enjoyment of the senses must be used according to the rules of reason, like a food, medicine, or exercise. But the pleasure which the soul finds in itself through understanding is a present joy such as can conserve our joy for the future as well. It follows from this that nothing serves our happiness better than the illumination of our understanding and the exercise of our will to act always according to our understanding, and that this illumination is to be sought especially in the knowledge of such things as can bring our understanding ever further into a higher light. For there springs from such knowledge an enduring progress in wisdom and virtue, and therefore also in perfection and joy, the advantage of which remains with the soul even after this life. A separate discussion would be needed to show what the things are whose knowledge causes so happy a progress. Meanwhile we can say that no one can rise more easily to a higher stage of happiness than can persons of rank, yet that no one finds it more
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 427 difficult than they actually to achieve this happiness, as Christ himself tells us. The reason is that though they have the power to do much good, they rarely put their minds to it. For having opportunities constantly for sensual indulgence, they grow used to seeking their joys mostly in the pleasures which come from the body. And even when they rise higher, they seek praise and honor from others more than a true satisfaction within themselves. Hence their self-deceit ends when the pleasures of the body are destroyed by illness, and their glory by misfortunes, and they find that they are unhappy. From their youth they have followed the drive of external things for the sake of the pleasure which they found in it, and especially because it is hard, at first, to resist this stream. Thus they have for the most part lost their freedom of mind. It is a great thing, therefore, when a person of rank can enjoy himself even in illness, misfortune, and disgrace 12 , especially if he can find contentment, not out of necessity because he sees that things must be as they are (this is no more comfort than that of taking a sleeping potion to escape feeling pain), but out of the awakening within himself of a great joy which overcomes these pains and misfortunes. Such joy, which a person can always create for himself when his mind is well ordered, consists in the perception of pleasure in himself and in the powers of his mind, when a man feels within himself a strong inclination and readiness for the good and the true, and particularly through the profound knowledge which an enlightened understanding provides for us, namely, that we experience the chief source, the course, and the purpose of everything, and the incomprehensible excellence of that Supreme Nature which comprises all things within it. Thus are we lifted above the unknowing, just as if we were looking down from the stars and could see all earthly things under our feet. Then at last we learn that we have reason to find the highest joy in all things that have happened and are yet to happen, but that we must also seek, as far as is in our power, to direct what has not yet happened for the best. For it is one of the eternal laws of nature that we shall enjoy the perfection of things and the pleasure which results from it, only in the measure of our knowledge, our good will, and our contribution to this perfection. When a person of rank attains this and finds his joy in the actions of his understanding and his virtue, even in the midst of all abundance and honor, I consider him doubly exalted. He is exalted unto himself because of this, his happiness and true joy; he is exalted before others because it is entirely certain that such a person can and will share his light and virtue with many others because of his power and reputation, since such sharing will reflect glory upon himself and so give new light to all those who have the same common purpose of helping each other in the search for truth, the knowledge of nature, the multiplication of human powers, and the advancement of the common good. The great happiness of persons who are both exalted in rank and enlightened as well is therefore apparent, because they can do as much for their happiness as if they had a thousand hands and a thousand lives - indeed, as if they lived a thousand times as long as they do. For only so much of our life is to be valued as truly living as the good we do in it. One who does much good in a short time is thus equal to one who lives a thousand times as long. This is the case with those who can make thousands upon thousands of hands work with them, so that more good can be brought about in a few years, to their supreme glory and enjoyment, than could otherwise be achieved in many hundreds of years. For references see p. 430
428 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS The beauty of nature is so great, its contemplation is so sweet, and the light and good inclination which arise from these bring such glorious fruitage even in this life that he who has tasted them considers all other delights small by contrast. But when we add that the soul does not perish but that every perfection within her must be preserved to bring forth fruit, then it can be seen in full how the true happiness which arises from wisdom and virtue is incomparably and immeasurably high above all that we may imagine about it. IV. ON NATURAL LAW 13 [Guh. DS., I, 414-19] Justice is a social virtue, or a virtue which preserves society. A society is a union of different men for a common purpose. A natural society is one which is demanded by nature. The signs by which one can conclude that nature demands something are, first, that nature has given us a desire and the power or effectiveness to fulfil it, for nature does nothing in vain; and then, more especially when the matter involves a necessity or a permanent benefit, for nature everywhere achieves the best. The most perfect society is that whose purpose is the universal and supreme happiness. Natural law is that which preserves or furthers natural societies. The first natural society is that between man and woman, for it is necessary to preserve the human race. The second is between parents and children; this arises at once out of the first, for when children are procreated or freely adopted, they must be reared, that is, governed and nourished. In return they owe their parents obedience and help after they are reared. For such a society is conceived and furthered by the hope of this gratitude, though nature maintains it principally for the sake of the children - that they may sometime achieve perfection. Parents exist primarily for the sake of children; the present, which does not last long, for the sake of the future. The third natural society exists between master and servant. This is natural when a person lacks understanding but does not lack strength to nourish himself. Such a person is by nature a servant who must work as another directs him. From his work he receives his maintenance; the rest belongs to his master. For whatever the servant is, he is for the sake of his master, since all other powers exist for the sake of the understanding. But understanding is in the master, only the other powers are in the servant. Since such a servant exists for the sake of his master, his master owes him only his maintenance, and that for his own sake, in order not to ruin his servant. This might be understood if there were no hope of bringing the servant himself to understanding; otherwise the master would be obligated to advance his servant's freedom through education, at least as far as this is necessary for the happiness of the servant. To confess the truth, I doubt whether an instance can be found of a servitude such that the servant exists entirely for the sake of the master, especially since souls are immortal and hence can sometime achieve understanding and the blessedness of a life based upon it. In my opinion, therefore, this society exists only between men and cattle. For even if a man were born entirely brutish and incapable of any instruction, we should still not have the right to martyr, kill, or sell him to barbarians for our own good. But if souls were only mortal, this servitude might occur in entire races which are almost as dumb as cattle, and so could be kept in this stupidity for the advantage of
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 429 their masters - at least to the extent that children can be reared not to advance beyond cattle. Now since the universal rules of justice are taught, and even atheists must accept them, it seems that the natural servants of men can be dealt with, provided, that is, any such servants are to be found. Even if such servitude is not to be endured in its full force among men, something similar and approaching it sometimes conforms to nature. To summarize, natural servitude applies to unintelligent men insofar as it is not restricted by the rules of piety. The fourth natural society is the household, which is composed of all the societies mentioned above - some or all. Its purpose is man's daily needs. The fifth natural society is civil society. If this is small, it is called a city; a province is a society of different cities, and a kingdom or a great dominion is a society of different provinces - all to achieve happiness or to be secure in it. The members of a civil society sometimes live together in a city, sometimes spread out over the land. Its purpose is temporal welfare. The sixth natural society is the church of God, which would probably have existed among men even without revelation and have been preserved by pious and holy men. Its purpose is eternal happiness. No one need wonder that I call it a natural society, since there is a natural religion and a desire for immortality implanted within us. This society of the saints is catholic or universal and binds the entire human race together. If a revelation is added, this bond is not tom apart but merely strengthened by it. A CLASSIFICATION OF SOCIETIES OR COMMUNITIES Every society is equal or unequal. It is equal when one has as much power in it as another, unequal when one rules over another. Every society is either unlimited or limited. An unlimited society concerns the whole life and the common good. A limited society concerns certain purposes, for example, trade and commerce, navigation, warfare, and travel. An unlimited equal society exists between true friends. Particularly does such a society exist between man and wife, between parents and grown children, between masters and freedmen, and in general between all intelligent men who have an adequate acquaintance with each other. An unlimited unequal society exists between rulers and their subjects. Such rule occurs for the sake either of improvement or of conservation. If for the sake of improvement, it really takes place between parents and children, and also between us and those whom we accept in the place of children, or whom we so rear that they receive their welfare from us and are under our rule alone. It has no place between teacher and pupil, since the latter is subject to the former only in a certain degree or way, while we are here talking about an unlimited society which involves the whole life and welfare. Brutish men are grown children. But if such rule is for the sake of conservation, it exists between master and servant and consists in the master assuring the servant's welfare, while the servant submits to the master's rule. All these societies are simple or composite, and also between few or many men. Hence all unlimited societies or communities [Lebensgesellschaften] can be reduced to certain points, namely, to education and instruction, rule and obedience, friendship and co-operation, etc. To the extent that they have been reared, children already owe obedience as far as For references see p. 430
430 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS their powers permit, and as they grow in understanding, they owe friendship and assistance to the master as well, even though their education is not completed. Man and wife are bound by nature to friendship and mutual aid [Lebenshiilfe] in a brotherly way. Similarly parents and children, and also relatives and people in a community, must have an understanding of each other, for to friendship belongs understanding. One who is himself being educated may educate, and one who is ruled may at the same time rule. But in this case there must be subordination. All unlimited societies do indeed aim at welfare, but they cannot always achieve it. Hence more and more societies have had to unite and build greater and stronger societies. Thus households, clans, villages, monasteries, orders, cities, provinces, and finally the whole human race, which also constitutes a community under the rule of God. If everything in the world were arranged in the most perfect way, then first of all, parents, children, and relatives would be the best of friends, and whole families would have chosen an art of living, would have arranged all that they have to this end, would abide in it and continue to perfect themselves in their art and direct their children to the same end. They would marry people of the same calling in order to be united through education from their parents. These clans would make up guilds or castes out of which cities would arise; these would enter into provinces, and all countries, finally, would stand under the church of God. REFERENCES Cf. p. 138, note 3. Jus may be translated either as Right or as Law, depending upon the context. 2 Cameades' statement is found in Cicero De rep. iii. 23, though Leibniz seems to have taken it from Grotius. 3 Leibniz here anticipated the bitter debate on the issue of disinterested love, which broke out between Fenelon and Bossuet (cf. p. 328, note 6) after the appearance of the former's Explication des maximes des saints sur la vie interieure in 1697. Fenelon asserted that pure love must "exclude every interested motive" and that "the soul must make the absolute sacrifice of its self-interest for eternity'~. The theological conflict which followed led to Fenelon's banishment from the court in August, 1697, and the pope's condemnation of the Explication in March, 1699 (see A. Cherel, Fenelon ou la religion du pure amour, 1934). On Leibniz's conception of the relation between law and theology see the concluding section of No. 1. 4 See No.2. The three precepts of Law are in Ulpian Institutes i. i. 3. 5 Hugo Grotius, Dejure belli et pacis, I, i, 5. We use Whewell's translation of the termsfacultas and aptitudo, which correspond in general to 'strict' legal right and to moral right, respectively. 6 The follo~ing paragraphs are not given by G. but are taken from the Codex juris gentium diplomaticus (Hanover 1693) itself. The Preface does not have numbered pages. 7 From the third page (unnumbered) of the Preface to the Mantissa codicis juris gentium diplomatici (Hanover 1700) a supplementary miscellany of political and diplomatic documents from the medieval and modem periods. 8 See note 3 above. 9 For the quietist movement of the 17th century and Miguel de Molinos see p. 328, note 6. Valentine Weigel, Evangelical pastor and mystic (1533-88), wrote many mystical works and had attributed to him many which he did not write. New editions of works attributed to him were appearing at Amsterdam and at Frankfurt in the years at the end of the 17th and the 1
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 431 beginning of the 18th century. The Cherubinischer Wandersmann of 'Angelus Silesius' appeared in its second edition (the first to bear this title) in 1675. 10 Fenelon's drama Telemaque had appeared in 1699. 11 The date of this paper, written in German, is uncertain, though Guh. DS. places it in the last decade of the 17th century, "when Leibniz stood at the height of his philosophical convictions". He had written a French 'de la Sagesse'in the Paris period (G., VII, 82ff), and was occupied with such statements of his ethics throughout his life. This paper is obviously addressed to 'persons of rank' and contains echoes of the tragedies undergone by the house of Hanover at this time. 12 Family disasters were striking at the court of Hanover in the early nineties: the deaths of the Princes Frederick August and Karl Philip in battle in 1690; the abortive attempt of Maximilian, the youngest son of Ernest August, to break the newly established law of primogeniture, which failed in 1691; and the notorious Konigsmark incident leading to the divorce of George Louis, later George I, king of England, and to the exile of his wife Dorothea, in 1694. 13 These are Leibniz's notes on John Felden, Elementa juris universi et in specie publici Justiniani, Frankfurt 1664, I, i. Fe1den's jurisprudence is Aristotelian and directed against Hobbes.
45 ON THE CORRECTION OF METAPHYSICS AND THE CONCEPT OF SUBSTANCE Acta eruditorum, March, 1694 Leibniz's increasing inclination to publish his philosophical conclusions is shown in this brief article inserted in the Leipzig scholarly journal. In it he urges greater exactness in metaphysics and distinguishes his conception of active force from the ambiguous Scholastic principle of power. The article led to a correspondence with John Christopher Sturm on the problem of substance, of which No. 53, On Nature Itself, was one result. [G., IV, 468-70] I find that most people who take pleasure in the mathematical sciences shrink away from metaphysics, because they find light in the former but darkness in the latter. The most important reason for this, I believe, is that general concepts which are thought to be very well known to everyone have become ambiguous and obscure through the carelessness and changeableness of human thinking and that the definitions commonly given of these concepts are not even nominal definitions and in fact explain nothing. And there is no doubt that this has spread to other fields subordinate to this primary and architectonic discipline. So instead of clear definitions, we make trivial distinctions, and, in place of truly universal axioms, we set up limited rules [regulae topicae] which are more frequently broken by exceptions than supported by examples. Yet by a sort of necessity men continue to use metaphysical terms and, flattering themselves, believe that they understand the words they have learned to say. It is obvious that the true and fruitful concepts, not only of substance, but of cause, action, relation, similarity, and many other general terms as well, are hidden from popular understanding. No one should be astonished, therefore, that this regal science, which goes by the name of 'first philosophy', and which Aristotle called desired or soughtafter [Cl1fOV!livl1], has hitherto remained to be sought. Plato, of course, studies the force of concepts throughout his dialogues, and Aristotle does the same in the books which are commonly called the Metaphysics, but it does not seem that much was accomplished. The later Platonists lapsed into uttering omens, and the Aristotelians, especially the Scholastics, cared more about asking questions than about answering them. Some distinguished men in our own times have also set their minds on metaphysics, but so far without great success. It cannot be denied that Descartes has contributed some admirable things. Above all, he both rightly restored the study of Plato by leading the mind away from the senses and thereupon also added to it the doubts of the Academy. But he missed the mark because of a certain wavering or a license in making assertions and failed to distinguish the certain from the uncertain. And so he absurdly put the nature of corporeal substance in extension. Nor did he
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 433 have any sound understanding of the union of soul and body. The cause of these errors was a failure to understand the nature of substance in general. For he proceeded to the solution of the most serious questions in a kind of leap, without having explained the concepts involved. Thus the failure of his Meditations on Metaphysics to achieve certainty is nowhere more apparent than in the writing in which, urged by Mersenne and others, he tried in vain to clothe them in mathematical dress. 1 I know that other men as well, of outstanding insight, have touched upon metaphysics and thought profoundly about some matters, but they have enveloped them in such darkness that they seem to have used divination rather than demonstrations. Yet it seems to me that light and certainty are more needed in metaphysics than in mathematics itself, because mathematical matters carry their own tests and verification with them, this being the strongest reason for success in mathematics. But in metaphysics we lack this advantage entirely. And so a certain distinctive order of procedure is necessary, which, like a thread in a labyrinth, will serve us, no less than the method of Euclid, to analyze our questions in the form of a calculus, yet nonetheless preserve the clarity which should never be lacking from popular speech. The importance of these matters will be particularly apparent from the concept of substance which I offer. This is so fruitful that there follow from it primary truths, even about God and minds and the nature of bodies - truths heretofore known in part though hardly demonstrated, and unknown in part, but of the greatest utility for the future in the other sciences. To give a foretaste of this, I will say for the present that the concept of forces or powers, which the Germans call Kraft and the French ta force, and for whose explanation I have set up a distinct science of dynamics, brings the strongest light to bear upon our understanding of the true concept of substance. Active force differs from the mere power familiar to the Schools, for the active power or faculty of the Scholastics is nothing but a close [propinqua] possibility of acting, which needs an external excitation or a stimulus, as it were, to be transferred into action. Active force, in contrast, contains a certain act or entelechy and is thus midway between the faculty of acting and the act itself and involves a conatus. It is thus carried into action by itself and needs no help but only the removal of an impediment. 2 This can be illustrated by the example of a heavy hanging body which strains at the rope which holds it or by a bent bow. For though gravity and elasticity can and ought to be explained mechanically by the motion of the ether, the ultimate reason for motion in matter is nevertheless the force impressed upon it in creation, which inheres in every body but is variously limited and restrained in nature through the impact of bodies upon each other. I say that this power of acting inheres in all substance and that some action always arises from it, so that the corporeal substance itself does not, any more than spiritual substance, ever cease to act. This seems not to have been perceived clearly by those who have found the essence of bodies to be in extension, alone or together with the addition of impenetrability, and who seem to conceive of bodies as absolutely at rest. It will be apparent from our meditations that one created substance receives from another created substance, not the force of acting itself, but only the limits and the determination of its own pre-existent striving or power of action. Not to speak now of other matters, I shall leave the solution of the difficult problem of the mutual action of substances upon each other for the future. 3 For references see p. 434
434 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS REFERENCES 1 In the Responsio ad secundas objectiones (ed. Adam and Tannery, VII, 160-70). The difference between Leibniz's conception of an originating force and the Scholastic concept of a capacity or the possibility of action is thus clear. But as primary force something of the Scholastic notion is retained in his system, since this force inheres potentially in the concept of the individual. The concept of force is more fully developed in No. 46, Part I. 3 See No. 47. 2
46 SPECIMEN DYNAMICUM 1695 While in Italy Leibniz had written an extensive Dynamics (GM., VI, 281-514) which summarized his criticism of Descartes's physical principles and at the same time supplemented what he regarded as an incompleteness in Newton's hypotheses. The manuscript of this work he left at Florence with the Baron Bodenhausen, tutor of the sons of the Duke of Tuscany, with the intention ofpublishing it after it had undergone the criticism of hisfriends (see his letter toL'Hospital, January 15,1696 [GM., II, 305-11]). Thepresent work is a summary of this longer one, made in response to a general demand for his new ideas. Part I was printed in the Acta eruditorum in April, 1695; the second part remained unpublished and was found by Gerhardt among the Hanover manuscripts. The two parts together comprise a mature statement of Leibniz's theory of dynamics. SPECIMEN DYNAMICUM; FOR TH'E DISCOVERY OF THE ADMIRABLE LAWS OF NATURE CONCERNING CORPOREAL FORCES, THEIR MUTUAL ACTIONS, AND THEIR REDUCTION TO THEIR CAUSES [GM., VI, 234-54] Part I Since we first mentioned a new science of dynamics, which was still to be founded, many prominent men in various places have asked for a fuller explanation of its teachings. But as we have not yet found leisure to write a book, we shall here set down some things which may cast some light on it - light which will be returned to us with interest if we succeed in eliciting the opinions of men who combine force of insight with distinction of style. We confess that their judgment will be most welcome and we hope, useful in advancing the perfection of the work. We have suggested elsewhere that there is something besides extension in corporeal things; indeed, that there is something prior to extension, namely, a natural force everywhere implanted by the Author of nature - a force which does not consist merely in a simple faculty such as that with which the Scholastics seem to have contented themselves but which is provided besides with a striving or effort [conatus seu nisus] which has its full effect unless impeded by a contrary striving. 1 This nisus sometimes appears to the senses, and is in my opinion to be understood on rational grounds, as present everywhere in matter, even where it does not appear to sense. But if we cannot ascribe it to God by some miracle, it is certainly necessary that this force be produced by him within bodies themselves. 2 Indeed, it must constitute the inmost nature of the body, since it is the character of substance to act, and extension means only the continuation or diffusion of an already presupposed acting and resisting substance. So far is extension itself from comprising substance! It is beside the point here that all corporeal action arises from motion and that moFor references see p. 450
436 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS tion itself comes only from other motion already existing in the body or impressed upon it from without. For like time, motion taken in an exact sense never exists, because a whole does not exist if it has no coexisting parts. Thus there is nothing real in motion itself except that momentaneous state which must consist of a force striving toward change. Whatever there is in corporeal nature besides the object of geometry, or extension, must be reduced to this force. This reasoning does justice, at last, both to truth and to the teachings of the ancients. Our age has already saved from contempt the corpuscles of Democritus, the ideas of Plato, and the tranquillity of the Stoics which arises from the best possible connection [nexus] of things; now we shall reduce the Peripatetic tradition of forms or entelechies, which has rightly seemed enigmatic and scarcely understood by its authors themselves, to intelligible concepts. Thus we believe that this philosophy, accepted for so many centuries, must not be discarded but be explained in a way that makes it consistent within itself (where this is possible) and clarifies and amplifies it with new truths. This method of study seems to me best suited both for the wisdom of the teacher and for the advancement of the learners; we must guard against being more eager to destroy than to construct, and against being tossed about uncertainly, as if by the wind, among the perpetually changing teachings put forth by certain freethinkers. Then after it has curbed the passion of sects, which is stimulated by the vain lust for novelty, mankind will at length advance with firm steps to ultimate principles in philosophy no less than in mathematics. For if we overlook entirely the harsher things which they say against others, the writings of outstanding men, both ancient and modem, usually contain many true and good things which deserve to be collected and arranged in the public treasury of knowledge. Would that men might choose to do this rather than to waste their time with criticisms that serve only to satisfy their own vanity. Indeed, though fortune has so favored me with the discovery of certain new things of my own that friends often urge me to think only about these, I nevertheless find pleasure in the views of others and appraise each according to its own worth, however this may vary. This may be because I have learned in my widespread activities not to despise anything. But now let us get back on the road. Active force, which may well be called power, as it is by some, is of two kinds. The first is primitive force, which is in all corporeal substance as such, since I believe that a body entirely at rest is contrary to the nature of things. The second is derivative force, which is exercised in various ways through a limitation of primitive force resulting from the conflict of bodies with each other. Primitive force, which is nothing but the first entelechy, corresponds to the soul or substantial form, but for this very reason it relates only to general causes which cannot suffice to explain phenomena. Therefore I agree with those who deny that forms are to be used in investigating the specific and special causes of sensible things. 3 This I must emphasize to make it clear that in restoring to the forms their proper function of revealing the sources of things to us, I am not trying to return to the word battles of the more popular Scholastics. A knowledge of forms is necessary, meanwhile, for philosophizing rightly, and no one can claim to have grasped the nature of body adequately unless he has paid some attention to such things and has come to understand that the crude concept of a corporeal substance which depends only on sensory imagery and has recently been carelessly introduced by an abuse of the corpuscular philosophy (which is excellent and most true in itself) is imperfect, not to say false. 4 This can also be shown by considering that such a concept
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 437 of body does not exclude cessation or rest from matter and cannot provide reasons for the laws of nature which apply to derivative force. Passive force is likewise of two kinds - primitive and derivative. The primitive force of suffering or of resisting constitutes the very thing which the Scholastics call materia prima, if rightly interpreted. It brings it about, namely, that one body is not penetrated by another but opposes an obstacle to it and is at the same time possessed of a kind of laziness, so to speak, or a repugnance to motion, and so does not allow itself to be set in motion without somewhat breaking the force of the body acting upon it. Hence the derivative force of suffering thereafter shows itself in various ways in secondary matter. 5 But setting aside these general and primary considerations, and having established the fact that every body acts by virtue of its form and suffers or resists by virtue of its matter, we must now proceed to the doctrine of derivative forces and resistances and discuss the question of how bodies prevail over or resist each other in various ways by their varied impulses. For to these derivative forces apply the laws of action, which are not only known by reason but also verified by sense itself through phenomena. Here, therefore, we understand by derivative force, or the force by which bodies actually act and are acted upon by each other, only that force which is connected with motion (local motion, that is) and which in turn tends to produce further local motion. For we admit that all other material phenomena can be explained through local motion. Motion is the continuous change of place and thus requires time. But as the moving body has its motion in time, so it has a velocity at every moment of time, a velocity which is the greater in the degree that more space is passed through in less expenditure of time. This velocity along with direction is called conatus. Impetus, however, consists in the product of the mass [molis] 6 of the body by its velocity, and so its quantity is that which Cartesians usually call the quantity of motion, that is, the momentaneous quantity, although speaking more accurately, the quantity of motion, having an existence in time, is an integral of the impetuses (whether equal or unequal) existing in the moving body multiplied by the corresponding intervals of time. In our debate with the Cartesians, however, we have followed their way of speaking. Yet in the scientific use of terms, as we may conveniently distinguish an increase which has already taken place, or one still to come, from one which is now occurring, designating this latter as the increment or element of the increase; so we can distinguish the falling of a body at the present moment from the fall which has already taken place which it increases. So we can also distinguish the present or instantaneous element of motion from the motion extended through time and call it 'motion'. Then what is popularly called motion would be called quantity of motion. But although we can readily comply with any accepted terminology after its meaning is established, we must be careful about terms until this is done, in order not to be misled by their ambiguity. 7 Furthermore, just as the calculation of motion carried out through time is integrated from an infinite number of impetuses, so in turn the impetus itself (even though it is a momentaneous thing) arises from a succession of an infinite number of impacts on the same moving body; so it too contains a certain element from which it can arise only through infinite repetitions. Assume a tube AC rotating about a fixed center C with a definite uniform velocity and in the horizontal plane of this page (Figure 29). Assume a ball B moving within the tube without any chain or impediment and hence beginning to move by centrifugal force. It is obvious that the beginning of the conatus of receding from the center (the conatus, namely, by which the ball B tends toward the end of the For references see p. 450
438 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS tube A) is infinitely small with respect to the impetus which it already has from the rotation or that by which the ball B tends from D to D' along with the tube itself, while retaining its distance from the center. But if the centrifugal impulsion proceeding from the rotation is continued for some time, there must arise in the ball, from its own progression, a certain complete centrifugal impetus D'B' comparable to the impetus of rotation DD'. Hence the nisus is obviously twofold, an elementary or infinitely small one which I also call a solicitation and one formed by the continuation or repetition of these elementary impulsions, that is, the impetus itself. But I do not mean that these mathematical entities are really found in nature as such but merely that they are means of making accurate calculations of an abstract mental kind. A c Fig. 29. Hence force is also of two kinds: the one elementary, which I also call dead force 8, because motion does not yet exist in it but only a solicitation to motion, such as that of the ball in the tube or a stone in a sling even while it is still held by the string; the other is ordinary force combined with actual motion, which I call living force [vis viva]. An example of dead force is centrifugal force, and likewise the force of gravity or centripetal force; also the force with which a stretched elastic body begins to restore itself. But in impact, whether this arises from a heavy body which has been falling for some time, or from a bow which has been restoring itself for some time, or from some similar cause, the force is living and arises from an infinite number of continuous impressions of dead force. This is what Galileo meant when in an enigmatic way, he called the force of impact infinite as compared with the simple impulsion of gravity. But even though impetus is always combined with living force, the two are nonetheless different, as we shall show below.
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 439 Living force in any aggregate of bodies can further be understood in two senses namely, as total and partial. Partial force in turn is either relative or directive, that is, either proper to the parts themselves or common to all. Respective or proper force is that by which the bodies included in an aggregate can interact upon each other; directive or common force is that by which the aggregate can itself also act externally. I call this 'directive' because the integral force of total direction is conserved in this partial force. Moreover, if it were assumed that the aggregate should suddenly become rigid by the cessation of the motion of the parts relative to each other, this alone would be left. Thus absolute total force is composed of relative and directive force taken together. But this can be understood better from the rules to be treated below. 9 So far as we know, the ancients had a knowledge of dead force only, and it is this which is commonly called mechanics, which deals with the lever, the pulley, the inclined plane (applicable to the wedge and screw), the equilibrium ofliquids, and similar matters concerned only with the primary conatus of bodies in itself, before they take on an impetus through action. Although the laws of dead force can be carried over, in a certain way, to living force, yet great caution is necessary, for it is at this point that those who confused force in general with the quantity resulting from the product of mass by velocity were misled because they saw that dead force is proportional to these factors. As we pointed out long ago, this happens for a special reason, namely, that when for example, different heavy bodies fall, the descent itself or the quantities of space passed through in the descent are, at the very beginning of motion while they remain infinitely small or elementary, proportional to the velocities or to the conatuses of descent. But when some progress has been made and living force has developed, the acquired velocities are no longer proportional to the spaces already passed through in the descent but only to their elements. lo Yet we have already shown, and will show more fully, that the force must be calculated in terms of these spaces themselves. Though he used another name, and indeed, another concept, Galileo began the treatment of living force and was the first to explain how motion arises from the acceleration of heavy falling bodies. Descartes rightly distinguished between velocity and direction and also saw that in the collision of bodies that state results which least changes the prior conditions. But he did not rightly estimate this minimum change, since he changes either the direction alone or the velocity alone, while the whole change must be determined by the joint effect of both together. He failed to see how this was possible, however, because two such heterogeneous things did not seem to him to be capable of comparison or of simultaneous treatment - he being concerned with modalities rather than with realities in this connection l l ; not to speak of his other errors in his teachings on this problem. Honoratius Fabri, Marcus Marci, John Alph. Borelli, Ignatius Baptista Pardies, Claude Deschales, and other most acute men have given us things that are not to be despised in the doctrine of motion, yet they have not avoided these capital errors.12 So far as I know, Huygens, whose brilliant discoveries have enlightened our age, was also the first to arrive at the pure and transparent truth in this matter, and to free this doctrine from fallacies, by formulating certain rules which were published long ago. Almost the same rules were obtained by Wren, Wallis, and Mariotte, all excellent men in this field, though in differing measure. 13 But there is no unity of opinion about the causes; hence men who are outstanding in these studies do not always accept the same conclusions. It would seem, indeed, that the true foundations of this science have not yet been For references see p. 450
440 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS revealed. Not everyone has accepted the proposition which seems certain to me - that rebound or reflection results only from elastic force, that is, from the resistance offered by an internal motion. Nor has anyone before me explained the concept of forces itself, a matter which has always disturbed the Cartesians and others who could not understand that the sum of motion or of impetuses, which they take for the quantity of forces, can be different after collision than it was before, because they believed that such a change would change the quantity of forces as well. While I was still a youth and followed Democritus, and Gassendi and Descartes, his disciples in this matter, in holding that the nature of body consists in inert mass alone, I brought out a small book entitled A PhYSical Hypothesis, in which I expounded a theory of both abstract and concrete motion. This writing seems to have pleased many distinguished men far more than its mediocrity deserved. There I set up the proposition that assuming this conception of the nature of body to be true, every colliding body must give its conatus to the body receiving the blow or directly opposing it as such. For since it tries to proceed in the moment of impact, and thus to carry the opposing body with it, and (because of the indifference to motion and rest which I then held bodies to have) this conatus must have its full effect upon the opposing body unless it is impeded by a contrary conatus, and indeed, even if it is impeded, since these diverse conatuses must be compounded with each other, it was obvious that no reason could be given why the colliding body should not attain the effect to which it strives, or why the opposing body should not receive the full conatus of the colliding one, so that the motion of the opposing body would be compounded of its own original motion and of that newly received from the external conatus. From this I showed further that if the body is understood in mathematical terms only - magnitude, figure, position, and their change - and conatus is admitted only at the moment of impact itself, no use being made of metaphysical notions such as active power in form, or of passive power and resistance to motion in matter, if therefore it is necessary to determine the outcome of the collision solely by the geometric composition of conatuses, as I have explained; then it must follow that the conatus of even the smallest colliding body must be transmitted to even the largest receiving body, and thus that the largest body at rest will be carried away by a colliding body, no matter how small, without any retardation of its motion, since such a notion of matter involves no resistance to motion but rather indifference to it. Thus it would be no more difficult to move a large body than a small one, and hence there would be action without reaction, and no estimation of power would be possible, since anything could be accomplished by any thing. 14 Since this and many other matters of the same kind are contrary to the order of things, and in conflict with the principles of a true metaphysics, I believed at that time (and indeed, rightly) that in this construction of the system the most wise Author of things had particularly avoided these things which would have followed per se from the bare laws of motion derived from pure geometry. Later, however, after I had examined everything more thoroughly, I saw wherein the systematic explanation of things consists and discovered that my earlier hypothesis about the definition of a body was incomplete. In this very fact, along with other arguments, I found a proof that something more than magnitude and impenetrability must be assumed in body, from which an interpretation of forces may arise. By adding the metaphysical laws of this factor to the laws of extension, there arise those rules of motion which I should call systematic - namely, that all change occurs gradually, that
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 441 every action involves a reaction, that no new force is produced without diminishing the earlier force, so that a body which carries another with it is retarded by the body carried away, and that there is neither more nor less power in the effect than in the cause. Since this law is not derived from the concept of mass, it must follow from something else which is in bodies, namely, from force itself, which always preserves the same quantity even though it is used by different bodies. I concluded, therefore, that besides purely mathematical principles subject to the imagination, there must be admitted certain metaphysical principles perceptible only by the mind and that a certain higher and so to speak, formal principle must be added to that of material mass, since all the truths about corporeal things cannot be derived from logical and geometrical axioms alone, namely, those of great and small, whole and part, figure and situation, but that there must be added those of cause and effect, action and passion, in order to give a reasonable account of the order of things. Whether we call this principle form, entelechy, or force does not matter provided that we remember that it can be explained intelligibly only through the concept of forces. I cannot agree with certain prominent men today, however, who see the inadequacy of the popular concept of matter, but call in God ex machina and remove all force of action from things themselves, as is done in a work on the Mosaic Philosophy, as Fludd called it. For although I should agree that they have shown clearly that there can be no distinct influx of one created substance into another, if the matter is taken in metaphysical rigor, and I also admit freely that all things arise by a continuous creation from God, yet I think that there is no natural truth in things for which we must find the reason in the divine action or will but that God has always put into things themselves some properties by which all their predicates can be explained. Certainly God has created not only bodies but also souls, to which the primitive entelechies correspond. But I shall demonstrate these matters elsewhere by following out their proper reasons more thoroughly. Meanwhile, even though I hold that an active principle which is superior to material concepts and so to speak, vital exists everywhere in bodies, I do not agree with Henry More and other men distinguished for piety and spirit, who make use of some Archeus - I know not what - or hylarchic principle, even to explain phenomena; as if there are some things in nature which cannot be explained mechanically and as if those who undertake a mechanical explanation aim to deny incorporeal beings, with a suspicion of impiety - or as if it were necessary to appoint intelligences for the revolving starry orbs as Aristotle did, or to say that the elements are driven upward and downward by their own form, a teaching that is certainly as naive as it is fruitIess. 1 5 With these things, I say, I do not agree, and this philosophy pleases me no more than the theology of those who believed so firmly that Jupiter thunders and snows that they even branded those who sought after the specific causes of these things with the crime of atheism. In my judgment the best answer, which satisfies piety and science alike, is to acknowledge that all phenomena are indeed to be explained by mechanical efficient causes but that these mechanical laws are themselves to be derived in general from higher reasons and that we thus use a higher efficient cause only to establish the general and remote principles. Once this is established, we need not admit entelechies any more than we admit superfluous faculties or inexplicable sympathies, as long as we are dealing only with the immediate and particular efficient causes of natural things. For the first and most universal efficient cause must not enter into special problems, For references see p. 450
442 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS aside from our viewing the ends to which the Divine Wisdom adhered in ordering things in such a way, lest we neglect any opportunity to sing the most beautiful hymns in his praise. In fact, as I have shown by the remarkable example of the principles of optics, the celebrated Molyneux having warmly approved my interpretation in his Dioptrics 16 , final causes may be introduced with great fruitfulness even into the special problems of physics, not merely to increase our admiration for the most beautiful works of the supreme Author, but also to help us make predictions by means of them which would not be as apparent, except perhaps hypothetically, through the use of efficient causes. Philosophers have in the past perhaps not sufficiently observed this advantage of final causes. It must be maintained in general that all existent facts can be explained in two ways - through a kingdom ofpower or effiCient causes and through a kingdom of wisdom or final causes; that God regulates bodies as machines in an architectural manner according to laws of magnitude or of mathematics but does so for the benefit of souls and that he rules over souls, on the other hand, which are capable of wisdom, as over citizens and members of the same society with himself, in the manner of a prince or indeed of a father, ruling to his own glory according to the laws of goodness or of morality. Thus these two kingdoms everywhere permeate each other, yet their laws are never confused and never disturbed, so that the maximum in the kingdom of power, and the best in the kingdom of wisdom, take place together. But here we have undertaken to set up the general rules for effective forces, which we can then use in explaining special efficient causes. Next I arrived at a true estimation of forces and at exactly the same one, moreover, by widely different ways. One was a priori, based on the most simple consideration of space, time, and action; this I shall explain elsewhere. The other was a posteriori, by calculating force by the effect it produces in expending itself. For by effect I mean here not any effect whatever but that for which force is expended or consumed and which may therefore be called violent. The force which a heavy body exercises in moving along a perfectly horizontal plane is not of this kind, because however far such an effect is prolonged, it always retains the same force, and though we use the same principle in calculating this effect also, which we may call harmless, we now exclude it from consideration. Moreover, I choose that particular form of violent force which is most capable of homogeneity or of division into similar and equal parts, such as is found in the ascent of a body endowed with gravity. For the elevation of a heavy body to 2 or 3 feet is exactly double or triple the elevation of the same weight to 1 foot. Hence the elevation of a body twice as heavy to 3 feet is exactly six times as great as the elevation of a simple body for 1 foot, assuming of course, for the sake of exposition, that heavy bodies have the same weight at different heights, for though this is not true in fact, the error will be imperceptible. Homogeneity is not so easily established in elastic bodies. Therefore, since I wanted to compare bodies with different masses and different velocities, I saw of course that if body A is a simple unit and body B twice as large, but the velocity is equal in the two cases, the force of the former must be a simple unit and that of the latter double, since whatever is assumed to occur once in the former must be taken to occur exactly twice in the latter. For in B the matter is twice the equal and equivalent of A, and nothing more. But if the bodies A and C are equal, but the velocity of A is simple and that of C twice as large, I saw that the properties of A would not be exactly doubled in C, since, though the velocity
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 443 is doubled, the body is not also. I saw that an error had been committed here by those who think that force is itself doubled merely by the doubling of a property. I have already observed and explained long ago that we do not yet have the true art of calculating in spite of the many 'Elements of Universal Mathematics' that have been written and that this art consists in arriving at length at homogeneous things, that is, at an accurate and complete duplication of things as well as their properties. No better or more illuminating example of this method can be given than the one shown in this argument. 1 7 In order to obtain these results, therefore, I considered whether these two bodies, equal in magnitude but different in velocity, could produce any effects that were both equipollent with their causes and homogeneous with each other. In this way things which cannot easily be compared directly can at least be compared accurately through their effects. I assumed that an effect must be equal to its cause if the entire force is expended or consumed in producing it; the length of time taken to produce the effect does not matter here. Assume therefore that bodies A and C are equally heavy and that their force is converted into an ascent, as happens if they are understood to be at the ends of vertical pendulums P A and EC at the moment at which they receive the given velocities, A's velocity being simple and C's twice as large (Figure 30). But the P E demonstrations of Galileo and others have established the fact that if body A, with a velocity of 1, ascends to a maximum height A zH of 1 foot over the horizontal, the body C, with a velocity of 2, will ascend to a height C 2R of 4 feet. Hence it follows that a heavy body whose velocity is double that of another has a force four times that of the other, since the expenditure of all its force can accomplish exactly four times as much. In lifting 1 pound (that is, itself) 4 feet, it lifts 1 pound 1 foot exactly four times. In the same way we can conclude in general that the forces of equal bodies are proportional to the squares of their velocities and that the forces of bodies in general are proportional, compositely, to their simple masses and the squares of their velocities. I have confirmed the same thing by reducing the contrary opinion, which is popularly accepted, especially among the Cartesians, to an absurdity, namely, to perpetual motion. According to this opinion, forces are believed to be proportional to the proFor references see p. 450
444 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS ducts of their masses and velocities. I have also sometimes used this method to give an a posteriori definition of two states unequal in force and at the same time to provide a sure criterion for distinguishing the greater from the smaller. If by substituting either for the other, we can get a perpetual mechanical motion or an effect greater than its cause, then these forces are not in the least equipollent, but that which was substituted for the other was more powerful, since it brought something greater to pass. I assume it to be certain, however, that nature never substitutes for forces something unequal to them but that the whole effect is always equal to the full cause. Thus we, in turn, can safely substitute things which are equal to these forces in our reckoning, freely assuming that this is just as if we actually carried out the substitution itself, without any fear 18 of perpetual mechanical motion. If it were true, as men are commonly persuaded, that a heavy body A of magnitude 2 (for this is now our assumption) and velocity 1, and heavy body C with magnitude 1 and velocity 2, are equipollent to each other we should be able to substitute one for the other with impunity - a thing which is not true. For let us assume that A, with magnitude 2, has acquired a velocity of 1 in its descent A 2A 1 from the height A 2H, which is 1 foot1 9 ; and then let us substitute for it, as it exists on the level of A h the weight C (which they claim is equipollent to it) with magnitude 1 and velocity 2, which ascends to C 2, a height of 4 feet. Thus, merely by the descent of a 2-pound weight A from the height of 1 foot A 2H, we have, by substituting its supposed equipollential, brought about a rise of 1 pound to 4 feet, which is double the former effect. Therefore we have gained this much force or achieved a perpetual mechanical motion, which is absurd. Whether we can actually accomplish this substitution through the laws of motion is irrevelant, for equipollents can safely be substituted for each other in the mind. But I have also thought out various methods by which we can actually carry out, as nearly as we wish, the transfer of the whole force of the body A to the body C, previously at rest, so that C alone is placed in motion while A is brought to rest. The result should be that to the double weight of velocity 1 there would succeed a I-pound weight with velocity 2, if these are equipollent, and as we have shown, an absurdity arises from this. These considerations are not worthless, nor are they merely verbal, for they have important applications in the comparison of machines and motions. For if enough force is received, from water power, animals, or some other cause, to keep a heavy body of 100 pounds in constant motion, so that it can complete a horizontal circle 30 feet in diameter in a fourth of a minute, and someone claims that a weight twice as large put in its place would complete half the circle in the same time, and with less expenditure of power, and claims that this means a profit to you, you may know that you are being deceived and are losing half of the force. But having now put these errors to flight, we will propound the true and genuinely admirable laws of nature a little more distinctly in the second part of this study.20 Part II The fact that the nature of body, and indeed of substance in general, is not well enough understood has resulted, as we have already suggested, in outstanding philosophers of our time locating the notion of body in extension alone and being driven therefore to take refuge in God to explain the union between soul and body and even the communication between bodies themselves. For it must be admitted that it is impossible for mere extension, which involves only geometric concepts, to be capable of action and
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 445 passion. So only one possibility seemed to remain for them - that when man thinks and starts to move his arm, God, as if by an original agreement, moves his arm for him; and conversely, that when there is a motion in the blood and animal spirits, God excites a perception in the soul. But such views are foreign to the true method of philosophizing and should have shown their authors that they were depending on a false principle and had not set up a correct concept of substance, since such consequences followed from it. We show, therefore, that there is in every substance a force of action and that if it is created substance, there is also a force of suffering. We show too that the concept of extension is not complete in itself but requires a relation to something which is extended and whose diffusion or continuous repetition it implies, and therefore that it presupposes also a bodily substance which involves the power to act and resist, and which exists everywhere as corporeal mass, the diffusion of which is contained in extension. Sometime we shall use this view to throw new light on the union of body and soul. 21 But now we must show that there follow from it wonderful and most useful practical theorems which apply to dynamics, the science which deals particularly with the laws of corporeal forces. First of all, we must recognize that force is something absolutely real even in created substances but that space, time, and motion have something akin to a mental construction [de ente rationis) and are not true and real per se but only insofar as they involve the divine attributes of immensity, eternity, and activity or the force of created substances. Hence it follows at once that there is no vacuum in space and time; that motion apart from force (or insofar as it involves only a consideration of the geometric concepts of magnitude, figure, and their variations) is in fact nothing but change of situation; and thus that motion insofar as it is phenomenal consists in a mere relationship. Descartes, too, acknowledged this when he defined it as translation from the position of one body to the position of another. But he forgot his definition when he deduced its consequences and set up rules of motion as if motion were something real and absolute. Therefore, we must hold that if any number of bodies are in motion, we cannot determine from the phenomena which of them are in absolute determinate motion or rest; rest can be attributed to anyone of them you may choose, and yet the same phenomena will be produced. It follows therefore (Descartes did not notice this) that the equivalence of hypotheses is not changed by the impact of bodies upon each other and that such rules of motion must be set up that the relative nature of motion is saved, that is, so that the phenomena resulting from the collision provide no basis for determining where there was rest or determinate absolute motion before the collision. Thus the rule of Descartes, which claims that a body at rest can in no way be driven from its place by a smaller body, hardly squares with the truth. He has other rules of this kind, too, than which nothing is further from the truth. It also folIows from the relative nature of motion that the action of bodies upon each other or their force ofpercussion is the same, prOVided they approach each other at the same velocity. That is to say, if the given phenomena appear the same, whatever may be the true hypothesis or however we may ascribe motion or rest to them, the same result will be produced in the unknown or the resulting phenomena, even with respect to the action of bodies upon each other. This conforms to our experience; we will feel the same pain whether our hand strikes a stone which is at rest, suspended from a thread, if you will, or the stone strikes our hand at rest with the same velocity. Meanwhile we speak as the situation demands, in whatever way provides the more fitting and simpler explanation of the For references see p. 450
446 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS phenomena, just as we make use of the motion of a primum mobile in the study of spheres and must use the Copernican hypothesis in planetary theory. Thus we already cause those violent arguments which have been carried on with so much energy, even by theologians, to disappear completely.22 For even though force is something real and absolute, motion belongs to the class of relative phenomena, and truth is found not so much in phenomena as in their causes. From our concepts of body and of forces there arises also this principle - that whatever happens in substances must be understood to happen spontaneously and in an orderly way. With this is connected the principle that no change occurs through a leap. If this is established, it follows also that there can be no atoms. That the force of this conclusion may be grasped, let us assume that bodies A and B collide, that A 1 comes to A 2 and B 1 to B 2, and that, colliding at A 2B 2, they are deflected from A 2 to A 3 and from Bl to B3 (Figure 31). Assuming then, that there are atoms, that is, bodies of o 81 Fig. 31. maximum hardness and therefore inflexible, change would obviously occur through a leap or in a moment, for the direct motion becomes retrograde at the very moment of collision, unless we assume that the bodies rest instantaneously after the collision, that is, that they lose their force - a thing which, besides being absurd on other grounds, would still contain a change through a leap, namely, an instantaneous change from motion to rest without passing through intermediate degrees. We must thus recognize that if bodies A and B collide and come from A 1 and B 1 to the place of collision AlB 2, they are there gradually compressed like two inflated balls, and approach each other more and more as the pressure is continuously increased; but that the motion is weakened by this very fact and the force of the conatus carried over into the elasticity of the bodies, so that they then come entirely to rest (Figure 32). Then as o r--II I ! IL ___ _ Fig. 32. the elasticity of the bodies restores itself, they rebound from each other in a retrograde motion beginning from rest and increasing continuously, at last regaining the same velocity with which they had approached each other, but in the opposite direction so that they regress and return to the positions A 3 and B 3, which coincide with A 1 and
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 447 B 1 if the bodies are assumed equal and with equal velocities. From this it is now clear that no change occurs through a leap but only by a gradually diminished progression finally reduced to rest, after which regression begins. Just so, one figure is not made from another (an oval from a circle, for instance) except by innumerable intermediate figures, and nothing passes from one place to another or from one time to another except by passing through all the intermediate places or times. Thus rest, and much less a motion in the opposite direction, cannot come from motion except through all the intervening degrees of motion. This is of such great importance in nature that I wonder that it has been so little noticed. There follows also from these matters the view which Descartes attacked in his letters and which some great men are even now unwilling to admit - that all rebound arises from elasticity, and a reason is given for many brilliant experiments which show that a body is bent before it is propelled; Mariotte has shown this most beautifully. Finally, there follows also that most admirable principle of all- that there is no body, however small, which has no elasticity and is not thus permeated by a still subtler fluid; and thus that there are no elementary bodies, nor any most fluid matter, nor any solid globes of some second element, I know not what; but that analysis proceeds to the infinite. It is also in agreement with this law of continuity, which excludes a leap from change, that the case of rest can be considered as a special case of motion, namely, the case of a disappearing or minimal motion, and that the case of equality can be held for a case of disappearing inequality. The consequence is that the laws of motion must be set up in such a way that particular rules are not necessary for equal and resting bodies, but that these arise from the rules for unequal and moving bodies as such. Or if we wish to formulate particular rules for rest and equality, we must be careful not to set up such rules as do not agree with a hypothesis which considers rest as the limit of motion, and equality as the smallest inequality. Otherwise we shall violate the harmony of things, and our rules will not agree with each other. I first published this new device for testing our own rules and those of others in the Nouvelles de la republique des lettres for July, 1687, Article 8, and called it a general principle of order arising from the concept of the infinite and the continuous, adding to this the axiom that as the data are ordered, the unknowns are also ordered [datis ordinatis etiam quaesita sunt ordinata]. I expressed the matter universally in this way - if in a given series one value approaches another value continuously, andat length disappears into it, the results dependent on these values in the unknown series must also necessarily approach each other continuously and at length end in each other. So in geometry, for example, the case of an ellipse continuously approaches that of a parabola as one focus remains fixed and the other is moved farther and farther away, until the ellipse goes over into a parabola when the focus is removed infinitely. Therefore all the rules for the ellipse must of necessity be verified in the parabola (understood as an ellipse whose second focus is at an infinite distance). Hence rays striking a parabola in parallel lines can be conceived as coming from the other focus or as tending toward it. Therefore, since the case in which the body A strikes B in motion can be varied continuously in the same way, so that as the motion of A remains constant, the motion of B can be assumed to be greater or smaller and at length to disappear into rest and then into increasing motion in the contrary direction, I maintain that the result of the collision when both are in motion, whether it be the result in A or in B, must continuously approach the result of the collision in the case when B is at rest, and must finally merge with it. So the case of For references see p. 450
448 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS rest in the given series as well as its results in the unknown series is the limit of the cases of directed motion, or the common limit of linear or continuous motion, and so, as it were, a special case of both. When I examined the Cartesian rules of motion by means of this touchstone, which I carried over from geometry into physics, it turned out that a kind of hiatus or leap was revealed which is contrary to the nature of things, for when the quantities involved were expressed graphically, the motion of B before collision in all its cases being taken for the abscissas, and the motion of B after collision as the unknown, for the ordinates, and a line was drawn through the ordinates according to their values by Descartes's rules, this line proved not to be one continuum but something with amazing gaps, with leaps of an absurd and unintelligible kind. 23 On that occasion I had also observed that the rules of the Reverend Father Malebranche did not meet this test in all respects, and after weighing the matter again with his usual candor, that distinguished man admitted that this led him to change his rules, and he brought out a small book to this effect. Yet it must be admitted that he had not yet sufficiently mastered the use of this new device and has left things which even now do not yet fit together completely.24 From what has been said it also follows, remarkably, that every passion of a body is spontaneous or arises from an internal force. though upon an external occasion. But I mean by this the passion proper to it, which arises from percussion, or which remains the same whatever hypothesis may be chosen or to whatever body we may ascribe rest or motion. For since the percussion is the same regardless of what body the true motion belongs to, it follows that the effect of percussion will be equally distributed between both, and thus that both act equally in the collision, so that half of the effect comes from the action of one, the other half from the action of the other. And since half of the effect or passion is also in one and half in the other, it suffices to derive the passion which is in one from the action which is in it, so that we need no influence of one upon the other 25 ; even though the action of one provides an occasion for the other to produce a change within itself. Certainly when A and B collide, the resistance of the bodies combined with elasticity causes them to be compressed through the percussion, and the compression is equal in both, whatever may be the hypothesis about their original motion. Experiments show this, too, if we let two inflated balls collide, whether both are in motion or one is at rest, and even if the one at rest is suspended from a string so that it can swing back with ease, for if the velocity of approach or relative velocity is always the same, the compression or elastic tension will be the same and will be equal in both. Then the baIls A and B will restore themselves by force of the active elasticity compressed within them, repel each other, and burst apart as if driven by a bow, each being driven back from the other with equal force, and thus receding, not by force of the other, but by its own force. But what is true of inflated balls must be understood of every body insofar as it suffers in percussion. Repercussion and repulsion, namely, arise from elasticity within the body itself, or from the motion of an ethereal fluid matter which permeates it, and so from an internal force existing within it. But, as I have said, I mean the proper motion, belonging to the bodies, separate from the common motion, or motion which can be ascribed to their common center of gravity; hence their proper motion is to be thought of (in a hypothetical way) as if they were carried in a ship which has a motion common to their center of gravity, while they themselves move in such a way that the phenomena can be saved, both with regard to the composite motion common to the ship or to their center and that proper
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 449 to themselves. 26 It is also understood from what has been said that there is never an action ofbodies without reaction and that both are equal to each other and in contrary directions. Also, since only force and the effort arising from it at any moment exist (for as we have explained above, motion never truly exists), and every effort tends in a straight line, it follows that all motion is in straight lines, or compounded of straight lines. Hence it not only follows that whatever moves in a curve strives always to proceed in a straight line tangent to it, but there also arises here, the true notion offirmness, which one would hardly expect. For if we assume that some one of those bodies which we call firm (although nothing is in fact absolutely firm or fluid but has a certain degree of firmness and fluidity, being called firm by us only out of a predominant regard for our senses)if we assume one of these bodies to rotate about its center, its parts will strive to fly off on a tangent; indeed, they really begin to fly off. But because this separation from each other disturbs the motion ofthe body surrounding them, they are thus repelled or crowded into each other again, as if there were a magnetic force in the center which attracts them, or as if there were a centripetal force in the parts themselves. The result is a rotation compounded of the rectilinear effort along the tangent and this centripetal impulse together. So all curvilinear motion arises as a continuous composition of rectilinear efforts with centripetal ones, and at the same time we understand that this crowding together by the surrounding bodies is the cause of all firmness. Otherwise it would be impossible for all curvilinear motion to be composed of mere rectilinear motions. This gives us another unexpected argument against atoms. Nothing more foreign to nature can be conceived, moreover, than to seek firmness in rest, for there is never any true rest in bodies, and nothing but rest can arise from rest. But though A and B may be at rest in relation to each other, if not actually, at least relatively (accurately speaking, however, this never occurs, for no body ever preserves exactly the same distance from another for any length of time, however small), and though whatever once rests will always be at rest unless a new cause is added yet it does not follow that, because B resists a striking body, it will also resist that which separates it from others, so that A would at once follow when the resistance of B is overcome or B is itself propelled. But if true attraction, which is not found in nature, were explained from a primitive firmness, or through rest or something similar, this would certainly follow. Firmness is therefore not to be explained except as made by the crowding together by the surrounding matter. For pressure alone does not adequately explain the problem, as if only the separation of B from A is prevented; it must be understood that they do in fact separate from each other but are again driven together by the surrounding matter, so that this conservation of their union is produced by the composition of two motions. Thus those who conceive of certain slabs or imperceptible layers in bodies, like two slabs of polished marble which fit together exactly, which it is difficult to separate because of the resistance of the surrounding matter, and who explain the firmness of two sensible bodies in this way, may indeed often be speaking the truth; but since they presuppose some firmness in the slabs themselves, they have given no ultimate explanation of firmness. From these considerations it can be understood why I cannot support some of the philosophical opinions of certain great mathematicians on this matter, who admit empty space and seem not to shrink from the theory of attraction but also hold motion to be an absolute thing and claim to prove this from rotation and the centrifugal force arising from it. But since rotation arises only from a composition of rectilinear motions, it follows that For references see p. 450
450 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS if the equipollence of hypotheses is saved in rectilinear motions, however they are a:ssumed, it will also be saved in curvilinear motions. 27 It can also be understood from what has been said that the motion common to a system 0/ bodies does not change their actions among themselves, because the relative velocity with which they approach each other and so the force of collision with which they approach each other are not changed. There follow from this the outstanding experiments which Gassendi reported in his letters about a motion imparted by a moving body which is itself being translated; he did this to answer those who thought they could infer that the earth is at rest from the motion of projectiles. It is certain, however, that if people are being transported in a large ship (assumed to be closed, or at least so constructed that the passengers cannot observe external things), and the ship moves at a great velocity, yet smoothly and without acceleration, they will have no principle by which to discern whether the ship is at rest or in motion (on the basis, that is, of what is happening within the ship), even if they play ball or carry out other motions. This must be noted in support of those who believe in the Coperniean theory, which they do not rightly understand. According to them, bodies projected from the earth into the air are caught up by the air which is turning with the earth, and so follow the motion of the earth, and likewise fall back to earth as if this were at rest. This view is rightly to be judged inadequate, since the most learned men who use the Copernican hypothesis think rather that whatever is on the surface of the earth moves with the earth, and if it is shot by a bow or catapult, it carries with it the impetus impressed on it by the rotation of the earth, together with the impetus impressed by its projection. Hence, since its twofold motion is in part common with the earth, in part peculiar to its projection, it is not surprising that this common motion changes nothing. Meanwhile it must not be concealed that if projectiles can be driven so far, or the ship be conceived as so large and moving with so great a velocity that before the descent the earth or the ship will describe an arc perceptibly different from a straight line, a difference would be perceived, because then the motion of the earth or ship, being circular, would not remain common with the motion impressed on the missile by the ship or by the rotation of the earth, which was rectilinear. In the striving of heavy bodies toward a center, moreover, an external action is added which can produce a diversity of phenomena, no less than if there were a compass in the enclosed ship which pointed to the pole and which would certainly indicate a variation in the ship's direction. But whenever the equipollence of hypotheses is involved, every factor contributing to the phenomena must be included. It is also understood from these matters that the composition of motions or the resolution of one motion into two or any number whatever can safely be used, even though, according to Wallis, one brilliant man has raised plausible doubts. For the matter certainly deserves to be proved and cannot be assumed to be known in itself, as many have done. REFERENCES See No. 45, which had appeared in the samejoumal the preceding year. The criticism here implied of the occasionalists and Malebranche becomes explicit in the New System (No. 47) and even more so in On Nature Itse/f(No. 53). The continuous miracle imputed to the occasionalists was involved in the denial of any proper activity according to law within created beings themselves. 3 Primitive force thus belongs to the realm of metaphysics, not of mechanical science. But it 1 2
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 451 inheres in the individual monads and the laws of their functional dependence, which would be revealed if physical analysis and synthesis could be completed. 4 On the nature of the corpuscular philosophy see p. 349, note 14. It is abused by any theory which regards mechanism as ultimate or applicable to substance itself. The "crude notion of a corporeal substance" advocated by Descartes thus exceeds the limits of a sound corpuscular philosophy by reducing substance to extension. 5 Materia prima is here defined in relation to the quality of resistance and inertia in the phenomenal body. Contrast No. 39, and p. 366, note 4, where it is related to the monad or individual substance. This dual function of materia prima appears throughout the subsequent discussion of matter. Cf. Introduction, Sees. III and VII. Secondary matter, on the other hand, includes the physical property of inertia and resistance in the composite body involved in physical transactions. 6 On Leibniz's concept of mass see p. 103, note 8, and p. 329, note 21. Mass is not equivalent to matter but is a quantitative measure of inertia or materia prima as experienced in materia secunda. But compare the distinction between moles and massa on p. 508, note 12. 7 See p. 301, note 2. Leibniz now defines momentary motion and aggregate motion in the sense in which he used quantity of motion and quantity of force in 1686. Every body has a velocity at a particular moment oftime: v=(ds/dt). The product of the mass by this velocity is here called the quantity of momentary motion, or merely 'motion': mv=(mds/dt), while the quantity of motion over a period of time would be the integral: m s~ ds/dtdt = ms. But, since distance is proportional to v2 , this is Leibniz's own quantity of force as defined in No. 34. The following table presents the mathematical equivalents of Leibniz's concepts: Leibniz Conatus, momentary velocity Impetus, momentarymotion (quantity of motion for Descartes) Quantity of motion for Leibniz Dead force (sollicitation) Living force (i) In a single body (ii) In a compound system (a) Absolute or total force (b) Progress of direction Modem Formula Velocity (vectorial) Momentum v=ds/dt mv m Force of acceleration (cf. potential energy) Vis viva (cf. kinetic energy) S: vdt a=dv/dt ma m S~ vdt=m S~ ds/dt dt=ms or mv 2 I:mv I. e., force of acceleration. Not only the total living force of a material system is conserved, therefore, but also (1) the internal relative force of its members with regard to each other and (2) the total directive progress of the system. The result of (1) is that the center of gravity of the system is not changed by the motions of its component members. The principle of the conservation of direction of 8 9
452 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS progress differs from Descartes's principle of the conservation of quantity of motion in considering the algebraic, not merely the arithmetic, sum of the progressive motion (mv) of its members; thus motion in opposite directions would carry opposite numerical signs (cf. p. 44, note 25). In this connection see H. Poincare, 'Note sur les principes de la mecanique dans Descartes et dans Leibnitz', in Emile Boutroux's edition of La Monadologie, Paris 1881, pp.225-31. 10 That is, to the derivative of the distance, dsfdt, orv. See p. 301, note 3. 11 See No. 42, Part II, on Arts. 40--44. Among Descartes's reifications of modal or conceptual differences which Leibniz had criticized are the distinction between rest and motion, the reduction of direction to the same and contrary motions, and now, the absolute separation of direction and speed. Descartes's distinction had saved his interactionism. Leibniz has just asserted that both force and direction of motion are conserved in a material system, and this implies that mind can effect neither; parallelism is thus inevitable. 12 See p. 302, note 4. Johannes Marcus Marci von Kronland, De proportione motus (1639); Ignace Gaston Pardies, Discours du mouvement locale (1670). 13 On Huygens see p. 301, note 2, and p. 302, note 8. It was the laws of motion of Huygens and Wren, formulated in 1668 in response to an invitation of the Royal Society, which occasioned Leibniz's own first efforts to develop laws of motion in 1669 (see Kabitz, Phil. des jungen Leibniz, pp. 65-68, 135-48). Mariotte had further developed some of Wren's work. 14 See p. 329, note 23. 15 Henry More's Opera omnia reached Leibniz soon after publication in 1679, but his influence is probably negligible beyond a few figures of speech which Leibniz appropriated from him. His argument that force and motion are due to a hylarchic principle which imparts an 'essential spissitude' to the bodies in which it inheres is developed in the Metaphysical Enchiridion, chap. xiii, scholium. Cf. p. 204, note 20; p. 328, note 14; and p. 508, note 2. 16 William Molyneux's Dioptrica nova appeared in two volumes (1692 and 1709). His reference was to the 'Unicum opticae, catoptricae, et dioptricae principium', which Leibniz published in the Acta eruditorum in 1682 (see No. 50). 17 Though the following argument has already been given three times (Nos. 34, 35, and 42), it is here developed with an emphasis upon methodology, which is a special case of the general method of analysis and synthesis. In No. 34 Leibniz attributed his method of analysis and the substitution of equivalents to Huygens' analysis of the compound pendulum (see p. 302, note 8). 18 Reading metu (Dut.) for motu (G.). 19 Reading unus for minus (G.). 20 Dut. adds "in the month of May". The second part was not published, however. The dynamic interpretation which Leibniz gives of his principles in this second part should be compared with their a priori logical exposition in the 'First Truths' earlier (No. 30). 21 The New System was published this same year (No. 47). 22 See the last letter in No. 43, and p. 420, note 12, for Leibniz's attempt to have his reconciliation of the two views accepted at Rome. 23 Leibniz's graph is on p. 412, note 34. 24 See No. 37. Malebranche undertook to correct his laws of motion as presented in the 'Recherche' in his Traite des lois de la communication des mouvements (1692). 25 The passive force involved here corresponds to relative or proper force as defined in Part I, not to directive or total force. The instance of the ship (the prototype of popular expositions of relativity?) makes this clearer. 26 To 'save phenomena' means not merely to avoid theories which contradict them but to provide analyses (here causal) that explain them. 27 This criticism is directed at both Newton and Huygens, who had held that circular motion is an argument for absolute motion (see No. 43, II, III).
47 A NEW SYSTEM OF THE NATURE AND THE COMMUNICATION OF SUBSTANCES, AS WELL AS THE UNION BETWEEN THE SOUL AND THE BODY Journal des savants, June 27, 1695 Leibniz's first published account of his metaphysical 'system'1 appeared in the wellestablished Paris journal to which he had contributed scientific articles since his Paris days. Since its contents are directly related to the writings and controversies on dynamics in which he had been involved, its emphasis is not theological, like that of the Discourse of 1686 (No. 35), but falls upon the problem of the individuality of created substance; the mind-body relation is treated by analogy to his analysis of the relationships of force in a compound material system. The essay brought Leibniz's thinking to a focus, since it stimulated the first public discussion of his metaphysics as such, Foucher, Beauval, Bayle, and Lami soon publishing criticisms of it, to which Leibniz wrote careful replies. The 'second explanation' made in reply to these critics is added as a supplement. The text is that of the published article, which Schmalenbach reproduces; G. gives a later revision. The paragraph numbers were added by Erdmann. [Sch., I, 119-31 (G., IV, 477-87)] 1. It is some years ago that I conceived this system and began communicating with learned men about it, especially with one of the greatest theologians and philosophers of our time, who had been told about certain of my opinions by a person of the highest nobility and had found them very paradoxical. 2 After receiving my explanations, however, he retracted in the most generous and edifying way possible, and after approving a part of my propositions, he withheld his censure of the others upon which he still did not agree with me. Since that time I have continued my meditations as occasions offered, so as to give to the public only well-examined opinions, and I have tried also to answer the criticisms raised against my essays on dynamics which have some connection with this. Since some eminent persons have asked to see my opinions more clearly developed, I have ventured upon these meditations, though they are not at all popular or suited to the enjoyment of all sorts of minds. I have decided upon this chiefly in order to profit by the criticisms of those who are informed on such matters, since it would be too burdensome to seek out and call to my aid individually those who would be disposed to give me instruction. This I shall always be pleased to receive, provided that the love of truth be shown in it rather than a passionate attachment for preconceived opinions. 2. Although I am one of those who have done much work in mathematics, I have constantly meditated on philosophy from my youth up, for it has always seemed to me For references see p. 460
454 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS that here, too, there is a way to establish something sound through clear demonstrations. I had penetrated deeply into the land of the Scholastics, when mathematics and modem authors made me withdraw from it while I was still young. Their beautiful ways of explaining nature mechanically charmed me, and with good reason I despised the method of those who use only forms or faculties of which nothing is understood. But later, after trying to explore the principles of mechanics itself in order to account for the laws of nature which we learn from experience, I perceived that the sole consideration of extended mass was not enough but that it was necessary, in addition, to use the concept of force, which is fully intelligible, although it falls within the sphere of metaphysics. It seemed to me also that though the opinion of those who transform or degrade beasts into pure machines seems possible, it goes beyond appearances and is even contrary to the order of things. 3. At first, after freeing myself from bondage to Aristotle, I accepted the void and the atoms, for it is these that best satisfy the imagination. But in turning back to them after much thought, I perceived that it is impossible to find the principles of a true unity in matter alone or in what is merely passive, since everything in it is but a collection or aggregation of parts to infinity. Now a: multitude can derive its reality only from the true unities, which have some other origin and are entirely different from points, for it is certain that the continuum cannot be compounded of points. To find these real unities, therefore, I was forced to have recourse to a formal atom, since a material being cannot be at the same time material and perfectly indivisible, or endowed with true unity. 3 It was thus necessary to restore and as it were, to rehabilitate the substantial forms which are in such disrepute today, but in a way which makes them intelligible and separates their proper use from their previous abuse. I found then that their nature consists of force and that there follows from this something analogous to sense and appetite, so that we must think of them in terms similar to the concept which we have of souls. But just as the soul ought not to be used to explain the details of the economy of the animal's body, so I concluded that one ought not to use these forms to explain the particular problems of nature, though they are necessary to establish its true general principles. Aristotle calls them first entelechies. I call them, more intelligibly perhaps, primitive forces, which contain not only the actuality or the completion of possibility but an original activity as well. 4 4. I saw that these forms and these souls must be indivisible, just as is our mind; in fact, I remembered that this was the opinion of St. Thomas with regard to the souls of beasts.5 But this truth revived the great difficulties about the origin and duration of souls and forms. For since every substance 6 which has a true unity can begin and end only by a miracle, it follows that souls can begin only by creation and end only by annihilation. So I was obliged to recognize that except for the souls which God still expressly wills to create, the forms which constitute substances have been created with the world and that they will subsist always. Moreover, certain Scholastics like Albert the Great and John Bacon had glimpsed a part of the truth about the origin of these forms. Nor should this opinion appear extraordinary, since we are merely ascribing to the forms the duration which the Gassendists grant to their atoms. 5. I concluded, nevertheless, that we must not mix up indifferently, or confuse, minds or rational souls with other forms or souls, for they are of a superior order and have incomparably more perfection than have the forms which are sunk in matter, which I believe are found everywhere. For in comparison with these, minds or rational
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 455 souls are as little gods made in the image of God and having in them some ray of the light of the Divinity. This is why God governs minds as a prince governs his subjects or indeed as a father cares for his children, while he deals with other substances, instead, as an engineer handles his machines. Minds thus have special laws which place them beyond the revolutions of matter 7, and one can say that all the rest is made only for them, these revolutions themselves being adapted to the happiness of the good and the punishment of the evil. 6. To return to ordinary forms, however, or to material souls 8, this duration which we must acribe to them instead of that which was attributed to the atoms could lead us to doubt whether they do not pass from body to body. This would be metempsychosis, somewhat like the transmission of motion and of species in which some philosophers have believed. 9 But such a fancy is far from the nature of things. There is no such transfer; at this point the transformations of Swammerdam, Malpighi, and Leeuwenhoek, the best observers of our times, have come to my aid and led me to admit the more readily that animals and all other organized substances do not at all begin when we believe them to and that their apparent generation is merely a development and a form of augmentation. I have noticed, too, that the author of the Recherche de ta verite and Mr. Regis, Mr. Hartsoeker, and other able men have held opinions not far removed from this.tO 7. The greatest question still remained, however: What becomes of the souls or forms at the death of the animal or at the destruction of the individual unit of organized substance? This question is the more difficult, inasmuch as it hardly seems reasonable that souls should remain, useless in a chaos of confused matter. This led me at length to conclude that there is only one reasonable view to take - that of the conservation not only of the soul but also of the animal itself and its organic machine, even though the destruction of its grosser parts may have reduced this machine to a size so small that it escapes our senses just as it did before birth. Moreover, no one can mark exactly the true time of death, which may for a long time be taken to be a simple suspension of observable actions and in the last analysis is never anything but this in the simple animals. Witness the resuscitation of flies which have been drowned and then buried under powdered chalk, and a number of similar examples which suffice to show that there would be other resuscitations, in cases much further gone, if men were in a position to restore the mechanism. It seems that the great Democritus spoke of something approaching this, extreme atomist though he was, though Pliny laughed at his opinion. tt It is natural, then, that animals which have always been living and organized (as people of great penetration are beginning to recognize) will also always remain so. And since an animal has thus no first birth or entirely new generation, it follows that there will be no final extinction or complete death, in a strict metaphysical sense, and that as a result, there is no transmigration of souls but only a transformation of the same animal, as its organs are differently folded and are more or less developed. 8. Rational souls, however, follow much more elevated laws and are exempt from everything which might make them lose the quality of citizens of the society of minds, since God has provided so well that no changes in matter can make them lose the moral qualities of their personality. And one can say that everything tends to the perfection not merely of the universe in general but also of these created beings in particular, which are destined for so high a degree of happiness that the universe itself For references see p. 460
456 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS is concerned in it by virtue of the divine goodness which is communicated to each being to the extent which the sovereign wisdom can permit. 9. As for the ordinary course 12 of animals and other corporeal substances, which have hitherto been thought to be entirely extinguished, and whose changes depend on mechanical rather than on moral laws, I have noted with pleasure that the ancient author of the book De diaeta, which is attributed to Hippocrates, caught sight of a part of the truth when he expressly said that animals neither are born nor die and that the things which are thought to have a beginning and to perish actually merely appear and disappear. According to Aristotle, this is also the opinion of Parmenides and Melissus, for these ancient thinkers were sounder than we think. 13 10. I am as ready as any man to do justice to the modems. Yet I find that they have carried reform too far, among other things in confusing natural with artificial matters, because they have not held high enough ideas of the majesty of nature. They think that the difference between natural machines and ours is merely the difference between great and small. This led a very able man, the author of the Conversations on the Plurality of Worlds, to say recently that when we examine nature closely we find it less admirable than has been thought, it being merely like a craftsman's workshop - a conception which I consider neither just enough nor worthy enough of it. 14 It is only our system which shows us, at length, the real and immense distance which lies between the least productions and mechanisms of the Divine Wisdom and the greatest masterpieces of the craft of a finite mind. This difference consists not merely in degree but also in kind. We must recognize that the machines of nature have a truly infinite number of organs, and are so well equipped and so completely proof against all accidents, that it is impossible to destroy them. A natural machine remains a machine even in its smallest parts, and what is more, it always remains the same machine that it has been, being merely transformed through the different foldings which it undergoes, and being now extended, now compressed and, as it were, concentrated, when it is thought to have perished. 11. Furthermore, by means of the soul or form there is a true unity corresponding to what is called 'I' in us. Such a unity could not occur in artificial machines or in a simple mass of matter, however organized it may be. For such a mass can be compared only to an army or a herd, or to a pond full of fish, or a watch made of springs and wheels. If there were no true substantial unities, however, there would be nothing substantial or real in the collection. It was this that forced Cordemoi to abandon Descartes and to support the Democritean theory of atoms in order to find a true unity in them. 15 But material atoms are contrary to reason, besides being still further composed of parts, since an invincible attachment of one part to another (if we could reasonably conceive or assume this) would not at all destroy the diversity of these parts. It is only atoms of substance, that is to say, real unities that are absolutely destitute of parts, which are the sources of action and the absolute first principles out of which things are compounded, and as it were, the ultimate elements in the analysis of substance. One could call them metaphysical points. They have something vital, and a kind of perception, and mathematical points are the points of view from which they express the universe. But when a corporeal substance is contracted, all its organs together make only one physical point with respect to us. Physical points are thus indivisible in appearance only, while mathematical points are exact but are nothing but modalities. It is only metaphysical points, or points of substance, constituted by forms or souls,
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 457 which are exact and real, and without them there would be nothing real, since there could be no multitude without true unities. 16 12. Having established these things, I thought I had reached port. But when I began to think about the union of the soul with the body, it was like casting me back into the open sea, for I found no way to explain how the body causes anything to take place in the soul, or vice versa, or how one substance can communicate with another created substance. So far as we can know from his writings, Descartes gave up the struggle over this problem. 17 But seeing that the common opinion is inconceivable, his disciples concluded that we sense the qualities of bodies because God causes thoughts to arise in our soul on the occasion of material movements and that when our soul in its turn wishes to move the body, God moves the body for it. And since the communication of motion also seemed inconceivable to them, they believed that God imparts motion to a body on the occasion of the motion of another body. This they call the System of Occasional Causes; it has had great vogue as a result of the beautiful reflections of the author ofthe Recherche de la verite. 13. It must be admitted that this has definitely penetrated the difficulty in showing us what cannot take place. But it does not seem to have removed the difficulty by showing us what actually does happen. It is quite true that speaking with metaphysical rigor, there is no real influence of one created substance upon another and that all things, with all their reality, are continually produced by the power of God. But problems are not solved merely by making use of a general cause and calling in what is called the deus ex mach ina. To do this without offering any other explanation drawn from the order of secondary causes is, properly speaking, to have recourse to miracle. In philosophy we must try to give a reason which will show how things are brought about by the Divine Wisdom in conformity with the particular concept of the subject in question. 14. Being constrained, then, to admit that it is impossible for the soul or any other true substance to receive something from without, except by the divine omnipotence, I was led insensibly to an opinion which surprised me, but which seems inevitable, and which has in fact very great advantages and very significant beauties. This is that we must say that God has originally created the soul, and every other real unity, in such a way that everything in it must arise from its own nature by a perfect spontaneity with regard to itself, yet by a perfect conformity to things without. And thus, since our internal sensations, that is, those which are in the soul itself and not in the brain or in the subtle parts of the body, are merely phenomena which follow upon external events or better, are really appearances or like well-ordered dreams, it follows that these perceptions internal to the soul itself come to it through its own original constitution, that is to say, through its representative nature, which is capable of expressing entities outside of itself in agreement with its organs - this nature having been given it from its creation and constituting its individual character. It is this that makes each substance represent the entire universe accurately in its own way and according to a definite point of view. And the perceptions or expressions of external things reach the soul at the proper time by virtue of its own laws, as in a world apart, and as if there existed nothing but God and itself (to make use of the expression of a person of exalted mind and renowned piety). So there will be a perfect accord between all these substances which produces the same effect that would be noticed if they all communicated with each other by a transmission of species or of qualities, as the common run of philoFor references see p. 460
458 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS sophers imagine. Furthermore, the organized mass in which the point of view of the soul is found is itself expressed more immediately by the soul and is in tum ready to act by itself following the laws of the corporeal mechanism, at the moment at which the soul wills but without either disturbing the laws of the other, the animal spirits and the blood taking on, at exactly the right moment, the motions required to correspond to the passions and the perceptions of the soul. It is this mutual agreement, regulated in advance in every substance of the universe, which produces what we call their communication and which alone constitutes the union of soul and body. This makes it clear how the soul has its seat in the body by an immediate presence which could not be closer, since the soul is in it as a unity is in the resultant of unities which is a multitude. 15. This hypothesis is entirely possible. For why should God be unable to give to substance in the beginning a nature or internal force which enables it to produce in regular order - as in an automaton that is spiritual or formal but free in the case of that substance which has a share of reason - everything which is to happen to it, that is, all the appearances or expressions which it is to have, and this without the help of any created being? Especially since the nature of substance necessarily demands and essentially involves progress or change and would have no force of action without it. And since it is the nature of the soul to represent the universe in a very exact way, though with relative degrees of distinctness, the sequence of representations which the soul produces will correspond naturally to the sequence of changes in the universe itself. So the body, in tum, has also been adapted to the soul to fit those situations in which the soul is thought of as acting externally. This is all the more reasonable inasmuch as bodies are made solely for the spirits themselves, who are capable of entering into a society with God and of extolling his glory. Thus as soon as one sees the possibility of this hypothesis of agreement, one sees also that it is the most reasonable one and that it gives a wonderful idea of the harmony of the universe and of the perfection of the works of God. 16. There is also in it the great advantage that instead of saying that we are free only in appearance and in a manner adequate for practical purposes, as several intelligent persons have thought, we must rather say that we are determined only in appearance and that in metaphysical strictness we are in a state of perfect independence as concerns the influence of all the other created beings. This throws a wonderful light on the immortality of our soul as well and on the always uniform conservation of our individual being, which is perfectly regulated by its own nature and fully sheltered from all accidents from without, whatever appearance there may be to the contrary. Never has a system so clearly exhibited our elevation. Since each mind is as a world apart and sufficient unto itself, independent of every other created being, enveloping the infinite and expressing the universe, it is as durable, as subsistent, as absolute as the universe of creatures itself. We must therefore conclude that it must always play such a part as is most fitting to contribute to the perfection of the society of all minds, which is their moral union in the City of God. A new proof of the existence of God can also be found here, one of surprising clarity. For the perfect agreement of so many substances which have no communication whatever with each other can come only from a common source. 17. In addition to all these advantages which recommend this hypothesis, we can say that it is something more than a hypothesis, since it seems hardly possible to explain things in any other intelligible way, and since a number of serious difficulties
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 459 which have heretofore troubled thinkers seem to disappear of themselves when we rightly understand it. Ordinary ways of speaking can still be preserved. For one may say that when the particular disposition of one substance provides a reason for a change occurring in an intelligible manner, in such a way that we can conclude that the other substances have been adapted to it on this point from the beginning according to the order of the divine decree, then that substance should be thought of as acting upon the others in this sense. Further, the action of one substance upon another is not an emission or a transplanting of some entity, as is commonly supposed; and it can be understood reasonably only in the way just shown. It is true that we can easily conceive of both the emission and the reception of parts in matter and can in this way reasonably explain all the phenomena of physics mechanically. But since material mass is not a substance, it is clear that the action of substance itself can be only what I have just described. 18. However metaphysical these considerations may seem, they are also of remarkable service to physics in establishing the laws of motion, as my Dynamics will be able to show. For it can be said that in the collision of bodies each suffers only from its own elasticity, caused by the motion which is already within it. As for absolute motion, nothing can determine it mathematically, since everything ends in relations. The results is always a perfect equivalence in hypotheses, as in astronomy, so that no matter how many bodies one takes, one may arbitrarily assign rest or some degree of velocity to anyone of them we wish, without possibly being refuted by the phenomena of straight, circular, or composite motion. 1s However, it is reasonable to attribute true motions to bodies if we follow the assumption which explains the phenomena in the most intelligible way, for to do this is in confrormity with the concept of activity which we have just established. II. "SECOND EXPLANATION OF THE NEW SYSTEM"19 (Postscript of a Letter to Basnage de Beauval, January 3/13, 1696) [G., IV, 498-500] I see clearly from your reflections that my thoughts, which a friend has had inserted in the Paris journal, are in need of clarification. You say that you do not understand how I can prove what I have suggested about the communication or harmony of two substances as different as the soul and the body. It is true that I thought I provided a way to do so. And this is how I propose to satisfy you. Imagine two clocks or watches which are in perfect agreement. 20 Now this can happen in three ways. Theftrst is that ofa natural influence. This is the way with which Mr. Huygens experimented, with results that greatly surprised him. He suspended two pendulums from the same piece of wood. The continued strokes of the pendulums transmitted similar vibrations to the particles of wood, but these vibrations could not continue in their own frequency without interfering with each other, at least when the two pendulums did not beat together. The result, by a kind of miracle, was that even when their strokes had been intentionally disturbed, they came to beat together again, somewhat like two strings tuned to each other. The second way of making two clocks, even poor ones, agree always is to assign a skilled craftsman to them who adjusts them For references see p. 460
460 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS and constantly sets them in agreement. The third way is to construct these two timepieces at the beginning with such skill and accuracy that one can be assured of their subsequent agreement. Now put the soul and the body in the place of these two timepieces. Then their agreement or sympathy will also come about in one of these three ways. The way of influence is that of the common philosophy. But since it is impossible to conceive of material particles or of species or immaterial qualities which can pass from one of these substances into the other, this view must be rejected. The way of assistance is that of the system of occasional causes. But I hold that this makes a deus ex machina intervene in a natural and ordinary matter where reason requires that God should help only in the way in which he concurs in all other natural things. Thus there remains only my hypothesis, that is, the way ofpreestablished harmony 21, according to which God has made each of the two substances from the beginning in such a way that though each follows only its own laws which it has received with its being, each agrees throughout with the other, entirely as if they were mutually influenced or as if God were always putting forth his hand, beyond his general concurrence. I do not think that there is anything more than this that I need to prove - unless someone should demand that I prove that God is skilful enough to make use of this foresighted artifice, of which we see samples even among men, to the extent that they are able men. And assuming that God can do it, it is clear that this way is the most beautiful and the most worthy of him. You had suspected that my explanation would be opposed to the different idea we have of the mind and of the body. But now you clearly see that no one could establish their independence more effectively. For as long as one was obliged to explain their communication by means of a miracle, one always gave opportunity for some people to fear that the distinction between body and soul is not as real as is thought, since we were forced to go to such lengths to maintain it. Now all these scruples will cease. My Essays on Dynamics are related to this, for in them it was necessary to explore the concept of corporeal substance, which I found in the force of action and resistance rather than in extension, the latter being merely a repetition or diffusion of something prior to it, namely, this force. These thoughts, which some people found paradoxical, have led to an exchange of letters with several famous people. I could publish a commercium epistolicum from them, which would also contain my correspondence with Mr. Arnauld, of which I spoke in my preceding letter. It would contain an interesting mixture of philosophic and mathematical ideas, which would perhaps sometimes have the grace of novelty. You yourself can judge, Sir, whether the explanations which I have given are suitable for sounding out the opinions of intelligent people if published in your journal - though without my name, as I was also unnamed in the Paris journal. REFERENCES Leibniz soon found it necessary to deny that he had a system (see Nos. 49, I, and 54). Leibniz notes, "Mr. Arnauld" (cf. Nos. 35 and 36). 3 In his final revision Leibniz altered the last two sentences as follows: "Now a multitude can derive its reality only from true unities which have some other origin and are entirely different from mathematical points, these being merely the extremities of what is extended, and modifications of which it is certain the continuum cannot be composed. To find the real unities, therefore, I was forced to have recourse to a real and animated point, so to speak, or an atom of substance which mus t include a certain active form to make a complete being." 1 2
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 461 See No. 45 and p. 434, note 2. Leibniz is in error in ascribing to Thomas Aquinas the doctrine of the indivisibility and immortality of all souls. In the Summa theologica, Part II, chap. 82, Aquinas argues against the immortality of beasts, holding that only perfect souls are indivisible. 6 Later revision: "every simple substance". 7 Later addition: "through the very order which God has put in them". 8 Later revision: "brute souls". 9 That is, abstracted qualities whether regarded as immaterial or material, like the Scholastic 'species volantes', which are passed from one substance to another (see p. 329, note 30). 10 Pierre Sylvain Regis, Cours entier de philosophie ou systeme general d' apres les principes de Descartes (1691). Nicolas Hartsoeker, Dutch microscopist, published an Essai de dioptrique in 1694 in which he developed an atomic theory. Regis criticized Leibniz's attacks on Descartes in 1697 (G., IV, 333-36), and Hartsoeker later corresponded with Leibniz on problems in the philosophy of nature (G., III, 488-90). 11 In the 'Doctrine of a Single Universal Spirit' (1702) (No. 58), Leibniz attributes this account of Democritus' theory of resuscitation to Plotinus. Pliny had ridiculed the concept as "put forth by Democritus, who did not himself come to life again". 12 Reading cours with Erd. and Sch., instead of corps (G .). 13 De caelo iii. 1. 298b. 14 Fontenelle's Entretiens sur la pluralite des mondes was published in 1686. 15 See p. 271, note 12. Cordemoi had supplemented Descartes with an atomic and an occasionalistic theory. 16 Metaphysical points are not spatial in Leibniz's mature thought, though he has not yet asserted, in 1695, that there is no absolute motion, but only that it cannot be known in a closed physical system. The spatial correlates to the three kinds of points are perceptual space to physical points, conceptual space to mathematical points, and the complex harmony of representational perspectives or points of view to metaphysical points. 17 Leibniz probably alludes here to Descartes's letter to Elizabeth, June 18, 1643 (Correspondence, ed. Adam and Tannery, III, 690-91). 18 Cf. No. 42, Part II, Art. 25, and No. 43. The allusion to relativism in astronomy is to the interpretations of celestial motions by Copernicus, Ptolemy, and Brahe, which Leibniz was interested in harmonizing through a phenomenalistic interpretation (cf. p. 420, note 12). 19 In 1697 Leibniz wrote brief replies to three critics of his New System - Foucher, Beauval, and Hartsoeker. Since the most thorough criticism was that of Bayle, and Leibniz's answer is most extended (No. 52), we print only one ofthe 'three explanations' made earlier - the 'second explanation' sent to Beauval, editor of the Histoire des ouvrages des savants. 20 The figure of the two clocks is not original with Leibniz but was in general use among the occasionalists. Its first use is generally attributed to Geulincx, Ethica, I, ii, 2, n. 19, though Leibniz need not have secured it from that source. The figure is not a fortunate one for Leibniz, since it throws no light upon the representative and functional nature of the relations between monads and also neglects the distinction between the passive and active roles of the monads in the divine harmony. 21 It is noteworthy that the adjective 'pre-established', so popular in the descriptions of Leibniz's system, does not appear until late in his thought, and then with particular reference to the mind-body problem. Any deistic implications are inconsistent with the immediacy of God in the perceptions and appetites ofthe monads. Leibniz was, however, already charged with deism by his contemporaries (see the Philosophical Transactions of the Royal Society, 1714-1716, p. 4 5 224).
48 LETTER TO GABRIEL WAGNER ON THE VALUE OF LOGIC 1696 Gabriel Wagner was a man of extended learning but with an insatiable appetite for controversy and conflict. Under the name of Realis de Vienna he published several works, including a criticism of Christian Thomasius which brought him into correspondence with Leibniz. Forced to leave Vienna, he settled in Hamburg in 1696 and there began a German weekly with the title Vernunftiibungen, which he devoted to bitter attacks upon contemporary Scholasticism. An attack on logic in that paper gave occasion for the following letter, written in German. [G., VII, 514-27] Honorable Sir, The fact that you had expressed your inclination and good opinion toward me publicly - and indeed, far beyond my deserts - even before you made my acquaintance, made it all the more pleasant to receive your recent letter, together with your scholarly and thoughtful publication, the Vernunftiibungen. I am under obligation to you to offer my thanks and my services, but especially to reveal to you sincerely my well-meant but tentative opinions on several matters, with the hope that you will accept them in good spirit and perhaps, after ripe consideration, find something useful in them. I note, therefore, that your Vernunftiibungen has given certain people an opportunity to grow indignant and to interpret it as a declaration of war against a kind of farcical learning which is now carried on in the higher schools and in others as well and which is universally praised and sought after. They hold that you oppose it in part, and especially insofar as it is removed from the knowledge of nature, and they view this as a deliberate effort to bring into derision and abuse by other people the whole class of those who deal in such learning. Now I am assured that this is not entirely your intention, and I cannot approve this extreme interpretation of it, especially since you have defended yourself against it and since I perceive from your Latin writings that you are yourself far from devoid of such learning, the style which you use in Latin (as well as in German) having an unusual amount of ornateness and expressiveness in the tradition of the ancients - which proves that you are not entirely lacking in, or opposed to, .an acquaintance with them. But since there are several things which create the opposite impression, I am inclined to think that you would do well, Sir, to clear up a few matters, either in further issues of the Vernun/tiibungen or in some other public way, and thus rescue the honor of these scholars and remove a burden from yourself by giving assurance that you had no intention of finding fault either with the sciences or types of learning or with those who pursue and understand them and least of all, that you wanted to scold or deride anyone. For my part, I confess that in my early youth I was inclined to reject much of what had been introduced into the learned world. But with growing years and deeper
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 463 insight I discovered the value of many things which I had before considered trivial, and I learned not to condemn anything too easily, a rule which I consider better and safer than that taught by certain Stoic lovers of wisdom and after them by Horace not to wonder at anything. I have made this clear to the so-called Cartesians in France and elsewhere and have warned them that by attacking the schools, they are helping neither themselves nor scholarship but are merely making learned men more bitter toward new ideas, however good. To some extent this actually happened, as the not entirely undeserved criticism by the learned Huet, Bishop of Avranches, proves. 1 And though Father Malebranche is otherwise my good friend, I have never been able to approve of his eforts to rule out, first, the critical study of Greek and Roman antiquities, then the reading of the rabbinical and Arabic literature, then the industry of the astronomers, and then something else, for after all, these things all have their value, and it is good that there are people working at them, who must therefore be encouraged through praise further to pursue their great work, which they often carry on without reward, instead of being frightened away from it through contempt. I have no doubt that you are for the most part in agreement with this, since you have expressed yourself ably on oriental languages, astronomy, and other fields. However, since you have in the main tended, in understand you, to reject the art of reasoning or logic entirely and to ban it and its close relative, the universal science or metaphysics, and since you have explicitly included me (upon whom you bestow too much praise) among those who despise logic, I consider it all the more important to explain my position to you. I have no doubt that you have written as you have because of a sincere zeal for the true and useful sciences, so that men need not be delayed and led to lose valuable time through fruitless grubbing; and I do not doubt that you have honored me by calling upon me as witness to such a worthy aim. But as my opinion on the matter is in a certain measure different from yours, I should like to see if we can understand and compare each other's positions. I believe that you are right in your intentions but that your expressions say more than you mean. By logic or the art of reasoning I understand the art of using the understanding not only to judge proposed truth but also to discover hidden truth. If such an art is possible, in other words, if there are marked advantages to be found in such processes, it follows that it ought by all means to be sought and val~ed highly, indeed, to be considered as the key to all the arts and sciences. You seem to admit that there are excellent advantages to be gained by thought and investigation; if you are merely unwilling to admit that this procedure should be named logic, our controversy concerns only a word. But since I do not think that this is your purpose, I can take your position to mean only that you are rejecting, not the true logic, but what we have heretofore honored by that name. If this is your opinion, I must indeed confess that all our logics until now are but a shadow of what I should wish and what I see from afar; but I must also confess, to stick to the truth and give everyone his due, that I also find much that is good and useful in the logic of the past. Gratitude as well compels me to say this, for I think I can truthfully say that even the logic taught me in school has been most fruitful for me. Before I entered a class in which it was taught, I was steeped in the historians and poets, for I had begun to read history as soon as I could read at all, and I found great pleasure and value in verse. But as soon as I began to learn logic, I was greatly stirred by the classification and order which I perceived in its principles. I came at once to notice that there must be something great in it, as far as a lad of thirteen years could notice such a For references see p. 471
464 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS thing. My greatest pleasure lay in the categories, which seemed to me to be a standard roll of everything in the world, and I examined many logics to see where the best and most exhaustive lists could be found. I often asked myself and my companions into which category and subdivision of it this or that concept might belong, although I was not at all pleased to find that so many things were entirely excluded, and I found, too, that some of the categories, especially the last two or perhaps four, dropped away completely for me because they were included in the earlier ones or because I could find no actual use for them. I soon made the amusing discovery of a method of guessing or of recalling to mind, by means of the categories, something forgotten when one has a picture of it but cannot get at it in his brain. One needs only to ask one's self or others about certain categories and their subdivisions (of which I had compiled an extensive table out of various logics) and examine the answers, and one can readily exclude all irrelevant matters and narrow the problem down until the missing thing can be discovered. Nebuchadnezzar could perhaps have reconstructed his forgotten dream in this way. In such tabulations of knowledge I attained practice in division and subdivision as a basis of order and a bond of thoughts. Here the Ramists and Semi-Ramists were heavily drawn upon. 2 Whenever I found a list of things belonging together, and especially whenever I found a genus or universal under which a number of particular species was subsumed, as for example, the number of the emotions or of the virtues and vices, I had to put them into a table and to see if the species fell into a successive order. I always found that the enumeration was incomplete and that more species could be added. I took great pleasure in such matters and wrote out all kinds of stuff, but then forgot it and let it be lost. Many years later, however, I found some of it and discovered that it did not entirely displease me. Later on I found the value of these exercises when I came to work out certain problems. I recall that once, when I had set up a construction of some kind, a learned friend asked me how I could think of everything that I had put in, even when its applicability was not at once apparent. I replied - what was true - that I did it by division and subdivision, using these as a net or snare to capture the elusive game. I found too that such division served to make for accurate descriptions of things, not to mention other advantages. Fortunately I was well advanced in the so-called humanities before this occurred to me, or I could hardly have prevailed upon myself to return again from the things to the words. Many other ideas 'occurred to me, some of which I took to my teachers; among others whether, since simple terms or concepts are ordered through the known categories, one could not set up categories and ordered series for complex terms or truths as well. For at that time I did not know that mathematical demonstrations were what I was seeking. I also observed that the topics or loci of the methods of explanation and demonstration were of great use in recalling for us, at the proper time, things already in our head but not in our thoughts, so that we might not merely prate about things but investigate them better. I observed that such loci or principles are to be used as sources, not merely for the methods of proving a represented truth, but also for the methods of explaining an object directly presented, and that we may thus speak of them not merely as principles of proof (argumentabilia) but also as principles of description (predicabilia).3 Hence the five well-known predicables of Porphyry are totally inadequate, since they contain only predicates in recto, or denominations, and not even all these; one must add limitation (dejinitio; the Dutch call it bepae/ing) and division, for it too is a predicable, for example, that every regular solid is either 4-, 6-,
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690 -98 465 8-, 12-, or 20-sided. But Porphyry overlooked the predicables which serve for predicates in obliquo or as sources of the secondary predicates [anbeylagen], if I may use such a word, and these are found in the topics, since cause, effect, whole, part, etc., are in fact of this kind. 4 I find that Placcius, the famed jurisconsult of Hamburg, whose learning, industry, profundity, and good opinion I esteem highly and whose patronage I would wish for you, has treated the loci ably and grasped the heart of the matter. 5 Jurists have made good use of these things in their legal loci and elsewhere. Upon them we may also develop a certain art of questioning which is useful not only for judges and recorders but also on journeys and in opportunities to see unusual things and speak with unusual persons from whom one may learn much, so that one can make the best use of such transient and never returning opportunities and not be angry with one's self later for having failed to ask questions or to observe this thing or that. Here belongs also the art of inquiry into nature itself and of putting it on the rack - the art of experimenting which Lord Bacon began so ably. You will reply that the ablest heads have no need of such advantages but get along well enough with their natural understanding and that simpletons cannot achieve as much with all such aids. There is some truth in this, but it is also true that there are few who know or make use of their advantages and that it is a misfortune for the human race that it has taken so little advantage of the grace revealed by God and of the treasures of benevolent nature. For I am of the opinion that men could accomplish things deemed incredible until now, ifthey really wanted to apply themselves to it, but their eyes are still holden, and everything takes time to ripen. So I am convinced that with the advantage of these aids and the willingness to use them, a poor head could excel the best, just as a child with a ruler can draw better lines than the greatest master with free hand. The greatest geniuses, however, would make unbelievable progress if they added these advantages. So far I have discussed only that part of the accepted logic which serves discovery and which, in a sense, should precede; now the part which concerns judgment must be considered. Here we come to the syllogisms and their figures and modes. This is the part which people hold to be the most useless; they make fun of Barbara and Celarent. My own observation has been different, however, and although Mr. Arnauld, in his Art of Thinking, thinks that men do not easily make errors in the form but almost always in the materials of thought, the situation is in fact quite otherwise. 6 Mr. Huygens has observed, as have I, that mathematical errors themselves, of the kind called paraiogisms, usually arise through a neglect of form. It is certainly no small matter that Aristotle reduced these forms to unerring laws, having been the first actuaJIy to write mathematically outside of mathematics. For those who are interested, I too have contributed something, having demonstrated by my art of knowing that each of the four figures has exactly six valid modes and that therefore, in contrast to the popular doctrine, one figure has as many as another, nature being regular in everything. 7 This seems to me no less worthy of our consideration than the number of regular bodies. Aristotle's work is indeed but a beginning, virtually the ABC's, for there are other more complex and difficult forms which can be used only after these first and simple forms have been established, as for example, the Euclidean inferences in which proportions are transposed and ratios inverted, compounded, divided, etc. Even addition, multiplication, and division of numbers, as they are learned in the arithmetic schools, are demonstrations in form, and we can depend upon them because they prove by virtue of their form. In this sense one may say that an entire bookkeeping For references see p. 471
466 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS calculation is formally demonstrable and consists in demonstrations inform. This is also true of algebra and many other formal proofs, which are indeed empty yet perfect. It is simply unnecessary for all forms of proof to be labeled omnis, atque, and ergo. Into all infallible sciences that are exactly demonstrated, higher logical forms are incorporated, some of which come from Aristotle, some of which must find their source elsewhere. Cardan saw this in his Logic. Just as counting on fingers and the use of lines and crosses are left to peasants, mathematicians having higher devices, so, when one has raised logic higher in the true sciences, one leaves to pupils this calculating by the fingers as it were, by means of omnis, atque, and ergo, by means of which they cannot count beyond three at a time, so to speak, because their inferences and syllogisms can have only three terms and three propositions. It is sometimes advisable, however, to stick to such peasant-calculating and child's logic. We sometimes accept small change in bunches but prefer to count over larger pieces, say, of gold, separately, and if we had to count diamonds, we should gladly count them on our fingers, because such counting, though of the poorest type, is also the surest, whereas the higher, the more artificial, and the more rapid the counting, the greater the danger of error. So in logic also; in important matters such as theological controversies which concern the nature and will of God and also our soul we do well to analyze matters most industriously and reduce everything to the simplest and most easily grasped inferences, so that even the most insignificant student cannot fail to see what follows and what does not. It will be found that men have often reached a standstill and remain stuck in important discussions because they abandon form, just as we can change a ball of twine into a Gordian knot by trying to unwind it in a disorderly way. In this connection I must set down my thoughts about the proper use of formal disputation. This has been banned from the lecture halls of both higher and lower schools, and one of the most important means of avoiding human errors has thus come to be considered almost as a child's game of which one is ashamed after he has progressed to something sounder. And it is no wonder that it is treated in this way, for it often seems that we do not want to use it to get behind the truth but only to give young people a little courage in showing themselves and defending themselves in public. Thus they commonly begin a syllogism, but the proposition which is denied or otherwise criticized is not in its turn established by a new syllogism, much less the disputed proposition in the pro syllogism, etc., as should be done in a true disputation in form. Instead, it is common to break off into conversation and informal discourse and to end in a word of honor or a compliment. Now I admit that it can hardly be otherwise if its purpose is merely to give youth practice. For if we wanted to carry through a formal disputation, several days would be spent on a syllogism, and where would the audience and the other opponents be then? The large number of prosyllogisms, moreover, would compose a real labyrinth from which we could not escape without a protocol, to say nothing of the great understanding and unusual acuteness needed to carry a demonstration back to its primary sources and fundamental truths on the spur of the moment. It is thus a human perversity to use logical form only where it can be of little help and must soon be stopped - that is, in oral controversies, and by young people, merely for practice. But where form might help us out of great difficulties, that is, in written theses for disputation, especially in important religious conflicts, we neglect it, with the result that there often arise harmful errors which are retained because in free discourse we think more of skill, eloquence, and subtlety, and
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 467 of approval and esteem as well, than of the foundation of truth. The result is that when both sides are defended by able and alert people, no decision is reached, but both sides are merely stiffened. I have often thought about this matter and have made some tests, and I find that whoever undertakes to prove something and constructs a syllogism for every wholly or partially denied proposition must inevitably finally stop because of the lack of proof and confess this or drive his opponents back to undeniable propositions and thus to an admission of truth, or (what sometimes happens in contingent matters) he must shift the burden of proof to his opponent. Thus the form of disputation has been shown to be necessary in necessary matters where eternal truths occur but not in contingent matters where the most probable must be chosen. In this case two further problems arise. The first concerns presumption, that is, when and how one has the right to shift the demonstration from one's self to someone else; the second concerns the degrees of probability, how to weigh and evaluate considerations which do not constitute a perfect demonstration but run counter to each other (indicantia and contraindicantia, the medics call them), and to reach a decision. For the common saying is true enough - rationes non esse numerandas sed ponderandas; arguments are not to be counted but weighed. But no one has as yet pointed out the scales, though no one has come closer to doing so and offered more help than the jurists. I have therefore thought a good bit about this matter and hope sometime to fill this need. This will also serve the art of exegesis and therefore be of use in theology. And it contains an infallible judge of conflicts, not indeed permitting us always to discover the truth, since God has often kept that for himself in the supreme secrets and has not revealed to us what we should like to know. But one can at least determine, first, whether the matter is perfectly proved, and then, if it is not, whether and to wha:t extent it has been given credibility. I once carried out an experiment with a scholar in a semimathematical controversy. We were both seeking the truth, and we exchanged letters which, though courteous, were not without mutual complaints that each unintentionally distorted the meanings and utterances of the other. So I proposed the syllogistic form, which was agreeable to my opponent. We carried the matter beyond the twelfth prosyllogism, and from the time we began this, complaints ceased, and we understood each other, to the advantage of both sides. 8 Since it is an easy and pleasant practice to arrange and rearrange syllogisms and prosyllogisms in formal replies, we should be able to use this method to get to the bottom of important scientific problems and to help free ourselves of dreams and conjectures. For the very nature of our procedure will eliminate all repetition, irrelevance, and unnecessary prolixity, as well as all deficiencies and omissions, whether intentional or unintentional, and finally, all disorder, misunderstanding, and dishonest conduct of the argument as well. This is what I wanted to say about the great, and for the most part tested, advantages of the known logic when it is rightly used. But I consider it certain that the art of reasoning can be carried incomparably higher and believe not only that I see this but that I already have a foretaste of it, which I could hardly have attained, however, without mathematics. Though I found some basis for it even before I was a novice in mathematics, and had already printed something about it in my twentieth year, I have finally come to see how blocked are the ways to it and how hard it would have been to open them without the aid of the deeper mathematics. What can actually be accomplished here is in my judgment of such scope that I cannot expect adequately to be believed without actual examples, and so must postpone a further exposition. For references see p. 471
468 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS I shall therefore break off for this time and comment on the objections which you raise to logic. I find that they apply only to its abuse or misuse. 1. Logic as the art of reasoning may serve the purposes of order and of good discourse, even though those who teach it neither order nor speak well. This merely means that they do not well understand or at least do not well practice their art. For one may understand everything that Ptolemy, Aristoxenus, and Zarlinus have written about music and yet not be able to sing or play. 2. If no one is convinced by logic, the reason for this is that no one takes the form or the orderly process seriously but uses it only for the amusement of youth or rather, hardly tries to use it at all. 3. There is some truth in the assertion that a great part of the arts were discovered and can be taught with a purely natural logic. But a reasonable man who understands neither writing nor numbers can also calculate with a natural arithmetic when necessary; does this prove that mathematics amounts to nothing? I myself am of the opinion that mathematics, history, and other subjects should be learned before an extensive mastery of logic, for how can one order one's thoughts who has never thought of much? But once provided with a store of good ideas, one can survey and measure them, and with the help of the order that is uncovered in them, one can all the more readily discover something new. This is similar to the art of speech. I am of the opinion that in learning a language one should stick to practice rather than to grammar. But once one is fairly proficient in the language, its grammar will help carry him further in it. In addition to all this, I must also mention the fact that Plato achieved a good bit in logic and that disputation by means of questions also has its uses. I do not think that Archimedes and Descartes can be considered as despisers of logic; Descartes at least studied it most industriously under the Jesuits at la Fleche and was well at home in the Scholastic philosophy, which contains much that is good if it can only be dug out. I value Jung very highly and cannot adequately lament the loss of his manuscripts. 9 Nor do I put Felden in any low category, and the other scholars whom you mention are also not to be despised. 4. But I cannot admit that logic has made no discoveries. Everything discovered by the understanding has been discovered through the good rules of logic, although they may not have been explicitly noted or written down at the start. A good painter who has through practice mastered true proportions uses the art of measuring and perspective, for even though he has not described or expressly known of these arts, their basis is in him. Meanwhile painting has become far more perfect since perspective has become a part of the art ofknowledge. 5. There is no doubt that a man who is skilled in the advantages of the art of reasoning proceeds with more acuteness than others. 6. Men are reasonable without a formulated science of reasoning, just as they can sing without the art of music. But if as much industry had been applied to the true art of reasoning as has been expended on the art of singing, men would have accomplished wonders. We have neglected this because we pay little attention to things which are not immediately noticeable to the external senses. Cicero has well said that nothing is more beautiful than virtue, but how few see it! As for your remarks on the explanation of words, it will suffice to point out that these explanations at once involve the discovery of their cause, provided they are made by means of the definitions which I call real and which I have explained elsewhere. To take an example which is a little
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 469 more difficult than the one you offer (why 3 times 4 is 12), why are the results of the successive addition of odd numbers always perfect squares? Thus 1+3+5+7 +9 +11+13 I 1 I 4 I 9 I 16 I 25 I 36 I 49, etc. 1= 1 or 3 + 1 = 4 5+ 4= 9 7 + 9 = 16, 9+16= 25, etc. In discovering the reason for this, we shall also discover the right use of the art of thought. 7. I have already admitted your assertion that everything may be learned without the art of judgment and have replied to it. Just as the Chinese have done many excellent things with only a natural art of measurement, so most things have been found out without using a proper art of thinking. Yet the value and utility of the art of thinking is established, as is that of the art of measuring. 8. It is true that the art of thinking must first be sought in examples of good thinking about things used as models. But after it has been found in these, we may attend directly to the art, so that it may itself become good and serve as a model, though without abandoning the practice and study of good thinking. A painter, sculptor, or architect studies ancient models and formulates an ideal from them. But these matters have also been reduced to rules which can be followed. Yet no one stops viewing beautiful works of art. 9. In spite of the transience and the complexity of human attitudes, there is only one art of thinking, although each person may follow his own inclinations in practice, just as there is only one art of riding which applies to all riders and horses, though not every saddle fits all horses. Numbers themselves may be grasped in many different ways. It is true that mathematics is not in itself logic, but it is one of its firstborn and applies it to magnitudes or to number, measure, and weight. I have discovered, too, that algebra derives its advantages from a much higher art, namely, the true logic. 10. Logic contains much that is difficult and much that is easy, just as does mathematics. What is easier than the first lesson in numbers, and what is more difficult than finding irrational roots? One may reasonably begin with the easiest and save the difficult until other sciences have been mastered. The beginnings will serve as a foretaste for youth, but the higher truths, both in logic and in arithmetic, belong to those who have come far in knowledge and in expression and wish to rise even higher. It is well known that Aristotle says of ethics, and Grotius of rhetoric, that they do not belong to students. I understand this to mean the higher use of these sciences, for Aristotle would not deprive youth of the Civilitas Morum, nor would Grotius forbid the Progymnasmata of Aphthonius. 10 11. I should hold that all the consequences lie in the conclusions and not in the premises except only insofar as the latter involve something commensurate with the conclusions. This is true in all applications of science to contingent matters.11 The art of practice consists in bringing accidents themselves under the yoke of science. The more we do this, the more does theory conform to practice. For example, long ago only the force of motion was considered in mechanics. Galileo began to study mathematically the strength of the bodies used in motion and raised the question of which forms of the For references see p. 471
470 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS same matter offer the most resistance. Later I bettered and increased his rules. GaIiIeo treated the motion of heavy bodies without considering the resistance of air. Blondel, in writing on bombs, also thinks that this is not necessary. On both rational and empirical grounds I hold the contrary. 12. The common logic is indeed often in error. What it says of genus and differentia needs improvement, for one can make a differentia out of the genus and vice versa, or to speak whimsically but truthfully, one can say that man is an animal rational being with as much right as that man is a rational animal. When I say that a cube is a regular parallelopiped, I can take either term for genus or differentia. 13. I leave undecided the question of how far one may say that the pure logician is an ass. Scaliger said the same thing about mathematicians. Even a coachman could serve no purpose among men away from his coach or stable, if he showed no signs of understanding. 14. Pure mathematics proves nothing against logic. For it has borrowed much from logic, and it also comes to the rescue of logic, for its example serves to warn people, as may be seen in your twenty-third exercise. The spiral of Archimedes, which you mention there, is not so wonderful as may be thought. If something is continuously lifted more than it falls, is there any wonder that it is finally elevated? What you say of tangent angles also has its limits, if rightly understood. If you admit infinite extension, it follows of course that one angle is greater than another. Your remark in the twentieth exercise, that there may be a moving object that is without motion, is not opposed to reason but only to the common semblance of it, and hence it is a paradox. It must also be observed that the axis is not a part [of a revolving sphere]. Furthermore, just as it is not proper to be always making verses, so it is improper to be always throwing syllogisms about. To define or limit all terms is as little needed as to divide all numbers into their factors. I hold that juristic definitions too are logical. 15. IfIogicis nothing but a bag full of good reminders, it is certainly not futile. I have no praise for the new logicians who condemn the old rather than improve it. It is not always in our power to find the truth when not enough data are at hand, but we can always guard against error if we have time to think about a matter and to discover everything possible from the data - if we bring logic to full perfection. I have brought matters so far with my infinitesimal calculus of differences and sums that many problems can now be solved in mathematical physics which one could not even venture to try before. Even when data are lacking, we can at least observe what data we do need. If we had adequate practice in the true art of reason, it would also help us to thoughts which we must grasp on the spur of the moment, but for the time being, we still lack most of such an art, and I have not had time to examine this point. I also admit that when a logician gives a rule without an example, it is like trying to learn to duel with mere verbal instructions. 17. There is much that is excellent in Realis de Vienna, and this may be why he is not generally refuted. As for me, I lay little importance in refutation but much in exposition. When a new book reaches me, I search for what I can learn, not for what I can critize in it. 18. I think that the Sorbonne and other colleges are not to be despised. So far as I know, logic is in no more disrepute in France and England than in Germany. Yet I must agree that the most learned people do well to use few Scholastic terms, especially in writing for general readers. Otherwise they are like a tailor who lets the seams show,
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 471 as Mr. Dilher once appropriately said to me in discussing the use of such terms in pulpits. In conclusion, I agree with you that without making much ado about logic and such fields, we should lead youth at once into the factual sciences, just as I hold that languages are to be learned primarily through use, even through grammar is not to be rejected but to be used at the proper time for greater accuracy of speech. I hope these remarks, which have grown more extended than I had planned, will suffice to show you my thoughts and that they may serve to conciliate or moderate, since both sides do presuppose the art of reason, even though you try to restrict it to pure mathematics only, where it appears in its most beautiful form, though not entirely or exclusively. If I should have the good fortune to make peace between you and the common teaching tradition, it would give me much pleasure, for the result would be that you could find a greater opportunity not merely to attack what is useless but to construct, without being hindered, something of value for our common use. REFERENCES On Huetsee No. 31, and p. 276, note 11. Huet had written a Censuraphilosophiae Cartesianae in 1689, in which he charged that Cartesianism was subversive to the church. The work is discussed in Leibniz's correspondence with Nicaise. 2 Peter Ramus (1515-72), Calvinistic philosopher, attacked the Aristotelian logic as artificial and remote from the natural logic of the mind and proposed a logic of discovery and judgment which he conceived as being closely related to rhetoric. The Semi-Ramists or Philippo-Ramists sought a mediating position in the controversy between Ramists and Aristotelians (or in the Protestant universities, Philippists, after Melanchthon). Leibniz's combination, a little later in the letter, of Aristotelian topics with Ramist loci suggests the influence of Semi-Ramism. 3 The German terms used by Leibniz are Beweisslichkeiten and Beleglichkeiten. They correspond in general to the two dimensions of thought - ratiocination and representation - corresponding to the formal relational and the empirical aspects of knowledge (see Introduction, Sec. V). 4 On relations in recto and obliquo see p. 246, note 3. Leibniz's extension of the predicables beyond Porphyry's, to include the oblique relations of subjects, points to a fundamental difficulty in his theory that the predicate is included in the subject in every true affirmative proposition. S Vincent Placcius (1642-99), lawyer and patron of scholars, was engaged in correspondence with Leibniz at this time. 6 See The Art o/Thinking, Book III, chap. I. On Leibniz's knowledge of the authorship of this work see p. 60, note 28. 7 The classification of the valid modes of the four figures was one of the more important applications of the first two problems in the Art 0/ Combinations (1666) (Vol. I, No.1). 8 The allusion is probably to the correspondence with Papin on the Cartesian theory of gravity and the conservation of quantity of motion, which resulted in Leibniz publishing 'De legibus naturae et vera aestimatione virium motricium contra Cartesianos', Acta eruditorum, September, 1691 (cf. Cout. L., p. 2, n. 1). 9 See p. 130, note 4. Both Jung and Felden had been mentioned with approval in the letter to Thomasius in 1669 and the Preface to Nizolius in 1670. 10 Aphthonius of Antioch, a rhetorician of the late 3rd and early 4th centuries, edited the Progymnasmata of Hermogenes of Tarsus as a textbook. The De civilitate morum puerilium (1530) was the best known of Desiderius Erasmus' pedagogical works. Both books were still widely used as schoolbooks in the 17th century. 11 All inference is therefore synthetic in matters of fact, and predicates are only incompletely or partially in their subjects. 1
49 LETTERS TO DES BILLETTES 1696-97 Gilles Filleau (or Failaiseau) des Billettes was a pensioner of the Academy of Sciences in Paris and a distinguished expert in the arts and crafts, with wide and in/luental acquaintances. Like the Duke de Roanez, he had been a close friend ofPascal. Leibniz had known him during his Paris years and later called him "one of my oldest friends in France". The letters written to him contain popular expositions of Leibniz's philosophical ideas and throw some light upon his motives as a thinker. [G., VII, 451-54] December 4/14, 1696 Your health and your welfare, Sir, of which health is the more essential, have given me great joy. I am glad, too, that one can go to La Trappe without losing his fine curiosity and taking an aversion to terrestrial things; this could be good for certain people only. The gazette has already informed me of the death of the Duke de Roanez, for which I am sorry. You say, Sir, that the Duke had gone to the country in the interest of your works of navigation. Be so good as to tell me what these are and continue your kindness in sending me incidents which have to do with the sciences, as you have begun. Imagine that I were in Paris, having the honor of seeing you in the suburb St. Jacques as in former times, where the meetings seem since to have been banned. I thank you very much for what you wrote about Mr. Dalesme, inventor of the pneumatic tubes for carrying forces a great distance, and also for your story about the calculation of games of chance. But you forgot to give me the name of the Poitevin gentleman, the great gambler who thought of this application of mathematics. Most games could in fact give occasion for sound thinking, and I should like to have his views, as well as those of other gamesters. A small discourse of Mr. Huygens on the game of dice [de ludo aleae] is printed in the Exercitationes of Francis Schooten. It is a work separate from his commentary on Descartes's geometry. 1 My system, about which you are interested in hearing some news, Sir, is not a complete body of philosophy, and I do not at all claim to give a reason for everything that others have claimed to explain. One must advance slowly to advance with sure steps. I begin with the principles, and I hope to be able to satisfy most doubts like those which perplexed the late Mr. Bernier. I believe that everything really happens mechanically in nature, and can be explained by efficient causes, but that at the same time everything also takes place morally, so to speak, and can be explained by final causes. These two kingdoms, the moral one of minds and souls and the mechanical one of bodies, penetrate each other and are in perfect accord through the agency of the Author of things, who is at the same time the first efficient cause and the last end. I
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 473 claim, then, that just as there is no vacuum in bodies, no more is there one in souls; that is, that there are souls everywhere, and that souls which once exist cannot perish. Bodies are multitudes and souls are unities, but they are unities which express or represent within themselves the multitude. Every soul is a mirror of the entire world according to its point of view. But minds are souls of the first order or the highest genus, which represent not only the world but also God in the world. So they are not only immortal but conserve for always their moral qualities as citizens of the republic of the universe, which lacks nothing because it is God who rules it. My explanation of the union of soul and body is found in the thirty-eighth issue of the Journal des savants for this year.2 But I come to the points which you raise. As for gravity, Mr. Newton has shown us a proportion of which, however, I already knew something; the planets show us that weights or attractions are reciprocally proportional to the squares of their distances. A heavy body, that is three times as far from the center of attraction will have only one-ninth of the weight. Now I find that this agrees with the action of light rays, for a fluid that is thin but solid will also take the form of emitted rays as it becomes distant from the center. It agrees also with motion away from the center along a tangent, which Kepler was the first to apply to gravity, Descartes following him in this. But merely the instantaneous conatus of the centrifugal force is not sufficient to form either light or gravity, as Descartes believed; a true motion of emission must be developed, like a puffing wind, which requires time. Now the emission of a heavier or more compact fluid necessarily creates the attraction of bodies which are less so. As for light, I believe that an explosion is involved in the luminous body, as if an infinite number of air guns [arquebuses a vent] were being discharged continuously. I hold also that all perceptible bodies are remarkably porous and permit more passage through them than we imagine. But when these passages are irregular, as when bodies are very dense or very mixed, they turn from transparent, as they really are, to opaque. I imagine that everything is continuous as well as contiguous, that is that things differ in degree and in appearance. The whole world is like a pond of matter in which there are different currents and waves. As for the sensibility o/matter, I have already mentioned the souls which exist throughout it, and I believe that it is not properly the matter which is sensitive, since this is nothing but an aggregate of substances rather than one substance, but that it is rather the corporeal substance, which always has something analogous to feeling and life, being provided with an organic matter as well as a soul or if you will, a form. The action of percussion comes solely from elasticity, the operation of which arises only from the fact that the motion of the surrounding matter is troubled and impeded when it is inclosed, a little like the current of a river when it is narrowed. The force of fermentation, of cold and hot, of gunpowder, etc., can be explained by something analogous to the force of air guns or of a spring. For instance, it is not the little mass of gunpowder which causes so great an effect but the surrounding matter, as I have already said about elasticity. Calculating the action of powder, I find that the compression of air easily suffices to explain it. But I dare not hope that we shall very soon enter into the details of such matters. The origin 0/ winds is due in part to the motion of the earth and to that of the light and heat from the sun on the earth, and even in part, from the moon. Without speaking of exhalations to explain the magnet, these particles twisted into folds seem quite unnecessary; it suffices that the openings are so adjusted For references see p. 475
474 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS to what passes through them that after this passage has continued for some time, its return is prevented and is against the grain, so to speak. A contrary effort changes these folds, however, and reverses them. As for the variation, we must labor to inform ourselves further about the fact. Except for the general principles on the nature of corporeal substance, of force, and of the structure of the universe, which it is important to establish firmly, 1 find that our progress in physics is not yet very notable. All that we can do at present for medicine and the arts (I exclude mathematics, and mechanics which depends on mathematics) is to observe the universal customs of nature, so to speak, in order to rule ourselves according to them. It is true that 1 believe that men will soon go much further if they press their point and profit by the methods which they have at hand. The Marquis de l'Hospital has himself had the goodness to throw light on my new infinitesimal calculus in the notable work which he has recently published. 3 1 also call it the calculus of differences and sums. If peace is made, 1 believe there will be a way to introduce my arithmetical machine in France and that you will do me the honor of supporting it with your approval if you find it worthy.4 1 beg you to send a few more details about Mr. Gayot, whose ability in mechanics you esteem so highly. Your testimony in such a matter is worth more than letters patent of the king. 1 must ask you a question. Can't one make some small bellows entirely out of steel of or some other metal, similar to a folding lantern? There would have to be thin strips at the places which must be flexible. This could be used to make a portable barometer like a watch, which would last a long time and would need no mercury or any other liquid, nor a fixed position. The use of barometers is important, as you know, in predicting the changes in the air. 5 You have many excellent ideas, Sir, of a mechanical as well as an economic-political nature. Why let them perish? Reflect on them a little, 1 pray you; you owe it to the public and to the honor of your nation. The Duke de Roanez had good ideas about water courses. Did he put anything in writing? 1 do not know whether you have seen the book on this subject by Mr. Guglielmini of Bologna. Mr. Papin has found many difficulties in it. Why haven't the Perier brothers published the mathematical essays of Pascal which they showed me? 6 Someone has told me that you have ideas for the improvement of printing; that would also be most useful. What is the present condition of what was once called the party of Port Royal? Does it still subsist in spite of the death of Mr. Arnauld and Mr. Nicole, and who are its buttresses? It seems to me that there are tools fit to facilitate the manufacture of clock wheels. This would help my arithmetical machine, which contains many such wheels. 1 beg you, Sir, to send me your opinion. II [GM., VII, 455-581 Hanover, October 11/21, 1697 .,. Certainly we cannot gain over force; all that depends on us is to use it well. My fundamental maxim in mechanics, drawn from metaphysics, is that the cause and the total effect are always equivalent in such a way that the effect, if it were completely turned around, could always reproduce its cause exactly, and neither more nor less. So if the machinist who is trying to improve coaches sins against this principle, he will accomplish nothing of value. Thus someone told me, one day in Paris, that some
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 475 German was said to have made a wooden horse which drew a carriage six German leagues in six hours by means of banded steel springs, as if it were possible to store so much force in so small a number of these springs. When I investigated, there was nothing to it. Yet it is true that we do not take enough advantage of the forces which nature supplies .... Peace is made, and so I expect to hear that the arts and sciences are regaining force and vigor in France. You charm me besides, Sir, by telling me such beautiful things about the intentions and the zeal of the Abbe Bignon for advancing them. 7 My correspondence with Mr. PeIlisson went further than with him, because our letters were more frequent. Aside from the very kind expressions of which the letters of the Abbe Bignon were full, no opportunity was found for a greater communication of our views. He must have greater and more beautiful ones than I, and what is the main thing, he has the opportunity to carry them out. This pleases me, for often those who have the authority do not have enough light or enough ardor. I give way to him in everything except zeal. Provided that something of importance is achieved, I am indifferent whether it is done in Germany or in France, for I seek the good of mankind. I am neither a phil-Hellene nor a philo-Roman but a phil-anthropos. And I seek this, too, without desiring the slightest advantage from it, so that if I can contribute to his excellent plans, he may make free use of me without fear of being embarrassed. It is this that I beg you to tell him when an occasion arises. My work is not yet finished, so there is no hurry about it, and if there is some other difficulty which prevents the kind of printing of which he spoke, I will appreciate being informed of it in order to guide myself accordingly. I do not want to be importunate to anyone, and I have scruples against receiving a favor which I am not sure is being done me with pleasure. Since I know that some of your able geometricians often speak against the methods which I have proposed and which persons of importance and merit have carried further, without our having been able to get the critics to offer their objections in writing, I imagine that these men fear to give authority to my work by such a printing. 8 And it would be an injustice for me to wish the Abbe Bignon, in order to do me a favor, to disfavor persons whom he sees every day. If this is the cause of the difficulty, I shall esteem and honor him no less, and I shall be no less eager to give witness to my zeal toward him on every other occasion. I tell you these things sincerely and frankly, as to a common friend. And you will oblige me, Sir, if you will enlighten me about them. What good is dissimulation between people who ought to treat each other with realism and who ought to place themselves above the trifles which embarrass common people. I believe that the descriptions of a good part of the arts can be made within the time which you mention, and I say that this will already be much. But since time is, in my opinion, the most precious of all things outside of ourselves over which we have control, I believe that one should almost double the number of persons in order to gain half of the time, if possible .... REFERENCES 1 Francis Schooten's Exercitationes mathematicae (1657) contained Huygen's paper De ratiociniis in aleae ludo, the beginning of the modem study of probability. The gambler mentioned was Antoine Gomboult, the Chevalier de Mere, as the account in the New Essays, IV, 16,9,
476 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS shows. On Leibniz's conception of the importance of games see p. 61, note 39. 2 See No. 47. 3 See p. 420, note 8. 4 The Treaty of Ryswick was signed September 20, 1697. 5 The first aneroid barometer was patented by Vidie in 1845. 6 To the inquiry about Pascal's mathematical manuscripts, Des Billettes replied as follows (May 28, 1697): "There remains only the one Perier who is priest and dean of some chapter in Clermont in Auvergne, his birthplace, and a sister worthy of them and their uncle [pascal]. You need not expect the works of the latter. Either they would have published them, or they did not judge them fitting to be brought to light." 7 Jean Paul Bignon, abbot of St. Quentin, was president of the Academy and director of the Royal Library, one of the co-founders of the Journal des savants. On the work which Leibniz sought to have published at the Louvre see p. 420, note 8. S On the controversies already in process about the validity and clarity of Leibniz's calculus of infinitesimals see the introduction to No. 56, below.
50 TENTAMEN ANAGOGICUM: AN ANAGOGICAL ESSAY IN THE INVESTIGATION OF CAUSES Ca. 1696 Leibniz agreed with the Cartesians that natural events are to be explained mechanistically. but he insisted that the consideration of.final causes was of significance in the derivation of mechanical laws themselves. As example he submitted a demonstration of the laws of refraction and reflection as a special case, maximally determined, of an infinite number of possible laws. His argument, historically important as the beginning of the famous dispute on the principle of least action in the 18th century, and the revived interest in a principle of the extremum today, was first published in the Acta eruditorum in June, 1682.1 This clear and concise formulation is obviously later. The form and content suggest that it may be a continuation of the Specimen dynamicum (No. 46). The mention of the celebrated brachistochrone problem dates it after June, 1696, however, when John Bernoulli first proposed this problem. The essay remained unpublished until Gerhardt included it in his edition. [G., VII, 270-79] 12 have shown on several occasions that the final analysis of the laws of nature leads us to the most sublime principles of order and perfection, which indicate that the universe is the effect of a universal intelligent power. As the ancients already held, this truth is the chieffruit of our investigations; without mentioning Pythagoras and Plato, whose primary aim was such an analysis, even Aristotle sought to demonstrate a prime mover in his works, particularly in his Metaphysics. It is true that these ancient thinkers were not informed about the laws of nature as are we, since they lacked many of the methods which we have and of which we ought to take advantage. The knowledge of nature gives birth to the arts, it gives us many means of conserving life, and it even provides us with conveniences; but the satisfaction of spirit which comes from wisdom and virtue, in addition to being the greatest ornament of life, raises us to what is eternal, whereas this life, in contrast, is most brief. As a result, whatever serves to establish maxims which locate happiness in virtue and show that everything follows the principle of perfection is infinitely more useful to man, and even to the state, than all that serves the arts. Discoveries useful to life, moreover, are very often merely the corollaries of more important insights; it is true here too that those who seek the kingdom of God find the rest on their way. The inquiry into final causes in physics is precisely the application of the method which I think ought to be used, and those who have sought to banish it from their philosophy have not adequately considered its usefulness. For I do not wish to do them the injury of thinking that they have evil designs in doing this. Others followed them, however, who have abused their position, and who, not content with excluding For references see p. 484
478 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS final causes from physics but restoring them elsewhere, have tried to destroy them entirely and to show that the Creator of the universe is most powerful, indeed, but without any intelligence. There have been still others who have not admitted any universal cause, like the ancients who recognized nothing in the universe but a concourse of corpuscles. This seems plausible to those minds in whom the imaginative faculty predominates 3, because they believe that they need to use only mathematical principles, without having any need either for metaphysical principles, which they treat as illusory, or for principles of the good, which they reduce to human morals; as if perfection and the good were only a particular result of our thinking and not to be found in universal nature. I recognize that it is rather easy to fall into this error, especially when one's thinking stops at what imagination alone can supply, namely, at magnitudes and figures and their modifications. But when one pushes forward his inquiry after reasons, it is found that the laws of motion cannot be explained through purely geometric principles or by imagination alone. This is also why some very able philosophers of our day have held that the laws of motion are purely arbitrary. They are right in this if they take arbitrary to mean coming from choice and not from geometric necessity, but it is wrong to extend this concept to mean that laws are entirely indifferent, since it can be shown that they originate in the wisdom of their Author or in the principle of greatest perfection, which has led to their choice. This consideration gives us the true middle term that is needed for satisfying truth as well as piety. We know that while there have been, on the one hand, able philosophers who recognized nothing except what is material in the universe, there are, on the other hand, learned and zealous theologians who, shocked at the corpuscular philosophy and not content with checking its misuse, have felt obliged to maintain that there are phenomena in nature which cannot be explained by mechanical principles; as for example, light, weight, and elastic force. But since they do not reason with exactness in this matter, and it is easy for the corpuscular philosophers to reply to them, they injure religion in trying to render it a service, for they merely confirm those in their error who recognize only material principles. The true middle term for satisfying both truth and piety is this: all natural phenomena could be explained mechanically if we understood them well enough, but the principles of mechanics themselves cannot be explained geometrically, since they depend on more sublime principles which show the wisdom of the Author in the order and perfection of his work. The most beautiful thing about this view seems to me to be that the principle of perfection is not limited to the general but descends also to the particulars of things and of phenomena and that in this respect it closely resembles the method of optimal forms, that is to say, of forms which provide a maximum or minimum, as the case may be - a method which I have introduced into geometry in addition to the ancient method of maximal lind minimal quantities. For in these forms or figures the optimum is found not only in the whole but also in each part, and it would not even suffice in the whole without this. For example, if in the case of the curve of shortest descent between two given points, we choose any two points on this curve at will, the part of the line intercepted between them is also necessarily the line of shortest descent with regard to them:' It is in this way that the smallest parts of the universe are ruled in accordance with the order of greatest perfection; otherwise the whole would not be so ruled. It is for this reason that I usually say that there are, so to speak, two kingdoms even
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 479 in corporeal nature, which interpenetrate without confusing or interfering with each other - the realm of power, according to which everything can be explained mechanically by efficient causes when we have sufficiently penetrated into its interior, and the realm of wisdom, according to which everything can be explained architectonically 5, so to speak, or by final causes when we understand its ways sufficiently. In this sense one can say with Lucretius not only that animals see because they have eyes but also that eyes have been given them in order to see, :though I know that some people, in order the better to pass as free thinkers, admit only the former. Those who enter into the details of natural machines, however, must have need of a strong bias to resist the attractions of their beauty. Even Galen, after learning something about the function of the parts of animals, was so stirred with admiration that he held that to explain them was essentially to sing hymns to the honor of divinity. I have often wished that an able physicist would undertake to prepare a special work whose title - or whose aim at least - would be The Hymn olGalen. What is more, our thinking sometimes furnishes us with considerations revealing the value of final causes, not merely in increasing our admiration for the supreme Author, but also in making discoveries among his works. Some day I shall show this in a special case in which I shall propose as a general principle of optics that a ray of light moves from one point to another by the path which is found to be easiest in relation to the plane surfaces which must serve as the rule for other surfaces. For it must be kept in mind that if we claimed to use this principle as an efficient cause, and as if the easiest path would prevail among all the possible competing rays, it would be necessary to consider the whole surface as it is, without considering the plane tangent to it, and then the principle would not always work out successfully, as I shall show presently. 6 But far from concealing that there is a certain final cause involved in this principle - an objection which was once made against Mr. Fermat, who had used it in his Dioptrics - I have found it more beautiful and more important than that of mechanism for a more sublime application. And an able author who has published a work on optics in England has expressed his indebtedness to my view. 7 Order demands that curved lines and surfaces be treated as composed of straight lines and planes, and a ray is determined by the plane on which it falls, which is considered as forming the curved surface at that point. But the same order demands that the effect of the greatest ease be obtained in relation to the planes, at least those which serve as elements to other surfaces, since it cannot be obtained with regard to these surfaces also. This is all the more true since it thus satisfies, with respect to these curves, another principle which now supersedes the preceding one, and which holds that in the absence of a minimum it is necessary to hold to the most determined, which can be the simplest even when it is a maximum. Now we find that the ancients, and among others Ptolemy, already used this hypothesis of the easiest path of a ray which falls on a plane, to account for the equality of the angles of incidence and reflection, the principle at the basis of catoptrics. It is by this same hypothesis that Mr. Fermat provided a reason for the law of refraction according to the sines, or to formulate it in other terms as Snell did, according to the secants. But what is more, I have no doubt whatever that this law was first discovered by this method. It is known that Willebrord Snell, one of the greatest geometricians of his time and well versed in the methods of the ancients, invented it, having even written a work which was not published because of its author's death. But since he had For references see p. 484
480 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS taught it to his disciples, all appearances point to the conclusion that Descartes, who had come to Holland a little later and who was most interested in this problem, learned it there. For the way in which Descartes has tried to explain the law of refraction by efficient causes or by the composition of directions in imitation of the reflection of bullets is extremely forced and not intelligible enough. To say no more about it here, it shows clearly that it is an afterthought adjusted somehow to the conclusion and was not discovered by the method he gives. So we may well believe that we should not have had this beautiful discovery so soon without the method of final causes. I recall that capable writers have frequently objected that this principle does not seem to work in reflection itself when applied to curved surfaces and that in concave mirrors the path of reflection happens sometimes to be the longest. But in addition to what I have already said, that according to architectonic principles, curved surfaces must be ruled by the planes tangent to them, I shall now explain how it remains always universally true that the ray is directed in the most determined or unique path, even in relation to curves. It is also worth noting that in the method of analysis by maxima and minima, the same operation suffices for the problems of the greatest and the smallest, without distinguishing between them except in applying the method to different cases, since we seek the most determined magnitude in both cases, which is sometimes the greatest and sometimes the smallest in its order, the analysis being based solely on the disappearance of a difference or on the unique result of reuniting twins, and not at all on a comparison of the greatest and smallest with all other magnitudes. For given a curve AB, concave or convex, and an axis ST to which the ordinates of the curve are referred; then it is seen that to each ordinate, like Q or R, there corresponds another one equal to it, its twin, q or r (Figure 33). But there is one particular ordinate T q G Fig. 33. Ee which is unique, or the only determinate one of its magnitude, and has no twin, since the two twins Ee and ec coincide in it and make but one. And this Ee is the greatest ordinate of the concave curve and the smallest of the convex curve. So instead of two infinitely near ordinates in all other cases, having a difference of dm if the ordinate is called m, whose ratio to Ee, a correspondingly small part of the axis, would give the angle of the curve or of its tangent to the axis ST, the infinitely close
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 481 ordinates or twins become coincident in this case at C and have no difference; dm becomes 0, and the tangent at C is parallel to the axis. Thus the basis of the analysis is this uniqueness caused by the union of the twins, without any concern as to whether the ordinate is the greatest or smallest. The calculus shows us this in particular, in this very matter. Let ACB be any mirror whatever, plane, concave, or convex; and let two points Fand G be given (Figure 34). To find the point of reflection C, such that the path FCG G A B A B A-3-~~~-B F Fig. 34. is the unique, singular, or most determined path in size, or what the ancients once called the /-IOVIXXOV, either the greatest or the smallest, that is, whichever it happens to be. For those which are not unique in this sense are doubles or twins, having another of the same length corresponding to them. Draw FG, whose middle point is H, and between C and FG draw CB perpendicular to FG, and CP perpendicular to the mirror. Call HF or HG a, H B x, CB y; then BP will be - ydy, dx being taken negatively. Then CF will be v y2 + shortest, though it is in fact the shortest when that which should provide the rule is i2 -2ax--t- a 2, and CG will be y2 + x 2 + 2ax + a 2. Now CF + CG = m. Differentiating, one gets d· CF + d· CG = 0; that is, v ydy + xdx - adx --~-- + ydy +xdx + adx CG -- = 0 or CF CG (a - x - ydy) dx (a + x + ydy) dx . But a - x is BF and a + x is GB. Therefore CF CG BF+BP GB - BP,' CF CG PF PG or This shows that the angle of direction FCG is bisected by CP, the perpendicular to the curve 8, or that the angles of incidence and of reflection are equal, whatever may be the reflecting surface. The same truth holds also with regard to refraction; that is, whether the surface of For references see p. 484
482 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS separation be plane or curved, provided only that it be uniformly determined, the broken ray always passes from a point in one medium to a point in the other medium by the most determined or unique path, which has, so to speak, no twin brother in length of time. This is something I do not remember having seen commented on before. It is easy to prove it by an analysis similar to that given above. Let a figure be set up just like that above, except that instead of a mirror there is a surface A CB, fiat, concave, or convex, which separates two media penetrated by the ray, and which changes its direction. The ratio of the resistance of the medium ACBF to that of the medium AGCBshaII be as/tog; then/·CF+g·CG = m. Differentiating, we get / (y'ly + xdx CF adx) + 9 (ydy + xdx + adx) CG _ 0 - , and as a result (calculating as above), CF /·PF CG=g'PG' Now it is easy to derive from this theorem the proportionality of sines. For let the G' A B A----~~~~~~~~----B A B M' M Fig. 35.
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 483 ray FC strike the refracting surface ACB at C, and let the refracted ray, CG, be taken equal to the incident ray FC. Draw FG cutting the straight line CP perpendicular to the surface, at P. From points F and G draw normals FL and GN to CP (Figure 35). Now since CG and CF are taken equal, it follows by the equation of the preceding paragraph that PF is to PG as 9 to f. Then because of the similar triangles PLF and PNG the sine FL will be to the sine GN as 9 to [9, that is, reciprocally as the resistances of the media. And the sines of the angles of refraction will be proportional to the sines of the angles of incidence. 1 0 This makes us see, finally, that the rule of the unique path, or the path most determined in length of time, applies generally to the direct and the broken ray, whether reflected or refracted, whether by plane or by curved surfaces, whether convex or concave, without distinguishing in the process whether the time is the longest or the shortest, though it is in fact the shortest when that which should provide the rule is taken into consideration, that is, the tangent plane; nature being governed, as it is, by sovereign wisdom, shows the general design throughout of controlling curves by straight lines or planes tangent to them, as if the curves were composed of these, although this is not strictly true. One also comes in this way to understand some general theorems common to catoptries and dioptrics. For the rectangle constructed by multiplying the rayon one side of the surface by the opposite segment of the base line (namely, the rectangle CF·PG) is always proportional to the corresponding rectangle on the opposite side, made by multiplying the ray of the oth~r side by the segment of the base opposite it (that is, the rectangle CG· P F); or the ratio of the product of one side of the broken ray times the opposite segment of the base, to the product of the other side of the ray by its opposite segment is equal to the ratio of the resistances of the opposite media. In the case of simple reflection, where the media have the same nature, this becomes the ratio of equals, and then this theorem gives CF·P"G" ~:---,:- - 111 CG" ·P"F- or CF· P"G" = CG" • P"F, or, as above, CF CG" = P"F P"GH ; that is, the angles of incidence and reflection are equal. But there could still be a case of reflection mixed with refraction, of which the solution is easy; for that proposed by Descartes does not seem consistent with the nature of light. The ray FC could at the same time meet the mirror A CB and the new medium MCA or M'CA at C, in which case it would be reflected backward, but the angle of reflection would not be equal to the angle of incidence. It will not be difficult to determine this, since one has only to think, in place of the ray FC, of the ray VIC which would pass, if continued directly, into CG", and it will be found that the ray FC, falling upon the mirror CB and into the new medium CM at the same time, will then be turned, by reflection and refraction together. to go as the ray VIC would go if turned by the refraction ofthe medium CM alone. For references see p. 484
484 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS This principle still deserves to be studied empirically, however, not to determine the quantity, but to see whether it can perhaps give us something specific, especially with regard to colors. Thus I should also like to have someone investigate empirically another transition from refraction to reflection, which occurs when the ray which strikes the medium has taken on an obliqueness too great to penetrate it; I should like to have this case, too, applied to colors as well as to a crystal of double reflection. 12 This also deserves application, furthermore, to the experiences of color arising from refraction. But this is said in passing. This principle of nature, that it acts in the most determined ways which we may use, is purely architectonic in fact, yet it never fails to be observed. Assume the case that nature were obliged in general to construct a triangle and that for this purpose only the perimeter or the sum of the sides were given, and nothing else; then nature would construct an equilateral triangle. This example shows the difference between architectonic and geometric determinations. Geometric determinations introduce an absolute necessity, the contrary of which implies a contradiction, but architectonic determinations introduce only a necessity of choice whose contrary means imperfection - a little like the saying in jurisprudence: Quae contra bonos mores sunt, ea nec facere nos posse credendum est. 13 So there is even in the algebraic calculus what I call the law of justice, which greatly aids us in finding good solutions. If nature were brutish, so to speak, that is, purely material or geometrical, the above case would be impossible, and unless something more determinative were given than merely the perimeter, nature would not produce a triangle. But since nature is governed architectonically, the half-determinations of geometry are sufficient for it to achieve its work; otherwise it would most often have been stopped. And this is particularly true with regard to the laws of nature. Perhaps someone will deny that what I have said above applies to the laws of motion and will maintain that an entirely geometric demonstration can be given of them. I reserve the proof of the contrary for another discourse, where I shall show that they cannot be derived from their sources without assuming architectonic grounds. One of the most important of these, which I believe I am the first to have introduced into physics, is the law of continuity, which I discussed many years ago in the Nouvelles de la republique des lettres, where I showed with examples how it serves as the touchstone of theories. 14 It serves not merely to test, however, but also as a very fruitful principle of discovery, as I plan to show some day. But I have also found other very beautiful and extended laws of nature, quite different, however, from those usually employed, yet always depending on architectonic principles. Nothing seems to me to be more effectual in proving and admiring the sovereign wisdom of the Author of things as shown in the very principles of things themselves. REFERENCES 1 See Introduction, Sec. V and p, 61, note 36. The text as given in G. begins with what is really a note added later by Leibniz (Cout. OF., p. 587). This note is as follows: "Whatever leads us to the supreme cause is called anagogical by philosophers as well as theologians. So we begin here to show that no other reason can be given for the laws of nature than the assumption of an intelligent cause. Or we show also that in the investigation of final causes there are cases in which it is necessary to consider the simplest or most determinate, without distinguishing whether this is a maximum or a minimum; that 2
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 485 the same thing is to be seen in the differential calculus; that the general laws for the direction of a ray, derived from final causes, give a beautiful example of this, without distinguishing whether the ray is reflected or refracted or whether the surface is curved or a plane. Certain new general theorems can be derived which apply equally to refraction and reflection. We show that the analysis of the laws of nature and the investigation of causes lead us to God; and how, in the method of final causes as in the differential calculus, we do not consider maxima and minima only, but the most determined and most simple in general." Leibniz also notes: "See if some of these propositions are already to be found in Barrow or elsewhere." 3 That is, the faculty of interpretation within the limits of sensory perception (see p. 41, note 12, and p. 553, note 3). 4 This is a clear allusion to the brachistochrone problem propounded by John Bernoulli in 1696; Leibniz restates the principle used by James Bernoulli in his solution: "If a curve has a certain property of maximum or minimum, every portion or element in the curve also has the same property" (see Mach, The Science of Mechanics, 5th English ed., pp. 521-29). 5 Leibniz follows the Aristotelian meaning ofthe term (Nic. Ethics i. 1) which applies to final causes or ends as explanatory of subordinate ends. Leibniz's architectonic therefore differs from Kant's in being metaphysical as well as methodological, though both rest upon a harmony offorms or possibilities. 6 Leibniz's meaning in this difficult paragraph is made clearer by his actual analyses of reflection and refraction which follow, in which he uses the plane tangent at the point of incidence in place of the curved reflecting or refracting surface itself. His argument rests upon the old discovery that maxima or minima involve in their determination the reduction of two equal values to a single one. This principle he views as an instance of the metaphysical principle of maximal determination or ofthe optimum. 7 Leibniz notes, "Mr. Molyneux" (see p. 452, note 16). On Fermat's interpretation of the problem see Mach, The Principles ofPhysical Optics, New York 1925, p. 34. 8 A line drawn from a vertex of a triangle dividing the opposite side into segments proportional to the adjacent sides bisects the angle at the vertex. g Leibniz's marginal note: "From this another theorem can also be derived which is common to catoptrics and dioptrics, and which seems most elegant to me. It as as follows. If two points are taken in a broken ray in such a way that the line which joins them is divided equally by the perpendicular to the surface of separation, the ratio of the two rays is always constant and proportional to the resistances of the media. For example, if Fand G' are taken so that CP' cuts FG' in two equal parts FP' and G'P', the ratio of ray FC to ray CG' will always be constant, namely, as fto g. For this reason they are equal in the same medium, which is the case in reflection. " 10 That is, the sines of angles FCL and GCP, since CF = CG. 11 The equation of G. is obviously incorrectly copied. 12 Iceland spar, whose property of double refraction had been discovered by Huygens and was discussed in the correspondence of Leibniz with him in 1694. 13 "Things which are contrary to moral principles, we ought also to believe we are unable to do." 14 See No. 37.
51 ON THE RADICAL ORIGINATION OF THINGS· November 23,1697 Leibniz's shift of emphasis to a posteriori reasoning for the existence of God is nowhere better exemplified than in this essay, unpublished until 1840, when Erdmann included it in his edition. The new phase ofhis metaphysics is concerned with the implications ofparticularity and its difference from mere possibility. The problem of the paper is the implication of this particular natural order for the nature of the ultimate harmony of ideas, and it is therefore also important for his hedonistic perfectionism in ethics and aesthetics. The close relationship with the preceding and following essays will be apparent (Nos. 50, 52, and 53). At the close there is a growing emphasis on temporal progress which is characteristic ofLeibniz's later thought. [G., VII, 302-8] Besides the world or aggregate of finite things, there is a certain One which is dominant, not only as the soul is dominant in me or rather, as the Ego itself is dominant in my body, but also by a much higher reason. For the dominant One of the universe not only rules the world but fabricates or makes it; it is superior to the world and, so to speak, extramundane, and hence is the ultimate reason for things. For a sufficient reason for existence cannot be found merely in anyone individual thing or even in the whole aggregate and series of things. Let us imagine the book on the Elements of Geometry to have been eternal, one copy always being made from another; then it is clear that though we can give a reason for the present book based on ,the preceding book from which it was copied, we can never arrive at a complete reasbn, no matter how many books we may assume in the past, for one can always wond{!r why such books should have existed at all times; why there should be books at all, and why they should be written in this way. What is true qf books is true also of the different states of the world; every subsequent state is somehow copied from the preceding one (although according to certain laws of change). No matter how far we may have gone back to earlier states, therefore, we will never discover in them a full reason why there should be a world at all, and why it should be such as it is. Even if we should imagine the world to be eternal, therefore, the reason for it would clearly have to be sought elsewhere, since we would still be assuming nothing but a succession of states, in anyone of which we can find no sufficient reason, nor can we advance the slightest toward establishing a reason, no matter how many of these states we assume. For even though there be no cause for eternal things, there must yet be understood to be a reason for them. For permanent things this reason is their necessity or essence itself; but in a series of changing things (if this is taken a priorP to be eternal) it is a prevailing of inclinations, as we shall see presently, for here reasons do not necessitate (in the sense of an absolute or metaphysical necessity. whose contrary implies a contradiction) but incline. These considerations show clearly that we
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 487 cannot escape an ultimate extramundane reason for things, or God, even by assuming the eternity of the world. The reasons for the world therefore lie in something extramundane, different from the chain of states or series of things whose aggregate constitutes the world. And so we must go from physical or hypothetical necessity, which determines later things in the world from earlier ones, to something which has absolute or metaphysical necessity, for which no reason can be given. The present world is necessary in a physical or hypothetical sense, not absolutely or metaphysically. That is, once it is established to be such as it is, it follows that things such as they are will come into being. Therefore, since there must be an ultimate root in something, which has metaphysical necessity, and since there is no reason for an existing thing except in another existing thing, there must necessarily exist some one being of metaphysical necessity, or a being to whose essence belongs existence. So there must exist something which is distinct from the plurality of beings, or from the world, which, as we have admitted and shown, has no metaphysical necessity. To explain a little more distinctly, however, how temporal, contingent, or physical truths arise out of truths that are eternal and essential, or if you like, metaphysical, we should first acknowledge that from the very fact that something exists rather than nothing, there is a certain urgency [exigentia] toward existence in possible things or in possibility or essence itself - a pre-tension to exist, so to speak - and in a word, that essence in itself tends to exist. From this it follows further that all possible things, or things expressing an essence or possible reality, tend toward existence 2 with equal right in proportion to the quantity of essence or reality, or to the degree of perfection which they involve; for perfection is nothing but quantity of essence. Hence it is very clearly understood that out of the infinite combinations and series of possible things, one exists through which the greatest amount of essence or possibility is brought into existence. There is always a principle of determination in nature which must be sought by maxima and minima; namely, that a maximum effect should be achieved with a minimum outlay, so to speak. And at this point time and place, or in a word, the receptivity or capacity to the world, can be taken for the outlay, or the terrain on which a building is to be erected as commodiously as possible, the variety of forms corresponding t4 the spaciousness of the building and the number and elegance of its chambers. The Case is like that of certain games in which all the spaces on a board are to be filled according to definite rules, but unless we use a certain device, we find ourself at the end blocked from the difficult spaces and compelled to leave more spaces vacant than we needed or wished to. Yet there is a definite rule by which a maximum number of spaces can be filled in the easiest way. Therefore, assuming that ,t is ordered that there shall be a triangle with no other further determining principle, the result is that an equilateral triangle is produced. 3 And assuming that there is to be motion from one point to another without anything more determining the route, that path will be chosen which is easiest or shortest. Similarly, once having assumed that being involves more perfection than nonbeing, or that there is a reason why something should come to exist rather than nothing, or that a transition from possibility to actuality must take place, it follows that even ifthere is no further determining principle, there does exist the greatest amount possible in proportion to the given capacity of time and space (or the possible order of existence), in much the same way as tiles are laid so that as many as possible are contained in a given space. For 'references see p. 491
488 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS We can now understand in a wonderful way how a kind of divine mathematics or metaphysical mechanism is used in the origin of things and how the determination of the maximum takes place. So the right angle is the determined one of all angles in geometry, and so liquids placed in a different medium compose themselves in the most spacious figure, a sphere. But best of all is the example in ordinary mechanics itself; when many heavy bodies pull upon each other, the resulting motion is such that the maximum possible total descent is secured. 4 For just as all possibilities tend with equal right to existence in proportion to their reality, so all heavy objects tend to descend with equal right in proportion to their weight. And just as, in the latter case, that motion is produced which involves the greatest possible descent of these weights, so in the former a world is produced in which a maximum production of possible things takes place. Thus we now have a physical necessity derived from a metaphysical necessity. For even if the world is not necessary metaphysically, in the sense that its contrary would imply a contradiction or logical absurdity, it is nonetheless necessary physically, or determined in such a way that its contrary would imply imperfection or moral absurdity. And just as possibility is the principle of essence, so perfection or degree of essence is the principle of existence (since the degree of perfection determines the largest number of things that are compossible). This shows at once how there may be freedom in the Author of the world, even though he does all things determinately because he acts on the principle of wisdom or perfection. Indifference arises from ignorance, and the wiser a man is, the more determined he is toward the most perfect. But, you will say, however elegant this comparison of a kind of determining metaphysical mechanism with the physical mechanism of heavy bodies may seem, it is faulty in this respect - heavy bodies which act against each other truly exist, whereas possibilities or essences, whether prior to or abstracted from existence, are imaginary or fictitious, and therefore we cannot look for a reason for existence in them. I answer that neither these essences nor the so-called eternal truths about them are fictitious but exist in a certain region of ideas, if I may so call it, namely, in God himself, who is the source of all essence and of the existence of the rest. The very existence of the actual series of things shows that this is not merely a gratuitous assertion of mine. For since no reason can be found for this series within itself, as I have shown above, but this reason is to be sought in metaphysical necessity or in eternal truth, and since, furthermore, existing things can come into being only from existing things, as I have also explained, it is necessary for eternal truths to have their existence in an absolutely or metaphysically necessary subject, that is, in God, through whom those possibilities which would otherwise be imaginary are (to use an outlandish but expressive word) realized. s And we do in fact observe that everything in the world takes place in accordance with the laws of the eternal truths and not merely geometric but also metaphysical laws; that is, not merely according to material necessities but also according to formal reasons. And not only is this true in general, on the principle which we have just explained that there should exist a world rather than none and that this world should exist rather than another. (This may be learned in any case from the tendency of possibles toward existence.) But it is true also when we descend to special cases and see the wonderful way in which metaphysical laws of cause, power, and action are present throughout all nature, and how they predominate over the purely geometric laws of
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 489 matter themselves, as I found to my great admiration when I was explaining the laws of motion. As I have fully explained elsewhere, I was at length compelled to give up the law of the geometric composition of conatuses which I had formerly defended when, as a youth, I was more materialistic. 6 We therefore have the ultimate reason for the reality of essences as well as existences in one being, which must necessarily be greater, higher, and prior to the world itself, since not only the existing things which compose the world but also all possibilities have their reality through it. But because of the interconnection of all these things, this ultimate reason can be found only in a single source. It is evident, however, that existing things are continuously issuing from this source and are being produced and have been produced by it, since no reason appears why one state of the world should issue from it rather than another, that of yesterday rather than today's. It is clear, too, how God acts not merely physically but freely as well, and how there is in him not only the efficient but the final cause of the world. Thus we have in him the reason not merely for the greatness and power in the world mechanism as already established, but also for the goodness and wisdom exerted in establishing it. In case anyone may think that this confuses moral perfection or goodness with metaphysical perfection or greatness, and may deny the former while granting the latter, it must be recognized that it follows from what has been said that the world is not only the most perfect naturally or if you prefer, metaphysically - in other words, that that series of things has been produced which actually presents the greatest amount of reality - but also that it is the most perfect morally, because moral perfection is truly natural' in minds themselves. Hence the world not only is the most wonderful mechanism but is also, insofar as it consists of minds, the best commonwealth, through which there is conferred on minds as much felicity or joy as possible; it is in this that their natural perfection consists. You may object, however, that we experience the very opposite of this in the world, for often the very worst things happen to the best; innocent beings, not only beasts but men, are struck down and killed, even tortured. In fact, especially if we consider the government of mankind, the world seems rather a kind of confused chaos than something ordained by a supreme wisdom. So it seems at first sight, I admit, but when we look more deeply, the opposite can be established. A priori it is obvious from the principles which I have already given that the highest perfection possible is obtained for all things and therefore also for minds. And as the jurisconsults say, it is truly unjust to render a judgment without having studied the whole law. We know but a very small part of an eternity stretching out beyond all measure. How tiny is the memory of the few thousand years which history imparts to us! Yet from such slight experience we venture to judge about the immeasurable and the eternal; as if men born and reared in prison or in the underground salt mines of Sarmatia should think that there is no other light in the world but the wretched torch which is scarcely sufficient to guide their steps. If we look at a very beautiful picture but cover up all of it but a tiny spot, what more will appear in it, no matter how closely we study it, indeed, all the more, the more closely we examine it, than a confused mixture of colors without beauty and without art. Yet when the covering is removed and the whole painting is viewed from a position that suits it, we come to understand that what seemed to be a thoughtless smear on the canvas has really been done with the highest artistry by the creator of the work. And what the For references see p. 491
490 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS eyes experience in painting is experienced by the ears in music. Great composers very often mix dissonances with harmonious chords to stimulate the hearer and to sting him, as it were, so that he becomes concerned about the outcome and is all the more pleased when everything is restored to order. Similarly we may enjoy trivial dangers or the experience of evils from the very sense they give us of our own power or our happiness or our fondness for display. Or again, in witnessing performances of ropedancing or sword-dancing [sauls peril/eux], we are delighted by the very fears they arouse, and we playfully half-drop children, pretending to be about to throw them away for much the same reason that the ape carried King Christian of Denmark, when he was still a baby dressed in long clothes, to a rooftop and then, while everyone waited in terror, returned him, as if in play, to his cradle. By the same principle it is insipid always to eat sweets; sharp, sour, and even bitter things should be mixed with them to excite the taste. He who has not tasted the bitter does not deserve the sweet; indeed, he will not appreciate it. This is the very law of enjoyment, that pleasure does not run an even course, for this produces aversion and makes us dul1, not joyful. But what I have said about a part being disordered without destroying the harmony in the whole must not be interpreted as if there is no reason for the parts or as if it were enough for the world to be perfect as a whole, even though the human race should be wretched and there should be no concern in the universe for justice and no account taken of us, as is held by some people who have not made sound judgments about the totality of things. For we must recognize that just as care is taken in the best-ordered republic that individuals shall fare as well as possible, so the universe would not be perfect enough unless as much care is shown for individuals as is consistent with the universal harmony. No better measure for this matter can be set up than the law of justice itself, which dictates that each one shall take part in the perfection of the universe and his own happiness according to the measure of his own virtue and the degree to which his will is moved toward 8 the common good. And in this very thing is fulfil1ed what we call the charity and the love of God, in which alone the force and power of the Christian religion also consist, according to the opinion of wise theologians. Nor should it seem remarkable that so much respect should be shown to minds in the universe, since they resemble most closely the image of the supreme Author and are related to him not merely as machines to their maker - as are other beings - but also as citizens to their prince. Moreover, they are to endure as long as the universe itself and in some way to express the whole and concentrate it in themselves, so that it can be said that minds are total-parts. As for the afflictions, especially of good men, however, we must take it as certain that these lead to their greater good and that this is true not only theological1y but also naturally. So a seed sown in the earth suffers before it bears fruit. In general, one may say that though afflictions are temporary evils, they are good in effect, for they are short cuts to greater perfection. So in physics the liquids which ferment slowly also are slower to settle, while those in which there is a stronger disturbance settle more promptly, throwing off impurities with greater force. We may well call this stepping back in order to spring forward with greater force [qu'on recule pour mieux sauter]. These views must therefore be affirmed not merely as gratifying and comforting but also as most true. And in general, I hold that there is nothing truer than happiness and nothing happier and sweeter than truth. As the crown of the universal beauty and perfection of the works of God, we must
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 491 also recognize that the entire universe is involved in a perpetual and most free progress, so that it is always advancing toward greater culture. Thus a great part of our earth has now received cultivation and will receive it more and more. And though it is true that some sections occasionally revert into wilderness or are destroyed and sink back again, this must be understood in the same sense in which I have just explained the nature of afflictions, namely, that this very destruction and decline lead to a better result, so that we somehow gain through our very loss. To the objection which could be offered, moreover, that if this were so, the world should long since have become a paradise, there is an answer near at hand. Although many substances have already attained great perfection, yet because of the infinite divisibility of the continuum, there always remain in the abyss of things parts which are still asleep. These are to be aroused and developed into something greater and better and in a word, to a better culture. And hence progress never comes to an end. REFERENCES • The fuller and more exact meaning of this title, here translated literally, is 'On the Process by Which the World Comes into Being from Its Roots', that is, 'On the First Principles of Creation'. 1 Both G. and E. have a priore; Professor Paul Schrecker is authority for reading a priori, with the Hanover manuscript. 2 Reading existentiam (with E.'s errata) for essentiam (G.). 3 For Leibniz's more specific argument on this point see the preceding selection (No. 50), particularly the closing paragraph. 4 The example apparently alluded to is the catenary, discovered by John and James Bernoulli, and solved by Leibniz, Huygens, and others in 1696. It was easily solved as a problem in maxima (see Mach, The Science 0/ Mechanics, pp. 85-89). 5 The barbarism is the word realisentur. The verb occurs frequently in crucial passages in the correspondence with Des Bosses (see p. 600, and p. 615, note 9). 6 The allusion is to the Theory 0/ Abstract Motion (1671) (No.8). Leibniz explains his change of opinion in detail in No. 46, Part I. 7 Physico. The extension of nature to include human purposes and actions is characteristic of much of Leibniz's writing (see p. 62, note 65). 8 Reading ergo (Brd.) for ergo (G.).
52 CLARIFICATION OF THE DIFFICULTIES WHICH MR. BAYLE HAS FOUND IN THE NEW SYSTEM OF THE UNION OF SOUL AND BODY Histoire des ouvrages des savants, July, 1698 Of the criticisms which the New System (No. 47) evoked, none was more penetrating than than that which Pierre Bayle attached to the article 'Rorarius'in the second volume of his Dictionnaire historique et critique appearing in 1697. His criticism covered many points but centered on the interpretation of the relation between mind and body. Leibniz sent the following reply in the form of a letter to Basnage de Beauval, editor of the Histoire, which had succeeded Bayle's own Nouvelles de la republique des lettres. [G., IV, 517-24] I take the liberty, Sir, of sending you this clarification of the difficulties which Mr. Bayle has found in the hypothesis I proposed to explain the union of soul and body. Nothing is kinder than the consideration which he shows for me, and I hold myself honored by the objections which he has put in his excelIent Dictionary, in the article on 'Rorarius'. So great and profound a mind as his, moreover, cannot but instruct, and I shall strive to profit by the light which he has shed on these matters in this article and at many other points in his work. He does not reject what I have said about the conservation of the soul or even that of the animal, but he still does not seem satisfied with the way in which I have tried to explain the union and intercourse of the soul and the body in the Journal des savants for June 27 and July 4, 1695, and in the Histoire des ouvrages des savants for February, 1696. 1 These are the words which seem to indicate where he finds the difficulty. He says: I am unable to understand the chain of internal and spontaneous actions which would cause the soul of a dog to feel pain immediately after having felt joy, even if it were alone in the universe. I reply that when I said that even if only it and God existed in the world, the soul would feel all that it feels now, I was merely using a fiction, assuming something which cannot happen naturaIly, in order to show that the feelings of the soul are entirely a result of what is already in it. I do not know whether the proof of the incomprehensibility which Mr. Bayle finds in this 'chain' is to be sought only in what he says later or whether he already means to suggest it in the example of the spontaneous transition from joy to pain, perhaps by trying to show that such a transition is contrary to the axiom that a thing always remains in the state in which it is at a certain time, unless something occurs to compel it to change, and that therefore, if an animal once is in a state of joy, it will always be in such a state if it is alone or if there is
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 493 nothing external to make it pass over into pain. In any case, I agree with the axiom; I even maintain that it favors my position, since it is in fact one of its foundations. For do we not conclude from this axiom, not only that a body at rest always remains at rest, but also that a body in motion will always retain its motion or its process of change, that is to say, the same speed and direction, if nothing occurs to impede it? Thus a thing not only remains in the state in which it is, insofar as it depends on itself, but also continues to change when it is in a state of change, always following one and the same law. But in my opinion it is in nature of created substance to change continually following a certain order which leads it spontaneously (if I may be allowed to use this word) through all the states which it encounters, in such a way that he who sees all things sees all its past and future states in its present. And this law of order, which constitutes the individuality of each particular substance, is in exact agreement with what occurs to every other substance and throughout the whole universe. Perhaps I shall not claim too much if I say that I can demonstrate all this, but for the present the question is merely to maintain it as a possible hypothesis which is suitable for explaining phenomena. Now it is in this way that the law of change in the substance of the animal carries it from joy to pain in that moment in which there takes place a break in the continuous processes in its body, because it is the law of the indivisible substance of the animal to represent what occurs in its body in the way in which we experience it, and even to represent in some way, through its relation to this body, everything which occurs in the world. For the substantial unities are nothing but different concentrations of the universe represented according to the different points of view by which they are distinguished. 2 Mr. Bayle continues: I understand why a dog passes immediately from pleasure to pain if we strike him with a stick just when he is very hungry and is eating some bread. I am not sure that we do fully understand this. No one knows better than Mr. Bayle himself that it is just here that the great difficulty lies in explaining why whatever occurs in the body makes a change in the soul, and that it is this which has forced the defenders of occasional causes to have recourse to the care which God must take to represent continually in the soul the changes which occur in its body. I believe instead that it is the soul's own God-given nature to represent everything that takes place in its organs by virtue of its own laws. Bayle continues: But that his soul is constructed in such a way that he should feel pain at the moment he is struck even if no one were to strike him, and even if he were to continue to eat bread without difficulty or interruption - this I cannot understand. Nor do I recall having said this. And one can speak in this way only by a metaphysical fiction, as when one assumes that God destroys a body in order to create a vacuum; the one is as contrary to the order of things as the other. For since the nature of the soul has been made in such a way from the beginning as to represent successively the changes of matter, the situation which we assume could not arise in the natural order. God could give to each substance its own phenomena independent of those of others, but in this way he would have made as many worlds without connection, so to speak, as there are substances, almost as we say that when we dream, we are in a world apart and that we enter into the common world when we wake up. Not that dreams do not For references see p. 497
494 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS also correspond with the organs and the rest of the body, but in a less distinct way. Let us continue with Mr. Bayle. He says: I find too that the spontaneity of this soul is most incompatible with the feelings of pain and in general, with all perceptions which are displeasing to it. This incompatibility would certainly exist if spontaneous and voluntary meant the same thing. Everything voluntary is spontaneous, but there are spontaneous actions which are not chosen and therefore are not voluntary. It does not rest with the soul always to give itself feelings which please it, since the feelings which it will have are dependent upon those which it has had. Mr. Bayle says further: Furthermore, it seems to me that this able man dislikes the Cartesian system because of a false assumption, for one cannot say that the system of occasional causes makes the action of God intervene by a miracle (deus ex machina) in the reciprocal dependence of body and soul. For since God's intervention follows only general laws, he does not therein act in an extraordinary way. This is not the only reason why I dislike the Cartesian system. And when my own is given a little consideration, it becomes clear what I find in it that makes me adopt it. Even if the hypothesis of occasional causes should have no need for miracles, it seems to me that my own would still have other advantages. I have pointed out that we can imagine three systems to explain the intercourse which we find between body and soul; namely, (1) the system of the mutual influence of one upon the other, which when taken in the popular sense is that of the Scholastics, and which I consider impossible, as do the Cartesians; (2) that of a perpetual supervisor who represents in the one everything which happens in the other, a little as if a man were charged with constantly synchronizing two bad clocks which are in themselves incapable of agreeing - this is the system of occasional causes; and (3) that of the natural agreement of two substances such as would exist between two very exact clocks. I find this view fully as possible as that of a supervisor and more worthy of the author of these substances, clocks or automata. But let us see whether the system of occasional causes does not in fact imply a perpetual miracle. Here it is said that it does not, because God would act only through general laws according to this system. I agree, but in my opinion that does not suffice to remove the miracles. Even if God should do thiS continuously, they would not cease being miracles, if we take this term, not in the popular sense of a rare and wonderful thing, but in the philosophical sense of that which exceeds the powers of created beings. It is not enough to say that God has made a general law, for besides the decree there is also necessary a natural means of carrying it out, that is, all that happens must also be explained through the nature which God gives to things. The laws of nature are not so arbitrary and so indifferent as many people imagine. For example, if God were to decree that all bodies should have a tendency to move in circles and that the radii of the circles should be proportional to the magnitude of the bodies, one would either have to say that there is a method of carrying this out by means of simpler laws, or one would surely have to admit that God must carry it out miraculously, or at least through angels charged expressly with this responsibility, somewhat in the manner of those that were once assigned to the celestial spheres. It would be the same if someone said that God has given natural and primitive gravities to bodies by which each tends to the center ofits globe without being pushed by anoth-
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 495 er body, for in my opinion such a system would need a perpetual miracle, or at least the help of the angels. 3 Does the internal and active power communicated to the forms of bodies know the series of actions which it must produce? By no means, for we know by experience that we are ignorant of what kinds of perceptions we shall have in an hour. I reply that this power, or better, this soul or form itself, does not know them distinctly but that it does feel them confusedly. In each substance there are traces of everything which has happened to it and of everything which will happen to it. But this infinite multitude of perceptions prevents us from distinguishing them, just as I cannot distinguish one voice from another when I hear the loud confused noise of a crowd. Then it would be necessary for the forms to be directed by some external principle in producing their acts. But would this not be the deus ex machina exactly as in the system of occasional causes? This deduction is avoided by the preceding answer. On the contrary, the present state of each substance is a natural result of its preceding state, but there is only one infinite intelligence which, because it envelops the universe, can see this result in souls as well as in each portion of matter. Mr. Bayle ends with these words: Finally, since he assumes with good reason that all souls are simple and indivisible, we cannot understand how they can be compared to a clock. That is, they are able to vary their operations by their original constitution, making use of the spontaneous activity which they receive from their creator. We conceive clearly that a simple being will always act uniformly if no external cause interferes with it. If it were composed of many pieces, like a machine, it would act diversely because the particular activity of each piece could at any moment change the course of all the others. But in a single substance, where can you find the cause of a change in operation? I find this objection worthy of Mr. Bayle, and one of those which are most in need of clarification. But I also believe that if I had not taken care of it from the start, my system would not deserve study. I have compared the soul with a clock only with regard to the regulated precision of its changes, which is only imperfect even in the best clocks, but which is perfect in the works of God. And one can say that the soul is a most exact immaterial autopiaton. When it is said that a simple being will always act uniformly, a distinction needs to be made. If to act uniformly is to follow perpetually the same law of order or of succession, as in a certain scale or series of numbers, I agree that in this sense every simple being and even every composite being acts uniformly. But if uniformly means similarly\ I do not agree. To explain the difference this meaning makes by means of an example, a movement in a parabolic path is uniform in the former sense but not in the latter, for the parts of the parabolic curve are not similar to each other as are the parts of a straight line. It is true, I may say in passing, that a simple body left to itself will describe only straight lines, speaking only of the center which represents the movement of the whole body. But when a simple and rigid body has once received a rotation or circular motion about its center, and retains it in uniform direction and uniform speed, the result is that such a body, left to itself, can describe circular lines at points other than its center when the center is at rest, and even certain quadratrices when the center is in motion, curves whose ordinates are compounded of the straight line traversed by the center and of the sine [of the rotated For references see p. 497
496 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS angles], the cosine being the abscissa, and the arc being related to the circumference as the straight line traversed is to a given line. S We must also take into consideration that the soul, however simple it may be, always has a feeling [sentiment] composed of many perceptions at once, a fact which serves our purpose as well as if it were composed of parts like a machine. For each preceding perception influences those which follow in conformity with a law of order which is found in perceptions as well as in movements. For many centuries, too, most philosophers, who ascribe thoughts to souls and to angels, whom they believe to be without any bodies (not to speak of the intellects of Aristotle), have admitted spontaneous change in simple beings. I add that the perceptions which are found together in one soul at the same time include a veritably infinite multitude of little indistinguishable feelings, which the subsequent series must develop, so that we need not be astonished at the infinite variety of what must result from it in time. All this is only a consequence of the representative nature ofthe soul, which must express what happens, and even what will happen in its body and in some way in all other bodies, through the connection or correspondence between all the parts of the world. Perhaps it would have sufficed to say that God, having made material automatons, could also make immaterial ones which represent the former ones, but I believed that it would be well to elaborate my views a little more fully. As for the rest, I have read with pleasure what Mr. Bayle says in the article on Zeno. 6 Perhaps he could perceive that the conclusions which can be drawn from it agree better with my system than with any other, for what is real in extension and movement consists of nothing but the foundation of order and the regular sequence of phenomena and perceptions. Also, the Academics and skeptics, as well as those who tried to answer them, seem chiefly to have been involved in difficulties merely because they sought a greater reality in things outside of us than that of well-regulated phenomena. We conceive of extension in conceiving an order in coexistences, but we should not conceive of it, any more than of space, in the nature of a substance. The same is true of time, which presents to the mind only an order in changes. As for motion, that which is real in it is force or power, namely, something in the present state which carries with it a change for the future. The rest is only phenomena and relations. Consideration of this system also shows that when we penetrate to the foundations of things, we observe more reason than most of the philosophical sects believed in. The lack of substantial reality in the sensible things of the skeptics; the reduction of everything to harmonies or numbers, ideas, and perceptions by the Pythagoreans and Platonists; the one and the whole of Parmenides and Plotinus, yet without any Spinozism; the Stoic connectedness, which is yet compatible with the spontaneity held to by others; the vitalism of the Cabalists and hermetic philosophers who put a kind of feeling into everything; the forms and entelechies of Artistotle and the Scholastics; and even the mechanical explanation of all particular phenomena by Democritus and the moderns; etc. - all of these are found united as if in a single perspective center from which the object, which is obscured when considered from any other approach, reveals its regularity and the correspondence of its parts. Our greatest failure has been the sectarian spirit which imposes limits upon itself by spurning others. The formalist philosophers find fault with the materialists or corpuscular philosophers, and vice versa. We wrongly impose limits upon the divisibility and subtlety, as well as on the riches and beauty of nature, when we assume atoms and a void, when we imagine cer-
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 497 tain first elements (as do even the Cartesians) 7 in place of veritable unities, and when we do not recognize the infinite in everything, and the exact expression of the greatest in the smallest, combined with the tendency of each one to develop itself in a perfect order. This is the most admirable and the most beautiful effect of the sovereign principle whose wisdom and bounty leave nothing better to be desired by those who are able to understand its economy. REFERENCES These references are to the New System itself and to the first two of the short explanations, the second of which is given in No. 46, Part II (cf. p. 461, note 19). 2 Meanwhile Leibniz has not answered Bayle's criticism, which Arnauld (see No. 36) and Foucher had already suggested. This concerns the unnecessary character of the physical world, if every modification of the soul arises solely out of its own nature. Leibniz does return to this problem briefly later in this essay, as well as in Nos. 53 and 62 and elsewhere. His basic argument for the existence of an external world of monads and a universal harmony is based upon the principle of perfection and plenitude (see his argument for the existence of other minds in No. 39). 3 The ambiguity of Leibniz's definition of miracle (as that which exceeds the power of creatures) is shown by his inclusion of Newton's theory of 'attraction' among miraculous explanations. The test of what lies within the power of creatures (or of nature) is never indicated; here his inclination to restrict motion, as did the Cartesians, to motion imparted by impact led him to views hardly consistent with his own metaphysics. Leibniz did not take into consideration the celebrated general scholium to Book III of Newton's Principia, in which the assumption of an attractive power on bodies is rejected, for the obvious reason that it appeared only in the second edition in 1713. 4 I.e., with a constancy or invariance in its states, analogous to a curve each part of which is similar to every other part, that is, a straight line. S The quadratrix, first discovered by Hippias of Elis, is a compound of a closed rotary and an open progressive motion (see Cantor, op. cit., I, 195-97, 246-48). To construct the figure described by Leibniz, let the center of the circle move on the Y-axis. 6 In this article Bayle had discussed the inconsistency of infinite divisibility with perceptual limits to analysis and had suggested that solid physical figures, as well as plane geometrical ones, have only 'ideal' existence. 7 Cf. p. 506, (No. 53), and p. 508, note 14. 1
53 ON NATURE ITSELF, OR ON THE INHERENT FORCE AND ACTIONS OF CREATED THINGS· Acta eruditorum, September, 1698 Robert Boyle's proposal, in his Free Inquiry into the Vulgarly Received Notion of Nature (1682), that the term 'nature' should be avoided and 'mechanism' substituted for it occasioned a controversy between John Christopher Sturm of Altdorf and Gunther Christopher Schelhammer of Kiel in 1692-98, in which Sturm defended Boyle's opinion, while Schelhammer defended the concept of nature. One of the points argued concerned the source and nature of motion, Sturm defending the Cartesian position that God is its only source. Though the correspondence which began between Leibniz and Sturm in 1695 avoided the central question of the status of nature, it turned on the independent reality of the natural order, including man, Sturm maintaining that it is pagan and unChristian to attribute properties to 'the nature of things' and that nature has no energy or force proper to itself. Leibniz's published reply is directed not only at Sturm but at the occasionalists and others who in effect deny the reality of the physical world. It contains a careful exposition of his reasons for a pluralistic. energistic system, and one pre-eminent for its revelation of the motives and the nature ofhis argument. [G., IV, 504-16] 1. I have recently had sent to me the apology published in Altdorf by that most noted and, in mathematical and physical matters, deservedly famous man, John Christopher Sturm, in defense of his dissertation De idolo naturae, which had been attacked by an outstanding and most gifted physician of Kiel, Gunther Christopher Schelhammer, in a book on nature. 1 I too had long ago pondered the same problem, and I had also carried on a kind of disputation by letter with the famous author of the dissertation, which he himself has recently mentioned in a way that honors me, since he makes public mention of certain papers which passed between us in the first volume of his Elective Physics (Book I, Sec, 1, chap. iii; Epilogue, Sec. 5). I was therefore all the more willing to set my mind and attention to this argument which is so important in itself, judging it necessary to explain my own opinion and the problem itself a little more clearly in terms of the principles which I have now stated so many times. His apologetic dissertation seems to offer a convenient occasion for beginning this, for we may judge that the author has here set forth, in few words and from a single perspective, the most important issues involved in the matter. I am not making the quarrel between these famous men my own, however. 2. Two questions are, I believe, of most importance. The first: In what does the nature consist which we customarily ascribe to things, whose attributes, as they are usually understood, Mr. Sturm considers to reek somewhat of paganism? The second: Whether there is any energy in created things. This he seems to deny. As for the first question,
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 499 on nature itself, if we are to discover both what it is and what it is not, I agree that there is no world soul; and I admit also that the wonderful events which occur daily and because of which we commonly say, rightly, that the work of nature is a work of intelligence are not to be ascribed to certain created intelligences endowed with wisdom and power proportional to such a task. But universal nature is, so to speak, the artifice of God, and such a work, indeed, that any natural machine whatever consists further of infinite organs (this is the true, but little noted, distinction between nature and art) and so entails an infinite wisdom and power on the part of its author and governor. So I consider the omniscient heat of Hippocrates, the soul-giving cholcodea of Avicenna, the most wise plastic power of Scaliger and others, and Henry More's hylarchic principle to be in part impossible and in part superfluous. 2 I consider it sufficient that the mechanism of the world is built with such wisdom that these wonderful things depend upon the progression of the machine itself, organic things particularly, as I believe, evolving by a certain predetermined order. And I agree when this illustrious man rejects the figment of a certain wise created nature which forms and governs the mechanisms of physical bodies. But I do not agree, and I do not think it conformable to reason, that we should deny that any active creative force resides in things. 3. I have said what nature is not; let us now examine a little more closely what this nature is which Aristotle has well called the principle of motion and of rest, though that philosopher seems to me to take the term more broadly than its accepted meaning, and to understand by it not only local motion and rest in a place, but change and Ul'aU1C; or permanence in general. 3 I may also point out in passing that the definition which he gives of motion, though more obscure than it should be, is not as inept as it seems to those who assume that he meant to define only local motioll. But to return to the point, Robert Boyle, a man of distinction and thoroughly at home in the observation of nature, wrote a little work On Nature Itself, the argument of which, if I remember rightly, amounted to this - that we must hold nature to be the mechanism of bodies itself. Superficially this can be approved, but to examine the matter with greater care, we must distinguish principles from derivative matters within this same mechanism; thus it is not enough in explaining a clock to say that it is moved by a mechanical principle, without further distinguishing whether it is driven by a weight or by a spring. I have already expressed, more than once, a view which I believe will be of use in preventing mechanical explanations of natural things from being carried to abuse in injuring piety, as if matter can stand by itself and mechanism needs no intelligence or spiritual substance - the view, namely, that the origin of this mechanism itself has come, not from a material principle and mathematical reasons alone, but from a higher and so to speak, a metaphysical source. 4. One important indication of this, among others, is provided by the foundation of the laws of nature, which is not to be found in the principle that the same quantity of motion is conserved, as had commonly been held, but rather in the principle that the same quantity of active power is necessarily conserved, and indeed - a thing which I discovered happens for a most beautiful reason - the same quantity of motive action also, the value of which is far different from what the Cartesians think of as the quantity of motion. After two mathematicians who easily rank among the foremost in ability had discussed this matter with me, partly in letters and partly in publications, one of them came over to my camp completely, and the other, after long and accurate For references see p. 508
500 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS thought, came to the point of abandoning all his objections and frankly confessed that he had not yet thought of any answer to my demonstration. 4 I have therefore been all the more astonished that in explaining the laws of motion in the published part of his Elective Physics, this famous man has accepted the popular opinion about these matters as if no doubt of it were possible, though he himself acknowledges that it rests upon no demonstration but only upon a kind of probability; this he has repeated in his latest discussion, chapter iii, Section 2. But perhaps he wrote this before my own views had appeared, and then either had no time to revise what he had written or did not think of it, especially since he believed that the Jaws of motion are arbitrary - a view which does not seem to me to be entirely consistent. For I think that God has been led to set in motion the laws which are observed in nature through determined principles of wisdom and by reasons of order; and that this makes clear what I once pointed out in discussing the laws of optics (a view to which the famous Molyneux later gave his approval in his Dioptrics), that final causes are useful not only for virtue and piety, in ethics and natural theology, but also for discovering and detecting hidden truths in physics itself.5 So I could have wished that when the famous Sturm, in dealing with final causes in his Elective Physics, referred to my opinion among the hypotheses, he might also have appraised it fully in his criticism, for he would then undoubtedly have taken occasion to say many excellent things in behalf of the excellence and fruitfulness of the argument - things which would be useful for piety as well. 5. But now we must examine what he says in this apologetic dissertation of his about the concept of nature and what seems still to be lacking in what he says. He admits (chap. iv, Sees. 2, 3, and elsewhere) that motions now taking place result by virtue of an eternal law once established by God, which law he then calls a volition and command, and that no new command or new volition of God is then necessary, much less a new conatus or some laborious effort (Sec. 3). And he rejects as wronbly ascribed to him by his opponent the opinion that God moves things as a woodchopper moves his ax or a miller controls his mill by shutting off the water or turning it into the wheel. But this explanation does not seem to me to do justice to the truth. For I ask whether this volition or command, or if you prefer, this divine law once established, has bestowed upon things only an extrinsic denomination or whether it has truly conferred upon them some created impression which endures within them, or as Mr. Schelhammer, who is as distinguished in judgment as in experience, very well puts it, an internal law from which their actions and passions follow, even if this law is mostly not understood by the creatures in which it inheres. The former view seems to be that of the anthors of the system of occasional causes, especially of the ingenious Mr. Ma:lebranche; the latter is the accepted view, and I believe the truest. 6. For since this command in the past no longer exists at present, it can accomplish nothing unless it has left some subsistent effect behind which has lasted and operated until now, and whoever thinks otherwise renounces any distinct explanation of things, if I am any judge, for if that which is remote in time and space can operate here and now without any intermediary, anything can be said to follow from anything else with equal right. It is not enough, therefore, to say that in creating things in the beginning, God willed that they should observe a certain law in their progression, if his will is imagined to have been so ineffective that things were not affected by it and no durable result was produced in them. In any case it also conflicts with the concept of the divine power and will, which are pure and absolute, for God to will and yet to produce or
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 501 change nothing by his willing, for him always to act but never to achieve and not to leave behind any work or any accomplishment [anorBAeupa]. Surely if nothing has been impressed upon creatures by that divine word producat terra, multipticemini animafia 6, if things are affected after the command just as ifno command had intervened, it follows - since some connection, either immediate or mediated by something, is necessary between cause and effect - either that nothing conforming to the command is now happening or that the command was valid only in the present and must always be renewed in the future. But the learned author rightly repudiates this view. If on the other hand, the law set up by God does in fact leave some vestige of him expressed. in things, if things have been so formed by the command that they are made capable of fulfilling the will of him who commanded them, then it must be granted that there is a certain efficacy residing in things, a form or force such as we usually designate by the name of nature, from which the series of phenomena follows according to the prescription of the first command. 7. This inherent force can indeed be understood distinctly, though it cannot be explained by sense perception. It is no more to be thus explained than is the nature of the soul, for this force belongs among those things which are grasped, not by the imagination but by the understanding. Therefore I interpret this learned man's request (in chap. iv, Sec. 6, of his 'Apologetic Dissertation') that we explain to the imagination the way in which such an inherent law can operate in bodies ignorant of law, as meaning that he wants it explained to the understanding, for otherwise it might be thought that he was asking for sounds to be painted or colors heard. Furthermore, if difficulty in explaining something is a sufficient reason for rejecting it, this must also be applied, to be consistent, to the view which he complains is ascribed to him unjustly (chap. i, Sec. 2), namely, that he prefers to hold that all things are moved by divine force alone rather than to admit anything by the name of nature of whose nature he is ignorant. Certainly Hobbes and others who try to make everything corporeal could also depend on this argument with as much right, since they have convinced themselves that only body can be explained distinctly and in sensible imagery. But these men are rightly refuted by the very fact that there is a power of action in things which we do not derive from sensible images. And simply to refer this back to a command of God, given at one time in the past and in no way affecting things or leaving an effect behind it, is so far from explaining the matter that it is rather to put aside the role of the philosopher and to cut the Gordian knot with a sword. For the rest, a more distinct and accurate explanation of active force than has heretofore been given may be drawn from my Dynamics, which contains an appraisal of the laws of nature and of motion that is true and in harmony with things. 8. But if some advocate of the new philosophy which maintains the inertness and deadness of things should go so far as to deprive God's commands of all lasting effect and efficiency in the future, and to regard it as nothing to demand of him always new arrangements (a view which Mr. Sturm wisely rejects as foreign to his own), it is his own affair to decide how worthy he considers this of God. But we cannot excuse him from giving us a reason why things themselves can have an enduring permanence while the attributes of things, which we designate as their 'nature', cannot have this permanence. For it is nevertheless consistent that just as the word fiat leaves behind it something permanent, namely, the persisting thing itself, so the word benedictio leaves behind it something in things no less wonderful - a fruitfulness or an impulse to proFor references see p. 508
502 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS duce their actions and to operate, from which activity follows if nothing interferes. 7 To this can be added the point I have made elsewhere, though perhaps not everyone has understood it adequately as yet, namely, that the substance of things itself consists in the force of acting and being acted upon; hence it follows that no enduring thing can be produced ifno force that long endures can be impressed upon it by the divine power. Then it would follow that no created substance, no identical soul, would be permanent, and hence that nothing would be conserved by God, but everything would reduce to certain evanescent and flowing modifications or phantasms, so to speak, of the one permanent divine substance. And, what reduces to the same thing, God would be the nature and substance of all things - a doctrine of most evil repute, which a writer who was subtle indeed but irreligious, in recent years imposed upon the world, or at least revived. 8 Surely if corporeal things contained nothing but matter, they could most truly be said to consist of a flux and to have nothing substantial, as the Platonists long ago recognized. 9. The second question is whether created beings may be said properly and truly to act. If we once understand that their internal nature is no different from the force of acting and suffering, this question reduces to the former one, for there can be no action without a force of acting, and conversely, a power which can never be exercised is meaningless. Yet since action and power are different things, the former a matter of succession, the latter permanent, let us examine action also. Here I confess I find no little difficulty in explaining the opinion of the famous Mr. Sturm. For he denies that created things by themselves properly act, yet he nonetheless admits that they do act, since he is unwilling to have ascribed to him the comparison of created things with an ax moved by a woodcutter. I can make out nothing certain from this; he does not seem to me to have explained very clearly how much he departs from accepted opinions, nor what sort of distinct concept of action he has in mind - for that the concept of action is not an easy or obvious one is clear from the conflicts of the metaphysicians. So far as I have made the concept of action clear to myself, I believe that there follows from it and is established by it that most widely accepted principle of philosophy - that actions belong to substances [actiones esse suppositorum). And hence I hold it also to be true that this is a reciprocal proposition, so that not only is everything that acts an individual substance but also every individual substance acts without interruption, not excepting body itself, in which no absolute rest is ever to be found. 9 10. But let us now consider a little more carefully the opinion of those who deny a true and proper activity to created things, as Robert Fludd, the author of the Mosaic Philosophy long ago did, and as some of the Cartesians now do who believe that things do not act but that God acts in the presence of things and according to the fitness of things, so that things are occasions, not causes, and merely receive but never effect or produce. While this doctrine had been proposed by Cordemoi, La Forge, and other Cartesians, it was particularly Malebranche, who, with his characteristic acumen, embellished it in luminous phrases. lO But so far as I know, no one has given sound reasons for it. Certainly if this doctrine is extended so far as to deny even the immanent actions of substances - an interpretation which Mr. Sturm shows his conspicuous caution in rejecting, in his Elective Physics, Book I, chapter iv, Epilogue, Section 11 it seems foreign to reason as no other view can be. For who will doubt that the mind thinks and wills, that many thoughts and volitions are produced in us and by us, and
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 503 that there is something spontaneous about us? To doubt this would be to deny human freedom and to thrust the cause of evil back into God but also to contradict the testimony of our internal experience and consciousness, by which we feel that what these opponents have transferred to God without even the appearance of a reason belongs to ourselves. But if we ascribe to our mind an inherent force of producing immanent actions or what is the same thing, of acting immanently, then nothing prevents the same force from residing in other souls or forms or if you prefer, in the natures of other substances; indeed, it is entirely consistent for it to be so - unless it is believed that in the nature of things which is open to us, our minds alone are active or that all power of action is immanently, and hence vitally, so to speak, coupled with the understanding. But such assertions are certainly not confirmed by any reason, nor can they be defended without coercing the truth. What we can establish about the external [transeunt] actions of creatures may better be explained elsewhere; in fact, I have already partly explained it - the intercourse of substances or of monads 11 , namely, arises not from an influence but from a consensus originating in their preformation by God, so that each one is adjusted to the outside while it follows the internal force and laws of its own nature. It is also in this that the union ofsoul and body consists. 11. It is indeed true, however, that bodies in themselves are inert if this is understood in the right sense, namely, insofar as what is once assumed for some reason to be at rest cannot impel itself to motion, or suffer being impelled by some other body without resistance, any more than it can of its own accord change the degree of velocity or the direction which it once has had or suffer such change from the outside easily and without resistance. So it must be admitted that extension, or the geometric nature of a body, taken alone contains nothing from which action and motion can arise. Indeed, matter rather resists being moved by its own natural inertia, as Kepler has fittingly named it, and is thus not indifferent to rest and motion as it is popularly interpreted to be, but strives toward motion with an active force proportional to its magnitude. Hence it is in this passive force of resistance, which involves impenetrability but something more, that I locate the concept of primary matter or mass [molis], which is everywhere proportional in a body to its magnitude. And hence I show that far different laws of motion follow from it than would be the case if the body, or matter itself, possessed only impenetrability with extension. And just as there is a natural inertia opposed to motion in matter, so there is in the body itself, and indeed, in every substance, a natural constancy opposed to change. This view does not justify those who deny action in things but rather opposes them, for as certain as it is that matter in itself does not begin motion, so certain is it also (as the well-known experiments on motion arising from the impact of a moving body also show) that taken by itself, a body retains an impetus and remains constant in its speed or that it has a tendency to persevere in the series of changes which it has once begun. Now since these activities and entelechies cannot be modes of primary matter or of mass, which is something essentially passive, as the judicious Sturm has himself clearly recognized (as I shall show in the next paragraph), it can be concluded that there must be found in corporeal substance a primary entelechy or first recipient [npwTov OeKTIICOV] of activity, that is, a primitive motive force which, superadded to extension, or what is merely geometrical, and mass, or what is merely material, always acts indeed and yet is modified in various ways by the concourse of bodies, through a conatus or impetus. It is this substantial principle itself which is called the soul in living beings and For references see p. 508
504 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS substantial form in other beings, and inasmuch as it truly constitutes one substance with matter, or a unit in itself, it makes up what I call a monad. For if these true and real unities were dispensed with, only beings through aggregation would remain; indeed, it would follow that there would be left no true beings within bodies. For even though there are atoms of substance, namely, my monads, which lack parts, there are no atoms of mass or of minimum extension, or any last elements, since a continuum is not composed of points. Furthermore, there is no being that is greatest in mass or infinite in extension, even if there are always things greater than any given things; there is only a being greatest in intension of perfection or infinite in power. 12. I observe, however, that in his 'Apologetic Dissertation' (chap. iv, Secs. 7ff.) the famous Sturm has undertaken to combat a moving force resident in bodies by means of certain arguments. "I will show abundantly", he says, "that no corporeal substance is capable of any active moving power" - though I do not grasp what a power can be which is not actively motive. He says, however, that he will use twin arguments - one from the nature of matter and body, the other from the nature of motion. The former reduces to this: matter is by its nature an essentially passive substance, and so it is no more possible to give it an active force than for God to will a stone, while it remains a stone, to be alive and reasonable, that is, not to be a stone. In the next place, the things we assume in body are only modifications of matter, but a modification (this I admit is excellently expressed) of something essentially passive cannot make it something active. But to this it is easy to make the following reply from the point of view of the accepted as well as of the true philosophy. Matter may be understood as either secondary or primary. Secondary matter is indeed complete substance but not merely passive. 12 Primary matter is merely passive but not a complete substance; there must be added to it a soul or a form analogous to the soul a first entelechy, that is, or a kind of nisus or primitive force of action which is itself the inherent law impressed upon it by divine command. I do not expect this famous and brilliant man to shrink back from this opinion, since he recently defended the view that body is composed of matter and spirit; except that spirit is not here to be taken for an intelligent being, as is usually done, but for a soul or a form analogous to the soul. Neither is it to be taken for a simple modification but for something which perseveres and is constitutive and substantial. This I customarily call a monad, which contains perception and appetite, as it were. The accepted doctrine, which is consistent with Scholastic teaching favorably expounded, must therefore first be refuted if the argument of the famous man is to have force. Similarly, it is clear from this that we cannot concede his assumption that whatever is in a corporeal substance must be a modification of matter. For it is well known that according to the accepted philosophy there are souls in the bodies of living beings which are certainly no modifications of these bodies. For though the learned man may assert the contrary, and seem to deny to dumb animals all sensibility in any true sense, and a proper soul, he cannot assume this opinion as the basis of his demonstration until it has itself been demonstrated. I believe on the contrary that it is consistent neither with the order nor with the beauty or the reason of things that there should be something vital or immanently active only in a small part of matter, when it would imply greater perfection if it were in all. And even if dominant sou!:', and hence intelligent souls such as there are in men, cannot be everywhere, this is no objection to the view that there should everywhere be souls, or at least things analogous to souls.
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 505 13. The second argument, which the illustriuous man takes from the nature of motion, seems to me to be no more necessarily conclusive than the first. Motion, he says, is merely the successive existence of the thing moved in different places. Let us concede this for the present, though it is not entirely satisfactory and expresses the result of motion rather than what we call its formal reason. However, it does not hereby exclude a moving force. For in the present moment of its motion, a body is not merely in a place of the same size as itself, but it also has a tendency or urge toward changing its place, so that its future state follows from its present one, per se, by the force of nature. Otherwise the body A which is in motion would be no different at the present moment (and therefore at any moment whatever) from the body B which is at rest, and it would follow from the opinion of the distinguished man, if it is opposed to mine at this point, that there would be no way whatever of distinguishing between bodies, since there is no basis for such a distinction in a plenum of mass uniform in itself other than that which concerns motion. This view would thus also have the further effect that there could be absolutely no variation in bodies and that everything would always remain the same. For if there is no difference between any portion of matter and another portion equal and congruent to it (which the illustrious man must admit, since he has destroyed active forces or impetuses and all other qualities and modifications except for existence in this place and successively some future existence or other, all qualities and modifications having been removed), and furthermore, if the state of this matter at one moment does not differ from its state at another moment except through the transposition of equal and congruent portions of matter which agree in everything, it obviously follows that because of the perpetual substitution of indistinguishables, the state of the corporeal world can in no way be distinguished at different moments. For the denomination by which one part of matter is to be distinguished from another, that is, a future one, would be purely extrinsic, namely, that it will be in one place or another in the future. In the present there is in fact no distinction; indeed, neither can one be assumed with any ground in the future, because even in the future there will never be available any present distinction, since there will be no mark whatever by which one place can be distinguished from another or one part of matter from another in the same place (by the hypothesis of such a perfect uniformity in matter itself). It would also be vain to have recourse to figure in addition to motion. For in a perfectly similar, undifferentiated, and filled mass there can arise no shape or limitation or distinction of different parts, except through motion itself. It therefore motion contains no distinguishing mark, it can also bestow none upon figure, and since everything which is substituted for a prior thing must be perfectly equivalent to it, no observer, not even an omniscient one, will see even the smallest indication of a change. And so everything will be the same as if no change or differentiation had taken place in the bodies, and no reason can be given for the diverse appearances which we experience by sense. 13 This would be as if we assumed two perfect concentric spheres perfectly similar, each to the other as wholes as well as in their parts, the one included in the other so that not even the slightest gap existed; then if we assumed the included sphere to revolve or to be at rest, not even an angel (not to say more) could observe a distinction between the states of the two spheres at different times or have any criterion by which to distinguish whether the included sphere is at rest or turning, and according to what law of motion. In fact, not even a boundary between the different spheres could be defined For references see p. 508
506 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS because of the lack, at the same time, of a gap and a difference, just as the motion could not be recognized, solely because of the lack of a difference. Hence we must hold it for certain - even if those who have not penetrated sufficiently deeply into these matters may not perceive it - that such things are foreign to the nature and order of things and that there is no perfect similarity anywhere; this is one of my new and most important axioms. A consequence of this is also that there are to be found in nature no corpuscles of extreme hardness, no fluids of greatest thinness, no universally diffused subtle matter, no ultimate elements such as some thinkers call primary and secondary.14 It is because Aristotle had seen something of these principles, I believe, that he concluded (he being in my opinion more profound than many people think) that there is needed some alteration besides change in place, and that matter is not similar to itself everywhere and does not remain invariable. But this dissimilarity or diversity of qualities, and this d).).o[Q)(JI~ or alteration, which Aristotle did not adequately explain, come from the different degrees and directions of the impulses and therefore from the modifications existing within the monads themselves. I think we understand further from these considerations that something must necessarily be assumed in bodies other than a uniform mass and its transportation - which certainly changes nothing. Of course those who hold to atoms and a vacuum at least diversify matter somewhat, by making it divisible in one place, indivisible in another, full in one place, with intervening spaces in another. But a long time ago, after ridding myself of youthful prejudices, I saw that we must reject atoms and a vacuum. The famous man adds that the existence of matter through different moments of time is to be ascribed to the divine will; why not then, he asks, also ascribe to the same being the fact that it exists here and now? 1 reply that this is undoubtedly due to God, as are all other things insofar as they involve some degree of perfection. But just as that first and universal cause which conserves all things does not destroy but rather supports the natural permanence of a thing which comes into existence and the perseverance in existence once bestowed upon it, so this same cause will not destroy, but rather confirm, the natural efficacy of a thing which is set in motion, and the perseverance in action once impressed upon it. 14. Many other things appear in this 'Apologetic Dissertation' which involve difficulties; for instance, what he says in the chapter (chap. iv., Sec. 11) about a moving globe being translated through many intermediate positions into collision with another globe-to the effect that the last globe is moved with the same force by which the first is moved. Here it seems to me that they are moved with equivalent forces, but not with the same force, since each one is set in motion by its own force, namely, by elastic force, when driven back by the body striking it, though this may seem remarkable. (I am not now discussing the cause of this elasticity, nor do I deny that it must be explained mechanically by the motion of a fluid existing in and moving through it.) His remark in Section 12, that a thing which cannot give itself original motion cannot continue its motion by itself, will therefore also rightly seem strange. For it is clear that on the contrary, as force is necessary to impart motion, so, once the impulse is imparted, far from being needed to continue this motion, it is rather needed to stop it. Such conservation is made necessary in things by a universal cause, which this is not the place to discuss, but which, as I have already cautioned, would destroy the substance of things if it destroyed their efficacy. 15. These considerations make it clear, further, that the doctrine of occasional
HANOVER TO THE DEATH OF ERNEST AUGUST, 1690-98 507 causes which some defend (unless it is interpreted in a way that makes possible some moderations, as Sturm has partly admitted and partly seems to want to admit) is fraught with dangerous consequences, even if its learned defenders do not, as is undoubtedly true, intend them. So far is this doctrine from increasing the glory of God by removing the idol of nature that it seems rather, like Spinoza, to make out of God the nature of the world itself, by causing created things to disappear into mere modifications of the one divine substance, since that which does not act, which lacks active force, and which is despoiled of all distinctiveness and even of all reason and ground for subsistence can in no way be a substance. I am most certainly convinced that Mr. Sturm, a man distinguished in piety and learning, is far removed from such monstrosities. So there is no doubt that he will either show clearly on what ground any substance or even any change is left in things, according to his doctrine, or he will extend his hand to the truth. 16. There are many things, in fact, which make me suspect all the more that I have failed adequately to understand his opinion, and he mine. He has somewhere admitted to me that a certain particle 0/ the divine power can, and indeed must, be understood in a sense as belonging to and attributed to things. (In my opinion such a particle must be an expression, an imitation, a proximate effect of the divine power, for this power itself cannot be cut up into parts in any case.) This is shown in his letters to me and repeated in the passage of the Elective Physics cited at the beginning of this paper. If, as appears from his words, this is to be understood in the sense in which we call the soul a part of the divine breath, the controversy between us at this point is already ended. But I hesitate the more to affirm that this is what he means, because I do not see him saying anything of this sort elsewhere or expounding any consequences from this view. On the contrary, I observe that his other remarks have very little coherence with this opinion, while the 'Apologetic Dissertation' leads to entirely different conclusions. It is true that when my opinions on an inherent force were first published in the Leipzig Acta eruditorum of March, 1694, and further elaborated in my Specimen dynamicum in the same journal for April, 1695 15 , he raised certain objections in a letter and after receiving my reply, generously said that there was no difference between us except in our way of speaking. But when I commented on this and still raised several issues, he turned about and pointed out many differences between us, which I acknowledge. These had hardly been uncovered, however, when it occurred to him again, very recently, to write me that except for a difference in terms there is no difference between us. This would be most pleasing to me. I have therefore tried, on the occasion of this latest 'Apologetic Dissertation', to explain the matter so that our individual opinions and their truth can at length be established more easily. For this distinguished man possesses great ingenuity of insight and keenness in exposition, so that I hope his study will throw no small light upon our problem and that my work will not prove useless because it has provided him an occasion for weighing and throwing light with his customary industry and force of judgment upon important aspects of the present discussion which have so far been overlooked by other authors and myself. Thus these considerations will be supplemented by new, more profound, and more widely extended axioms, from which there can sometime come a restored and revised system of philosophy midway between the formal and the material but rightly combining and preserving both. For references see p. 508
508 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS REFERENCES * The full title adds: 'To Serve to Confirm and Illustrate the Author's Dynamics.' The following bibliographical notes may make the references in the essay clearer: Robert Boyle's Tractatus de ipsa natura (1688) repeated the mechanical conception of nature which he formulated in his Free Inquiry of 1682. On it Sturm based his De naturae agentis idolo (1692), to which Schelhammer replied in Natura sibi et medicis vindicata in 1697. Sturm's reply, De natura sibi incassum vindicata (1698), is the work to which Leibniz here refers as the 'Apologetic Dissertation'. The Elective Physics is Sturm's Physica electiva sive hypothetica, published in 1697. 2 On the various vitalistic theories of nature which Leibniz had critized since 1669, see p. 104, note 20; p. 328, note 14; p. 412, note 37; and p. 452, note 15. He frequently cited the pseudoHippocratic work, Peri diaites (especially in his correspondence with Arnauld), in connection with his view that animals are never truly generated or destroyed. 3 See Aristotle's Physics iii. 1. Leibniz returns to Aristotle's conception of motion at greater length in the New Essays, III, i, 9. 4 The two mathematicians were probably John Bernoulli and Christian Huygens, who had died in 1695. See the letter to Bayle, December 27,1698 (G., III, 57), and Gueroult, Dynamique et mitaphysique leibniziennes, chap. IV, esp. pp. 98-109. 5 See No. 50 and p. 452, note 16. 6 "Let the earth produce and animals bring forth their kind." 7 The allusions are to the phrases "let there be" and "it is good" in chapter 1 of Genesis. 8 The sharpening of Leibniz's condeInnation of Spinoza since the papers following 1678 is conspicuous. 9 The conversion of the proposition actiones sunt suppositorum (see Introduction, Sec. V, and p. 119, note 11 into "every substance acts" is in need of empirical grounding; Leibniz's entire physics, biology, and psychology are efforts to do so. It is difficult to see, however, how the principle really establishes pluralism .Leibniz merges two things - God's impression of a law of individuality and of force upon creatures. 10 Louis de la Forge anticipated occasionalism in his Traite de ['ame humaine, de sesfacultes 1 etfonctions et de son union avec Ie corps suivant les Principes de R. Descartes (1666). 11 The term 'monad', which here appears for the first time in these selections, is widely held to have been used first by Leibniz in a letter to Fardella on September 3/13,1696, and to have been borrowed from the younger Van Helmont, who visited Hanover early in 1696 (see L. Stein, Leibniz und Spinoza, pp. 209-10). But the term had been in use since Bruno, and Leibniz had used related terms such as monas and monades in his early writings. 12 This is a misleading remark, since secondary matter, as matter, is phenomenal, and only the aggregated monads whose passive force is expressed as resistance or inertia are substantial. Cf. the letter to John Bernoulli in the same year mc., 11,370-71): "Matter in itself, or mass [moles], which may be called primary matter, is no substance, not even an aggregate of substances, but something incomplete. Secondary matter [massa] is not one substance but a plurality of substances." 13 Leibniz's argument that we have no criterion for individual differences and change without an intrinsic force seems to have full effect against all purely logical and mathematical analyses of the physical world. But it is not clear how it establishes an internal force in addition to motion. His use of the principle of geometric similarity, and its limitation by his injection of change and force, must be understood in terms of his separation of dynamics, phorometry, and geometry after his criticism of Descartes's physics in the 1680's. 14 A reference to Descartes's distinction, in the Principles of Philosophy, Part III, Sec. 52, between three levels of matter or "elements of the visible world". 15 See Nos. 45 and 46.
PART IV HANOVER UNDER GEORGE LOUIS 1698-1716
54 CORRESPONDENCE WITH JOHN BERNOULLI 1698-99 The Bernoulli brothers, John and James (the nephew Daniel had not yet come on the scientific scene), were among Europe's outstanding mathematicians and among the first to champion Leibniz's new infinitesimal analysiS. They had entered into the solution of the great test problems of the 1690's in keen, jealous rivalry with each other as well as with other scientists - John at Groningen, James at Bern. Leibniz's correspondence with both was extensive but chiefly mathematical and physical in content. Near the end of the century a three-cornered exchange developed between Leibniz, John Bernoulli, and Burcher de Voider (No. 55) in which certain issues connected with the nature of matter and the infinite were discussed. Earlier in 1698 Leibniz had suggested that the infinites and infinitesimals of his calculus are "imaginary, yet fitted for determining reals, as are imaginary roots. They have their place in the ideal reasons by which things are ruled as by laws, even though they have no existence in the parts of matter." He suggested also that "the real infinite is perhaps the absolute itself, which is not made up ofparts but which includes beings having parts, in an eminent way and in proportion to the degree of their perfection" (June 7,1698; GM., III,499-500}.lThe following letter summarizes the discussion about this point. The mathematical portions, concerned primarily with the solution of the catenary, are omitted. [GM., Ill, 551-53] Hanover, November 18, 1698 ... You say that my discussions of more metaphysical matters are entirely too laconic, but I took pains, I believe, to speak accurately and fully. If there remain some doubts however, I shall try to satisfy you by replying to them. You say that I have given definitions rather than explanations. But would that definitions might always be given, for they virtually contain the explanations! As concerns infinitesimal terms, it seems to me not only that we cannot penetrate to them but that there are none in nature, that is, that they are not possible. Otherwise, as I have already said, I admit that if I could concede their possibility, I should concede their being. z We must see, therefore, what reason can be used to demonstrate that a straight line, for example, is possible which is infinite yet terminated on both ends. But I come to your points. On 1. When I said that primary matter is that which is merely passive and separated from souls or forms, I said the same thing twice, for it would be the same if I had said that it is merely passive and separate from all activity. Forms are for me nothing but activities or entelechies, and substantial forms are the primaryentelechies. On 2. I have preferred to say that the active is incomplete without the passive, and the passive without the active, rather than to speak of matter without form and form For references see p. 514
512 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS without matter, in crder to use terms already explained rather than terms still to be explained - and also somehow to apply your advice before you give it, for our moderns will popularly take less offense at the term 'activities' than at that of 'forms'. On 3. We need not be stopped by the fact that the Cartesians deny anything in the body analogous to the soul, for they have no reasons for denying it, and it does not follow that a thing has no being merely because we cannot have a sensory image of it. On 4. It has long seemed ridiculous to me that the nature of the universe should be so niggardly or grudging that it has provided souls only to such insignificant masses as the human bodies on this earth of ours, when it could have provided them to all bodies without interfering with its other goals. On 5. How far a piece of flint must be divided in order to arrive at organic bodies and hence at monads, I do not know. But it is easy to see that our ignorance in these things does not at all prejudice the matter itself. On 6. I do not believe that there is any minimal animal or living being, that there is any without an organic body, or any whose body is not further divisible into more substances. Therefore we never arrive at living points or points endowed with forms. If you have a: clear idea of the soul, you will also have one of forms, for they are the same genus but different species. You are right in concluding that we ought not to reject something merely because we do not perceive it clearly and distinctly. No matter how much the good Cartesians talk about their clear and distinct perceptions, they do not seem to me to perceive even extension in this way. For the rest, if we conceive of soul or form as the primary activity, from whose modifications the secondary forces arise as figures arise from the modifications of extension, I believe we shall have satisfied the demands of understanding. 3 There can be, that is, no active modifications of something whose essence is purely passive, because modifications limit rather than increase or add. Hence we must assume, besides extension, which is the seat or the principle of figures, a seat or first bearer [proton dektikon]4 of actions, namely soul, form, life, primary entelechy, or whatever you wish to call it. I approve thoroughly of your advice that we should refrain from mentioning primary matter and substantial forms in our discussions with Cartesians and similar people and content ourselves with mentioning only passive mass in itself and entelechy or primary activity, soul, or life. You are also entirely right in thinking that all the bodies in the world arise from an interaction of internal forces, and I have no doubt that these forces are coeval with matter itself, for I believe that matter cannot subsist in itself without forces. I think, nevertheless, that primary or living entelechies are different from dead forces, which themselves probably always arise from living forces, as is apparent when a centrifugal tendency, which must be considered a dead force, arises from the living force causing rotation. Life, or the first entelechy, is something more than any simple dead tendency for I believe it includes also perception and appetite, both corresponding to the present state of the organs in an animal. Your discussion is in full agreement with my opinion, and you confirm my principle that changes do not occur by a leap. Besides, it is no jest, but a firm conviction of mine, that there are animals in the world as much greater than ours as ours are greater than the animalcules of the microscope. Nature knows no limits. And so it is possible
HANOVER UNDER GEORGE LOUIS, 1698-1716 513 on the other hand - indeed, it is necessary - that there should be worlds not inferior to our own in beauty and variety, in the smallest bits of dust, in fact, in atoms. And though this may seem even more wonderful, nothing prevents animals from passing over into such worlds when they die. For I am of the opinion that death is nothing but the contraction of an animal, as generation is nothing but its unfolding [evolutio). It was my opinion long before Newton's work, that gravity is inversely proportional to the square of the distance, a theory at which I arrived not merely by a posteriori processes but also by an a priori reason, which I am surprised that he did not notice. Leaving out of consideration the physical basis of gravity, namely, and remaining within mathematical concepts, I consider gravity as an attraction caused by certain radii or attractive lines going out from an attracting center; so, like the density of illumination in rays of light, the density of radiation in gravitational attraction will be inversely proportional to the square of the distance from the radiant point. ... II [GM., III, 574-75] February 21, 1699 ... Possible things are those which do not imply a contradiction; actual things are nothing but the best of possibles, everything considered. And so things that are less perfect are not therefore impossible, for we must distinguish between the things which God can do and those which he wills to do; he can do all things, but he wills the best. When I say that God elects out of infinite possibilities, I mean the same as you when you say that he has elected from eternity. Your remark that it is impossible for him to revoke his decisions and then to create other things than those he has decided to create, pertains to hypothetical necessity, which we are not discussing here. I know that, as you imply, there are many who doubt that we can know what conforms to the divine wisdom and justice. Yet I believe that just as our geometry and our arithmetic are true for God as weIl, so general laws of the good and the just, of mathematical certainty, are also valid for God. And even if evil in itself is less than nothing, it sometimes increases reality when conjoined to other things, as shadows are useful in pictures and dissonances in music. I have no doubt that evil is aIlowed when a greater good grows from it. It is most pleasing that my opinion about the union and intercourse between soul and body does not conflict with the view which you and Mr. Braun hold. But those who hold the problem to be so far inexplicable and miraculous, as it were, do not seem to have understood my view sufficiently, for if I am not mistaken, every difficulty is met in it. My reply to two objections which seemed of great importance to you has not displeased Mr. Bayle. Even if the soul does not consist of parts, yet in its perceptions it expresses a thing consisting of parts, namely, the body. Since it has many perceptions at the same time, therefore, and future consequences arise naturally from present perceptions, it is not strange that so many modifications flow spontaneously from the soul. There is also no doubt that our future states are already in some way involved in our present ones, though they cannot be distinguished because of the multitude and smaIlness of the perceptions occurring at the same time. I have sent this and other matters to Bayle in letters, and Mr. Basnage promised to insert my reply in his last quarterly review, issued in the fall oflast year, ifI am not mistaken. 5 ••• For references see p. 514
514 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS In your exposition of my theory about the subject matter of entelechies there are some things which I should not venture to affirm as you do. For in those matters where certainty can be had, I do not like to use hypotheses, yet it is sufficient to consider the whole of the matter. To your objections I should make this reply. When I say that the moment of death cannot be defined, I at once signify that in a metaphysical sense there is no such moment; nor do I see that it destroys the law of continuity to say that somehow a great change takes place in this very short time. It is quite consistent for such a thing to happen in nature, especially in deaths. For it happens that composite machines are slowly formed but easily destroyed. Yet the wisdom of the Author of the universe brings it about that what is best for the world as a whole is always considered. In this theater it is possible for the same animal to be pro~uced more than once, yet I believe that the contrary is also possible. Reason does not determine this question very easily, therefore, and I hold it for a deeper investigation. You do not reply to the reason which I have proposed for the view that, given infinitely many terms, it does not follow that there must also be an infinitesimal term. This reason is that we can conceive an infinite series consisting merely of finite terms or of terms ordered in a decreasing geometric progression. I concede the infinite plurality of terms, but this plurality itself does not constitute a number or a single whole. It means nothing, in fact, but that there are more terms than can be designated by a number. Just so there is a plurality or a complex of all numbers, but this plurality is not a number or a single whole ..... REFERENCES Compare the note to the letter to Des Bosses on September 1, 1706 (0., 11,314), on the distinction between a syncategorematic, a hypercategorematic, and a categorematic infinite. This note is translated in the Introduction, Sec. VI, p. 31. See also p. 541, note 21. S Leibniz obviously anticipates some of Berkeley's later empirical objections to the foundations of the calculus. Though he suggests a number of interpretations in the letter to Varignon (No. 56), his reply to Berkeley could be inferred from his reply to Locke. Ideas are for him not merely objects of the mind, but operators, and the concept of infinitesimal is ofthis kind. 3 Secondary or derivative force is the variable quantity of activity in the monad, and on the phenomenal level, of any material system and is therefore a function of time, while primary force is the permanent basis or co.urse of action. The two are related as law and its particular values. 4 See Aristotle Physics vi. 4. 248b, 249a. 5 See No. 52. 1
55 CORRESPONDENCE WITH DE VOLDER 1699-1706 Burcher de Voider (1643-1709) held the professorships of philosophy, physics, and mathematics in the University of Leyden. Highly esteemed by his contemporaries, appointed as his literary executor by his fellow-countryman Huygens, he was excellently qualified to test the consistency and clarity of Leibniz's philosophical analyses. Though considered a Cartesian, he had shown independence ofjudgment in examining Descartes's physics and metaphysics. De Voider was brought into correspondence with Leibniz through a criticism of the calculus which he offered to John Bernoulli. He took issue also, from a Cartesian viewpoint, with Leibniz's theory of the conservation of force and with his conviction that an elastic force must be assumed in bodies in addition to extension and impenetrability. Referred by Bernoulli to Leibniz, these objections called forth a metaphysical justification of the conservation of force and therefore a development of the notion of substance. At first Leibniz's letters, of which only the most important are here translated, show a reluctance to discuss his still unperfected concept of substance and express his feeling that his own efforts are hypothetical and incomplete and should be a part of a co-operative enterprise. Eventually, however, his letters reveal irritation at De Voider's persistence, and he finally affirms his own dynamic idealism as against the latter's realism. [G., II, 168-75] Hanover, March 24/April3, 1699 No more outstanding example could easily have been given, both of your very penetrating judgment and of your uncommon love of truth, than that which you have given me in your excellent and most friendly letter. I wish my capacity were as great as my will to do justice to it. But est aliquid prodire tenus 1; what is not yet ready to be defended by rigorous demonstrations will meanwhile commend itself as a hypothesis which is clear and beautifully consistent within itself and with phenomena. I believe also that to anyone who considers it attentively, most of it will seem certain. This is the axiom that I use - no transition is made through a leap. I hold that this follows from the law of order and rests upon the same reason by which everyone knows that motion does not occur in a leap; that is, that a body can move from one place to another only through intervening positions. I admit that once we have assumed that the Author of things has willed continuity of motion, this itself will exclude the possibility of leaps. But how can we prove that he has willed this, except through experience or by reason of order? For since all things happen by the perpetual production of God, or, as they say, by continuous creation, why could he not have transcreated a body, so to speak, from one place to another distant place, leaving For references see p. 539
516 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS behind a gap either in time or in space; producing a body at A, for example, and then forthwith at B, etc. ? Experience teaches us that this does not happen, but the principle of order proves it too, according to which, the more we analyze things, the more they satisfy our intel/ect. This is not true of leaps, for here analysis leads us to mysteries [apPI1ra:]. Thus I believe that the same thing applies not only in transitions from place to place but also in transitions from one form to another or from one state to another. For experience, as well, refutes all changes through a leap. And I do not believe that any reason a priori can be given against a leap from place to place which is not also effective against a leap from state to state... , •.. I do not think: that substance is constituted by extension alone, since the concept of extension is incomplete. Nor do I think that extension can be conceived in itself, but I consider it an analyzable and relative concept, for it can be resolved into plurality, continuity, and coexistence or the existence of parts at one and the same time. Plurality is also contained in number, and continuity also in time and motion; coexistence really applies to extension only. But it would appear from this that something must always be assumed which is continuous or diffused, such as the white in milk, the color, ductility, and weight in gold, and resistance in matter.2 For by itself, continuity (for extension is nothing but simultaneous continuity) no more constitutes substance than does multitude or number, where something is necessary to be numbered, repeated, and continued. So I believe that our thinking is completed and ended in the concept of force rather than in that of extension. And we need seek no other concept of power or force than that it is the attribute from which change arises, and whose subject is substance itself. I do not see anything here which escapes the understanding. The nature of the matter does not allow anything more explicit, such as a picture. I think that the extended has a unity only in an abstract sense, namely, when we leave out of consideration the internal motion of the parts, for each part of matter is itself subdivided further into actually different parts; this the plenitude does not at all prevent. Nor are the parts of matter different only in their modes, if they are distinguishable from each other by the souls and entelechies which subsist always. Somewhere in his letters I have observed that Descartes too, following Kepler's example, has acknowledged that there is inertia in matter. 3 This you derive from the power which you say everything has to remain in its own state and which is not different from the nature of that thing itself. So, you believe, the simple concept of extension suffices to explain this phenomenon too. But the axiom that a body conserves its own state needs itself to be changed, for a body moving in a curve, for example, does not conserve its curvilinear path but only its direction. But granted that there is in matter a force to maintain its state, this force can certainly not be derived in any way from extension alone. I admit that each thing remains in its state unless there is a reason for change; this is the principle of metaphysical necessity. But it is one thing to retain its state until there is something which changes it, which this may do even though it is in itself indifferent to either state; it is another and far more significant matter if a thing is not indifferent to change but has a force and an inclination, as it were, to retain its state and so to resist motion. Thus in a book written long ago when I was young, I proceeded on the assumption that matter in itself is indifferent to motion and rest and concluded from this that the largest body, at rest, must be moved by any impelling body, however small, without any weakening of the latter; from this I then derived the abstract rules of motion for the system. 4 And such a world in
HANOVER UNDER GEORGE LOUIS, 1698-1716 517 which matter at rest would obey the moving body without any resistance, could indeed be imagined as possible, but such a world would actually be pure chaos. So the two tests upon which I always depend - success in experiment and the principle of order caused me later to recognize that matter has been so created by God that there inheres in it a certain repugnance to motion and, to put it in a word, a resistance, insofar as the body in itself withstands being moved and thus opposes all motion if at rest, or all greater motive force applied in the same direction if in motion, so that it weakens the force of the impelling body. Since matter in itself therefore resists motion by a general passive force of resistance but is set in motion by a special force of action, or entelechy, it follows that inertia also constantly resists the entelechy or motive force during its motion. Hence I showed in the preceding letter that the united force is stronger, or that the force is twice as great if two degrees of speed are combined in 1 pound, than if they are dispersed through 2 pounds, and that the force of 1 pound moved at double velocity is therefore twice as great as that of 2 pounds moved at the simple velocity, because, though the quantity of velocity is the same in both cases, the inertia of matter offers only half the resistance in the case of 1 pound. This inequality in forces which exists between 1 pound and 2, with a velocity inversely reciprocal to their masses, has been demonstrated in another way from our measurement of forces, but it is also nicely demonstrable from this consideration of inertia, so completely is everything in agreement. Thus the resistance of matter contains two factors: impenetrability or antitypy, and resistance or inertia. And since these two factors are everywhere equal in a body or are proportional to its extension, it is in them that I locate the nature of the passive principle or of matter, even as I recognize, in the active force which exerts itself in various ways through motion, the primitive entelechy or in a word, something analogous to the soul, whose nature consists in a certain perpetual law of the same series of changes through which it runs unhindered. We cannot dispense with this active principle or ground of activity, for accidental or changing active forces and their motions are themselves certain modifications of some substantial thing, but forces and actions cannot be modifications of a merely passive thing such as matter. It follows, therefore, that there is a primary active or substantial being which is modified by an added disposition of matter or of passivity. Hence secondary or motive forces and motion itself must be ascribed to a secondary matter or to the complete body which results from the active and the passive together. And so I come to the communication between the soul or entelechy of the organic body and the mechanism of its organs. I am happy that my hypothesis about this does not entirely displease a man of your acumen and discernment. You make it very clear, in fact, when you ascribe an adequate idea of the corporeal mechanism to the soul; this is just what I mean when I say that it is the nature of the soul to represent the body. Therefore whatever follows from the laws of body must necessarily be represented in order by the soul to itself, some of it distinctly but some confusedly (that, namely, in which a multitude of bodies is involved). In the former case, the soul understands; in the latter, it senses. Meanwhile, I think that you agree with me that the soul is one thing, and the idea of the body another, for the soul remains the same, but the idea of the body changes as the body itself changes, whose present modifications it always reveals. Of course the idea of the present state of the body is always in the soul, but it is not simple and hence not purely passive but is combined with a tendency toward a new idea arising out of the earlier one, so that the soul is the source For references see p. 539
518 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS and foundation of different ideas of the same body, which arise according to a prescribed law. But if you take the term 'adequate idea' to mean not that which changes but the constant law of change itself, I have no objection; in this sense I will say that there is in the soul an idea of the body and also the phenomena which proceed from it. For the rest, there are in all of these matters certain things which should be discussed more thoroughly, which I shall not fail to do when occasion offers. For even though I cannot easily demonstrate everything a priori with geometric rigor, or give accurate explanations even where I see the reasons, I yet venture to promise that no objection can be offered which I shall be unable to satisfy. This in itself is, I believe, not to be disdained in matters so far removed from sense, especially since the agreement of scientific teachings, both with phenomena and among themselves, is among the most powerful tests of their truth. Objections which have any weight always serve to clarify the nature of any issue, and so I recognize how very much I and all lovers of truth are indebted to you, for I feel that you kindle such a light for me that I seem to understand my own ideas better by reading yours. If by your aid, and that of the Bemoullis and other men like them (would there were not so very few of them), I shall sometime be able to succeed in supporting with clear demonstrations what I can now only defend in one way or another - I shall not begrudge to others my light which lowe in great part to you. At least I shall dread the opinions of others the less for having relied upon your judgment. 5 ••• II [In his reply 0/ May 13, 1699, De Voider attacked Leibniz's analysis of substance as complex and insisted upon a return to a 'logical' approach to the problem instead of the physical and metaphysical ones. We have the idea of a substance, he held, only if we have a simple concept from which no essential can be removed without destroying the entire concept. Extension is such a concept; change, motion, and force are not. The concept of 'a subject of change' is a purely formal designation which throws no light on the nature of such substance, as extension does, for example, upon its accident, motion.] [G., 11,182-85]6 , Hanover,June23,1699 ... Your statements about the concept of substance are as usual subtle and ingenious. It is within the arbitrary choice of anyone to assign names to concepts, yet concepts thus named do not always correspond either to actually existing things or even to accepted usage. l' You assert that the notion of substance is formed out of concepts and not out of things. But are not concepts themselves formed from things? You say that the notion of substance is a concept of the mind, or a rational entity, as they say. But the same can be said of any concept, if I am not mistaken, and furthermore, it is not about concepts but about the objects of concepts that we say entities are either real or rational. But substance, I believe, is a real entity - indeed, the most real. You say there are two kinds of concepts, some representing a single unified something from which nothing can be separated without destroying the whole; in your opinion this is the concept of a substance, and you say that extension is such a concept. The other kind of concept may represent two or more things. This is a little obscure to me. Surely
HANOVER UNDER GEORGE LOUIS, 1698-1716 519 every concept or definition is such that you cannot remove anything without destroying the whole definition; yet in that case another concept may come into being in the definition. Thus if you remove the concept of equal sides from the' definition of a square, the square is destroyed but a rectangle remains. A concept from which nothing can be removed must be simple and primitive, but I do not think that the concept of substance should be established in this way or that the concept of extension is of this kind. Furthermore, you say that those "two or more things" ate so related to each other that one can be conceived without the other, and so perception and extension are thus related that neither involves the other; extension is involved in motion but not the contrary. And motion is thus an accident or mode. In all these things I hold very different opinions. I believe that perception is involved in extension, and motion as well, and that substance and accident equally involve and are involved in each other. Extension is an attribute; the extended, or matter, is not substance but substances. Moreover, duration, particular time, and the enduring thing are in a relation on the one hand, proportional to extension, place, and the placed thing on the other. It does not seem that there can be things which do not have common attributes. 7 Nor should I think that the concept of extension is primitive, or one from which nothing can be withdrawn, since it may be analyzed into plurality, which it has in common with number; into continuity, which it has in common with time; and into coexistence in common even with things that are not extended. I should not have believed that plurality is to be denied in the extended thing, especially if we admit that it has actual parts; we should in that case also have to deny plurality to a herd or army, in other words, everywhere. Continuity in motion is distinct from continuity of place, for it contains continuity both of time and of variation in degree of velocity. Time is neither more nor less a rational entity than space. To coexist and to exist before or after are something real; they would not be, I admit, as matter and substances are commonly understood. But it is easier to show what these concepts are not than to explain in words what they are and to prove it with reasons. You say that a subject of change is merely a logical concept; but it is enough that it is true, though you could just as well have called it metaphysical. We despise obvious things, yet the unobvious things sometimes follow from them. We must start with nominal definitions, and it is of such a definition that I spoke when I said that no other definition of power is needed than the one I had advanced. The other consideration then becomes the causal one of how change takes place. And here there can be things which escape our understanding. You say that the unity of an extended thing is perceived even if it is divided into parts moved in different ways, since one of these parts can n«ither exist nor be conceived without the others. Therefore you assume two things wtpch I cannot concede: that one part of an extended thing cannot exist or be conceived without the others and then, that such things form a unity. From this you show that a vacuum is impossible. But your arguments do not achieve this, and if it be conceded, it follows indeed that one part of matter cannot exist without some other part, but it hardly follows that it cannot exist without these particular others. Besides, unless I am deceived, this argument proves too much, for according to it things removed from each other would still be one. As I understand unity, such things are more properly to be called many, and they do not constitute a unity except as an aggregate while they are grasped together in one thought. In what is truly one substance there are not many substances. I recognize neither inertia nor For references see p. 539
520 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS motion in extension; in extended matter I recognize both, but not by reason of its extension. You very rightly observe, in agreement with my own opinion, that it is in opposition to the laws of power, cause, and effect, for a great body to be moved by a smaller without penalty. But from this fact I prove that the body contains something dymamic by virtue of which the laws of power are observed. It therefore contains something besides extension and antitypy, for no such thing can be proved from these two alone. I made this same reply to someone in the Parisian journal many years ago. I recognize that resistance involves something besides passivity, that secondary motive forces are not modifications of something merely passive, and that there must therefore be an active substantial principle. This I have thought it worth while to point out for the sake of those who do not yet hold that all substance is active. I think that an extended substance completely at rest belongs among those things of which we cannot form a distinct concept, like a most rapid motion. You ask, Sir, whether in my judgment "the active principle is extension, or a mode of extension, or a substance distinct from extension". I reply that the principle seems to me to be substantial, and constitutive of the extended itself or of matter, that is, of the thing which possesses not only extension and antitypy but also action and resistance. Extension is itself, for me, an attribute resulting from many substances existing continuously at the same time. So primitive force can be neither extension nor a mode of it. Nor does it act upon extension but in the extended. When you ask further if an inanimate body has its own entelechies "distinct from the soul", I reply that it has innumerable such entelechies, since it consists in turn of parts each of which is animated or as if animated. In the soul there is an adequate idea of matter, yet the soul is not, for me, the idea of matter itself but the source of ideas for itself and in itself - ideas born of its own nature but representing the different states of matter in order. An idea is, so to speak, something dead and unchangeable in itself, as is a figure; soul is rather something living and full of activity; and in this sense I do not say that it is anyone idea which tends to change out of itself, but only various ideas succeeding each other, one of which can, however, be derived from another. But in another sense of the word, I could say that in some way the soul is a living or substantial idea or more correctly, that it is an 'ideating' substance. Nor do I think that you intend anything else when you say that ideas act upon each other in representing each other, for I do not believe that you regard ideas as substances colliding with each other as do bodies.... These are the answers, illustrious Sir, which I thought could be made. I wish that they could all be explained more distinctly and proved more soundly, but in this infancy of our philosophy it is something to point out what seems to be irrefutable, and to derive the rest from hypotheses which are few in number and worthy of respect. Perhaps there will be a time when we can go further, especially if I continue to gather rays from your light. III [Instead of the above letter Leibniz sent a much shorter one. De Voider's reply of August 1,1699, returned to the principle of the conservation of force and particularly to the problem of continuity raised in an earlier letter (No. I), in which Leibniz asserted
HANOVER UNDER GEORGE LOUIS, 1698-1716 521 that no a priori argument could he given for continuous motion. Leihniz's reply, undated hut in 1699, once more summarized these problems.] [G., II, 192-95] ... For the rest, to mention a few other matters, you asked me to prove a priori the law of the continuity of changes; I replied that a proof a priori might with equal right ·be demanded of the law of the continuity of motion. You offered a reason based on direction, on the fact, namely, that moving bodies always adopt a straight line. To this I replied that I did not see that the conclusion follows, for a cause which translates bodies anywhere by a leap could still act in such a way as to translate them always in a straight line. So, unless I am mistaken, you would still have to show that this is impossible, in order to make your proof absolute. I added the hypothesis of transcreation for the sake of illustration, speaking philosophically and particularly like the Cartesians, who say, with some ground, that God creates all things continuously.a For them, therefore, moving a body is nothing but reproducing it in successively different places, and it would have to be shown that this reproduction cannot take place in leaps. Rather, this could not be shown without returning to the reason which I have proposed for the universal law of continuity. If you do not accept such a re-creation of things, however, the same thing must be said regardless of what the cause of motion may be. Then too, one can, in replying to an opponent, assume a hypothesis which he does not accept, until the hypothesis has been refuted. You are right in saying that an interruption of motion is inconsistent both with the velocity and with the direction of motion, once you assume, that is, that motion is something continuous in nature. But anyone who rejects continuity in things will say that motion in its essence is nothing but a succession of leaps through intervening intervals, which flow from the action of God and not from the nature of the thing moved, or which are recreations by God in separate places. His philosophizing will then be almost like that which would compound matter out of mere discrete points and would support this opinion on the ground of the labyrinthine difficulties which surround the nature of continuity, from which there do indeed follow, not the necessity of leaps, but some other things which are not usually well understood. However, this hypothesis of leaps cannot be refuted except by the principle of order, with the aid of the supreme reason, which does everything in the most perfect way. Since every extended body, as it is really found in the world, is in fact like an army of creatures, or a herd, or a place of confluence, like a cheese filled with worms, a connection between the parts of a body is no more necessary than is a connection between the parts of an army. 9 And just as some soldiers can be replaced by others in an army, so some parts can be replaced by others in every extended body. Thus no part has a necessary connection with any other part, even though it is true of matter in general that when any part is removed, it must necessarily be replaced by some other part, just as it is necessary, when soldiers are confined in a small inclosure or one which will not hold many, for another to take the place of anyone who goes out. I have already made enough suggestions about this in my previous letter, and I do not see any point that can be made about any body whatsoever, apart from the soul, which would not be equally valid for an army or a machine. Therefore I understand a true unit (and not merely a sensible one), or a monad, to exist only where there is something which does not contain many substances. For references see p. 539
522 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS I too ascribe to motion (including in this the causes of motion) every variety of bodies, yet I recognize a substantial distinction between the parts of matter. All others also recognize this who assign a rational soul to man as something substantial but without extension, though they do not always admit such a mind in all the parts of matter as well. You seem to designate as logical or metaphysical those concepts which explain nothing, but I do not recognize such as concepts at all. So far is the concept which I proposed from explaining nothing, however, that I think that proofs of great importance can be derived from it and from notions similar to it. But we are constituted so full of preconceptions that although we properly distinguish in theory intelligible things from those given in sense perception, so to speak, and declare that we distinguish them, we do not observe the distinction in practice and regard almost as nothing everything which is not to be grasped in images. In no other way can I take what you say about not being able to understand the things I asserted about an active principle prior to extension; you mean that you are unable to imagine them. Meanwhile, if an opinion follows necessarily from premises that are understood, we may consider it itself to be understood. If I am not mistaken, you certainly understand something when the Cartesians speak of the human soul, which I do not consider different in kind from other entelechies. To your first question (what this active principle may be) I must therefore give the same answer as to the question of what the soul may be, though I might also make a somewhat more distinct reply. Incidentally, it seems that the power of preconception and authority is so great that many people have convinced themselves that they understand in Descartes what they deny they understand in others. If you interpret your second question (whether a living body has an entelechy distinct from the soul) in such a way that it applies to the living body as a whole and not to its separately animated parts, I reply that such a body does not have any other entelechy except the soul and the entelechies of its separately activated parts. Indeed, there would be no such soul of the whole, aside from the soul of each separately animated part, if the soul did not dominate the whole by virtue of the structure of that whole. When you say that more causality or force is needed to move a larger body at a given velocity than to move a smaller one at the same velocity, you are already tacitly assuming that the body resists motion. For if it does not, but is indifferent and in a state of equilibrium, as it were, I do not see what obstacle its magnitude can offer to an impelling force, for no resistance can ever arise from an increase of such indifferent masses. And likewise, if it is unnecessary to pass through intervening stages, then any cause or impUlsion to motion whatever, which inclines or determines a body to a given velocity and direction, will be enough, and hence any moving body, however small, will be sufficient to carry with it any body, however large, without resistance or impediment to its own motion. Since this does not happen, but rather the contrary, namely, that a greater force must be expended and consumed to produce the motion of a larger body, we must understand that matter resists motion. Hence bodies also suffer compression before they allow themselves to be carried away; therefore, the law of continuity is always obeyed in changes, and no greater motion can be produced except by passing through the lesser stages of motion. If the entelechy is entirely different from extension, you infer from this that it can do nothing to extension. But does not motion differ from extension? Yet it can do
HANOVER UNDER GEORGE LOUIS, 1698-1716 523 something to it. Accurately speaking, moreover, extension is merely something modal like number and time, and not a thing, since it is an abstract designation of the continuous possible plurality of coexisting things, while matter is in fact this very plurality of things itself and hence an aggregate of the things which contain entelechies. So I do not admit an entelechy entirely separated from matter, if by the word "extension" you mean matter in this sense. Finally, it means nothing in metaphysical rigor for one thing to do something to another, except that one thing responds spontaneously to the other - as we have already agreed in the case of the intercourse between soul and body. Do not apologize for your dissent, for such things are not matters of choice. The pursuit of truth, care in investigation, and candor combined with moderation in speech - these should be enough for us, nor can they be anything but useful and pleasing to men of good will. P.S. From our friend Bernoulli I have learned that you find it more important to throw light upon the activity of substance than to estimate forces. I believe the same thing and approve your judgment. Yet it has always seemed to me that the latter question is the gateway through which to pass to the true metaphysics, since the mind is surely gradually freed from the false notions of matter, motion, and corporeal substance which are held popularly and by the Cartesians, when it comes to understand that the rules of force and action cannot be derived from these notions and that we must either take refuge in a deus ex machina or hold that there is something higher in bodies themselves. If the mind is led without preparation into this holy of holies, where it can suddenly view the entirely novel nature of substance and body fully and from the beginning, we must fear that it will be blinded by the very abundance of light. IV [Leibniz's efforts to sharpen his own analysis had little effect on De Voider, who in his reply returned to his own definition of substance as that which is conceived in itself as a simple idea from which nothing can be removed without destroying it. In his letter of February 13,1701 (G., II, 223), he went so far as to call the idea of substance a modus concipiendi independent of all attributes and repeated his challenge to Leibniz to develop his own idea further.] [G., II, 224-28] Hanover, July 6, 1701 I return to my meditations and the long-interrupted duty of my correspondence, and I beg your forgiveness for not having answered your last letter sooner. It is usually the case that I postpone longer than I ought the things with which I wish to take the most pains. I only wish that I could satisfy you the better for having delayed so long. But I turn to your letter. You say a substance is that whose concept so represents a unity that nothing of the thing represented can be removed without the whole perishing. But cannot there be a substance which adds new perfections to those of others? 1 0 But if I am not mistaken, each single perfection of the thing represented is matter. Thus the Democriteans think of space as a substance and of body as a more perfect substance which adds resistance to extension. (As you well observe, these examples do not need to be true; For references see p. 539
524 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS they are given merely to clarify.) Some of the moderns think that a new perfection can be added to certain bodies, namely, that of thought, and the School has long held that besides the simple animated body, there is a more perfect body which senses and a most perfect one of all which is rational. I say this to point out that your concept of substance does not seem to agree with those commonly so called but only with that of the most simple substance. This is also true when you say that substance is that which is conceived in itself, an opinion to which I have opposed the proposition that an effect cannot be conceived better than through its cause, but that all substances except the first have a cause. You reply that we need a cause to conceive the existence of a substance but not to conceive its essence. But to this I answer that the concept of a possible cause is needed for conceiving its essence, but to conceive its existence the concept of an actual cause is needed. I can already foresee the elegant rejOinder which you will make to this, based on an example in geometry. The essence of an ellipse, for instance, does not depend on a cause, since the same ellipse can be produced by different causes - the section of a cone, a cylindrical section, the motion of a string. But the existence of an ellipse cannot be thought of without assuming some determinate cause. My reply to this, however, is twofold. First, though it is not necessary to conceive a determinate mode of generation to think of the essence of an ellipse, this essence, whether of an ellipse or anything else, cannot be conceived perfectly unless its possibility can be demonstrated a priori through some formal cause which exists in every individual method of generation. And to do this we must necessarily add some simpler lines. In the second place, I have already established the fact that incomplete things such as lines or figures can be similar to each other even if they are produced by different causes, as an ellipse made by a conic section may be similar to an ellipse made by motion in a plane. But in completely determined things this cannot happen, and so one substance is not perfectly similar to another, nor can the same substance be generated in many different ways. 11 On this ground (as well as on other considerations) I once also concluded that there are no atoms, that space is not a substance, and that primary matter itself, or matter separate from all activity, cannot be included among substances. I come now to the modes, which I agree with you in distinguishing from other predicates, that is, from attributes and properties. Yet if we define them merely in terms of their needing another concept, properties will also be modes. It is common to both properties and modes to be in something. But this same definition will also fit things which are not contained in something, such as effects which need causes to be understood, as I have already said. On this basis all effects would be modifications of their causes, and the same thing could be the mode of many things at the same time, since the same thing can be the effect of many concurrent causes. Who will deny, too, that one substance is modified by the intervention of another, as when a body is repelled by some obstacle in its path? In order to conceive the rebound of one of these bodies, therefore, the concept of both of them will be necessary, yet the rebound can be the modification of only one, since the other may continue in its path without rebound. Something more is needed in the definition of a modification, therefore, than the necessity of another concept, and to be 'contained in' (a quality which is common to both properties and modes) is more than to need something else. In my opinion there is nothing in the whole created universe which does not need, for its perfect concept, the concept of everything else in the universality of things, since
HANOVER UNDER GEORGE LOUIS, 1698-1716 525 everything flows into 12 every other thing in such a way that if anything is removed or changed, everything in the world will be different from what it now is. For the rest, if A and B are two substances in the sense in which you define them, that is, most simple, I admit that they cannot have a common predicate; yet it does not necessarily follow from this that there cannot be some third thing C which needs both of them for its concept. For just as relations result from a plurality of absolute terms, so qualities and actions also result from a plurality of substances. And just as a relation is not compounded from as many relations as there are terms to be related, so neither are the other modes which depend upon many things resolvable into many modes. 13 It does not follow, then, that a mode which requires many things is not a unity but a composite of many modes. Besides, it is not clear how any modes could possibly arise, according to your notion of them. For a substance such as you define, which has only a simple representation or one attribute, will have only one mode, and it does not appear how any diversity can arise, since only one can come from one. Hence its mode will be invariant, contrary to your hypothesis. But even more, there will not even be any mode, since it does not appear how there can come to be a mode different from an attribute. So if we say, as is usually done, that a body contains nothing but extension, and then conceive extension as a kind of simple and primitive attribute, we can in no way explain how any variation can arise in bodies or how a plurality of bodies can exist. I have in fact demonstrated elsewhere, in my reply to Sturm which was published in the Leipzig Acts, that if matter were not heterogeneous (which it becomes through the entelechies), there could arise no variety of phenomena, and as a result equivalents would always replace each other. 14 For the rest, I make no distinction here between the general concept of substance and the concept of a determinate substance, for all substance is determinate, though different substances are determined in different ways. As for my own notion of substance, I should prefer to have it arise from our mutual discussion rather than to produce it myself and intrude it, so to speak; certainly ,we seem to me to have made a good beginning. In turning back to the earlier of your two letters, I noticed some matters which still need comment in order to form a better idea of the whole problem. It will be difficult to give examples of a concept from which no representative mark can be removed. Primitive concepts lie concealed in derivative ones but are hard to distinguish in them. I doubt that a body can be conceived apart from motion; I admit that motion cannot be conceived apart from body. But in the concept of motion there are included not only body and change but a reason and a determinant of change as well, which cannot be found in a body if its nature is considered to be purely passive, that is, to consist in extension alone or even in extension and impenetrability. In extension I think of many things together - on the one hand, continuity, which it has in common with time and motion, and on the other, coexistence. So it is not necessary to think of extension either as a whole or as nothing at all. To make extension possible, moreover, there must clearly be something which is repeated continuously, or a plurality of things which coexist continuously. You ask, Sir, what it is that we can think of in a thing to which we ascribe extension, aside from this extension itself. I reply that action and passion must be added to extension in the thing itself. Then, you reply, extension will be a mode of the extended. I answer that extension, in my sense of the term, will not be a mode of the substances from which it results, because it is itself For references see p. 539
526 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS invariable and designates a numerical determination of these things which remains the same in any change whatever. And you will surely agree with me that modes must be variable. Meanwhile I admit that not only extension but also action and passion cannot be thought of by themselves and that it is neither necessary nor easy to arrive at concepts of ultimate simplicity, as I have already remarked. So if we insist on such a concept alone as the concept of substance, I fear that we shall have to set aside all created substances - and this would be to cut the knot, not to untie it. .,. v [Further efforts by the two correspondents to refine their respective notions of substance, and of the relation of continuity, coexistence, and plurality in extension, led at length to the following clear statement by Leibniz.] [G., II, 239-41] Hanover, April, 1702 ... I do not believe that in the general concept of substance only one unique perfection is to be considered. You seem indeed not to accept any substance save with one attribute, and this is consistent with your concept of substance. For assuming that there is a substance with attributes A and B, then since there can, for you, be another substance with attribute A, it is evident that substance AB cannot be conceived through itself but only through substance A. Hence you will not consider it a substance. Nor can there be any reason, if one absolute, simple attribute can constitute a substance by itself, why another could not do so as well. But once you have assumed that every substance has one simple attribute, you cannot in the nature of things understand the origin of modifications and changes, for whence can these come but from substances? I, in contrast, hold that there is no substance which does not involve a relation to all the perfections of any other substances whatsoever. Hence no substance with but one attribute can be conceived, nor can we, so far as I know, conceive of an attribute or simple and absolute predicate by itself. I know that the Cartesians have felt otherwise about the former point, and Spinoza about the latter, but I know also that this resulted from a lack of adequate analysis, the touchstone of which is a demonstration of predicates from the subject. For every demonstrable proposition whose demonstration we do not have must contain an insufficiently analyzed term. When I say that every substance is simple, I understand by this that it lacks parts. Indeed, if all things which have a necessary connection with each other constituted one substance, it would follow, assuming that we exclude a vacuum, that all parts of matter would compose one substance, since they have a necessary connection. But this same reasoning would confuse substance with an aggregate of substances, whereas you point out quite correctly that we are here seeking the notion of substance, not that of an aggregate of substances. I do in fact accept the proposition against which, I believe, you argue that I ought not to accept it, namely, "that if the extended were conceived by itself alone, it would not be extended", for such an extended being would imply a contradiction. I also think it certain that what can be conceived by itself alone cannot be located in space. To be in a place is not a bare extrinsic denomination; indeed, there is no denomination
HANOVER UNDER GEORGE LOUIS, 1698-1716 527 extrinsic that it does not have an intrinsic denomination as its basis. This is itself one of my important doctrines. 15 ... If I am not mistaken, you said that if two predicates which belong together to the concept of a subject C are separable, that is, as I interpret it, if they can be found without each other in other subjects, then the concept C is not a unitary one. I offered the example of a square, whose predicates are those of being rectangular and equilateral, two predicates which do not occur together elsewhere. This separation, moreover, is certainly not merely one made in the mind; it exists in nature, since a quadrilateral may be rectangular but not equilateral, and a triangle may be equilateral and 110t rectangular. I cannot make a satisfactory application of your answer in your last letter. I admit that at least some proportion between its sides is inseparable from the concept of a rectangle, but such proportionality is one predicate, the proportion of equality is another, and the two differ as genus and species. It makes no difference whether the square has a 'prerogative of simplicity' over other rectangles if, indeed, it does have it. Moreover, these two predicates also generally require different causes. Let AB be moved along CD [perpendicular to it]; then the cause which makes A or C a right angle is one thing and that which makes AB equal to CD is another. It is easy to see, therefore, that this motion produces different effects. Yet the concept of the square is nonetheless one. Any two things A and B not only have in common that they are things or substances; they also have some kind of 'sympathy', as I remember saying in earlier letters to which you did not seem to object. The Cartesians think that some substance can be constituted by extension alone because they conceive of extension as something primitive. But if they undertook to analyze the concept, they would see that extension alone cannot suffice for an extended being, any more than number suffices for the things that are enumerated. I agree with you that just as the concept of the number 3 is not adequate to understand three particular things, so the concept of diffusion is inadequate to understand the nature of what is diffused. This is itself the very nature into which I think we ought to inquire. And I leave it to your judgment whether this can be anything but a force [10 ovva:JiIKOV] from which activity and passivity follow. Finally, granted that the a priori demonstration such as you desire for everything cannot be given, will this make my hypothesis accord any less with the facts? If you allow that it can be proved a posteriori, it will also be more valid than a hypothesis. And is any reason that can be adduced more valid against your concept of substance than the one which you yourself now acknowledge - that on the basis of it no modifications and changes can arise? Granted therefore that its impossibility is not to be demonstrated, it would suffice to build our concepts so that they agree with experience and practice, and to resolve our difficulties so that the road to higher reasons is opened. If any doubts are raised against my remarks, therefore, I shall try to reply freely and candidly, just as I have done until now. And perhaps you will look in vain for even this in other hypotheses. SO VI [On August 19, 1702, Leibniz sent De Voider a copy of his response to Bayle's second criticism (No. 60). In his next letter De Voider demanded that if mass and entelechy For references see p. 539
528 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS be combined in the same substance, a necessary connection should be demonstrated between them. Leibniz replied, in one of the most important letters in the series, with a comprehensive exposition of his notion of individual substance.] [G., II, 248-53] Hanover, June 20, 1703 16 I am replying to both of your deeply thoughtful letters in one and the same writing. I hope that my reply to Bayle has made my opinion about most matters clearer to you as well; if I am not mistaken, your letter shows that it has. Mr. Bayle himself writes that he now has a deeper insight into my hypothesis; his only remaining difficulty seems to concern the possibility of a spontaneous progression of thoughts in the soul. But there is no difficulty here for me, either from the side of experience - for since we often perceive such progression why cannot we believe it possible otherwise as well - or on a priori grounds, since I conclude that it is necessary from the very nature of all substance, which must act or have a tendency. Add to this also the fact that the present is everywhere pregnant with the future (in completely determined things, that is), so that all future states are pre-established in the present state. Your own objections arise from other sources. I turn back first to your earlier letter, in which you ask for a necessary connection between matter (or resistance) and active force, so that they need not be joined superficially only. But the cause of this connection is the fact that every substance is active and every finite substance is passive as well, and connected with this passivity is resistance. Such a conjunction is therefore demanded by the nature of things, which cannot be so impoverished as to lack a principle of action, and does not permit a vacuum of forms any more than of matter - not to mention the fact that the sources of action and of unity are the same. I do not at all approve of the doctrine of attributes which people are formulating today; as if one simple absolute predicate, which they call an attribute, constituted a substance. Nor do I find any entirely absolute predicates in concepts, that is, any which do not involve connections with other predicates. Certainly thought and extension, which are commonly proposed as examples, are far from being such attributes, as I have often shown. And, unless the predicate is taken concretely [in concreto], it is not the same as the subject; so the mind coincides with the thinker indeed (though not formally) but not with the thinking. For it is a property of the subject to involve future and past thoughts in addition to present ones. 17 Those who find the distinction between bodies to lie solely in what they think of as modes of extension (as almost everybody does today, you say) claim that in excluding a vacuum, they do not reject the view that bodies differ from each other only modally.ls But two individual substances must be distinguished more than modally. Besides, as the matter is commonly understood, they will not even be found to be distinguished modally. For if you assume two bodies A and B to be equal and with the same figure and motion, it will follow from such a concept of body, that is, a concept drawn solely from the putative modes of extension, that these bodies will have no intrinsic marks at all by which to be distinguished. Does this mean that A and B are not diverse individuals? Or is it possible for two things to be diverse which can in no way be distinguished? This and countless other considerations of the same kind show conclusively that this new philosophy which forms substances out of material or passive entities alone completely upsets the true conceptions of things.
HANOVER UNDER GEORGE LOUIS, 1698-1716 529 Things which are different must differ in something or must have within themselves some diversity that can be noted. It is strange that men have not applied this most obvious axiom, along with so many others. But people are generally content to satisfy their imaginations and do not worry about reasons; hence so many monstrosities introduced to the injury of the true philosophy. Thus they commonly use only incomplete and abstract concepts, which thought supports but which nature does not know in their bare form; such notions as that of time, also of space or of what is extended only mathematically, of merely passive mass, of motion considered mathematically, etc. Such concepts men can easily imagine to be diverse without diversityfor example, two equal parts of a straight line, since the straight line is something incomplete and abstract, which needs to be considered only in theory. But in nature every straight line is distinguishable by its contents from every other. Hence it cannot happen in nature that two bodies are at once perfectly similar and equal. Also, things which differ in position must express their position, that is, their surroundings, and are hence not to be distinguished merely by their location or by a solely extrinsic denomination, as such things are commonly understood. Hence there can be no bodies in nature as they are commonly conceived, like the atoms of the Democriteans and the perfect globules of the Cartesians, and these are nothing but the incomplete cogitations of philosophers who have not thoroughly investigated the natures of things.19 In my last reply to Sturm I used another unassailable argument besides to demonstrate that, given a plenum, it is impossible for matter as it is commonly thought of as formed solely out of the modifications of extension, or if you prefer, out of passive mass, to suffice for filling the universe, but that it is obviously necessary to assume something else in matter from which we may get a principle of change and one by which to distinguish among phenomena; and hence we need some alteration, and therefore some heterogeneity, in matter in addition to increase, diminution, and motion. But I do not admit any generation or corruption in substance itself. I turn now to your other letter. When I say that even if it is corporeal, a substance contains an infinity of machines, I think it must be added at the same time that it forms one machine composed of these machines and that it is actuated, besides, by one entelechy, without which it would contain no principle of true unity. I think that what has been said shows the evident necessity which forces us to admit entelechies. Also, if we are to have real beings and substances, I do not see how we can avoid true unities. Of course the arbitrary unities used in mathematics do not belong here, for they can be applied just as well to apparent entities such as all beings by aggregation - a herd, an army - whose unity comes from thought. This is the same in every aggregate; you will find no true unity if you take away the entelechy. Properly and exactly speaking, perhaps we should not say that the primitive entelechy impels the mass of its own body but that it is merely combined with a passive primitive power which it completes, or with which it constitutes a monad. Nor can it influence [in/luo in] the other entelechies or substances which exist in the same mass. But in phenomena, or in the resulting aggregate, everything is explained mechanically, and so masses are understood to impel each other. In these phenomena it is necessary to consider only derivative forces, once it is established whence these forces arise, namely, the phenomena of aggregates from the reality of the monads. In my opinion there never arises a natural organic mechanism that is new, because it always possesses infinite organs, so that it may express the whole universe in its For references see p. 539
530 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS way; indeed, it always involves all past and present time. This is the most certain nature of every substance. And we know that what is expressed in the soul is also expressed in the body; hence the soul as well as the machine animated by it, and the animal itself, are as indestructible as the very universe. It is for this reason that such a machine cannot be put together, any more than it can be destroyed, by any mechanical process. Nor can any primitive entelechy ever come into being or be extinguished naturally or ever lack an organic body. So far as my study of things carries me, at least, this cannot be otherwise, and my opinions on this score are not derived from our ignorance about the formation of the fetus but from higher principles. I regard substance itself, being endowed with primary active and passive power, as an indivisible or perfect monad - like the ego, or something similar to it - but I do not so regard the derivative forces, which are found to be changing continuously. But if there were no true one, then every true being would be eliminated. The forces which arise from mass and velocity are derivative and belong to aggregates or phenomena. When I speak of a primitive force as enduring, I do not mean the conservation of the total motive power, which we discussed together earlier, but an entelechy which always expresses this total force as well as other things. Derivative forces are in fact nothing but the modifications and echoes of primitive forces. So you see, esteemed Sir, that corporeal substances cannot be constituted solely out of derivative forces combined with their resistance, that is, out of vanishing modifications. Every modification presupposes something permanent. Therefore when you say, "Let us assume that there is nothing in bodies but derivative forces", I reply that such a hypothesis is impossible and that it again gives rise to the error of taking incomplete notions for the completely determined concepts of things. I do not admit any action of substances upon each other in the proper sense, since no reason can be found for one monad influencing another. But in appearances composed of aggregates, which are certainly nothing but phenomena (though well founded and regulated), no one will deny collision and impact. Meanwhile I discover that it is further true in phenomena and derivative forces that masses do not so much give new force to other masses as they give determinate direction to the force already existing in them, so that one body is repelled away from another by its own force rather than being propelled by the other. Entelechies must necessarily differ or not be completely similar to each other; in fact, they are principles of diversity, for they each express the universe from their own point of view. This is their office, that they should be so many living mirrors or so many concentrated worlds. Yet we rightly say that the souls of like-named animals, such as human souls, belong to the same species not in the mathematical but in the physical sense in which father and son are agreed to be of the same species. If you think of mass as an aggregate containing many substances, you can still conceive of a single pre-eminent substance or primary entelechy in it. For the rest, I arrange in the monad or the simple substance, complete with an entelechy, only one primitive passive force which is related to the whole mass of the organic body. The other subordinate monads placed in the organs do not make up a part of it, though they are immediately required by it, and they combine with the primary monad to make the organic corporeal substance, or the animal or plant. I therefore distinguish: (1) the primitive entelechy or soul; (2) primary matter or primitive passive power; (3) the complete monad formed by these two; (4) mass or secondary matter, or the
HANOVER UNDER GEORGE LOUIS, 1698-1716 531 organic machine in which innumerable subordinate monads concur; and (5) the animal or corporeal substance which the dominating monad makes into one machine. You doubt whether a single simple thing is subject to changes. But since only simple things are true things, and the rest are beings by aggregation and therefore phenomena, existing, as Democritus put it, by convention but not by nature [VOJlQ> not "'va8/], it is obvious that unless there is change in the simple things, there will be no change in things at all. Nor must every change be from without; on the contrary, an internal tendency to change is essential to finite substance, and no change can arise naturally in the monads in any other way. But in phenomena or aggregates every new change arises from an impact according to laws prescribed partly by metaphysics, partly by geometry; for abstractions are necessary for the scientific explanation of things. Hence we regard the individual parts within a mass as incomplete, and each as contributing its part, but completed only by the combination of all. So any body whatever, taken by itself, is understood to strive in the direction of a tangent, though its continuous motion in a curve may follow from the impressions of other bodies. But in a proper substance which is complete in itself and involves everything together, the construction of this curved line is itself contained and expressed, because everything future is predetermined in the present state of the substance. For there is as great a difference between substance and mass as there is between complete things as they are in themselves and incomplete things as we accept them through abstraction. It is by means of this abstraction that we can define in phenomena the role to be ascribed to each part of mass and can distinguish and explain the whole phenomenon rationally a thing which necessarily requires abstractions. You seem to have rightly grasped my doctrine of how every body whatever expresses all other things, and how every soul or entelechy whatever expresses its own body and through it all other things. But when you have uncovered the full force of this doctrine, you will find that I have said nothing else which does not follow from it. I had said that extension is the order of possible coexistents and that time is the order of possible inconsistents. If this is so, you say you wonder how time enters into all things, spiritual as well as corporeal, while extension enters only into corporeal things. I reply that the relations are the same in the one case as in the other, for every change, spiritual as well as material, has its own place [sedes], so to speak, in the order of time, as well as its own location in the order of coexistents, or in space. For although monads are not extended, they nevertheless have a certain kind of situation [situs] in extension, that is, they have a certain ordered relation of coexistence with others, namely, through the machine which they control. I do not think that any finite substances exist apart from a body and that they therefore lack a position or an order in relation to the other things coexisting in the universe. 2o Extended things involve a plurality of things endowed with position, but things which are simple, though they do not have extension, must yet have a position in extension, though it is impossible to designate these positions precisely as in the case of incomplete phenomena. VII [The letters which follow are largely repetitive of the points already made, but the sections here translated excel in the clarity and sharpness of Leibniz's statements.] For references see p. 539
532 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS [G., II, 257-59] Hanover, November 10, 1703 ... You seem to desire a cause from me where you yourself do not yet admit the effect. So we must first agree upon the 'that' [t'o Ot'I], that is, upon the question of fact, whether every substance, at least everyone known to us, can be considered as active. And this is a question which can be answered from phenomena. You are of the opinion that the resistance in a substance can accomplish nothing more than that the substance opposes its own active power. But this should not seem strange to you, since it happens even in quasi-substances or bodies that their mass limits the velocity which another body strives to impress upon them. But in things that are limited we need a principle of limitation, just as we need a principle of action in acting things. The intrinsic difference between bodies you attribute not so much to the things themselves as to my hypothesis. But I had added a demonstration taken from phenomena - to the effect that if this difference did not exist, one state of matter in a plenum could not be distinguished from another, for equivalents could always be substituted for each other. This applies chiefly to the Cartesians, who do not recognize qualities or forces in matter but only translation, as if God placed a body first in one position and then in another and then gave the mind arbitrary sensations which do not correspond to the properties of the body. It also applies especially to Malebranche, Sturm, and other occasionalists, who ascribe all force or active power to God alone, so that there is no principle of distinction in corporeal things themselves. You therefore disagree with both ofthese positions and agree with me in accepting derivative forces, hoping that in this way the diversities in phenomena can be explained. But then you should do justice to my other argument - that derivative or accidental forces are mere modifications and that an active thing cannot be the modification of something passive. since a modification is merely a varying limitation, and modes merely limit things but do not increase them and hence cannot contain any absolute perfection which is not in the thing itself which they modify. Otherwise, in fact, these accidents must be thought of in the manner of substances, namely, as something which stands per se. So you either must accept my opinion or take refuge in the misnomer [dU6yA.w0"0"ov] which you suggest in the view that perhaps the whole universe is merely one substance. To use the word "substance" in this sense is to twist it out of the sense others give it. And I do not see any argument by which such a paradox could be made probable; those offered by Benedict de Spinoza for such a view do not seem, if I am any judge, to contain even the shadow of a proof. Besides, even setting aside this discussion of the word 'substance', it is enough that you admit different subjects or things which contain modes; with this admission the argument which I have given, that a mode merely limits and does not augment its subject, is still valid. This makes it clear that motion is inadequate without forces, and derivative forces are inadequate without primary entelechies. In order to refute what I said about an internal tendency to change being essential to finite substance, you say, "Whatever follows from the nature of a thing is in that thing in an invariant mode, at least as long as the same nature persists in the thing, nor can it be taken away from it, since there is a necessary connection between it and the nature of the thing." But from this it would follow that nothing is active by
HANOVER UNDER GEORGE LOUIS, 1698-1716 533 nature, for action is always a change in the acting creature. I reply that we must distinguish between properties which are perpetual and modifications which are transitory. Whatever follows from the nature of a thing can either follow from it permanently or temporarily, and if temporarily, either at once and immediately, that is, in the present, or by the mediation of some prior modification, so that it is future. There is an image of this in quasi-substances or bodies which have force or are placed in motion. It follows from the nature of a body moving in a straight line at a given velocity, if no extraneous force be assumed, that after a given time has elapsed it will arrive at a given point on the straight line. Does this mean, therefore, that it arrives at this point permanently? Grant me therefore in the primitive tendenCies what it is necessary to recognize in the derivative. The case is like that of mathematical laws of series, or the nature of curves, where the entire progression is sufficiently contained in the beginning. Nature as a whole must be like this; otherwise it would be absurd and unworthy of wisdom. Nor do I see even the appearance of a reason for doubting it, except that we are frightened by the unusual. ... VIII [G., II, 262-65] Brunswick, January 21,1704 ... You speak as if you do not understand what I intend when I say that derivative forces are mere modifications and that the active cannot be a modification of the passive. Don't you understand, then, what is meant by modification, by active and passive? Meanwhile, reading I know not what obscurities into the argument, you have nibbled so cursorily at what I have written that you even ascribe to me what I did not say or rather, the very opposite of what I did say. For you interpret me as denying that derivative forces are active, since you say, "Therefore, I do not see why these (derivative) forces are not active." But so far am I from denying that they are active that I infer, from the very fact that they are active and yet modifications, that there is something primary and active of which they are modifications. You assert that motion, or the product of mass and velocity, constitutes the derivative forces. I, however, do not consider motion to be a derivative force but think rather that motion, being change, follows from such force. Derivative force is itself the present state when it tends toward or preinvolves a following state, as every present is great with the future. But that which persists, insofar as it involves all cases, contains primitive force, so that primitive force is the law of the series, as it were, while derivative force is the determinate value which distinguishes some term in the series. I do not recall who preceded Spinoza in saying that there is one sub~tance in the whole universe, so you will pardon my calling him to mind, especially since I used him merely as an illustration. If bodies are not substances insofar as they are this or that particular body, they are not individual substances. This would be like saying that Peter is a substance only insofar as he is a man or that species are substances but that individuals are not. Besides, the totality of bodies will also not be an individual substance in this sense, for what is this but the aggregate of all individual substances, unless you call in something else which is to persist - as the thinker of whom I spoke is compelled to do. For references see p. 539
534 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS And this enduring something will be a substance only because it is also a monad. In fact, he could have found an analogy of what he ascribed to the universe as a whole, in each of its parts. Substances are not mere wholes which contain parts formally but total things which contain their partials eminently. 21 If nothing is active by its own nature, there will be nothing active at all, for what reason for activity can there be if not in the nature of a thing? Yet you add the restriction that "a thing can be active by its own nature, if its action always maintains itself in the same mode". But since every action contains change, we must have in it precisely what you would seem to deny it, namely, a tendency toward internal change and a temporal succession following from the nature of the thing. You of course deny that "from the nature of a thing there follows that which belongs to it merely temporarily". You prove this by the nature of a triangle, but you do not distinguish between universal and particular natures. From universal natures there follow eternal consequences; from particular natures also temporal ones, unless you think that temporal things have no cause. "I do not see", you say, "how any succession can follow from the nature of a thing, viewed in itself." This is indeed impossible if we assume that this nature is not individual. "Unless", you add, "the thing itself is a succession." But all individual things are successions or are subject to succession, and so your view coincides with my own. For me nothing is permanent in things except the law itself which involves a continuous succession and which corresponds, in individual things, to that law which determines the whole world. Besides, you yourself recognize that in the case of quasi-substances, as 1 call them, it follows from the nature of a moving body that if nothing prevents it, it will arrive at a given point in a given time. You admit therefore that temporal things follow from the nature of particular things. What your objection is, 1 do not see. You say that in a series, such as one of numbers, nothing is thought of as successive. What of it? I do not say that every series is a temporal succession but only that a temporal succession is a series, which has in common with other series the property that the law of the series shows where it must arrive in continuing its progress or in other words, the order in which its terms will proceed when its beginning and the law of its progression are given, whether that order is a priority of essence!'. only or also one of time. 1 do not agree with your statement that "all of the terms in a series are contained in it in a single invariant way". This takes place in a certain way only in a uniform series, but there are series which contain maxima, minima, bend points, etc. When you say that "God bestowed upon matter at the beginning of the world only derivative forces", you are already tacitly assuming primitive forces in matter, because we cannot' understand what matter would be except through monads, since it would always be an aggregate or rather, the result of a plurality of phenomena, until we arrived at these simple beings. "Nothing", you say, "prevents substances of the same nature from acting upon each other." But you know that philosophers have rather denied any action between similar beings. And what is there that prevents substances which differ in nature from acting upon each other? When you have explained this, you will see that your explanation prevents all finite substances from influencing each other - not to mention the fact that all substances are different in nature, and there are no two things in nature
HANOVER UNDER GEORGE LOUIS, 1698-1716 535 which differ in number alone. When such a thing is conceived, it is by a fiction of the mind which is ignorant of the difference or is concealing it, or abstracting from it. There is only one case of one substance acting immediately upon another: the action, namely, of infinite substance upon finite substances - an action which consists in continuously producing or constituting them. For there must necessarily be a cause why these finite substances exist and correspond with each other, and this must necessarily arise from the infinite substance which is necessary per se. But if it is claimed that substances do not remain the same but that different substances which follow upon prior ones are always produced by God, this would be to quarrel about a word, for there is no further principle in things by which such a controversy can be decided. The succeeding substance will be considered the same as the preceding as long as the same law of the series or of simple continuous transition persists, which makes us believe in the same subject of change, or the monad. The fact that a certain law persists which involves all of the future states of that which we conceive to be the same this is the very fact, I say, which constitutes the enduring substance. And if anyone concedes to me that there is an infinity of percipients, in each of whom there is a fixed law of the progression of phenomena, that the phenomena of these different percipients correspond with each other, and that there is a common reason for both their existence and their correspondence in the thing which we call God, this is all that I claim in the matter, and all that I think can be claimed. All other positions and issues, I believe, arise only from poorly analyzed notions, and I shall be surprised if anyone shows that anything more can be added to these. If we had always kept this in mind in our dispute, we should have avoided much wrangling. You say, "Experience teaches us that changes take place, but our question was not what experience teaches but what follows from the nature of things." But do you think that I either could or should wish to prove anything in nature if change were not presupposed? But you say, "No experience teaches us that changes arise from within [ab intrinseco]." Nor have I urged this on the basis of experience. "The modes of action in the mind", you say, "are too obscure." I thought they were most clear; indeed, that they alone are clear and distinct. I thought you agreed that at least something in the mind comes from within, or not from any other finite substance, and hence I perhaps inferred that my opinion would be intelligible to you. But you take this to mean that I have assumed as axiomatic that everything in the mind is of such a nature. I admit that this is the view which I hold, but I do not postulate it .... IX [G., II, 268-71] Hanover, June 30, 1704 ... You continue by saying, "Nevertheless (your argument) does not convince me that a mathematical body has no reality, unless perhaps there is some ambiguity in the word 'reality'. For I conceive of the innumerable properties of such a body with the greatest evidence." To this I reply in two ways. First, it is a necessary inference from my principles that a mathematical body is not real and second, the arguments you urge, for saying that you conceive a body most clearly (as real), do not establish its reality. As for the first point, it follows from the very fact that a mathematical body cannot For references see p. 539
536 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS be analyzed into primary constituents that it is also not real but something mental and designates nothing but the possibility of parts, not something actual. A mathematicalline, namely, is in this respect like arithmetical unity; in both cases the parts are only possible and completely indefinite. A line is no more the aggregate of the lines into which it can be cut than unity is the aggregate of the fractions into which it can be split up. And, as in counting, the number is not a substance without the things counted, so neither is a mathematical body or extension without active and passive entities or motion. But in real things, that is, bodies, the parts are not indefinite as they are in space, which is a mental thing - but actually specified in a fixed way according to the divisions and subdivisions which nature actually introduces through the varieties of motion. And granted that these divisions proceed to infinity, they are nonetheless all the results of fixed primary constituents or real unities, though infinite in number. Accurately speaking, however. matter is not composed ofthese constitutive unities but results from them, since matter or extended mass is nothing but a phenomenon grounded in things, like the rainbow or the mock-sun, and all reality belongs only to unities. Phenomena can therefore always be divided into lesser phenomena which could be observed by other, more subtle, animals and we can never arrive at smallest phenomena. 22 Substantial unities are not parts but foundations of phenomena. I come now to the ground of your objection, esteemed Sir. "I conceive with greatest evidence", you say, "the innumerable properties of a mathematical body." I grant this, in the same sense, that is, in which the properties of number and time are conceived, concepts which are also only orders or relations pertaining to possibility and to the eternal truths of the world, and are then further applicable to actual events. But you add, "I conceive of a mathematical body as existing and inhering in nothing else." This I do not admit, unless we also conceive of time as existing or inhering in nothing. If you regard this mathematical body as space, it must be correlated with time; if as extension, it must be correlated with duration. For space is nothing but the order of existence of things possible at the same time, while time is the order of existence of things possible successively. As a physical body is to space, so the status or series of things is to time. The body and the series of things add to space and time, motion or action and passion, and the principle of motion. 23 For as I have repeatedly reminded you - though you seem to have neglected my reminders - extension is an abstraction from the extended and can no more be considered substance than can number or a multitude, for it expresses nothing but a certain nonsuccessive (i.e., unlike duration) but simultaneous diffusion or repetition of some particular nature, or what amounts to the same thing, a multitude of things of this same nature which exist together with some order between them; and it is this nature, I say, which is said to be extended or diffused. The notion of extension is thus relative, or extension is the extension of something, just as we say that a multitude or a duration is a multitude, or a duration, of something. But this nature which is said to be diffused, repeated, and continued is that which constitutes a physical body, and it can be found in no other principle but that of acting and enduring, since no other principle is suggested to us by the phenomena. But of what kind this action and passion are, I shall say later. So you see that once we begin an analysis of concepts, we always arrive at last at the view which 1 am urging. It is really not surprising that the Cartesians have failed to understand the nature of corporeal substance and to arrive at true principles, since they consider extension as
HANOVER UNDER GEORGE LOUIS, 1698-1716 537 something absolute, irresolvable, ineffable, or primitive. For trusting their sense perceptions, and perhaps also seeking the applause of men, they were content to stop where their sense perception stopped, even though they also boasted, elsewhere, that they had distinguished sharply between the sensible and the intelligible realms. "By forces", you say, "I have always meant something nonsubstantial but inhering in substance." And rightly so, if you mean mutable forces. But when force is taken to be the principle of action and passion, which is thus modified by derivative forces or by what is momentary in action, you can understand enough from what I have said that this is involved in the concept of extension itself, which is relative per se, and that by your own analysis of corporeal substance, we must come to this conclusion. This is even more clear, as was shown above, when we consider the analysis of aggregates and of the phenomena in unities and reality. You add, "I have always considered forces, viewed apart from the foundations from which they spring, as being in the nature of an external denomination." I should prefer to consider derivative forces in relation to their foundations, as a figure in relation to extension, that is, as a modification. And you know from my calculus, in which I have demonstrated the true measure of derivative forces a priori, that force multiplied by the time through which it acts equals action and that force is therefore the momentaneous factor in action but with a relation to the following state. I have often said - and do not remember ever to have deviated from this position - that unless there were some primary active principle in us, there could be no derivative forces and actions in us, since everything accidental or changeable must be a modification of something essential or perpetual and can contain nothing more positive than that which it modifies, since every modification is only a limitation - a figure of that which is varied and a derivative force of that which varies. You continue, "This foundation which was to be in the thing may perhaps be the same as what you call primitive forces, from which the derivative forces flow." I believe that this is most true, and so it appears that we are agreed on this point. You add, "But I perceive nothing of these - so feeble is the force of my understanding - except that you assert that all the remaining mutations flow from them." But you do yourself an injury through your excessive modesty, for you understand the matter as far as its nature allows. Would you seek to sense things which can only be understood, to see sounds, to hear colors? You do not in fact disagree with what I have asserted that mutations flow from them; do you regard it as nothing to know this? It is important, however, also to consider that this principle of action is most intelligible, because there is something in it analogous to what is in us, namely, perception and appetite. For the nature ofthings is uniform, and our nature cannot differ infinitely from the other simple substances of which the whole universe consists. Indeed, considering the matter carefully, it may be said that there is nothing in the world except simple substances and, in them, perception and appetite. Matter and motion, however, are not so much substances or things as they are the phenomena of percipient beings, whose reality is located in the harmony of the percipient with himself (at different times) and with other percipient beings. When Descartes and others say that "there is one substance for all corporeal beings", they mean one similar nature, and do not, I think, intend that all bodies together make one substance. Surely the fact itself shows the world to be an aggregate, like a herd or a machine. For references see p. 539
538 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS I had said that temporal events follow from particular things. You say that you do not object to this but that it remains to be explained how particulars differ from universals and why temporal events follow from the former and not from the latter. But if I am not mistaken, an essential order of particulars corresponds to the definite parts of time and space, and universals are abstracted from these particulars by the mind. Last of all, you add, "Particulars act upon each other and are thus subject to change with respect to actions. How this can be explained by substances which do not act upon each other is obscure to me." This seems to be aimed at my opinion about the pre-established harmony between simple substances, which cannot act upon each other. Yet they do produce a change in themselves, and it is necessary for this to happen from your own point of view as well. For you acknowledged above that there is an internal basis for forces or actions, and so we must recognize an internal principle of change. And unless we do, there will be no natural principle of change at all and therefore no natural change. For if the principle of change were external to all and internal to none, there would be none at all, and we should have to turn back with the occasionalists to God as the only agent. It is therefore truly internal to all simple substances, since there is no reason why it should be in one rather than in another, and it consists in the progress of the perceptions of each monad, the entire nature of things containing nothing besides. You see how simple the matter becomes when we have arrived at principles which are manifestly necessary and sufficient, so that it seems not only superfluous but inconsistent and without explanation to add anything further. To go beyond these principles and ask why there is perception and appetite in simple substances is to inquire about something ultramundane, so to speak, and to demand reasons of God why he has willed things to be such as we conceive them to be. I have been compelled to be more verbose in my answers in order to begin the reasoning by which I establish each point with a repetition of your own words. For I have noted that earlier, when we wrote more freely, we almost forgot what had gone before in the progression of the argument and sometimes turned in circles or digressed to other matters, which is sometimes an unintentional sign of impatience. For the rest, our esteemed common friend, John Bernoulli, has written that your health is not of the best; he himself has scarcely recovered from a serious illness. This is a great grief to me, who owe much to your thoughts and expect much fruitage still from them. So I think that you have need of gaiety, activity, and in brief, a kind of diet adapted to the body; such a diet is the true medicine for chronic illnesses and irregularities, though we often neglect it when pulled away by custom and business. x [G., II, 281-83] Hanover, January 19, 1706 ..• You rightly despair of obtaining from me what I can give you no hope of receiving and what I neither hope nor desire to find for myself. The Scholastics commonly sought things which were not only ultramundane but utopian. The brilliant French Jesuit, Tournemine, recently gave me an excellent example of this. He gave general approval to my pre-established harmony, which seemed to him to supply a reason
HANOVER UNDER GEORGE LOUIS, 1698-1716 539 for the agreement which we perceive between soul and body, but said that he still desired one thing - to know the reason for the union between the two, which he held to differ from their agreement. I replied that this metaphysical 'union' - I know not what - which the School assumes in addition to their agreement is not a phenomenon and that there is no concept and therefore no knowledge of it. So neither could I think of a reason that might be given for it. 24 I fear that the force which is thought to be in extension or mass, yet outside of the percipient beings and their perceptions, is of this nature. For there can be nothing real in nature except simple substances and the aggregates resulting from them. But in the simple substances themselves we know nothing besides perceptions or the reasons for them. Whoever assumes more must give the marks by which the additional natures are to be verified and explained. I consider it demonstrated - as I have written several times, although I cannot yet order everything in such a way as to present the demonstration conveniently to the eyes of others - that it is essential to substance that its present state involves its future states and vice versa. And there is nowhere else that force is to be found or a basis for the transition to new perceptions. From the things I have said it is also obvious that in actual bodies there is only a discrete quantity, that is, a multitude of monads or of simple substances, though in any sensible aggregate or one corresponding to phenomena, this may be greater than any given number. 25 But a continuous quantity is something ideal which pertains to possibles and to actualities only insofar as they are possible. A continuum, that is, involves indeterminate parts, while on the other hand, there is nothing indefinite in actual things, in which every division is made that can be made. Actual things are compounded as is a number out of unities, ideal things as is a number out of fractions; the parts are actually in the real whole but not in the ideal whole. But we confuse ideal with real substances when we seek for actual parts in the order of possibilities, and indeterminate parts in the aggregate of actual things, and so entangle ourselves in the labyrinth of the continuum and in contradictions that cannot be explained. Meanwhile the knowledge of the continuous, that is, of possibilities, contains eternal truths which are never violated by actual phenomena, since the difference is alway!} less than any given assignable amount. And we do not have, nor ought we to hope for, any other mark of reality in phenomena than that they correspond with each other and with eternal truths as well .... REFERENCES An allusion to Horace Ep. i. 32. "One can advance to a certain point, even though nothing further is possible." 2 It is noteworthy that in describing the extended, Leibniz chooses qualities on rising levels of distinctness and therefore also of well-founded phenomena, beginning with indistinct sense qualities (whiteness) and proceeding through quantitative properties (ductility and weight) to resistance and corporeal force. a See Descartes, Correspondence (ed. Adam and Tannery), II, 466,543,627. Compare Leibniz's discussions of inertia in the fifth letter to Clarke, Sec. 102, and in the Theodicy, Part I, Sec. 30. Leibniz does not use inertia, as Newton does in his first law of motion, as an absolute principle of matter but as a quantitative variable which together with velocity determines the constant amount of force in a material system. His physics is thus a phenomenal corroboration of his metaphysics, where force has active and passive aspects. 1
540 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Cf. the Discourse, No. 35, Sec. 21; also the Specimen dynamicum (No. 46, I). The close of the letter contains another exposition of the argument against Descartes that quantity of force rather than of motion is conserved. 6 This letter was not sent but is given here because it replies to De Voider's criticisms. The one of the same date which replaced it returns to the physical and empirical problems of substance. 7 Leibniz returns to this problem in his criticism of Malebranche (Conversation of Philarete and Ariste [No. 64]), where he makes clear that the difference between duration and extension on the one hand, and time and space, on the other, is a relational and practical one, the former abstractions being applied internally to things, the latter externally, and serving the purpose of measurement. But see also the letter of June 21, 1704, to De VoIder (lX, below) and the fifth letter to Clarke. 8 See the first letter of the series. Malebranche expounds this doctrine of creation in the Entretiens sur la metaphysique and the Recherche, Eclaircissement XV. 9 The discussion of a substantiating chain in the correspondence with Des Bosses (No. 63) turns about the adequacy of this statement. 10 BC.'s German translation renders perfectio as 'reality'. We have not taken this liberty, but the reader will do well to remember that for Leibniz and his correspondent the two are equivalent, since primary concepts or essences are the perfections of God. 11 A complete term is thus a concrete one, and an incomplete term abstract. This restates Leibniz's logical view that many real definitions are possible for an abstraction but that there is only one adequate or ultimate analysis possible of a determinate concept. 12 In the light of his rejection of the Scholastic doctrine of influence (cf. p. 83, note 6), Leibniz's use here of the verb influo is startling. The context makes clear, however, that he is talking oflogical and functional dependence and not of efficient causality. 13 It follows therefore that for Leibniz, independent substances are related in a harmonious complex and that relations are in this sense external to them (cf. New Essays, II, xxv, 10: "There is no term so absolute or so detached that it does not include relations so that its perfect analysis leads to other things and even to all other things"). It follows also that the essence of an individual substance, or an individual concept, involves properties not reducible to the properties of the concepts out of which it is compounded. 14 See No. 53. Leibniz has argued more fully in the Specimen dynamicum that individual bodies cannot be distinguished except through motion, and hence through their inherent force. 15 Leibniz uses the Epicurean term KOPla/ Meal. The doctrine of relations expounded in this and the preceding letters (cf. note 13, above) is far from unambiguous. If, as he said earlier, all substances are necessarily related yet independent, and if, as he says here, extrinsic relations depend upon internal denominations or relational qualities, he must hold that relations are necessary but not determinative of substance, while the relational qualities upon which the relations depend are thus determinative. 16 A postscript shows that the letter was originally sent in the early winter of 1703 from Berlin but that a copy was sent from Hanover on June 20,1703, after Bernoulli had reported that he had not received the original, which he was to have forwarded to De VoIder. 17 This passage, significantly, identifies the logical and the psychological subject. 'Formally' or metaphysically the 'I' is a functional law ; logically it is a subject which is identical with the 'concrete' totality of its predicates; psychologically it is the 'thinker', the self-conscious spirit which involves the whole of its perceptions. 18 See Descartes's Principles of Philosophy, Part I, Arts. 60 and 61, and Leibniz's comments in No. 42. 19 This distinction between material and abstract analysis, which is effective in theory but never adequate, though always applicable, to nature, supports Leibniz's distinction between truths of reason and of fact and between the connotative and denotative dimensions of truths 4 5
HANOVER UNDER GEORGE LOUIS, 1698-1716 541 of fact. Existing entities are concrete or completely determined; mathematical and logical entities are only partial. 20 Space is thus a phenomenon, but spatiality is a fundamental aspect of the functional relationships between coexistent and simultaneous perceptions ofthe monads. 21 Leibniz's sudden shifts from mathematical to Scholastic terms (from the law of the series to substances with formal and eminent properties) must not obscure the metaphysical truth herea creative order which determines its own acts and passive states is a unity which possesses reality beyond these changing modes themselves; it is not merely, after the analogy of spatial conceptions, the aggregate of its parts. 22 Here and elsewhere (cf. the letter to Varignon in No. 56) Leibniz has anticipated the criticisms of Berkeley and other empiricists who seek to limit analysis by minima sensibilia; for any empirical problem in which we must pass over into causal analysis, analysis is an endless task. 23 That is, primitive force and its several modes, active and passive. 24 See 'Remarque de l'auteur du systeme de l'harmonie preetablie sur un endroit des Memoires de Trevoux' (G., VI, 595). This appeared in the Memoires de Trevoux for March, 1708, in reply to Toumemine's criticism in the same journal for March, 1704. Leibniz did, however, return to the nature of the metaphysical union in bodies and discuss it extensively with Des Bosses (cf. No. 63, and see also note 9 above). 25 Thus there is no empirical meaning for infinity as applied to discrete existing beings, but only one of indefinite continuation. The continuum of mathematics, on the other hand, applies only to the realm of possibility (cf. p. 514, note 1, and No. 56).
56 LETTER TO VARIGNON, WITH A NOTE ON THE 'JUSTIFICATION OF THE INFINITESIMAL CALCULUS BY THAT OF ORDINARY ALGEBRA' 1702 The criticisms to which the new infinitesimal calculus was subjected during the last decade of the 17th century were often grounded upon nothing more than a failure to understand its value or a distrust of novelty. Thus Huygens himself, and the Abbe Gallois, an editor of the Journal des savants, seem not at once to have grasped the importance of the new instrument. With more veneration for Descartes than insight into mathematics, the Abbe Catelan once more rushed into print. Among the criticisms, however, was one aimed at an unclear foundation of the calculus itself, the uncertain status and nature of the infinite and the infinitesimals which were used. In 1694 and again in 1695 this issue was raised by Bernard Nieuwentift in two criticisms of the calculus; later the criticism was developed more convincingly by Michel Rolle, an abler mathematician. Among the defenders of the new methods were the Bernoulli brothers (cf. No. 53); the Marquis de I'Hospital, whose Analyse des infiniment petits (1696) was the first textbook in the field (cf. p. 420, note 8) ; Jacob Hermann (1678-1733); and Pierre Varignon (1654-1722), who had already made contributions to statics and was later to develop polar coordinates. Varignon was engaged at the time of this letter in replying to Rolle's criticisms and had asked Leibniz what he meant precisely by the infinitely small. The latter's reply was published in the Journal des savants, March 20, 1702; it suggested several levels ofinterpretation upon which the user ofthe calculus might stand. The supplement (II) had been sent to Pinson and Varignon sometime earlier and appeared in the Memoires de Trevoux, January, 1701. I. LETTER TO V ARIGNON [GM., IV, 91-95] Hanover, February 2, 1702 I am a little late in replying to the letter with which you honored me on November 29 of last yellr but which I did not receive until today. After Mr. Bernoulli sent it to me from Groningen, it did not arrive in Berlin until after I had left to return to Hanover with the Queen of Prussia, Her Majesty having been so gracious as to ask that I be in her suite. This had delayed my return. I am greatly obliged to you, Sir, and to your learned men who have done me the honor of reflecting upon what I wrote to one of my friends in reply to the criticisms against the calculus of differences and sums which were published in the Journal de Trevoux. I do not recall exactly what expressions I may have used, but my intention was to point out that it is unnecessary to make mathematical analysis depend on
HANOVER UNDER GEORGE LOUIS. 1698-1716 543 metaphysical controversies or to make sure that there are lines in nature which are infinitely small in a rigorous sense in contrast to our ordinary lines. or 'as a result, that there are lines infinitely greater than our ordinary ones (yet with ends; this is important inasmuch as it has seemed to me that the infinite. taken in a rigorous sense, must have its source in the unterminated; otherwise I see no way of finding an adequate ground for distinguishing it from the finite).l This is why I believed that in order to avoid subtleties and to make my reasoning clear to everyone. it would suffice here to explain the infinite through the incomparable. that is, to think of quantities incomparably greater or smaller than ours. This would provide as many degrees of incomparability as we may wish. since that which is incomparably much smaller has no value whatever in relation to the calculation of values which are incomparably greater than it. It is in this sense that a bit of magnetic matter which passes through glass is not comparable to a grain of sand, or this grain of sand to the terrestrial globe, or the globe to the firmament. It was to make this point that I once submitted some lemmas on incomparables to the Leipzig Acts. which could be understood as applicable either to infinites in the rigorous sense or merely to magnitudes which do not need to be considered in relation to others. But at the same time we must consider that these incomparable magnitudes themselves. as commonly understood. are not at all fixed or determined but can be taken to be as small as we wish in our geometrical reasoning and so have the effect of the infinitely small in the rigorous sense. If any opponent tries to contradict this proposition, it follows from our calculus that the error will be less than any possible assignable error, since it is in our power to make this incomparably small magnitude small enough for this purpose, inasmuch as we can always take a magnitude as small as we wish. Perhaps this is what you mean. Sir. when you speak of the inexhaustible, and the rigorous demonstration of the infinitesimal calculus which we use undoubtedly is to be found here. 2 It has the advantage of giving such a proof visibly and directly and in a way well fitted to reveal the source of the invention, while the ancients, like Archimedes. gave it indirectly in the form of their reductions to the absurd; but they were unable to arrive at complicated truths or solutions in default of such a calculus, though they possessed the foundation of the invention. It follows from this that even if someone refuses to admit infinite and infinitesimal lines in a rigorous metaphysical sense and as real things, he can still use them with confidence as ideal concepts which shorten his reasoning, similar to what we call imaginary roots in the ordinary algebra, for example, v'-2. Even though these are called imaginary, they continue to be useful and even necessary in expressing real magnitudes analytically. For example, it is impossible to express the analytic value of a straight line necessary to trisect a given angle without the aid of imaginaries. Just so it is impossible to establish our calculus of transcendent curves without using differences which are on the point of vanishing, and at last taking the incomparably small in place of the quantity to which we can assign smaller values to infinity. In the same way we can also conceive of dimensions beyond three. and even of powers whose exponents are not ordinary numbers - all in order to establish ideas fitting to shorten our reasoning and founded on realities. Yet we must not imagine that this explanation debases the science of the infinite and reduces it to fictions, for there always remains a 'syncategorematic' infinite. as the Scholastics say.3 And it remains true, for example. that 2=~+~+~+~+ 116 + 312 + ...• For references see p. 546
544 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS which is an infinite series containing all the fractions whose numerators are 1 and whose denominators are a geometric progression of powers of 2, although only ordinary numbers are used, and no infinitely small fraction, or one whose denominator is an infinite number, ever occurs in it. Furthermore, imaginary roots likewise have a real foundation [fundamentum in re]. So when I told the late Mr. Huygens that.J 1 + v -3 -.J 1 - v - 3 = V6, he found this so remarkable that he replied that there is something incomprehensible to us in the matter. So it can also be said that infinites and infinitesimals are grounded in such a way that everything in geometry, and even in nature, takes place as if they were perfect realities. Witness not only our geometrical analysis of transcendental curves but also my law of continuity, by virtue of which , we may consider rest as infinitely small motion (that is, as equivalent to a particular instance of its own contradictory), coincidence as infinitely small distance, equality as the limit of inequalities, etc. This law I once explained and applied in Mr. Bayle's Nouvelles de la republique des lettres and applied to the rules of motion of Descartes and Father Malebranche. I have since observed, by the second edition of the latter's rules which has since appeared, that the entire force of this principle is not yet understood. 4 Yet one can say in general that though continuity is something ideal and there is never anything in nature with perfectly uniform parts, the real, in turn, never ceases to be governed perfectly by the ideal and the abstract and that the rules of the finite are found to succeed in the infinite - as if there were atoms, that is, elements of an assignable size in nature, although there are none because matter is actually divisible without limit. And conversely the rules of the infinite apply to the finite, as if there were infinitely small metaphysical beings, although we have no need of them, and the division of matter never does proceed to infinitely small particles. This is because everything is governed by reason; otherwise there could be no science and no rule, and thIs would not at all conform with the nature of the sovereign principle. For the rest, when my reading of the Journal de Trevoux brought me to write about the attacks made there against the differential calculus, I assert that I was not thinking of the controversy which you, or rather those who use the calculus, are having with Mr. Rolle. It is only since your last letter, too, that I learned that the Abbe Gallois, whom I always honor greatly, has taken part. Perhaps his opposition comes only from his belief that we have founded the demonstration of this calculus on metaphysical paradoxes which I myself believe we can well discard .... I even find that it means much in establishing sound foundations for a science that it should have such critics. It is thus that the skeptics, with as much reason, fought the principles of geometry; that Father Gottignies, a Jesuit scholar, tried to throw out the best foundatioI1s of algebra; and that Mr. Cluver and Mr. Nieuwentijt have recently attacked our infinitesimal calculus, though on different grounds. Geometry and algebra have survived, and I hope that our science of infinites will survive also. But it will always owe you a great debt for the light which you have shed upon it. I have often thought that a reply by a geometrician to the objections of Sextus Empiricus and to the things which Francis Sanchez 5, author of the book Quod nihil scitur, sent to Clavi us, or to similar critics, would be something more useful than we can imagine. This is why we have no reason to regret the pains which are necessary to justify our analysis for all kinds of minds capable of understanding it ....
HANOVER UNDER GEORGE LOUIS, 1698-1716 545 II. JUSTIFICATION OF THE INFINITESIMAL CALCULUS BY THAT OF ORDINARY ALGEBRA [GM., IV, 104-6] Let two straight lines AX and EY meet at C, and from points E and Y drop EA and YX perpendicular to the straight line AX. CaU AC, c and AE, e; AX, x and XY, y (Figure 36). Then since triangles CAE and CXYare similar, it follows that (x-c)/ \ c\ :c 1 I \ \ I x<"I \ \ '\ " I I I I , I \ \ \ \ \ I I \ \ ---L--"-_--\ y X Fig. 36. y=c/e. Consequently, if the straight line EY more and more approaches the point A, always preserving the same angle at the variable point C, the straight lines c and e will obviously diminish steadily, yet the ratio of c to e will remain constant. Here we assume that this ratio is other than 1 and that the given angle is other than 45°, Now assume the case when the straight line EYpasses through A itself; it is obvious that the points C and E will fall on A, that the straight lines AC and AE, or c and e, will vanish, and that the proportion or equation (x - c)/y=c/e will become x/y=c/e. Then in the present case, assuming that it faUs under the general rule, x - c =x. Yet c and e will not be absolutely nothing, since they still preserve the ratio of CX to XY, or the ratio between the entire radius and the tangent of the angle at C 6 , the angle which we assumed to remain always the same as EYapproached the point A. For if c and e were nothing in an absolute sense in this calculation, in the case when the points C, E, and A coincide, c and e would be equal, since one zero equals another, and the equation or proportion x/y=c/e would become x/y=O/O=I; that is, x=y, which is an absurdity, since we assumed that the angle is not 45°. Hence c and e are not taken for zeros in this algebraic calculus, except comparatively in relation to x and y; but c and e still have an algebraic relation to each other. And so they are treated as infinitesimals, exactly as are the elements which our differential calculus recognizes in the ordinates of curves for momentary increments and decrements. Thus we find in the calculations of ordinary algebra traces of the transcendent difFor references see p. 546
546 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS ferential calculus and the same peculiarities about which some scholars have scruples. Even algebraic calculation cannot avoid them if it wishes to preserve its advantages, one of the most important of which is the universality which enables it to include all cases, even that where certain given lines disappear. It would be ridiculous not to accept this and so to deprive ourselves of one of its greatest uses. All capable analysts in ordinary algebra have made use of this universality in order to make their calculations and constructions general. And when this advantage is applied to physics as well, particularly to the laws of motion, it reduces in part to what I call the law of continuity, which has long served me as a principle of discovery in physics and also as a convenient test to see if certain proposed rules are good. Some years ago I published an example of this in the Nouvelles de la repub/ique des lettres, in which I take equality as a particular case of inequality, rest as a special case of motion, parallelism as a case of convergence, etc., assuming not that the difference of magnitudes which become equal is already zero but that it is in the act of vanishing; and similarly in the case of motion, not that it is already zero in an absolute sense but that it is on the point of becoming zero. And anyone who is not satisfied with this can be shown in the manner of Archimedes that the error is less than any assignable quantity and cannot be given by any construction. It is in this way that a mathematician, and a very capable one besides, was answered when he criticized the quadrature of the parabola on the basis of scruples similar to those now opposed to our calculus. For he was asked whether he could, by means of any construction, designate any magnitude that would be smaller than the difference he claimed existed between the area of the parabola given by Archimedes and its true area, as can always be done when the quadrature is false. Although it is not at all rigorously true that rest is a kind of motion or that equality is a kind of inequality, any more than it is true that a circle is a kind of regular polygon, it can be said, nevertheless, that rest, equality, and the circle terminate the motions, the inequalities, and the regular polygons which arrive at them by a continuous change and vanish in them. And although these terminations are excluded, that is, are not included in any rigorous sense in the variables which they limit, they nevertheless have the same properties as if they were included in the series, in accordance with the language of infinites and infinitesimals, which takes the circle, for example, as a regular polygon with an infinite number of sides. Otherwise the law of continuity would be violated, namely, that since we can move from polygons to a circle by a continuous change and without making a leap, it is also necessary not to make a leap in passing from the properties of polygons to those of a circle. REFERENCES The section enclosed in parentheses was to be omitted in the letter as sent. a If Leibniz had more clearly combined his conception of the infinitesimal as a quantity to be taken at will as less than any assignable quantity whatever with his own analysis of series and his functional conception of the law of continuity, he should have been led to the critical concept of limits upon which the calculus was at last theoretically grounded in the nineteenth century by Weierstrass and Cauchy. 8 I.e., a 'potential infinite'; see also the letters to John Bernoulli (No. 54) and p. 514, note 1. 4 See No. 37. 5 OM. has Suarez. • That is, assuming the angle at e to be at the center of a unit circle with radius ex. 1
57 ON WHAT IS INDEPENDENT OF SENSE AND OF MATTER (Letter to Queen Sophia Charlotte of Prussia, 1702) This and the following two selections (Nos. 58 and 59) show Leibniz's ability to popularize his ideas. The first two were certainly written at the instigation of his pupil, the Queen of Prussia, and the third, on ethics and law, belongs by style at least to the same group. This letter of Leibniz's was probably in reply to one by John Toland, who had visited the courts of Hanover and Berlin and had there had opportunity to expound his own empiricism and materialism. In any case, Sophia Charlotte submitted a letter of Toland's to Leibniz for criticism, and a rather short and unsatisfactory correspondence between the two men followed. Leibniz's paper is at certain points clearly aimed at Toland and probably also at Locke, whose Essay he was engaged in criticizing, but who avoided being drawn into correspondence. [0., VI, 499-508] I found the letter truly ingenious and beautiful which was sent some time ago from Paris to Osnabrtick, and which I recently read by your order at Hanover. Since it deals with two important questions on which I admit I do not entirely share the opinion of its author - whether there is something in our thoughts which does not come from sense and whether there is something in nature which is not material I wish I were able to explain myself with the same charm as his, in order to obey Your Majesty's orders and satisfy Your Majesty's curiosity. To use the analogy of an ancient writer, we use the external senses as a blind man uses his stick, and they help us to know their particular objects, which are colors, sounds, odors, tastes, and tactual qualities. But they do not help us to know what these sensible qualities are or in what they consist. For example, if red is the whirling of certain small globes which, it is claimed, make light; if heat is an eddy of very fine dust; if sound is made in the air as are circles in the water when a stone is thrown in, as some philosophers hold, we at least do not see this, and we cannot even understand how this whirling, these eddies and circles, if they are real, should bring about just the particular perceptions which we have of red, of heat, and of noise. So it can be said that sensible qualities are in fact occult qualities and that there must be others more manifest which could render them understandable. Far from understanding sensible things only, it is just these which we understand the least. And even though we are familiar with them, we do not understand them the better for that, just as a pilot does not understand the nature of the magnetic needle, which turns to the north, better than other men, although he has it constantly before his eyes in the compass, and as a result scarcely even has any more curiosity about it. I do not deny that many discoveries have been made about the nature of these For references see p. 553
548 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS occult qualities. So, for example, we know what kind of refraction produces blue and yellow and how these two colors mixed produce green. But we still cannot understand as a result how the perception we have of these three colors follows from these causes. Also, we do not have even nominal definitions of such qualities, in order to explain the terms. The purpose of nominal definitions is to give marks sufficient to aid in recognizing things. For example, assayers have marks by which they distinguish gold from all other metals, and even if a man has never even seen gold, these marks could be taught him so that he could recognize it unmistakably should he some day encounter it. But this is not the case with these sensible qualities; no mark for recognizing blue, for example, can be given to one who has never seen it. Thus blue is itself its own mark, and in order that a man may know what blue is, one must of necessity show it to him. For this reason it is usually said that the concepts of these qualities are clear, since they serve us in recognizing them, but that these same concepts are not distinct, because we cannot distinguish or develop the content included in them. It is an 'I know not what' which we perceive but for which we cannot account. On the other hand, we can make someone else understand what a thing is if we have some kind of description or nominal definition, even though we do not have the thing at hand to show him. We must do justice to the senses, however, by recognizing that besides these occult qualities, they enable us to know other qualities which are more manifest and furnish more distinct concepts. It is these which are ascribed to the common sense, because there is no external sense to which they are particularly attached and belong. 1 It is of these that definitions of the terms or words we use can be given. Such is the idea of numbers, which is found alike in sounds, colors, and the qualities of touch. It is thus, too, that we perceive the figures which are common to colors and to qualities of touch but which we do not observe in sounds. But it is true that in order to conceive numbers and even shapes distinctly and to build sciences from them, we must reach something which sense cannot furnish but which the understanding adds to it. 2 Since therefore our soul compares the numbers and the shapes of colors, for example, with the numbers and shapes discovered by touch, there must be an internal sense where the perceptions of these different external senses are found united. This is called the imagination, which comprises at once the concepts 0/ particular senses, which are clear but con/used, and the concepts 0/ the common sense, which are clear and distinct. 3 And these clear and distinct ideas which are subject to the imagination are the objects of the mathematical sciences, namely, arithmetic and geometry, which are the pure mathematical sciences, and their applications to nature, which make up mixed mathematics. It is seen also that particular sense qualities are capable of explanation and rationalization only insofar as they have a content common to the objects of several external senses and belong to the internal sense. For whenever one tries to explain sensible qualities distinctly, one always turns back to mathematical ideas, and these ideas always include magnitude, or multitude of parts. It is true that the mathematical sciences would not be demonstrative but would consist of a simple induction or observation which could never assure us of the perfect generality of the truths found in it, if something higher, which only the intellect can provide, did not come to the aid of imagination and sense. There are thus also objects of another nature, which are not at all included in what we have observed in the objects of either the particular senses or the common sense,
HANOVER UNDER GEORGE LOUIS, 1698-1716 549 and which consequently are also not to be considered objects of the imagination. Besides what is sensible and imaginable, therefore, there is that which is only intelligible, since it is the object of the understanding alone. And such is the object of my thought when I think of myself. This thought of myself. who perceive sensible objects, and of my own action which results from it, adds something to the objects of sense. To think of some color and to consider that I think of it - these two thoughts are very different, just as much as color itself differs from the ego who thinks of it. And since I conceive that there are other beings who also have the right to say 'I', or for whom this can be said, it is by this that I conceive what is called substance in general. It is the consideration of myself, also, which provides me with other concepts in metaphysics, such as those of cause, effect, action, similarity, etc., and even with those of logic and ethics. Thus it may be said that there is nothing in the understanding which has not come from the senses, except the understanding itself, or the one who understands. There are thus three levels of concepts: those which are sensible only, which are the objects produced by each sense in particular; those which are at once sensible and intelligible, which appertain to the common sense; and those which are intelligible only, which belong to the understanding. The first and second together are imaginable, but the third lie beyond the imagination. The second and third are intelligible and distinct, but the first are confused, although they may be clear and recognizable. 4 Being itself and truth are not understood completely through the senses. For it would not at all be impossible for a created being to have long and orderly dreams which resemble our lives, such that everything that it thought it perceived through the senses would be nothing but mere appearances. Something is thus needed beyond the senses, by which to distinguish the true from the apparent. But the truth of the demonstrative sciences is free 5 of such doubts and must even serve to judge the truth of sensible things. For as able ancient and modern philosophers have already well said, even if all that I think I see were only a dream, it would always be true that I who am thinking in my dream would be something and that I should in fact think in many ways for which there must always be a reason. What the ancient Platonists have said is thus quite true and quite worthy of consideration - that the existence of intelligible things, particularly of the I who think and am called a mind or soul, is incomparably more certain than the existence of sensible things and that it would thus not be impossible, speaking with metaphysical rigor, that there should exist at bottom only intelligible substances, of which sensible things would be only the appearances. Instead, our lack of attention causes us to take sensible things for the only true ones. It is also well to observe that if! should discover some demonstrative truth, mathematical or other, in a dream (and this can in fact be done), it would be just as certain as if I were awake. This shows us that intelligible truth is independent of the truth or existence of sensible and material things outside of us. This conception of being and of truth is thus found in the ego and in the understanding rather than in the external senses and the perception of exterior objects. In the understanding we discover also what it means to affirm, deny, doubt, will, and act. But above all, we find there the force of the conclusions in reasoning, which are a part of what is called the natural light. For example, by reversing the terms, one can draw from the premise that no wise man is vicious the conclusion that no vicious For references see p. 553
550 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS man is wise. On the other hand, from the premise that every wise man is praiseworthy, one cannot conclude by reversing terms that every praiseworthy man is wise, but only that some praiseworthy men are wise. Although one can always convert particular affirmative propositions, this is impossible with particular negatives. For example, if some wise men are rich, it is necessary also that some rich men are wise. Yet one can say that there are charitable beings who are not just, for this happens when charity is not regular enough, but one cannot infer from this that there are just beings who are not charitable, for charity and the rule of reason are at once included in justice. It is by this natural light that one may recognize also the axioms of mathematics; for example, that if the same quantity is taken away from two equals the remainders are equal and likewise that if both sides of a balance are equal neither will sink, a fact which we can foresee without ever having tried it. It is upon such foundations that arithmetic, geometry, mechanics, and the other demonstrative sciences are established, in which it is true that the senses are necessary to have definite ideas of sensible things, and experience is necessary to establish certain facts and even useful in verifying the reasoning involved, by a kind of check, as it were. But the force of the demonstrations depends upon intelligible concepts and truths, for it is these alone which enable us to draw conclusions which are necessary; they even make it possible for us, in the conjectural sciences, to determine demonstratively the degree of probability in certain given assumptions, so that we may choose reasonably, among conflicting appearances, that one whose probability is the greater. But this part of the art of reasoning has not yet been cultivated as much as it ought to be. To return to necessary truths, however, it is universally true that we know them only by this natural light and not at all by sense experiences. For the senses can indeed help us after a fashion to know what is, but they cannot help us to know what must be or what cannot be otherwise. For example, although we have countless times tested the fact that every heavy body falls toward the center of the earth, and is not sustained freely in the air, we are not sure that this is necessary until we have grasped the reason for it. Thus we cannot be sure that the same thing would happen in an altitude a hundred leagues or more higher than we are. There are philosophers who represent the earth as a magnet whose attractive force does not, they think, extend very, far, any more than the ordinary magnet attracts a needle some distance away from it. I am not saying that they are right but only that we cannot proceed with much certainty beyond the experiences which we have had, unless we are aided by reason. It is for this reason that the geometricians have always held that what has only been proved by induction or by examples, in geometry or arithmetic, has never been perfectly proved. For example, experience teaches us that the odd numbers when added together continuously in their order produce the square numbers in order, that is, the numbers produced by multiplying a number by itself. Thus 1 and 3 make 4, that is, 22; and 1 and 3 and 5 make 9, that is, 32 ; and 1 and 3 and 5 and 7 make 16, or 42 and 1 and 3 and 5 and 7 and 9 make 25, or 52; and so forth. However, if one had tried this a hundred thousand times, extending the calculation very far, one might well judge it reasonable that this will always be true, but one could never be absolutely certain of it as long as he does not grasp the demonstrative reason for it which mathematicians long ago discovered. It is on the basis of this uncertainty of induction, pushed a little too far, that an Englishman has recently tried
HANOVER UNDER GEORGE LOUIS, 1698-1716 551 to argue that we can avoid death. For, says he, the following conclusion is not sound: my father, my grandfather, my great-grandfather have died, and so have all the rest whom we know to have lived before us; therefore we too will die. For their death has no influence upon us. The trouble with this argument is that we resemble them a little too much, in that the causes of their death subsist in us as well. For the similarity between us would itself not be sufficient to draw conclusions of complete certainty, without considering the same reasons. There are in fact experiments which succeed countless times in ordinary circumstances, yet instances are found in some extraordinary cases in which the experiment does not succeed. FOf,example, if we have shown a hundred thousand times that iron sinks to the bottom when placed in water, we are still not sure that this must always happen. Without appealing to the miracle of the prophet Elisha, who made iron float, we know that an iron pot can be made so hollow that it floats and can even carry a considerable load besides, as do boats made of copper and of tinplate. Even the abstract sciences like geometry provide cases in which what ordinarily happens does not happen. Ordinarily, for example, we find that two lines which approach each other continuously finally meet, and many people would be quick to swear that it could never happen otherwise. Yet 'geometry does furnish exceptional lines called asymptotes for this reason, that when extended to infinity they approach each other continuously, yet never meet. This consideration also shows that there is a light which is born with us. For since the senses and induction can never teach us truths that are fully universal or absolutely necessary, but only what is and what is found in particular examples, and since we nonetheless know the universal and necessary truths of the sciences - in this we are privileged above the beasts - it follows that we have drawn these truths in part from what is within us. Thus one can lead a child to them by simple questions in the Socratic manner, without telling him anything, and without having him experiment at all about the truth of that which is asked him. This could most easily be carried out in numbers and similar matters. I agree, however, that in our present state the external senses are necessary for our thinking and that if we had none, we would not think. But what is necessary for something need not therefore make up its essence. The air is necessary for our life, but our life is (Iifferent from air. The senses furnish us with the matter for reasoning, and we never have thoughts so abstract that something is not mixed with them from sense. But reasoning demands something more than what is sensible. As for the second question, whether there are immaterial substances, one must first explain it in order to answer it. Heretofore matter has been understood to mean that which includes only purely passive and indifferent concepts, such as extension and impenetrability, which need to be given determinate form or activity by something else. Thus when it is said that there are immaterial substances, one means by this that there are substances which include other concepts, namely, perception and the principle of action or of change, which cannot be explained either by extension or by impenetrability. When these beings have feeling, they are called souls, and when they are capable of reason, they are called spirits. Hence if anyone says that force and perception are essential to matter, he is taking matter for the complete corporeal substance which includes form and matter, or the soul along with the organs. This is the same as if he had said that there are souls everywhere. This could be true, yet For re/eren ces see p. 553
552 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS not at all contrary to the doctrine of immaterial substances. For this does not require these souls to be free from matter but only to be something more than matter and not produced or destroyed by the change which matter undergoes or subject to dissolution, since they are not composed of parts. It must also be admitted, however, that there is some substance separate from matter. To make this clear, we need only to consider that there is an infinity of possible orders which the totality of matter might have received in place of this particular sequence of changes which it has actually taken on. For it is clear, for example, that the stars could have moved quite differently, since space and time are indifferent to every kind of motion and figure. Hence the reason, or the universal determining cause which makes things be, and makes them be as they are rather than otherwise, must of necessity be free of matter. Even the existence of matter depends upon it, since one does not find anything in the concept of matter which carries a reason for its existence with it. Now this ultimate reason for things which is common to all and universal because of the connection between all the parts of nature is what we call God, who must of necessity be an infinite and absolutely perfect substance. I am inclined to believe that all finite immaterial substances - in the opinion of the ancient Church Fathers, even the genii or angels - are joined to organs and accompany matter and even that souls or active forms are found everywhere. And to constitute a complete substance matter cannot dispense with them, since force and action are found everywhere in it. And the laws of force depend upon certain marvelous principles of metaphysics or upon intelligible concepts and cannot be explained by material or mathematical concepts alone or by those which fall within the jurisdiction of the imagination. Perception, too, cannot be explained by any mechanism, whatever it may be. We can conclude then that there is also something immaterial everywhere in created beings, and particularly in us, where this force is accompanied by a fairly distinct perception, and even by that light of which I have spoken above, which makes us resemble God in miniature not only through our knowledge of order but also through the order which we can ourselves impart to the things within our grasp, in imitation of that which God imparts to the universe. It is in this, also, that our virtue and perfection consist, as our feliCity consists in the pleasure which we take in it. Now whenever we penetrate to the basis of anything, we find there the most beautiful order we can desire, surpassing anything we had expected, as anyone knows who has understood the sciences. We can therefore conclude that it is the same in all the rest and that not only do immaterial substances subsist always but their lives, progress, and changes are controlled to lead to a definite end or better, to approach it more and more, as do the asymptotes. Even though we may sometimes slip back, like curves which descend, the progression must finally prevail and win. The natural light of reason is insufficient for us to recognize the details, and our experiences are still too limited to discover the laws of this order. Meanwhile the revealed light guides us when we heed it through faith. But there remains room to think that in the future we may know still more by experience itself and that there are spirits who already know more in this way than we. Meanwhile philosophers and poets, lacking this knowledge, have had recourse to the fictions of metempsychosis or of the Elysian fields in order to provide some ideas which might be popularly appealing. But a consideration of the perfection of things, or what amounts to the same thing, of the sovereign power, wisdom, and goodness
HANOVER UNDER GEORGE LOUIS, 1698-1716 553 of God, who does everything for the best, that is, for the greatest order, is enough to make all reasonable people content and to convince us that our contentment should be the greater in the measure in which we are inclined to follow order and reason. REFERENCES For Leibniz's interpretation of Aristotle's doctrine of the common sense as the "mind itself" in reply to Locke see p. 294, note 2. 2 The selection of number and figures as examples is significant, since Leibniz used them from the beginning as fundamental categories, subforms of quantity and quality, upon which to base and to extend mathematics, particularly geometry and the art of combinations (see Nos. 1, 27,and 70). 3 Leibniz's distinction between imagination and sensation itself marks a point of deviation from Locke, since he emphasizes the dependence of the former upon the common sense and therefore its close relation to reflection and understanding, 4 At about this time Leibniz was developing his theory of apperception (probably suggested by the reflexive form s' appercevoir, which Coste used to translate Locke's perceive). Apperception or reflection is the basis of understanding, for without it there would be no perception of the content of perceptions and therefore no gound upon which to discover the universal principles of reason operative in the mind. While memory is the precondition of consciousness for Leibniz, apperception is the essential relation involved in the continuity of consciousness. 5 Reading exempte for exemp/e (G.). 1
58 REFLECTIONS ON THE DOCTRINE OF A SINGLE UNIVERSAL SPIRIT 1702 This work, which returns to the theme of No. 53, On Nature Itself, was written at the summer palace, Liitzenburg (later Char/ottenburg), near Berlin. Like the preceding, it reflects the reply which Leibnizwas engaged in preparing to Locke's Essay. [G., VI, 529-38] Some discerning people have believed and still believe today, that there is only one single spirit, which is universal and animates the whole universe and all its parts, each according to its structure and the organs which it finds there, just as the same wind current causes different organ pipes to give off different sounds. Thus they also hold that when an animal has sound organs, this spirit produces the effect of a particular soul in it but that when the organs are corrupted, this particular soul reduces to nothing or returns, so to speak, to the ocean of the universal spirit. Aristotle has seemed to some to have had an opinion approaching this, which was later revived by Averroes, a celebrated Arabian philosopher. He believed that there is an intellectus agens, or active understanding, in us and also an intellectus patiens, or a passive understanding, and that the former, coming from without, is eternal and universal for all, while the passive understanding, being particular for each, disappears at man's death. This was the doctrine of certain Peripatetics two or three centuries ago, such as Pomponatius, Contarini, and others, and one recognizes traces of it in the late Mr. Naude, as his letters and his recently printed Naudaeana show. 1 These men taught the doctrine in secret to their closest and ablest disciples; in public they were cautious enough to say that though the doctrine was indeed true according to philosophy - by which they meant pre-eminently that of Aristotle - it was false from the viewpoint of faith. This finally resulted in the disputes concerning the twofold truth, a doctrine condemned in the last Lateran Council. I have been told that Queen Christina held a strong inclination toward this opinion, and since Mr. Naude, her librarian, was saturated with it, it would seem that he gave her information about these secret opinions of famous philosophers, with whom he had discoursed in Italy. Spinoza, who recognizes only one single substance, is not far from the doctrine of a single universal spirit, and even the Neo-Cartesians, who hold that only God acts, affirm it, seemingly unawares. It would also seem that Molinos and certain other modem quietists, among them an author who calls himself John Angelus Silesius, who wrote before Molinos and some of whose writings have recently been reprinted, and even before these, Weigel, shared this opinion of a Sabbath or a repose of souls in God. It is for this reason that they believed that the cessation of particular activities is the highest state of perfection. 2
HANOVER UNDER GEORGE LOUIS, 1698-1716 555 It is true that the Peripatetic philosophers did not make this spirit completely universal, for besides the inteiligences which they held animated the stars, they also assumed an intelligence for this lower world, holding that it is this intelligence which functions as active intellect in the souls of men. They were led to this doctrine of a universal immortal soul for all men by a fallacious argument. For they assumed that an actual infinite plurality is impossible and that it is therefore also impossible that there should be an infinite number of souls but that this would necessarily follow if particular souls were to subsist. For since it is their opinion that the world is eternal and the human race also, and since new souls are constantly being born, there would have to be an actual infinity by now if they were all to subsist. They regarded this reasoning as a demonstration. But it is full offalse assumptions. There are those who disagree with them on the impossibility of an actual infinite, on the eternity of the human race, and on the generation of new souls, since Platonists teach the pre-existence of souls and Pythagoreans teach metempsychosis, holding that there always remain a certain determined number of souls which pass through cycles. In itself the doctrine of a universal spirit is good, for all who teach it recognize in fact the existence of divinity, whether they believe that this universal spirit is supremein which case they hold that it itself is God - or whether they believe, like the Cabalists, that God created it. The latter is also the opinion of the Englishman Henry More and other newer philosophers, particularly of certain chemists who believe that there is a universal Archeus or world-soul; some of them have maintained that this is the spirit of the Lord moving over the waters, of which the beginning of Genesis speaks. 3 But to go so far as to say that this universal spirit is the only spirit and that there are no particular souls or spirits, or at least that these particular souls cease to subsist, is, I believe, to exceed the bounds of reason and to advance, without any basis, a doctrine of which we have not even a distinct concept. Let us examine briefly the apparent reasons upon which the attempt is made to support this doctrine which destroys the immortality of souls and degrades the human race, or rather, all living creatures, from the level on which they belong and which is commonly ascribed to them. For it seems to me that so important an opinion should be proved and that it is not enough merely to have an imaginary notion of it based in fact only upon a very lame comparison with the wind animating musical organs. I have shown above that the supposed demonstration of the Peripatetics, who maintained that there is only one spirit common to all men, has no force but is supported entirely by false premises. Spinoza undertook to demonstrate that there is only one substance in the world, but his demonstrations are pitiful or unintelligible. And the Neo-Cartesians, who believe that only God acts, have hardly given a proof, not to mention that Father Malebranche seems to admit at least the internal action of particular spirits. One of the most obvious arguments that have been urged against particular souls is the difficulty involved in their origin. The Scholastic philosophers held great disputes about the origin of forms, among which they included souls. Their opinions were sharply divided as to whether they were drawn forth from the potency of matter, like a figure worked out of marble [eduction], or whether there was a traduction of souls, so that a new soul is born from a preceding one as one fire is lighted from another, or whether souls had already pre-existed and merely made themselves known after For references see p. 560
556 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS the generation of the body, or finally, whether souls were created by God whenever there was a new generation. Those who denied particular souls believed that by doing so, they were escaping the whole difficulty, but they were really cutting the knot rather than untying it. There is no force at all in an argument which can be put as follows: There have been differing explanations of this doctrine; therefore, the whole doctrine is false. That is the way the skeptics reason, and, if it were acceptable, there would be almost nothing which one could not reject. Experiments in our own time lead us to believe that souls, and even animals, have always existed, although in minute size, and that generation is but a kind of augmentation. In this way all the difficulties connected with the generation of souls and forms disappear. We do not deny God the right to create new souls, however, or to give a higher degree of perfection to those already in nature. We are rather speaking only of what is-ordinary in nature without entering into God's particular economy with respect to human souls, which may be privileged because they are infinitely above those of animals. A factor which, in my opinion, has also contributed much to make intelligent men accept the doctrine of a single universal spirit is that the popular philosophers gave currency to a doctrine about separate souls and about soul functions separate from and independent of the body and its organs which they could not fully justify. They had a good reason in wanting to sustain the immortality of the soul as conforming to divine perfections and to true morality; but seeing that the organs observed in animals become disordered through death and are finally destroyed, they felt obliged to return to separate souls, that is, to believe that the soul subsists without any body yet does not cease having its thoughts and functions. The better to prove this, they tried to show that the soul already has thoughts in this life which are abstract and independent of material concepts. But those who rejected this separate state and independence as contrary to experience and to reason were thereby driven all the more to believe in the extinction of the individual soul and the conservation of the single universal spirit. I have examined this matter carefully and have shown that there are in truth certain materials of thought or objects of the understanding in the soul which have not been furnished by the external senses, namely, the soul itself and its functions (nihil est in intellectu quod non juerit in sensu, nisi ipse intellectus).4 Those who favor a universal spirit will readily assent to this, for they distinguish this spirit from matter. I find, however, that there is never any abstract thought which is not accompanied by some images or material traces, and I have established a perfect parallelism between what happens in the soul and what takes place in matter. I have shown that the soul with its functions is something distinct from matter but that it nevertheless is always accompanied by material organs and also that the soul's functions are always accompanied by organic functions which must correspond to them and that this relation is reciprocal and always will be. As for the complete separation of soul and body, I can say nothing about the laws of grace, and about the ordinances of God in regard to human souls in particular, beyond what the Holy Scriptures say, since these are things which cannot be known by reason, being dependent on the revelation of God himself. Nevertheless, I see no reason, either religious or philosophical, which compels me to abandon the doctrine of the parallelism of soul and body and to admit a perfect separation. For why cannot the soul always retain a subtle body organized after its own manner, which could
HANOVER UNDER GEORGE LOUIS, 1698-1716 557 even some day reassume the form of its visible body in the resurrection, since a glorified body is ascribed to the blessed, and since the ancient Fathers have ascribed a subtle body to angels? Furthermore, this doctrine conforms with the order of nature established through experience, for the observations of very capable observers have convinced us that animals do not begin when they are popularly believed to begin and that seminal animals or living seeds have existed from the beginning of things. 5 And both order and reason demand that what has existed since the beginning should no more have an end and that, since generation is thus merely the growth of a changed and developed animal, death will be nothing but the diminution of a changed and developed animal but that the animal itself will always remain throughout these transformations, just as the silkworm and the butterfly are one and the same animal. And it is appropriate to remark here that nature has this tact and goodness in revealing its secrets to us in small samples and thus making us infer the rest, everything being in correspondence and harmony. It is this which nature shows us in the transformation of caterpillars and other insects, for flies too come from worms, to help us grasp that there are transformations everywhere. Our experiments on insects have destroyed the popular notion that these animals are reproduced through nourishment, without propagation. Nature has likewise also given us, in birds, a sample of how all animals are generated by means of eggs, a fact which the new discoveries have now made us accept. There are also microscopic observations which have shown that the butterfly is merely a development of the caterpillar, but especially that seeds already contain the formed plant or animal, although it still needs transformation and nourishment, or growth, to become an animal of the kind which our ordinary senses can observe. And since even the smallest insects reproduce by the propagation of their kind, one must conclude the same to be true for these little seminal animals, that is, that they themselves come from other still smaller seminal animals, and thus have originated only with the world. This agrees well with the Holy Scriptures, which suggest that there were seeds in the beginning. In dreams and in unconsciousness nature has given us an example which should convince us that death is not a cessation of all functions but only a suspension of certain more noticeable ones. Elsewhere I have explained an important point whose neglect has led men the more easily to accept the opinion that the soul is mortal. It is that a large number of small perceptions which are equal and balanced among themselves, with nothing to give them relief or distinguish them from each other, are not noticed at all and cannot be remembered. But to conclude from this that the soul is without any function at all would be like the popular belief that there is a void or nothing at all wherever there is no noticeable matter or that the earth does not move because its movement, being uniform and without jerks, is unnoticeable. We have an infinity of little perceptions which we are incapable of distinguishing. A great stupefying roar, as, for example, the murmur of a large assemblage, is composed of all the little murmurs of individual persons which are not noticed at all but of which one must nevertheless have some sensation; otherwise one would not sense the whole. Thus when an animal is deprived of organs capable of giving it sufficiently distinct perceptions, it does not follow that the animal has left no smaller and more uniform perceptions or that it is deprived of all its organs and all its perceptions. Its organs are merely enveloped and reduced to a small volume, but the order of nature requires that everyFor references see p. 560
558 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS thing be developed again sometime and return to a noticeable state and that there be a definite well-regulated progression in its changes which helps to bring things to fruition and perfection. It seems that even Democritus noted this resuscitation of animals, .for Plotinus ascribed a doctrine of resurrection to him.6 These considerations all show that not only particular souls but animals themselves subsist and that there is no reason for believing in a complete extinction of souls or even a complete destruction of the animal. As a result, therefore, there is no need to have recourse to a single universal spirit and to rob nature of its own particular and subsisting perfections; thus also failing in fact adequately to recognize its order and harmony. There are also many things in the doctrine of a single universal spirit which cannot be maintained and are involved in much greater difficulties than the common doctrine. These are a few of them. One may see at once that the analogy of the wind which makes different pipes sound differently flatters the imagination but explains nothing or, rather, that it implies exactly the contrary. For this universal wind in the pipes is nothing but the sum of a number of individual winds. So each pipe is filled with its own air, which can even pass from one pipe into another, in a way which makes the analogy support, instead, particular souls and even the transmigration of souls from one body to another, as the air can change pipes. Moreover, if one imagines the universal spirit to be like an ocean composed of an infinity of drops which become detached when they animate some particular organic body but are reunited to the ocean after the organs are distroyed, one again forms a materialistic and crude concept which does not fit the matter and is involved in the same difficulties as those of the wind. For since the ocean is an aggregate of drops, God would be an assemblage of all souls, almost in the same way that a swarm of bees is an assemblage of small animals. But this swarm is not in itself a true substance, and it is clear that on this basis the universal spirit would not in itself be a true being. Instead of saying, then, that God is the only spirit, we should have to say that he is nothing at all by himself and that there are i'n nature only the particular souls of which he is the aggregate. Besides, the drops reunited to the ocean of universal spirit after the destruction of the organs would in fact be souls which were subsisting independently of matter. So we would fall back into the view which we sought to avoid, especially if these drops retain some trace of their preceding state or still hav~ certain functions and could perhaps even acquire more sublime ones in this ocear of divinity or of the universal spirit. But if we mean that these souls reunited to God are without any other functions of their own, we fall into an opinion contrary to reason and to all sound philosophy, as if any subsisting being could ever reach a state in which it is without any function or impression whatever. For when one thing is joined to another, it does not cease to have its particular functions, but these joined to the functions of others result in the functions of the whole. The whole would have none if the parts had none. Furthermore, I have shown elsewhere that each being preserves perfectly all the impressions which it has received, although these impressions may no longer be noticeable separately because they have been joined with others. Thus the soul, reunited with an ocean of souls, would always remain the particular soul which it had been separately. This shows that it is more reasonable and in greater conformity with the habits of
HANOVER UNDER GEORGE LOUIS, 1698-1716 559 nature to keep particular souls subsisting in animals themselves, and not outside of them in God, and so to conserve not merely the soul but also the animal, as I have explained above and elsewhere; thus particular souls would also remain on dutyalways, that is, they would retain the particular functions which belong to them and would contribute to the beauty and order of the universe, instead of being reduced to the Sabbath in God of the quietists, or to a state of idleness and uselessness. As for the beatific vision of blessed spirits, it is compatible with the functions of their glorified bodies, which will continue to be organic in their own manner. If anyone tries to maintain, however, that there are no particular souls at all, not even now, while the functions of sensation and thought take place with the help of organs, he is refuted by our experience, which teaches, it seems to me, that we are in ourselves something particular which thinks. which perceives, and which wills, and that we are distinguished from another being who thinks and wills something else. Otherwise we fall into the opinion of Spinoza or some similar authors who hold that there is only one substance, God, who thinks, believes, and wills one thing in me, but who thinks, believes, and wills an entirely contrary thing in someone else, an opinion which Mr. Bayle has well held up to ridicule in certain passages of his Dictionary.7 To go further, if there is nothing in nature but the universal spirit and matter, we shall have to say that if it is not the universal spirit who believes and wills contrary things in different persons, it is matter which is different and acts differently. But if matter acts, of what good is the universal spirit? If matter is only a passive first principle or better, a purely passive being, how then attribute these actions to it? It is far more reasonable, then, to believe that besides God, who is the supreme active principle, there are numerous particular active beings, since there are numerous actions and passions which are particular and contrary and should not be ascribed to the same subject. And these active beings are none other than individual souls. It is also known that there are degrees in all things. There is an infinity of degrees between motion of any kind whatever and perfect rest, between hardness and perfect fluidity without any resistance, between God and nothing. Thus there is likewise an infinity of degrees between an active being as great as it can be and pure passivity. It is unreasonable, therefore, to recognize only a single active being, that is, a universal spirit, and a single passive one, that is, matter. We must consider also that matter is not something opposed to God but that it must rather be bpposed to a limited active being, that is, to the soul or to the form. For God is the supreme being, opposed to nothingness; from him comes matter as well as forms, and the purely passive is something more than nothingness, since it is capable of something, whereas nothingness can have no attributes. So we must match each particular portion of matter with particular forms, that is to say, with the souls and spirits which correspond to it. I do not wish to return here to a demonstrative argument which I have used elsewhere, which is drawn from the nature of unities or simple things, with which particular souls are included. This argument compels us, unavoidably, not merely to admit particular souls but also to affirm that they are immortal by their nature and as indestructible as the universe and what is more, that each soul is a mirror of the universe in its own way, without any interruption, and contains in its depths an order corresponding to that of the universe itself; and that the souls vary and represent in an infinite number of ways, all different and all true, and thus multiply the universe, so to speak, as often as For references see p. 560
560 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS possible, and in such a way that they approach divinity as far as they can in their different degrees and give to the universe all the perfection of which it is capable. Consequently, I cannot see any basis, either in reason or in appearance, for combating the doctrine of individual souls. Those who do it agree that what is in us is an effect of the universal spirit. But the effects of God have subsistence, not to say that even the modifications and effects of created beings have permanence in some way and that their impressions are merely joined together without destroying each other. If therefore, as we have seen, it is in conformity with both reason and experience for the animal to subsist always, with its more or less distinct perceptions and with certain organs, and if, as a result, this effect of God always subsists in these organs, why should it not be permissible to call this the soul and to say that this effect of God is an immaterial and immortal soul which in some way imitates the universal spirit? Especially since this doctrine puts an end to all difficulties, as I have made fully clear in what I have said here and in other writings dealing with these matters? REFERENCES 1 Leibniz's easy identification of the differing positions of these men is inexact. Pomponazzi (De immortalitate animae [1516]) explicitly rejected the Averroistic doctrine of a single active intellect, and Cardinal Contarini (De immortalitate animae, adversus Petrum Pomponatium [1518]) rejected both Averroist and Alexandrist versions, as did the church in the Lateran Council on December 19, 1512, as Leibniz later points out. Cassirer (BC., II, 49, n. 314) cites Sponde, Annales ecc/esiae, as the source of Leibniz's error. The Naudaeana of the French bibliographer and librarian of Queen Christine of Sweden, Gabriel Naude (1600-1653), had appeared in 1701. 2 On the quietists, Valentine Weigel, and Angelus Silesius see p. 430, note 9. 3 Gen. 1 :2. On Henry More see p. 452, note 15; on the elder Van He1mont's popularization of Paracelsus' doctrine of archeus see p. 412, note 37; and p. 328, note 14. On the vitalistic movement see p 508, note 2. 4 "Nothing is in the intel1ect which has not already been in the senses - except the intel1ect itself. " 5 The capable observers alluded to are Malpighi, Leeuwenhoek, and Swanunerdam. Malpighi had formulated the cel1 theory in his Anatome plantarum (1675), Leeuwenhoek discovered spermatazoa, and Swammerdam was known for his studies of the transformations of insects. On the controversy between the ovulist followers of Harvey and the animalculists following Leeuwenhoek, Leibniz does not here take a position (see Wundt, Leibniz, pp. 54-56). 6 See p. 461, n. 11. 7 Especial1y in the articles on "Averroes" and on "Spinoza".
59 REFLECTIONS ON THE COMMON CONCEPT OF JUSTICE 1702(?) Though conclusive evidence for the date of this work, in French, is lacking, it is obviously in Leibniz's courtly style, and the allusion to the three queens (p.570) in whom the Electress Sophia was directly interested suggests that it was written for her at some time between the determination of the Hanoverian succession to the English throne and the death of the Queen ofPrussia in 1705. Not only is it a clear development of Leibniz's theory ofjustice and its application to government, but it contains clues to his theory of values, proposals for scientific co-operation, and a popular statement of his theodicy. His indictment of slavery is more vigorous than in No. 44, IV, and earlier writings, and Whig principles find expression in his justification of the people's right to resist the sovereign in extraordinary cases. [Mollat, pp. 41-70] It is generally agreed that whatever God wills is good and just. But there remains the question whether it is good and just because God wills it or whether God wills it because it is good and just; in other words, whether justice and goodness are arbitrary or whether they belong to the necessary and eternal truths about the nature of things, as do numbers and proportions. The former opinion has been held by certain philosophers and by theologians, both Roman and Reformed. But the Reformed theologians of today usually reject this teaching, as do also all our own theologians and most of those of the Roman church as well. As a matter of fact it would destroy the justice of God. For why praise him for acting justly if the concept of justice adds nothing to his act? And to say, Stat pro ratione voluntas - 'Let my will stand for the reason' - is definitely the motto of a tyrant. Moreover, this opinion would hardly distinguish God from the devil. For if the devil, that is, an intelligent, invisible power who is very great and very evil, were the master of the world, this devil or this god would still be evil even if we were forced to honor him, just as certain peoples honor imaginary gods of this kind in the hope of bringing them to do less evil. Consequently, some people, overly devoted to the absolute right of God, have believed that he could justly condemn innocent people and even that this may actually happen. This does violence to those attributes which make God love-worthy and destroys our love for God, leaving only fear. Those who believe, for example, that infants who die without baptism are cast into the eternal flames must in effect have a very weak idea of the goodness and the justice of God and thus thoughtlessly injure what is most essential to religion. The Sacred Scriptures also give us an entirely different idea of this sovereign substance, speaking, as they so often and so clearly do, of the goodness of God and presenting him as a person who justifies himself against complaints. In the story of the creation of the world, the Scripture says that God considered all that he had done For references see p. 573
562 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS and found it good; that is, he was content with his work and had reason to be so. This is a human way of speaking which seems to be used explicitly to point out that the goodness of the acts and products of God does not depend on his will but on their nature. Otherwise he would only have to see what he willed and did to determine if it is good and to justify himself to himself as a wise sovereign. All our theologians, therefore, and most of those of the Roman church, as well as the ancient Church Fathers and the wisest and most esteemed philosophers, have favored the second view, which holds that goodness and justice have grounds independent of will and of force. In his dialogues Plato introduces and refutes a certain Thrasymachus who tried to explain what justice is by a definition which, if acceptable, would strongly support the view which we are opposing. 1 That is just, he says, which suits or pleases the most powerful. If this were true, the sentence of a sovereign court or a supreme judge would never be unjust, nor would an evil but powerful man ever deserve condemnation. What is more, the same action could be just and unjust depending on the judges who decide, which is ridiculous. It is one thing to be just, another to pass for just and to take the place of justice. A celebrated English philosopher named Hobbes, who has a reputation for his paradoxes, has tried to maintain almost the same thing as Thrasymachus. 2 He holds that God has the right to do anything because he is all-powerful. This fails to distinguish between right and fact. For what can be is one thing; what ought to be is another. This same Hobbes believes, for almost the same reason, that the true religion is that of the state. 3 It would follow that if the emperor Claudius, who decreed in an edict that "in libera re publica crepitus atque ructus liberos esse debere" 4, had established the god Crepitus among the authorized gods, he would have been a true god worthy of worship. This amounts to saying, in concealed terms, that there is no true religion and that religion is merely an invention of men. And in the same vein, the remark that justice is that which pleases the most powerful is nothing but saying that there is no certain and determined rule of justice which prevents our doing what we wish to do and can do with impunity, however evil it may be. Thus treason, assassination, poisoning, the torture of innocents, would all be just if they succeeded. This is essentially to change the meaning of terms and to speak a language different from that of other men. Until now we have meant by justice something different from that which always prevails. We have believed that a happy man can be evil and that an unpunished act can nevertheless be unjust, that is, it may deserve punishment, so that the issue is solely to know why it deserves punishment, without raising the question of whether the punishment will actually follow or not, or whether there is any judge to impose it. There were once two tyrants in Sicily named Denis, father and son. The father was more evil than the son. He had established his tyranny by destroying many honorable men. His son was less cruel but more addicted to disorders and luxuries. The father was happy and kept himself in power; the son was overthrown and finally made himself schoolmaster at Corinth in order to have the pleasure of ruling always and of carrying a scepter, after a fashion at least, by wielding the switches used in punishing the children. Should we say that the actions of the father were more just than those of the son because he was happy and unpunished? Would such a view permit history
HANOVER UNDER GEORGE LOUIS, 1698-1716 563 to condemn a happy tyrant? We see too, every day, that men, whether interested or disinterested, complain of the actions of certain powerful people and find them unjust. So the question is only whether they have reason to complain and whether history can justly blame the inclinations and acts of any prince. If this be granted, we must acknowledge that men mean something else by justice and right than that which pleases a powerful being who remains unpunished because there is no judge capable of mending matters. In the universe as a whole, or in the government of the world, it is fortunately true that he who is the most powerful is at the same time just and does nothing against which anyone has a right to complain. We must hold for certain that if we understood that universal order, we should find it impossible to do anything better than he has done it. Yet his power is not the formal reason which makes him just. Otherwise, if power were the formal reason for justice, all powerful beings would be just, each in proportion to his power, which is contrary to experience. We must therefore search after this formal reason, that is, the 'wherefore' of this attribute or the concept which should teach us what justice is and what men mean when they call an act just or unjust. And this formal reason must be common to God and man. Otherwise we should be wrong in seeking to ascribe the same attribute to both without equivocation. These are fundamental rules for reasoning and discourse. I grant that there is a great difference between the way in which men are just and the way in which God is just, but this difference is only one of degree. For God is perfectly and entirely just, while the justice of men is mixed with injustice, with faults and sins, because of the imperfection of human nature. The perfections of God are infinite; ours are limited. Anyone, therefore, who tries to maintain that the justice and goodness of God have entirely different rules from those of men must at the same time admit that two entirely different concepts are involved and that to ascribe justice to both is either deliberate equivocation or gross self-deceit. But if we choose one of the two concepts as the proper conception of justice, it must follow either that there is no true justice in God or that there is none in man, or perhaps that there is none in either God or man, so that in the end we do not know what we are talking about when we speak of justice. This would in effect destroy justice and leave nothing but the name, as do those who make it arbitrary and dependent on the whim of a judge or ruler, since the same act will appear just and unjust to different judges. This is somewhat as if we should try to maintain that our science - for example, arithmetic, or the science of numbers - does not agree with the science of God or the angels, or perhaps that all truth is arbitrary and based on a whim. For example, 1,4, 9, 16,25, etc., are square numbers produced by multiplying 1, 2, 3,4,5, etc., by themselves. Thus 1 times 1 is 1; 2 times 2 is 4; 3 times 3 is 9, etc. We discover that the successive odd numbers are the differences between successive square numbers. Thus the difference between 1 and 4 is 3, that between 4 and 9 is 5, between 9 and 16 is 7, etc .... Now would one have any reason to maintain that this is not true for God and the angels and that they see or discover something in numbers entirely contrary to what we find in them? Would we not be right in laughing at a man who maintained this and who did not know the difference between eternal and necessary truths, which must be the same for all, and truths that are contingent and changeable or arbitrary? This same thing is true about justice. If it is a fixed term with determinate meaning in a word, if it is not a simple sound without sense, like blitiri - the term or word For references see p. 573
564 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS justice will have some definition or intelligible meaning. And, by using the incontestable rules of logic, one can draw definite consequences from every definition. This is precisely what we do in building the necessary and demonstrative sciences which do not depend at all on facts but solely on reason; such are logic, metaphysics, arithmetic, geometry, the science of motion, and the science of Right [droit] as well, which are not at all based on experience or facts but serve rather to give reasons for facts and to control them in advance. This would be true in regard to Right, even if there were no law [Ioi] in the world. 5 The error of those who have made justice depend upon power comes in part from their confusion of Right with law. Right cannot be unjust; this would be a contradiction. But law can be, for it is power which gives and maintains law; and if this power lacks wisdom or good will, it can give and maintain very bad laws. But happily for the world, the laws of God are always just, and he is in a position to maintain them, as- he without a doubt does, even though this has not always happened visibly and at once - for which he assuredly has good reasons. We must determine, then, the formal ptinciple of justice and the measure by which we should judge acts to know if they are just or unjust. After what has been said we can already foresee what this must be. Justice is nothing but what conforms to wisdom and goodness combined. The end of goodness [bonte] is the greatest good [bien]. But to recognize this we need wisdom, which is merely the knowledge of the good, as goodness is merely the inclination to do good to all and to prevent evil, at least if evil is not necessary for a greater good or to prevent a greater evil. Thus wisdom is in the understanding, and goodness is in the will, and as a result justice is in both. Power is another matter. But if power is added, it brings to pass the Right and causes that which should be to exist really as well, insofar as the nature of things permits. And this is what God does in the world. But since justice aims at the good, and wisdom and goodness together form justice and so refer to the good, we may ask what is the true good. I reply that it is merely whatever serves the perfection of intelligent substances. It is obvious, therefore, that order, contentment, joy, wisdom, goodness, and virtue are goods in an essential sense and can never be bad and that power is a good in a natural sense, that is, by itself, because, other things being equal, it is better to have it than not to have it. But power does not become an assured good until it is joined with wisdom and goodness. For the power of an evil man serves only sooner or later to plunge him further into misery, since it gives him the means of doing more evil and of earning a greater punishment, from which he will not escape, since the universe has a perfectly just monarch whose infinite penetration and sovereign power one cannot avoid. Since experience shows us that God, for reasons unknown to us but surely very wise and based on a greater good, permits many evil persons to be happy in this life and many good persons to be unhappy, a fact which would not conform to the rules of a perfect government such as God's if it had not been corrected, it follows necessarily that there will be another life and that souls will not perish with the visible bodies. Otherwise there would be crimes unpunished and good deeds un rewarded, which is contrary to order. There are demonstrative proofs, besides, of the immortality of the soul, for the principle of action and of consciousness could not derive from a purely passive extended thing indifferent to all motion, as is matter. Therefore action and consciousness must necessarily come from something simple or immaterial, without extension and
HANOVER UNDER GEORGE LOUIS, 1698-1716 565 without parts, which is called the soul. But whatever is simple and without parts is not subject to dissolution and as a result, cannot be destroyed. There are people who imagine that we are too small a thing in the sight of an infinite God for him to be concerned about us. It is thought that we are to God as are the worms which we crush without thinking, in relation to us. But this is to imagine that God is like man and that he cannot think of everything. God, according to this reasoning, being infinite, does things without work in a way that results from his will, just as it results from my will and that of my friend that we are in accord, without needing some action to produce the accord after our resolutions are made. But if mankind, or even the smallest thing, were not well governed, the whole universe would not be well governed, for the whole consists of its parts. We also find order and wonders in the smallest whole things when we are capable of distinguishing their parts and at the same time of seeing the whole, as we do in looking at insects and other small things in the microscope. There are thus the strongest reasons for holding that the same craftsmanship and harmony would be found in great things if we were capable of seeing them as a whole. Above all, they would be found in the whole economy of the government of spirits, which are the substances most similar to God because they are themselves capable of recognizing and inventing order and craftsmanship. As a result we must conclude that the Author of things who is so inclined to order will be concerned for those creatures who are naturally sources of order in the measure of their perfection and who are alone capable of imitating his workmanship. But it is impossible that this should seem so to us, in this small portion of life which we live here below, which is but a small bit of the life without bounds which no spirit can fail to achieve. To consider this bit separately is to consider things like a broken stick or like the bits of flesh of an animal taken separately, so that the craftsmanship of its organs cannot be made apparent. This is also true when one looks at the brain, which must undoubtedly be one of the greatest wonders of nature, since it contains the most immediate organs of sense. Yet one finds there only a confused mass in which nothing unusual appears but which nevertheless conceals some kind of filaments of a fineness much greater than that of a spider's web which are thought to be the vessels for that very subtle fluid called the animal spirits. Thus this mass of brain contains a very great multitude of passages and of passages too small for us to overcome the labyrinth with our eyes, whatever microscope we may use. For the subtlety of the spirits contained in these passages is equal to that of light rays themselves. Yet our eyes and our sense of touch show us nothing extraordinary in the appearance of the brain. We may say that it is the same in the government of intelligent substances under the kingship of God, in which everything seems confused to our eyes. Nevertheless, it must be the most beautiful and most marvelous arrangement of the world, since it comes from an Author who is the source of all perfection. But it is too great and too beautiful for spirits with our present range to be able to perceive it so soon. To try to see it here is like wishing to take a novel by the tail and to claim to have deciphered the plot from the first book; the beauty of a novel, instead, is great in the degree that order emerges from very great apparent confusion. The composition would thus contain a fault if the reader could divine the entire issue at once. But what is only suspense [curiosite] and beauty in novels, which imitate creation, so to speak, is also utility and wisdom in this great and true poem, this word-by-word creation, the uniFor references see p. 573
566 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS verse. The beauty and justice of the divine government have been hidden in part from our eyes, not only because it could not be otherwise without changing the entire harmony of the world, but also because it is proper in order that there may be more exercise of free virtue, wisdom, and a love of God which is not mercenary, since the rewards and punishments are still outwardly invisible and appear only to the eyes of our reason or faith. This I find to be a good thing here, since the true faith is based on reason. And since the wonders of nature show us that God's operations are admirably beautiful whenever we can envisage a whole in its setting, even though this beauty is not apparent when we consider things detached or torn from their whole, we must likewise conclude that all that we cannot yet disentangle or envisage as a whole with all its parts must no less have justice and beauty. To recognize this point is to have a natural foundation for faith, hope, and the love of God, since these virtues are based on a knowledge of the divine perfections. Now nothing better corroborates the incomparable wisdom of God than the structure of the works of nature, particularly the structure which appears when we study them more closely with a microscope. It is for this reason, as well as because of the great light which could be thrown upon bodies for the use of medicine, food, and mechanical ends, that it should be most necessary to push our knowledge further with the aid of microscopes. There are scarcely ten men in the world who are carefully at work on this, and if there were a hundred thousand, there would not be too many to discover the important wonders of this new world which makes up the interior of ours and which is capable of making our knowledge a hundred thousand times greater than it is. It is for this reason that I have more than once hoped that the great princes might be led to arrange for this and to induce men to work at it. Observatories have been founded for watching the stars, whose structures are spectacular and demand great apparatus, but telescopes are far from being as useful and from revealing the beauties and varieties of knowledge which microscopes reveal. A man in Delft has accomplished wonders at it, and if there were many others like him, our knowledge of physics would be advanced far beyond its present state. It behooves great princes to arrange this for the public welfare, in which they are most interested. And since this matter involves little cost and display, is very easy to direct, and needs very little but good will and attention to accomplish it, there is little reason to neglect it. As for me I have no other motive in recommending this research than to advance our knowledge of truth and the public good, which is strongly interested in the increase of the treasure of human knowledge. Most of the questions of Right, but especially of the right of sovereigns and nations, are confused because they do not agree on a common conception of justice, with the result that we do not understand the same thing by the same word, and this opens the way to endless dispute. Everyone would agree, perhaps, on this nominal definition that justice is a constant will to act in such a way that no person has reason to complain of us. But this is not enough unless the method is given for determining these reasons. Now I observe that some people restrict the reasons for human complaints very narrowly and that others extend them. There are those who believe that it is enough if no harm is done to them and if no one has deprived them of their possessions, holding that no one is obligated to seek the good of others or prevent evil for them, even if it should cost us nothing and give us no pain. Many who pass in the world for great judges keep themselves within these limits. They content themselves with harming
HANOVER UNDER GEORGE LOUIS, 1698-1716 567 no one, but they are not inclined to improve people's conditions. In a word, they believe one can be just without being charitable. There are others in the world who have greater and more beautiful views and who would not wish anyone to complain of their lack of goodness. They would approve what I have said in my preface to the Codex juris gentium 6 - that justice is the charity of the wise man, that is, a goodness toward others which ought to conform to wisdom. And wisdom, in my opinion, is nothing but the knowledge of happiness. Men may be permitted to vary in their use of words, and if anyone wants to insist on limiting the term just to what is the opposite of charitable, there is no way to force him to change his language, since names are arbitrary. Yet we have a right to learn the reasons which he has for being what he calls just, in order to see whether these same reasons will not bring him also to be good and to do good. I believe we will agree that those who are charged with the conduct of others, like tutors, the directors of societies, and certain magistrates, are obligated not merely to prevent evil but also to secure the good. But it might perhaps be questioned whether a man free from commitments, or the sovereign of a state, has such obligations, the former in relation to others involved in the situation, the latter in relation to his subjects. On top of this I shall ask that whoever can sustain a person must not do evil to others. One can give more than one reason for this. The most pressing will be the fear that someone will do the same thing to us. But are we not also subject to the fear that men will hate us if we refuse them aid which does not at all inconvenience us and if we neglect to prevent an evil which is about to crush them? Someone may say, 'I am content that others should not harm me. I do not ask at all for their aid and their good deeds and have no wish either to give or to claim more.' But can one sincerely maintain this? Let him ask himself what he would say or hope for if he should find himself actually on the point of falling into an evil which someone could help him avoid by a tum of his hand? Would one not hold him for a bad man and even for an enemy if he refused to save us in such a situation? ... It will be granted, then, that one ought to prevent evil for another if it can be done conveniently. But perhaps it will not be granted that justice orders us to do positive good to others. 1 now ask if one is not at least obligated to relieve others' ills. And 1 return again to the proof, that is, to the rule, quod Ubi non vis fieri. 7 Suppose that you were plunged into misery. Would you not complain about someone who did not help you, if he could easily do so? You have fallen into the water. If he refuses to throw a rope to you to give you a way of saving yourself, would you not judge him to be an evil man and even an enemy? Suppose that you suffered from violent pains and that someone had in his house, under his lock and key, a healing fountain capable of relieving your ills. What would you say and what would you do if he refused to give you a few glasses of its water? Led by degrees 8, people will agree not only that men ought to abstain from doing evil but also that they ought to prevent evil from being done and even to alleviate it when it is done, at least as far as they can without inconvenience to themselves. 1 am not now examining how far this inconvenience can go. Yet it will still be doubted, perhaps, that one is obligated to secure the good of another, even when this can be done without difficulty. Someone may say, 'I am not obligated to help you achieve. Each for himself, God for all.' But let me again suggest an intermediate case. A great good comeS to you, but an obstacle arises, and I can remove that obstacle without pain. Would For references see p. 573
568 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS you not think it right to ask me to do so and to remind me that I would ask it of you ifI were in a similar plight? If you grant this point, as you can hardly help doing, how can you refuse the only remaining request, that is, to procure a great good for me when you can do this without inconvenience of any kind to yourself and without being able to offer any reason for not doing it except a simple, 'I do not want to'? You could make me happy, and you refuse to do so. I complain, and you would complain in the same circumstances; therefore, I complain with justice. This gradation shows us that the same grounds for complaint subsist throughout. Whether one does evil or refuses to do good is a matter of degree, of more or less, but this does not alter the nature of the matter. It can also be said that the absence of the good is an evil and the absence of the evil a good. In general, if someone asks you to do something or not to do something, and you refuse his request, he has reason to complain if he can judge that you would make the same request if you were in his place. And this is the principle of equity or, what is the same thing, of equality or of the identity of reasons, which holds that one should grant to others whatever one would himself wish in a similar situation, without claiming any privilege contrary to reason or without claiming to be able to allege one's will as a reason. Perhaps we can say, then, that not to do evil to another, neminem laedere, is the precept of the Law which is called strict Right Uus strictum] but that equity demands that one also do good when this is fitting and that it is in this that the precept consists which orders us to give each one his due, suum cuique tribuere. But what determines fitness [convenance] or what each one is due can be known by the rule of equity or of equality: quod tibi non vis fieri aut quod tibi vis fieri, neque aliis jacito aut negato. 9 This is the rule of reason and of our Master. Put yourself in the place of another, and you will have the true point of view to judge what is just or not. Certain objections have been made against this great rule, but they come from the fact that it is not applied universally. For example, it has been objected that by virtue of this maxim a criminal can claim a pardon from the sovereign judge because the judge would wish the same thing if he were in a similar position. The reply is easy. The judge must put himself not only in the place of the criminal but also in that of the others whose interest lies in the crime being punished. And he must determine the greater good in which the lesser evil is included. The same is true of the objection that distributive justice demands an inequality among men, that a society ought to divide gains in proportion to what each has contributed, and that merit and lack of merit must be considered. Here the reply is also easy. Put yourself in the place of all and assume that they are well informed and enlightened. You will gather this conclusion from their votes: they will regard it fitting to their own interest that distinctions be made between one another. For example, if profits were not divided proportionalIy in a commercial society, some would not enter it at alI, and others would quickly leave it, which is contrary to the interest of the whole society. We may say, then, that justice, at least among men, is the constant will to act as far as possible in such a way that no one can complain of us if we would not complain of others in a similar situation. From this it is evident that when it is impossible to act so that the whole world is satisfied, we should try to satisfy people as much as possible. What is just thus conforms to the charity of the wise man. So wisdom, which is a knowledge of our own good, brings us to justice, that is to say, to a reasonable advance toward the good of others. So far we have proposed as a
HANOVER UNDER GEORGE LOUIS, 1698-1716 569 reason for this the fear that we will be harmed if we do otherwise. But there is also the hope that others will do the same for us. Nothing is surer than the proverbs, homo homini deus, homo homini lupus. 10 Nothing can contribute more to the happiness, or to the misery, of man than men themselves. If they were all wise and knew how to treat each other, they would all be happy, as far as happiness can be obtained by human reason. But we may be permitted to use fictions for a better insight into the nature of things. Assume a person who has nothing to fear from others; such a person as would be a superior power in relation to men - some higher spirit; some substance which pagans would have called a divinity; some immortal, invulnerable, invincible man - in short, a person who can neither hope for nor fear anything from us. Shall we say that such a person is nonetheless obligated to do us no harm and even to do us good? Mr. Hobbes would say 'No'. He would even add that this person would have an absolute right in making us his conquest, because we could not complain of such a conqueror on the grounds which we have just pointed out, since there is another condition which exempts him from all consideration for us. But without needing a fiction, what shall we say of the supreme divinity whom reason makes us recognize? Christians agree, and others should agree, that this great God is supremely just and supremely good. But it cannot be for his own repose or to maintain peace with us that he shows us so much goodness, for we should be unable to wage war against him. What then is the principle of his justice, and what is its law? It cannot be this equity or equality which exists among men and makes them envisage the common end of our human condition, 'to do unto others what we wish others to do unto us'. One cannot envisage any other motive in God than that of perfection or if you like, of his pleasure. Assuming, according to my definition, that pleasure is nothing but the feeling of perfection, he has nothing to consider outside of himself; on the contrary, everything depends upon him. But his happiness would not be supreme if he did not aim at as much good and perfection as possible. But what will you say if I show that this same motive is found in truly virtuous and generous men, whose highest function is to imitate divinity so far as human nature is able? The earlier reasons of fear and hope can bring men to be just in public and when necessary for their own interest. They will even obligate them to exercise and practice the rules of justice from childhood in order to acquire habits, out of fear of betraying themselves too easily, and so harming themselves along with others. Yet if there were no other notive, this would merely be political at bottom. And if someone who is just in this sense should find opportunity to make a great fortune through a great crime which would remain unknown, or at least unpunished, he would say as did Julius Caesar,following Euripides: Si violandum est jus, regnandi gratia Violandum est. l l But he whose justice is proof against such a temptation cannot have any motive but that of his own inclination, acquired by birth or exercise and regulated by reason, which makes him find so much pleasure in the practice of justice and so much ugliness in unjust acts that other pleasures and displeasures are compelled to give way. One can say that this serenity of spirit, which finds the greatest pleasure in virtue and the greatest evil in vice, that is, in the perfection and imperfection of the will, would be the greatest good of which man is capable here below, even if he had nothing to expect beyond this life. For what can be preferred to this internal harmony, this For references see p. 573
570 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS continual pleasure in the purest and greatest, of which one is always master and which one need never abandon? Yet it must also be said that it is difficult to attain this disposition of spirit and that the number of those who have achieved it is small, most men remaining insensible to this motive, great and beautiful though it be. This seems to be why the Siamese believed that those who attain this degree of perfection receive divinity as a reward. The goodness of the Author of things has therefore provided for it through a motive more nearly within the reach of all men, by making himself known to the human race, as he has done by the eternal light of reason which he has given us and by the wonderful effects which he has placed before our eyes of his power, wisdom, and infinite goodness. This knowledge should make us see God as the sovereign Monarch of the universe, whose government is the most perfect state conceivable, in which nothing is neglected, in which all the hairs on our heads are counted, in which everything right becomes a fact, either in itself or in some equivalent form, in such a way that justice coincides with the good pleasure of God and no divorce ever arises between the honorable [l'honnete] and the useful. After this it must be imprudent not to be just, because, according as he is just or unjust, a man will certainly experience good or bad for himself from what he has done. But there is something still more beautiful than all this in the government of God. What Cicero has said allegorically of ideal justice is really true in reference to this substantial justice - that if we could see it, we should be inflamed by its beauty.12 One can compare the divine Monarchy to a kingdom whose sovereign would be a queen more spiritual and more learned than Queen Elizabeth; more judicious, more happy, and in a word, greater than Queen Anne; cleverer, wiser, and more beautiful than the Queen of Prussia - in short, as accomplished as it is possible to be. 13 Conceive that the perfections of this queen make such an impression upon the minds of her subjects that it is their greatest pleasure to obey and to please her. In this case the whole world would be virtuous and just by inclination. It is this which occurs literally and beyond all description in relation to God and to those who know him. It is in him that wisdom, virtue, justice, and grandeur, are accompanied by sovereign beauty. One cannot know God as one should witho1f1t loving him above all things, and one cannot love him thus without willing what he wills. His perfections are infinite and cannot cease. This is why the pleasure which consists in the feeling of his perfections is the greatest and most durable possible; thl).t is, it is the greatest felicity. And that which causes one to love him at the same time makes one happy and virtuous.... This shows that justice can be taken In different ways. It can be opposed to charity, and then it is only the jus strictum. It can be opposed to the wisdom of him who must exercise justice, and then it conforms to the general good, but there will be cases in which the particular good will not be found in it. God and immortality would not enter into account. When one considers them, however, one always finds his own good in the general good. While justice is merely a particular virtue, moreover, when we leave out of consideration God or a government which imitated that of God, and while this virtue so limited includes only what is called commutative and distributive justice, it can be said that as soon as it is based on God or on the imitation of God it becomes universal justice and contains all the virtues. For when we are vicious not only do we harm ourselves but we also diminish, so far as depends on us, the perfection of the great state of which God is the monarch. And although the evil is in fact redressed by the wisdom of the
HANOVER UNDER GEORGE LOUIS, 1698-1716 571 sovereign Lord this is partly through our punishment. Universal justice is distinguished by the supreme precept - honeste (hoc est probe, pie) vivere; as suum cuique tribuere conforms to particular justice, whether in general or taken more narrowly as the distributive justice which distinguishes men in particular; and as neminem laedere stands for commutative justice or for jus strictum as opposed to equity, as one takes these terms.14 It is true that Aristotle has recognized this universal justice, though he has not related it to God; even so, I find it beautiful that he had so lofty an ideaY But a well-formed government or state takes the place of God on earth for him, and this government will do what it can to require men to be virtuous. But as I have already said, one cannot compel men to be always virtuous by the principle solely of selfinterest in this life; even less can one find the rare secret of lifting them up so that virtue constitutes their greatest pleasure, in the way I have just finished describing. Aristotle seems to have hoped for this rather than shown it. Yet I do not find it impossible that there should be times and places where one attains this, especially if piety is added. We can still distinguish jus strictum, equity, and piety when we are considering the right of sovereigns and of peoples. Hobbes and Filmer seem to have considered only jus strictum. 16 The Roman jurisconsults also sometimes adhere to this level of right alone. It can even be said that piety and equity regularly demand the jus strictum when they do not supply an exception to it. In insisting upon jus strictum, however, one must always add, 'except for the demands of equity and of piety.' Otherwise the proverb would hold: summum jus summa est injuria. 17 In examining the jus strictum, it is important to consider the origin of kingdoms or states. Hobbes seems to think that men were something like beasts at first and became more tractable little by little but that, as long as they were free, they were in a state of war of all against all and thus had no jus strictum, since each had a right in everything and was able, without injustice, to seize the possessions of his neighbor as he saw fit. For there was then no security or judge, and anyone had the right to forestall those whom one had grounds to fear greatly. But as this state of crude nature was a state of misery, men agreed upon the means to secure their safety, transferring their right to judge to the person of the state, represented by an individual or by some assembly. I 8 However, Hobbes acknowledges somewhere that a man has not, for this reason,lost the right to judge what is most agreeable to him and that a criminal is allowed to do what he can to save himself. But the citizens of a state must submit to the judgment of the state. 19 The same author must also recognize, however, that these same citizens, who have not lost their power of judgment, also cannot let their own safety be endangered in some situation where many of them are mistreated. 20 So in the end, in spite of what Hobbes says, each one has retained his right and his liberty regardless of the transfer to the state, and this transfer will be provisional and limited, that is, it will take place to the degree that we believe our safety is involved. The reasons which this illustrious author gives to prevent subjects from resisting their sovereign are nothing but plausible considerations based on the true principle that ordinarily such a remedy is worse than the evil itself. But what is ordinarily the case is not absolutely so. The one is like the jus strictum, the other like equity. It seems to me also that this author makes the mistake of confusing right with its factual application. A man who has acquired a good, who has built a house or forged For references see p. 573
572 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS a sword, is the proprietary master of it, although someone else, in time of war, has the right to drive him from his house and to take away his sword. And although there are cases where one cannot enjoy his right for want of a judge and of enforcement, the right does not cease to subsist. To try to destroy something because there is no way at once to prove it and to enjoy it is to confuse matters. Mr. Filmer seems to me to have recognized rightly that there is a right, even a jus strictum, before the foundation of states. Whoever produces something new or gains possession of something already existing but which no one has possessed before, and improves and adapts it to his use, cannot as a rule be deprived of it without injustice. This is also true if one acquires a thing from such an owner, either directly or through intermediates. The right of acquisition is a jus strictum which even equity approves. Hobbes believes that by virtue of this right children are the property of their mother unless society orders differently,.and Filmer, assuming the superiority of the father, gives him the right of property over his children as well as over the children of his slaves. Since all men from the beginning until now are, according to sacred history, descended from Adam and also from Noah, it follows, according to Filmer, that if Noah were living, he would have the right of an absolute monarch over all men. In his absence fathers always are, or should be, the sovereign masters of their descendants. This paternal power is the origin of kings, who replace progenitors, in the last analysis, either by force or by consent. And since the power of fathers is absolute, that of kings is absolute also. This conception ought not entirely to be condemned, but I think we can say that it has been pushed too far. We must admit that a father or a mother acquires a great power over children by their procreation and education. But I do not think that we can conclude from this that children are the property of their progenitors, as are the horses or dogs which are born to us and the works which we create. The objection may be raised that we can acquire slaves and that the children of slaves are also slaves. And according to the law of nations, slaves are the property of their masters, and no reason can be seen why children whom we have produced and nurtured by education should not be our slaves by an even juster title than those whom we have bought or captured. To this I reply that even if I were to agree that there is a right of slavery among men which conforms to natural reason, and that according to jus strictum the bodies of slaves and their infants are under the power of their masters, it will always be true that another stronger right opposes the abuse of this one. This is the right of reasonable souls, which are naturally and inalienably free. It is the Law of God who is the sovereign master of bodies and souls and under whom masters are the fellow-citizens of their slaves, since slaves have the right of citizenship in the kingdom of God as well as their masters. So it can be said that a man's body is the property of his soul and ought not to be taken from him as long as he lives. Since a man's soul cannot be acquired, neither can ownership of his body be acquired, so that the right of a master over his slave can be in the nature only of what is called servitude to another, or a kind of usufruct. But usufruct has its limits; it must be practiced without destroying itself, salva re, so that this right cannot be extended to the point of making a slave evil or unhappy. But even if I were to agree, contrary to the nature of things, that an enslaved man is the property of another man, the right of the master, however rigorous, would be limited by equity, which demands that one man shall care for another as he would
HANOVER UNDER GEORGE LOUIS, 573 1698-1716 wish another to care for himself in a similar situation, and by charity, which orders us to work for the happiness of others. And these obligations are perfected by piety, that is, by what we owe to God. If we wished to stop with jus strictum alone, the American cannibals would have a right to eat their prisoners. There are those among them who demand even more; they use their prisoners to have children, then fatten and eat the children, and afterward, when she produces no more, the mother. Such are the consequences of a pretended right of masters over slaves and of fathers over children .... REFERENCES n, 1 Republic 338c If. Note the change in Leibniz's opinion since 1666 (No.1, when he applied Hobbes's theory of justice to God. 2 De cive xv. 5. 3 Ibid., 16. 4 "In a free state the passing of wind and belching should be free." The ruling of Claudius is reported by Suetonius, chap. 32; Leibniz's bit of vulgarity is of a kind which Sophia seems to have enjoyed. 5 This reaffirms the position taken in the Mainz period around 1670 (No.7, I). 6 See No. 44, I, above. 7 "What you do not wish to have done to you." This is the Golden Rule in its negativeformulation(cf. Matt. 7:12; Luke 6:31). 8 Leibniz's method of reasoning is an application of his law of continuity to cases of justice, arranged from the narrowest legal concept (neminem laedere) in a continuous scale to the highest religious demands. Hence his device of seeking middle cases between the given cases, in which there may be disagreement; this approximates the method which he employed, for example, in his criticism of Descartes's laws of motion (No. 42). 9 "What you do not wish to have done to you (or what you do wish to have done to you), do not do to others (or do not deny to others)". The advance of the argument beyond the negative statement in note 7 above is obvious. 10 "Man is a god to man; man is a wolf to man." Symmachus Epistle ix, 114; Plautus Asin. ii, 4. 90. 11 According to Suetonius, chap. 30; Euripides' original lines are in the Phoenissae v. 524--25. Way translates, "If wrong e'er be right, for a throne's sake were wrong most right." 12 De officiis iii. 6.17. 13 This flattering example is obviously addressed to the Electress Sophia, for the three queens are those in whom that ambitious sovereign might well be most interested - her mother, the English rulel' to whose throne her own right had been established, and her daughter, the Queen of Prussia. 14 See p.430, note 4 for the source of these maxims: "To live honorably (Le., uprightly, piously), to give to each his due, to injure no one." 15 Nic. Ethics v.I. 19. 16 Robert Filmer's Patriarchia. or the Natural Power of Kings, derived royal sovereignty from patriarchal authority. His theory evoked Locke's Treatises on Government (1689). 17 "The more law, the more injustice." Cicero (De officiis i. 10.33) has summum ius, summa iniuria. 18 De cive ii, 5. 19 Leviathan, chap. 21. 20 Ibid., chap. 29.
60 REPLY TO THE THOUGHTS ON THE SYSTEM OF PREESTABLISHED HARMONY CONTAINED IN THE SECOND EDITION OF MR. BAYLE'S CRITICAL DICTIONARY, ARTICLE RORARIUS 1702 The second edition of the Dictionnaire historique et critique appeared in 1702, with an additional criticism of Leibniz's system attached as note L to the article on 'Rorarius'. The reply which Leibniz prepared the same year was sent to John Bernoulli and De Voider on August 19 and forwarded by the latter to Bayle, who returned it to Leibniz along with a letter now lost. Leibniz published his paper in Masson's Histoire critique de la republique des lettres in 1702 with the title given above. Leibniz's position is the same as that of the De Voider correspondence but directed to the explanation of body-and-soul processes; the reconciliation of mechanism and 'idealism' (this term itself appears) is particularly clear. [G., IV, 554--71] In June and July, 1695, I had published in the Journal des savants of Paris several essays on a new system which seemed to me adapted to explain the union of soul and body.1 Instead of the Scholastics' theory of influence and the Cartesians' theory of assistance, I have there made use of the theory of pre-established harmony. Mr. Bayle, who is able to impart to the most abstract meditations the charm which they need to attract the attention of readers, but who at the same time penetrates to their depths and brings them into clear light, took the pains to enrich this system by the comments which he inserted in his Dictionary in the article on Rorarius. But since he at the same time also discussed some difficulties which he held to be in need of clarification, I tried to do justice to these in the Histoire des ouvrages des savants for July, 1698. 2 To this Mr. Bayle has just replied in the second edition of his Dictionary, in the same article on Rorarius, page 2610, note L. He says, most honorably, that my replies have strengthened my position and that if the possibility of the hypothesis of pre-established harmony were well established, he would find no difficulty in preferring it to the Cartesian hypothesis, because it gives a noble idea of the Author of things and removes every concept of miraculous guidance in the ordinary course of nature. He still seems to find it difficult, however, to conceive that this pre-established harmony is possible. To show this, he begins with something which, in his opinion, is easier but which will nonetheless be found very implausible. He compares my hypothesis, namely, with the assumption of a ship which arrives at a desired port all by itself without any guidance. On this he says that we must admit that the infinity of God is not too great to communicate such a faculty to a ship. He does not assert absolutely that the thing is impossible, yet he does judge that others will so consider
HANOVER UNDER GEORGE LOUIS, 1698-1716 575 it, for "you yourself will admit [he adds] that the nature of a ship is incapable of receiving this particular faculty from God". Perhaps he believes that according to the hypothesis in question, we must think of God giving the ship, for this result, a faculty in the Scholastic sense, like that which the Schools ascribed to heavy bodies to draw them toward the center. If it is in this sense that he understands the doctrine, I am the first to reject this assumption. But if he means a faculty of the ship which can be explained by the laws of mechanics and by internal forces as well as by external circumstances, and still rejects this assumption as impossible, I should like him to give some reason for this judgment. For though I have no need of the possibility of something entirely resembling this ship in the way in which Mr. Bayle seems to think of it (as I shall show later), I still believe that when things are well considered, there is not only no difficulty involved from God's viewpoint, but it seems that there could even be a finite spirit skilful enough to bring this about. There is no doubt whatever that a man could make a machine capable of walking about for some time through a city and of turning exactly at the corners of certain streets. A spirit incomparably more perfect, though still finite, could also foresee and avoid an incomparably greater number of obstacles. This is so true that if this world were nothing but a composite of a finite number of atoms which move in accordance with the laws of mechanics, as the hypothesis of some thinkers holds, it is certain that a finite spirit could be so enlightened as to understand and to foresee demonstratively everything which would occur in a determinate time, so that this spirit not only could construct a ship capable of sailing by itself to a designated port, by giving it the needed route, direction, and force at the start, but could also form a body capable of counterfeiting a man. For this involves merely a matter of more or less, which does not alter matters in the realm of possibilities. However great may be the number of functions of a machine, the power and skill of the builder could increase proportionately in such a way that not to see this possibility would be to give insufficient consideration to the degrees of things. It is true that the world is not compounded of a finite number of atoms but is rather like a machine composed in each of its parts of a truly infinite number of forces. But it is also true that he who made it and who governs it has an even more infinite perfection, because it comes from an infinity of possible worlds which are in his understanding and from which he has chosen that which pleased him. To return to limited spirits, however, we can judge from the small examples which sometimes occur among us how far those which we do not know may extend their powers. For example, there are men capable of carrying out great arithmetical calculations at once and solely by thinking. M. de Monconis mentions such a man in Italy in his day, and there is now one in Sweden who never learned even the ordinary arithmetic, and whom, I hope, they will not neglect to sound out concerning his mode of procedure. And what is man, however excellent he is capable of being, in comparison with all the many possible, or even existing, creatures such as angels or genii, who could surpass us in every kind of understanding and reasoning incomparably more than these wonderful possessors of a natural arithmetic surpass us in the matter of numbers? I admit that people do not commonly consider these matters; they are confused by objections when they have to think of what is unusual or even of that of which we have no instance. But when we think of the greatness and variety of the universe, we judge entirely differently about it. Mr. Bayle especially cannot fail to see the justice of these conclusions. It is true that my hypothesis does not depend upon them, as I For references see p. 585
576 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS will show directly, but even if it did, and if one were right in saying that it is even more surprising than the hypothesis of automata (of which, as I shall show below, it carries forward only the good parts and what is sound), I should not be disturbed, granted that there were no other method of explaining things in conformity to the laws of nature. For in these matters we ought not to be guided by popular concepts to the injury of conclusions that are certain. Besides, the objection which a philosopher should make against automata does not lie in the wonderfulness of the assumption but in the failure of principles, since entelechies are necessary everywhere, and we hold a small idea of the Author of nature (who multiplies his little worlds or his active indivisible mirrors as much as he can) when we give them only to human bodies. It is even impossible for them not to be everywhere. So far we have spoken only of what a limited substance can do; in reference to God the matter is entirely different. Far from that which at first seemed impossible really being so, in his case we must rather say that it is impossible for God to have used any other way, being as he is infinitely powerful and wise and in everything preserving as much order and harmony as is possible. What is more, though this seems so strange when considered by itself, it is a certain consequence of the constitution of things, so that the universal wonder, so to speak, destroys and absorbs the particular wonder, since it provides a reason for it. For everything is so controlled and bound together that these infallible machines of nature, which are comparable to ships that would arrive at port by themselves in spite of all obstacles and storms, ought not to be considered any stranger than a rocket which glides along a string or a liquid which runs through a tube. Furthermore, since bodies are not atoms but are divisible, and are indeed divided to infinity, and everything is full of them, it follows that the very smallest body receives some impression from the slightest change in all the others, however distant and small they may be, and must thus be an exact mirror of the universe. The result is that a sufficiently penetrating spirit could, in the measure of his penetration, see and foresee in each corpuscle everything which has happened and will happen in that corpuscle and everything which has happened and will happen everywhere both within and outside of the corpuscle. So nothing happens to it, not even by the impact of surrounding bodies, which does not follow from what is already internal to it and which can disturb its order. This is still more obvious in the simple substances or in the active principles themselves, which I follow Aristotle in calling primitive entelechies, and which nothing can disturb, in my opinion. This is my reply to a marginal note of Mr. Bayle (p. 2612, b) in which he makes the objection that since an organic body is composed of many substances, each of which has a principle of action that is really distinct from the principle of each of the others, and since the action of each principle is spontaneous, this should vary the effects unto infinity. And the impact of neighboring bodies should add some constraint to the natural spontaneity of each. But we must take into consideration the fact that each one has already been adapted to every other one from all time and responds to what the others demand of it. Thus there is no constraint in substances, except externally and in appearance. This is so true that the motion of any point whatever in the world takes place in a line strictly determined in nature, which this point has taken once for all and which nothing can ever make it abandon.
HANOVER UNDER GEORGE LOUIS, 1698-1716 577 This is the most exact and clear explanation which I can give, I believe, for those who are geometrically minded, although these kinds of curves infinitely exceed those which a finite mind can grasp. It is true that if there could be but this one point in the world, its line would be straight, but that now it is the result, by virtue of the laws of mechanics, of the concourse of all bodies; it is also by this very concourse that it is pre-established. Thus I acknowledge that the spontaneity is not properly to be found in the mass (short of the universe in its entirety, to which there is no resistance). For if this point could begin to be by itself, it would continue, not in the pre-established curve, but in the straight line tangent to it. So it is properly in the entelechy, of which this point is the point of view, that spontaneity is found. And while the point can have by itself only a tendency to move in a line tangent to this curve, because it has no memory or presentiment, so to speak, the entelechy expresses the pre-established curve itself, since the surrounding bodies cannot have any influence upon this soul or entelechy, so that in this sense there can be no violence with respect to it. What is commonly called violence, however, does occur insofar as this soul has confused, and therefore involuntary, perceptions. 3 All this shows, finally, that the wonders of a ship which guides itself to port without a pilot, or of a machine which carries out the functions of man without having intelligence, and who knows what other fictions which can be presented in objection to my view and which make my assumptions appear absurd when considered separately, offer no more difficulties. It shows too that when we recognize that things are determined or inclined to what they ought to do, all the strangeness found in my view completely disappears. Everything which ambition or any other passion makes the soul of Caesar do is represented in his body as well, and the movements of these passions all come from impressions of objects joined to internal movements. The body is made in such a way that the soul never makes any resolutions to which the movements of the body do not correspond; even the most abstract reasonings play their part in this by means of the characters which represent them to the imagination. In a word, so far as the details of phenomena are concerned, everything takes place in the body as if the evil doctrine of those who believe, with Epicurus and Hobbes, that the soul is material were true, or as if man himself were only a body or an automaton. These materialists have thus extended to man as well what the Cartesians have held regarding all other animals, having shown in fact that nothing is done by man, with his whole reason, which is not a play of images, passions, and motions in the body. Those who have tried to prove the contrary have, by persisting in this bias, merely dishonored themselves and prepared the basis for error to triumph. The Cartesians have had poor success (a little like Epicurus with his declination of atoms, which Cicero so ably ridiculed) in trying to maintain that the soul cannot give motion to the body but that it can nevertheless give it its direction. But neither the one nor the other can or ought to take place, and the materialists have no need to resort to this, so that nothing which appears outside of man may succeed in refuting their teaching. This suffices to establish a part of my hypothesis. Those who point out to the Cartesians that their way of proving that beasts are only automatons tends at length to support the view that it is possible, metaphysically speaking, for all other men except themselves also to be simple automatons, have said exactly and precisely what I need in order to prove the half of my hypothesis which concerns the body. But in addition to the general principles which establish the monads of which compound things are For references see p. 585
578 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS merely the results, internal experience refutes the Epicurean doctrine. This experience is the consciousness within us of this Ego which perceives the things occurring in the body. And since this perception cannot be explained by figures and movements, it establishes the other half of my hypothesis and makes us recognize an indivisible substance in ourselves which must itself be the source of its phenomena. According to this second half of my hypothesis, therefore, everything occurs in the soul as if there were no body,just as everything occurs in the body as if there were no soul, according to the first half. And reason makes us conclude that other men have the same prerogative as we. Besides, I have frequently shown with regard to bodies themselves that although there are mechanical reasons for the details of phenomena, the final analysis of the laws of mechanics and the nature of substances compels us to resort to active indivisible principles. And the wonderful order which prevails here shows us that there is a universal principle whose intelligence is supreme as well as his power. Since it seems from this that there is something good and sound in the false and evil teaching of Epicurus, to the effect that there is no need to say that the soul changes the impulses of the body, we can readily conclude also that it is just as unnecessary to assume that the material mass sends thoughts to the soul through the influence of some unknown kind of chimerical 'species' such as is proposed by the Scholastics, or that God must always be the interpreter of the body to the soul, any more than he needs always to interpret the decisions of the soul to the body, as the Cartesians have held. The preestablished harmony is a good interpreter of each to the other. This shows that our view combines what is good in the hypothesis of both Epicurus and Plato, of both the greatest materialists and the greatest idealists, and that there is nothing surprising here except only the supreme perfection of the ruling principle, which is now shown in its works to be far above all that we have believed until now. What wonder, then, that everything goes well and with precision, since all things work together and lead each other by the hand, if we first assume that the whole has been perfectly thought out. It would rather be the greatest of all wonders or better, the strangest of absurdities, if this vessel, designed to go so well, if this machine whose route has been plotted for all time, should fail in spite of the measures which God has taken. Our hypothesis with respect to corporeal mass should therefore not be compared to a vessel which brings itself to port but to the ferry boats which are attached to a cable across the river. It is like the theatrical machines and fireworks whose regularity we no longer find strange when we know how everything is done. It is time to transfer our admiration from the work to its inventor, just as we now see that the planets do not need to be guided by intelligences. So far we have discussed almost nothing but the criticisms concerned with body or matter, and there remains no further difficulty that has been raised than that of the miracles, however beautiful, orderly, and universal they may be, which must occur in bodies in order that they may be in agreement with each other and with souls. In my opinion tlus should be understood as a proof rather than as an objection, at least by those persons who esteem as they ought "the power and the intelligence of the divine art", to quote Mr. Bayle, who also admits "that one can imagine nothing which gives a nobler idea of the intelligence and the power of the Author of all things". Now we must come to the soul, where Mr. Bayle still finds difficulties, even after my efforts to resolve his first ones. He begins by comparing this soul, alone and taken by itself, receiving nothing from without, with an atom of Epicurus surrounded
HANOVER UNDER GEORGE LOUIS, 1698-1716 579 by the void. And I do in fact regard souls, or rather monads, as the atoms of substance, since there are no material atoms in nature according to my view, and the smallest particle of matter still has parts. Since an atom such as Epicurus imagined has a moving force which gives it a certain direction, it will carry out this direction without hindrance and uniformly if it encounters no other atom. So it seems to Mr. Bayle that the soul also, being of a nature such that nothing from without can change it, should always retain a feeling of pleasure once it has felt it. For while the entire cause remains, the effect must always remain. If I protest that the soul must be considered as in a state of change, so that the entire cause does not remain, Mr. Bayle will reply that this change should be like the change of an atom which moves continuously in the same straight line at a uniform speed. And if he were to agree to the transformation of thoughts (so he says), it would at least be necessary for the passage which I maintain exists from one thought to another to contain some reason for the connection. I am in agreement with the basis of these objections, and I myself use them to explain my system. The state of the soul, like that of the atom, is a state of change. a tendency. The atom tends to change its place, the soul to change its thoughts; each changes by itself in the simplest and most uniform way which its state permits. Then how does it come, I will be asked, that there is such simplicity in the change of the atom, and such variety in the changes of the soul? It is because the atom (as it is assumed to be, although there is no such thing in nature), though it has parts, has nothing which causes some variety in its tendency, because we assume that its parts do not change their relations. The soul, on the other hand, though entirely indivisible, involves a composite tendency, that is to say, a multitude of present thoughts, each of which tends to a particular change according to what it involves and what is found in it at the time by virtue of its essential relationship to all the other things in the world. Among other things, it is also their lack of this relationship which bans the atoms of Epicurus from nature. For each thing or part of the universe must point to all the rest, in such a way that the soul, as concerns the variety of its modifications, must be compared, not with a material atom, but with the universe which it represents according to its point of view - and in some ways even with God himself, whose infinity it represents finitely because of its confused and imperfect perception of the infinite. The thought of pleasure seems to be simple, but it is not, and anyone who studies its anatomy will find that it involves everything that surrounds us and therefore everything which surrounds our environment. And the reason for the change of thoughts in the soul is the same as that of the change of things in the universe which it represents. The mechanical reasons which are developed in the bodies are united and concentrated, so to speak, in the souls or entelechies; indeed, they have their source there. It is true that not all the entelechies are, like our soul, images of God, for they are not all made to be members of a society or of a state of which he is the head. But they are always images of the universe. They are after their manner worlds in abridged form, fruitful simplicities, substantial unities, but virtually infinite by the multitude of their modifications, centers which express an infinite circumference; and they are necessarily so, as I once explained them in letters exchanged with Mr. Arnauld. 4 Their duration cannot embarrass anyone any more than the duration of the atoms of Gassendi's followers. For the rest, it is often but a step from pleasure to pain, as Socrates observed in Plato's Phaedo in speaking of a man scratching himself; "grief occupies the extremes of joy" [extrema gaudii luctus occupat]. 5 So one need not be surprised at this transition; Far references see p. 585
580 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS pleasure seems sometimes to be only a composite of little perceptions, each of which would be a grief if it were great. Mr. Bayle has already acknowledged that I have tried to reply to a good part of his criticisms and admits also that in the system of occasional causes it is necessary for God to be the executor of his own laws, whereas in my system the soul does this. But he objects that the soul has no instruments for such execution. I reply, as I have replied, that it does; they are the present thoughts from which future thoughts are born, and one can say that in the soul, as indeed everywhere, the present is great with the future. I believe that Mr. Bayle will agree, and all philosophers with him, that our thoughts are never simple and that with regard to certain thoughts the soul has the power to pass by itself from one to the other, as when it goes from premises to the conclusion or from the end to the means. Even Father Malebranche agrees that the soul has internal voluntary actions. What reason, then, to deny that this is the case in all our thoughts? Perhaps because it is believed that confused thoughts are entirely different in kind from distinct ones, whereas they are merely less distinguishable and less developed because of their multiplicity. The result is that certain movements, rightly called involuntary, have been ascribed to the body in such a way that nothing is believed to correspond to them in the soul; and reciprocally, it is believed that certain abstract thoughts are not represented at all in the body. But there is an error in both of these views, as usually happens in such distinctions, because we notice only what is most apparent. The most abstract thoughts are in need of some sense perception. And when we consider what these confused thoughts are which are never absent from even the most distinct thoughts which we can have - as, for example, those of colors, odors, tastes, heat, cold, etc. - we recognize that they always involve the infinite and not only that which takes place in our body but also, by means of it, that which happens outside of it. Thus they serve our purpose here even better than would the legion of substances of which Mr. Bayle speaks as an instrument which seems necessary for the functions which I have given to the soul. It is true that the soul has these legions at its service, but not inside itself. For there is no soul or entelechy which is not dominant with respect to an infinity of others which enter into its organs, and the soul is never without an organic body which fits its present state. It is therefore these present perceptions, along with their regulated tendency to change in conformity to what is outside, which form the musical score which the soul reads. "But", says Mr. Bayle, "must not the soul recognize the sequence of the notes (distinctly), and so actually think of them?" I answer 'No'; it suffices that the soul has included them in its confused thoughts in the same way that it has a thousand things in its memory without thinking of them distinctly. Otherwise every entelechy would be God, if it were distinctly conscious of the whole infinite which it includes. For God expresses everything perfectly all at once - possible and existent, past, present, and future. He is the universal source of all, and the created monads imitate him as much as it is possible for created beings to do so. He has made them sources of their phenomena, which contain relationships to everything, more or less distinct according to the degrees of perfection which the individual substances contain. Where then is the impossibility? It seems rather that it would have to be this way in order that creatures may be made to approach God as nearly as is reasonably possible. I should like to see some positive argument pointing to a contradiction or to a conflict with some known truth. To say that the view is surprising is no objection. On the contrary, everyone who recognizes
HANOVER UNDER GEORGE LOUIS, 1698-1716 581 immaterial and indivisible substances also attributes to them a multitude of simultaneous perceptions and a spontaneity in their reasoning and their voluntary acts. Thus lam only extending this spontaneity to confused and involuntary thoughts too and showing that it is their nature to include relations to everything outside of them. How prove that this cannot be, or that everything that is in us must necessarily be known distinctly by us? Is it not true that we cannot always remember even what we know, and then all of a sudden come upon it by a small chance reminiscence? And what a variety of matters we can carry in the soul, even when we are unable to discover them quickly. Otherwise the soul would be a God, whereas it must suffice for it to be a little world. But this world is found to be as imperturbable as the great world, when we consider that there is spontaneity in the confused as well as in the distinct. In another sense, however, we are justified in speaking, as did the ancients, of that which consists of confused thoughts, where there is an element of the involuntary and unknown, as perturbations or passions. Hence the common usage is not wrong in speaking of a conflict between body and spirit, since our confused thoughts represent the body or the flesh and constitute our imperfection. After having recorded this answer, which I have already given in substance - that confused perceptions include all external things and contain an infinity of relations Mr. Bayle does not refute it. He says instead that "when this hypothesis is well developed, it is the true means of solving all the difficulties", and he honors me by saying that he hopes that I will thoroughly solve his own. Even if he had said this only out of politeness, I should have spared no efforts to do so, and I believe I have overlooked none of his questions; if I have neglected anything without trying to offer a solution, it is because I have been unable to see where the difficulty lay which he sought to raise. It is this which sometimes gives me the greatest trouble in my reply. I should like to see why he thinks that this multitude of perceptions which I assume in an indivisible substance is impossible. For I believe that it would be permissible to assume them even if our experience and common opinion did not make us recognize a great variety in our soul. It is no proof of the impossibility of a matter merely to say that one cannot understand this thing or that without pointing out wherein it violates reason, and when the difficulty is only in sense perception, and there is none in the understanding. It is a pleasure to have to do with an opponent who is at once as just and as profound as Mr. Bayle, who is so fair that he often foresees my replies. This he has done in observing that my opinion, that the primitive constitution of each spirit is different from that of all the others, cannot seem any more extraordinary than what the Thomists hold, following their master, concerning the specific differences among all separate intelligences. I am happy to agree with him in this, for I have somewhere cited this same authority.6 It is true that, consistent with my own definition of a species, I do not call this difference specific, for since I believe that no two individuals ever resemble each other perfectly, I should have to say that no two individuals belong to the same species, which would not be accurate. I regret that I have not yet been able to see the objection which Dom Francis Lami made, as Mr. Bayle informs me, in his second treatise On the Cognition of Self (ed. 1699)7, or I should also be replying to them. Mr. Bayle has explicitly sought to spare me all the objections common to my system and other; for this too I am indebted to him. I shall only say that as concerns the force given to creatures, I think I have replied, in the Leipzig journal for September For references see p. 585
582 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 1698, to all the objections contained in a memoir which a scholarly man published in the same journal in 1697, and which Mr. Bayle cites in the margin, letter S.8 I think I have even demonstrated there that without an active force in the body there would be no variety in phenomena, which amounts to the same thing as there being nothing at all. It is true that my learned adversary replied to this (May, 1699), but he really only further explained his own opinion without adequately touching upon the reasons which I opposed to it. As a result, he did not remember to reply to this demonstration, especially since he considered it futile to tty to arrive at an agreement or to clarify this matter further; he even regarded it as capable of injuring our mutual understanding. I admit that this is commonly the result of such debates, but there are exceptions, and this discussion between Mr. Bayle and myself seems to be of another kind. For my part, I try always to take proper measures to preserve moderation and to push forward the clarification of problems, so that the dispute will not only be harmless but may even become fruitful. I do not know if I have achieved this last aim, but although I cannot flatter myself to give entire satisfaction to a mind as penetrating as Mr. Bayle's in a matter as difficult as the present one, I shall always be content if he finds that I have made some progress in so important an investigation. I have been unable to prevent myself from renewing the pleasure I once had in reading, with particular attention, a number of articles from his excellent and rich Dictionary, among others those concerned with philosophy, like the articles on the Paulicians, Origen, Pereira, Rorarius, Spinoza, and Zeno. I was surprised anew at the fecundity, force, and brilliance of his thoughts. No ancient academician, not even Carneades, could have brought out the difficulties better. Although Mr. Foucher was most able in such studies 9, he does not approach these, and I myself find nothing in the world more useful in solving these same old difficulties. It is this that pleases me so in the criticisms of able and moderate persons, for I feel that they give me new powers, like Antaeus hurled to earth in the fable. If I speak with some confidence, it is because my own views have become fixed only after my considering all sides and weighing them well, so that I can perhaps say, without vanity, omnia praecepi atque animo mecum peregi. 10 But criticisms put me back on the track and save me much trouble, for it is no small matter to have to retrace all the bypaths to anticipate and foresee everything that others may find to criticize, inasmuch as our points of view and inclinations are so different that there have been very penetrating persons who have accepted my hypothesis from the start and even urged it upon others, while other very able men have pointed out to me that they have in fact already held this view, and still others have even said that they understand the hypothesis of occasional causes in this same sense and cannot distinguish it from mine, which well satisfies me. But I am no less pleased when I see someone set out to examine it as it should be done. To say something about the articles of Mr. Bayle which I have just mentioned and whose subject matter has many connections with this question, it seems that the reason for permitting evil rests in the eternal possibilities, in accordance with which this kind of universe which allows evil and has admitted it to actual existence is found to be more perfect, considering the whole, than all other possible kinds. But we go astray in trying to show in detail the value of evil in revealing the good, as the Stoics do - a value which St. Augustine has well recognized in general, and according to which we step back, so to speak, in order to leap forward better.ll For can we enter
HANOVER UNDER GEORGE LOUIS, 1698-1716 583 into the infinite particulars of the universal harmony? If it were necessary, however, to choose reasonably between the two, I should always favor the Origenists and never the Manichees. 12 It does not seem necessary to me to deny action or force to creatures on the pretext that they would be creators if they produced their modifications. For it is God who conserves and continuously creates their forces, that is, who establishes a source of changing modifications in the creatures, or a state by which we can conclude that there will be a change of their modifications. Otherwise I find, as I have shown in the work cited above, that God would produce nothing and that there would be no substances beyond his own - a view which would lead us back into all the absurdities of Spinoza's God. It also seems to me that Spinoza's error comes entirely from his having pushed too far the consequences of the doctrine which denies force and action to creatures. I acknowledge that time, extension, motion, and the continuum in general, as we understand them in mathematics, are only ideal things - that is, they express possibilities, just as do numbers. Even Hobbes has defined space as a phantasm of the existent. But to speak more accurately, extension is the order of possible coexistence, just as time is the order of possibilities that are inconsistent but nevertheless have a connection. Thus the former considers simultaneous things or those which exist together, the latter those which are incompatible but which we nevertheless conceive as all existing; it is this which makes them successive. But space and time taken together constitute the order of possibilities of the one entire universe, so that these orders - space and time, that is - relate not only to what actually is but also to anything that could be put in its place, just as numbers are indifferent to the things which can be enumerated. This inclusion of the possible with the existent makes a continuity which is uniform and indifferent to every division. It is true that perfectly uniform change, such as the mathematical idea of motion, is never found in nature any more then are actual figures which possess in full force the properties which we learn in geometry, because the actual world does not remain in this indifference of possibilities but arises from the actual divisions or pluralities whose results are the phenomena which are presented in practice and which differ from each other down to their smallest parts. Yet the actual phenomena of nature are arranged, and must be, in such a way that nothing ever happens which violates the law of continuity, which I introduced into philosophy and first mentioned in Mr. Bayle's Nouvelles de la repub/ique des lettres 13, or any of the other most exact rules of mathematics. On the contrary, things can be rendered intelligible only by these rules, for they alone are capable, along with the rules of harmony or perfection which the true metaphysics provides, of leading us to the reasons and intentions of the Author of things. The result of this very great multitude of infinite compositions is that we are finally lost and are forced to stop in our application of metaphysical principles, and of mathematical ones as well, to physics. Yet these applications are never in error, and when a miscalculation appears after an exact chain of inference, it is because we cannot adequately examine the facts and because there is an imperfection in our assumption. We are even more able to advance in this application to the degree that we are able to make use of our thoughts of infinity, as our newest methods have shown us. Although mathematical thinking is ideal, therefore, this does not diminish its utility, because actual things cannot escape its rules. In fact, we can say that the reality of phenomena, which distinguishes them from dreams, consists in this fact. However, mathematicians For references see p. 585
584 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS do not need all these metaphysical discussions, nor need they embarrass themselves about the real existence of points, indivisibles, infinitesimals, and infinites in any rigorous sense. In my reply to a notice in the Memoires de Trevoux for May and June, 1701, which Mr. Bayle cites in the article on Zeno, I pointed this out, and in the same year I suggested that the mathematicians' demand for rigor in their demonstrations will be satisfied if we assume, instead of infinitely small sizes, sizes as small as are needed to show that the error is less than that which any opponent can assign, and consequently that no error can be assigned at all. 14 So even if the exact infinitesimals which end the decreasing series of assigned sizes were like imaginary roots, this would not at all injure the infinitesimal calculus, or the calculus of differences and sums, which I have proposed and which excellent mathematicians have cultivated so fruitfully. Error is impossible in this calculus except through a failure to understand it, or a false application, because it contains its own demonstration. It was later acknowledged in the Journal de Trevoux, in the same place, that the objections which had been raised before do not apply to my explanation. It was still maintained, it is true, that these objections do apply to the calculus of the Marquis de I'Hospital, but I believe that he has no more desire than I to burden geometry with metaphysical problems. I almost laughed at the airs which the Chevalier de Mere gave himself in the letter to Pascal which Mr. Bayle describes in the same article. But I can see that the chevalier knew that this great genius had his imperfections, which sometimes made him too susceptible to extreme spiritualistic impressions and even made him disgusted at intervals with sound knowledge. The same thing has since happened to Steno and Swammerdam, but without any restoration, because they failed to combine the true metaphysics with physics and mathematics. 1s De Mere took advantage of this fact to talk down to Pascal. It seems to me he was talking a little too frivolously, as is common with people of the world who have much spirit but mediocre knowledge. They try to convince us that what they do not fully understand is of slight importance; they should be sent to school with Mr. Roberval. Yet it is true that the chevalier had an unusual talent, especially for mathematics, and I have learned from Mr. des BiIlettes, a friend of Pascal's who excels in mechanics, what the discovery was of which the chevalier boasts in his letter. Being a great gambler, he made the first ventures into the calculation of wagers, and it was this that led to the beautiful studies of the game of hazard [de alea] by Fermat, Pascal, and Huygens which Roberval could not or would not understand. 16 The Pensionaire de Witt has pushed this study still further and applied it to other more important uses related to life insurance. Mr. Huygens told me that Mr. Hudde also had excellent ideas on the problem and that it is unfortunate that he suppressed these along with so many others. Games themselves deserve study, and if a penetrating mathematician were to investigate them, he would find many important truths, for men never show more spirit than when they are jesting. Let me add in passing that not only Cavalieri and Torricelli, of whom Gassendi spoke in the passage cited by Mr. Bayle, but also I myself and many others have found figures of infinite length whose areas are finite. There is nothing more extraordinary about this than about infinite series, where we find that ~+~+~+ :6 + ;2 +etc.=1. It may be, however, that the chevalier also experienced some fine enthusiasm which transported him "into that invisible world and into that infinite extension" of which
HANOVER UNDER GEORGE LOUIS, 1698-1716 585 he speaks and which I believe to be that of the ideas or forms of which certain Scholastics also speak in raising the question of whether "there is a vacuum of forms". For he says that "one can here discover the principles of things, the most hidden truths, the harmonies, the justice, the propositions, the true originals and perfect ideas of everything that one seeks". This intelligible world of which the ancients speak so much is in God and in some way also in us. But what the letter says against division to infinity makes it clear that its author was still too much of a stranger in this superior world and that the charms of the visible world of which he wrote did not leave him the time which he needed to acquire the rights of citizenship in the other. Mr. Bayle is right in saying, with the ancients, that God uses geometry and that mathematics makes up a part of the intelligible world and is therefore the more fit to be an entrance into it. But I myself believe that its interior is something more. I have suggested elsewhere that there is a calculus more important than those of arithmetic and geometry which depends on the analysis of ideas. This would be a universal characteristic, and its formation seems to me one of the most important things that can be undertaken. REFERENCES See No. 47. See No. 52. 3 Violent action, in the Scholastic sense, is action proceeding not from an internal cause but from an extraneous source. 4 See No. 36, I; No. 38. 5 Phaedo 60 b,J. 6 See Nos. 30 and 35 (Discourse, Sec. 9); also p. 271, note 7. 7 Fran<;ois Lami had attacked various aspects of the theory of pre-established harmony in the Connoissance de soy-meme, Paris 1699; Leibniz finally published a partial reply in the Supplement du Journal des savants in 1709 (G., IV, 572-95). 8 De ipsa natura (No. 53), the reply to John Chr. Sturm. 9 For Simon Foucher see No. 11, and the introduction to No. 47. The allusion is probably primarily to his Histoire des academiciens (1690). He had died in 1697. 10 "I have anticipated everything and gone through it in my mind." 11 Reculer pour mieux sauter. This is a favorite figure of Leibniz in interpreting the role of evil in history. 12 In his article on Manicheism, Bayle had formulated a dualistic theory of good and evil; much of the discussion in the Theodicy later is directed at Bayle's further development of this position. Jean Ie Clerc, French refugee and editor of the BibliotMque choisie, had replied to the article on Manicheism in a chapter of his Parrhasiana (1699), putting his answer in the mouth of an Origenist. 13 See No. 37. 14 See No. 56, II, and GM., V, 350ff. 15 On Steno see No. 23, introduction and p. 220, note 1. John Swammerdam became an enthusiast and follower of Mme de Bourignon. 16 See No. 49. Most of De Mere's letter to Pascal is reprinted in Bayle's article on Zeno. 1 2
61 CONSIDERATIONS ON VITAL PRINCIPLES AND PLASTIC NATURES, BY THE AUTHOR OF THE SYSTEM OF PRE-ESTABLISHED HARMONY 1705 This paper was published in the Histoire des ouvrages des savants in May, 1705, in the form of a letter to Basnage de Beauval, its editor. Leibniz had been asked by Jean Ie Clerc, editor of the Bibliotheque choisie, to give his opinion, based upon the theory of pre-established harmony, about the controversy between Bayle and Le Clerc over the existence of vital principles and plastic natures, such as Cudworth and others had proposed. 1 [G., VI, 539-46] Since the dispute which has arisen concerning plastic natures and the principles of life has given an occasion for well-known persons interested in it to speak of my system, and it seems that some clarification of it is desired (cf. Bibliotheque choisie, Vol. V, Art. 5, p. 301, and also Histoire des ouvrages des savants, 1704, Art. 7, p.393), I consider it fitting to add something to what I have already published on this subject in various articles in the journals cited by Mr. Bayle in his Dictionary, the article on Rorarius. I do indeed hold that vital principles are spread throughout all nature and are immortal, since they are indivisible substances or unities, while bodies are multitudes subject to destruction through the dissolution of their parts. These vital principles or souls have perception and appetite. When I am asked if they are substantial forms, I reply with a distinction. For if this term is taken to mean what Descartes meant in maintaining against Regis that the rational soul is the substantial form of man, I agree. 2 But I say 'No' to anyone who takes the term in the sense of those who imagine that there is a substantial form in a piece of stone or in any other inorganic body. For vital principles belong only to organic bodies. It is true according to my system that there is no part whatever of matter which does not contain an infinity of organic and animated bodies, among which I include not only animals and plants but perhaps also other kinds which are entirely unknown to us. But one cannot say that every portion of matter is therefore animated, any more than we should say that a pond full of fish is an animated body, although the fish are. My opinion on vital principles, however, is in certain respects different from what has previously been taught. One of these respects is that it has always been thought that vital principles change the course of motion in bodies, or at least that they provide God with the occasion for changing it. My system, instead, holds that this course is not at all changed within the order of nature, God having pre-established it as it should be. The Peripatetics believed that souls have an influence on bodies and that according to their will or appetite, they give certain impressions to the body. The
HANOVER UNDER GEORGE LOUIS, 1698-1716 587 celebrated authors who by their vital principles and plastic natures have occasioned the present controversy have been of the same opinion, although they are not Peripatetics. 3 One can say the same thing about those who have made use of an archeus or a hy/archic principle, or other immaterial principles with other names. 4 Descartes very well recognized that there is a law of nature by which the same quantity of force is conserved, though he made a mistake in applying this principle by confusing quantity of force with quality of motion; he therefore thought it unnecessary to give the soul the power of increasing or diminishing the force of the body but only that of changing its direction by changing the course of the animal spirits. And those Cartesians who have given vogue to the doctrine of occasional causes hold that since the soul can have no influence whatever upon the body, it is necessary for God to change the course and direction of the animal spirits in accordance with the wishes of the soul. But if this new law of nature which I have demonstrated had been known in Descartes's day, according to which not only the same quantity of total force of bodies in interrelation is conserved but also their total direction, he would undoubtedly have been led to my system of pre-established harmony, for he would have recognized that it is just as reasonable to say that the soul does not change the quantity of the direction of the body as it is to deny to the soul the power of changing the quantity of its force, both being equally contrary to the order of things and the laws of nature, since both are equally inexplicable. Therefore souls or vital principles, according to my system, change nothing in the ordinary course of bodies and do not even give God the occasion for doing so. The souls follow their laws, which consist in a definite development of perceptions according to goods and evils, and the bodies follow theirs, which consist in the laws of motion; nevertheless, these two beings of entirely different kind meet together and correspond to each other like two clocks perfectly regulated to the same time. It is this that I call the theory of pre-established harmony, which excludes every concept of miracle from purely natural actions and makes things run their course regulated in an intelligible manner. Instead of this, the common system has recourse to absolutely inexplainable influences, while in the system of occasional causes God is compelled at every moment, by a kind of general law and as if by compact, to change the natural couse of the thoughts of the soul to adapt them to the impressions of the body and to interfere with the natural course of bodily movements in accordance with the volitions of the soul. This can only be explained by a perpetual miracle, whereas I explain the whole intelligently by the natures which God has established in things. This system of pre-established harmony furnishes a new proof, hitherto unknown, of the existence of God, since it is very clear that the agreement of so many substances, none of which exerts an influence upon another, can only come from a general cause upon which all of them depend and that this cause must have infinite power and wisdom to pre-establish all these agreements. Even Mr. Bayle has expressed his judgment that no other hypothesis has ever given so much help to our knowledge of the divine wisdom. This system also has the advantage of conserving, in its full rigor and generality, the great principle of physics that a body never receives a change in motion except through another body in motion which pushes it: corpus non moveri nisi impulsum a corpore contiguo et moto. This law has until now been violated by all those who accept souls or other immaterial principles, including here even all of the Cartesians. The For references see p. 590
588 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Democriteans, Hobbes, and certain other outright materialists who have rejected every immaterial substance have heretofore been alone in preserving this law and think they have found a ground for abusing other philosophers, whom they believe to hold an unreasonable opinion in this. But the ground of their triumph is only apparent and ad hominem; far from serving their own view, this law serves to embarrass them. Now that their error is discovered and their assumed advantage turned against them, it can be said, it seems, that for the first time the preferable philosophy is also shown to be the more consistent with reason and that there is nothing left with which to oppose it. Though this general principle excludes particular prime movers, since it denies this quality to souls or created immaterial principles, it leaves us all the more certain and clear about the universal prime mover from whom come alike both the sequence and the correspondence of perceptions. These are like two kingdoms, one of efficient causes, the other of final, each of which separately suffices in detail to give a reason for the whole, as if the other did not exist. But neither is adequate without the other when we consider their origin, for they emanate from one source in which the power which makes efficient causes, and the wisdom which rules final causes, are found united. Even this maxim, that there is no motion which does not originate in another motion in accordance with mechanical rules, leads us again to a prime mover because matter, being in itself indifferent to motion or repose but nevertheless always possessing motion with its whole force and direction, cannot have been put in motion except through the author of matter himself. There is still another difference between the opinions of the other authors who favor vital principles and mine. This is that I believe that these vital principles are immortal and yet that they are everywhere. The common opinion holds instead that the souls of beasts perish. and according to the Cartesians, it is only man who truly has a soul and, indeed, who has perception and appetite - an opinion which will never receive general approval and into which they rushed only because it seemed necessary either to ascribe immortal souls to beasts or to admit that the soul of man could be mortal. But we must rather say that since all simple substance is imperishable, and consequently every soul immortal, the soul which one cannot reasonably deny to beasts must also subsist always, although in a way far different from ours, since the beasts, at least so far as we can judge, lack that reflection by which we think of ourselves. It is hard to see why men have found it so repugnant to ascribe imperishable and immortal substances to the bodies of other organic creatures, especially since the defenders of atoms have introduced material substances which do not perish, and since the soul of a beast has no more reflection than an atom. For there is a great difference between the sensation common to all these souls and the reflection which accompanies reason, since we may have a thousand sensations without reflecting about them. I do not find that the Cartesians have ever proved, or can prove, that all perception is accompanied by consciousness. It is just as reasonable that there should be substances capable of perception below us as above us, so that our soul, far from being the lowest of all, finds itself in the middle, from which one may rise or sink. Otherwise there would be a deficiency in order, or what some philosophers call a vacuum of forms. Thus both reason and nature lead men to the opinion which I have proposed but their prejudices have turned them away from it. This opinion leads us to another in which I am also forced to abandon the accepted view. Those who agree with me will be asked what becomes of the souls of beasts
HANOVER UNDER GEORGE LOUIS, 1698-1716 589 after the animals die, and we shall have imputed to us the doctrine of Pythagoras, who believed in the transmigration of souls, a theory which not only the late Van Helmont (the son) but also the clever author of certain Metaphysical Meditations, published in Paris, have sought to revive. 5 But it must be seen that my opinion is far different from this, because I believe that not merely the soul but the whole animal subsists. Very exact observers have noted before now that it is doubtful that an entirely new animal is ever produced but that living animals as well as plants already exist in miniature in the seeds before conception. Assuming this doctrine to be true, we may reasonably conclude that what does not begin to live does not stop living either and that death, like generation, is only the transformation of the same anim!ll, which is sometimes augmented and sometimes diminished. Thus we discover the marvels of divine artifice even where they have never been thought of. For since the mechanisms of nature are mechanisms down to their smallest parts, they are indestructible, since smaller machines are enfolded in greater machines into infinity. Thus one finds himself forced to maintain at the same time both the pre-existence of the soul with that of the animal and also the subsistence Ii of the animal with that of the soul. I have come, imperceptibly, to an explanation of my opinion of the formation of plants and animals, since it appears from what I have said that they are never formed entirely anew. I am thus of the opinion of Mr. Cudworth, whose excellent work for the most part well supports me, that the laws of mechanism by themselves could not form an animal where there is nothing already organized. 7 I find that he is right in opposing what certain ancients have sensed on the subject, and also Descartes's Traitt! de [,homme, whose man costs so little to form but also so little resembles a true man. I strengthen this opinion of Cudworth's with the consideration that if matter is arranged by divine wisdom, it must be essentially organized throughout and that there must thus be machines in the parts of the natural machine into infinity, so many enveloping structures and so many organic bodies enveloped, one within the other, that one can never produce any organic body entirely anew and without any preformation, nor any more destroy entirely an animal which already exists. So I have no need to resort, as does Cudworth, to certain immaterial plastic natures, though I recall that Julius Scaliger and other Peripatetics, as well as certain adherents of Van Helmont's doctrine of the archeus believed that the soul makes its own body. To this I can say non mi bisogna, e non me basta S , because this preformation and this infinitely complex organism provide me with material plastic natures that meet the need. Immaterial plastic natures, by contrast, are as unnecessary as they are incapable of satisfying it. For since animals are never formed naturally from an inorganic mass, the mechanism, though incapable of producing their infinitely varied organs anew, can at least draw them out of pre-existing organic bodies by a process of development and transformation. However, those who make use of plastic natures, whether material or immaterial, by no means weaken the prcof for the existence of God drawn from the wonders of nature, which appear with particular force in the structure of animals, assuming that the defenders of immaterial plastic natures add to them a particular guidance by God, and assuming that those who make use, as I do, of a material cause, agree that the plastic mechanism supports not only a continual preformation but also an original divine pre-establishment. In whatever way one interprets this, therefore, one cannot escape the divine existence in seeking to explain these wonders which have always been admired, but which have never been shown as well as in my system. For references see p. 590
590 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS This shows that not only the soul but also the animal must always subsist in the ordinary course of things. But the laws of nature are made and applied with so much order and wisdom that they serve more than one end. Thus God, who holds the place of inventor and architect in relation to the mechanism and the works of nature, holds the place of king and father to those substances which have intelligence and whose soul is a spirit formed in his image. With respect to spirits, his kingdom, of which they are citizens, is the most perfect monarchy which can be built. Here there is no sin without some punishment attached, no good action without some reward. Here all tends, finally, to the glory of the monarch and the happiness of the subjects, by the most beautiful combination of justice· and goodness which could be wished. I do not venture an assertion with regard to pre-existence, however, or with regard to the details of the future state of human souls, since God is able to use extraordinary methods in these matters within the realm of grace. Nevertheless, the ways favored by the natural reason are to be preferred, at least so far as revelation does not teach the contrary. I do not undertake to decide this matter here. Before closing, it may be well to point out, among the other advantages of my system, the universality of the rules which I use. These rules are always without exception in my general philosophy; in other systems the contrary is true. For example, I have here said that mechanical laws are ne~er violated in natural motion, that the same force and the same direction are always conserved, that everything occurs in souls as if there were no bodies and everything in bodies as if there were no souls, that there is no part of space which is empty, that there is no part of matter which is not actually divided and does not contain organic bodies, that there are also souls everywhere as there are bodies everywhere, that the souls and even the animals subsist always, that organic bodies are never without souls, and that souls are never separated from organic bodies, though it may be true, nevertheless, that there is no part of matter of which one can say that it is always affected by the same soul. Thus I do not at all recognize entirely separated souls in the natural order or created spirits entirely detached from any body. In this I share the opinion of many ancient Church Fathers. God alone is above all matter, since he is its author. But creatures free or freed from matter would at the same time be divorced from the universal bond, like deserters from the general order. This universality in my rules is confirmed by a great facility in explanation, since the uniformity which I believe is observed in the whole of nature makes us say that everywhere, at every time, and in every place things are just as they are here, almost to the very degrees of grandeur and perfection, so that the most remote and most hidden things can be explained perfectly by analogy to what is visible and near unto us. REFERENCES 1 In his Continuation des pensees diversees sur la com~te (1705) Bayle had made passing reference to the 'plastic natures' of Cudworth, charging that they served to make atheism easy. The occasion was Le Clerc's publication of selections from Cudworth's The True Intellectual System o/the Universe (1678) in his BibliotMque choisie. The ensuing controversy ran into 1707, Bayle's side appearing in the Reponse aux questions d' un provincial. Vol. III, chaps. 179/f. (1705), and the Entretiens de Maxime et de Themiste, ou reponse Ii ce que M. Ie Clerc a ecrit ... (1707). a This Regis is not the Cartesian Pierre Silvain Regis (p. 146, note 10) but Hemi Ie Roi (1598-
HANOVER UNDER GEORGE LOUIS, 1698-1716 591 1679), who became a critic of Descartes after 1645. Descartes wrote him in January, 1642, that a true 'substantial unity' exists between soul and body (Correspondence, ed. Adam and Tannery, V,508-9). 8 The allusion is to Henry More and Cudworth. On More see p. 452, note 15. 4 Seep. 412, note 37; p. 508, note 2, and p. 328, note 14, on the elder Van Helmont and the vitalistic movement in general. 5 On the younger Van Helmont (Franciscus Mercurius) and his monadology see also p. 508, note 11 and the New Essays, Part II, chap. xxvii. The Paris metaphysical meditations were probably those of Rene Fede, Meditations metaphysiques de I'Origine de l'arne, sa nature, sa beatitude, son desordre et sa restauration, which appeared anonymously in 1683. 6 Reading subsistence for substance, with Erd. On the contemporary biological backgro\j1ld see p. 560, note 5; p. 329, note 25; and p. 350, note 29. 7 In December, 1703, Lady Masham had sent Leibniz a copy of her father's work. The correspondence between her and Leibniz which followed contained not only a sympathetic discussion of that work but also one of Leibniz's system, probably based on Locke's difficulties with it. 8 "I do not need it, and it does not meet my need."
62 LETTER TO HANSCH ON THE PLATONIC PHILOSOPHY OR ON PLATONIC ENTHUSIASM July 25, 1707 Like Johann Christian Wolff, Michael Gottlieb Hansch (1683-1752) was one of the younger men who adopted Leibnizian ideas early in the new century and who entered into correspondence with their author. The following letter was published in his Diatriba de enthusiasmo Platonico in 1716; in 1728 he offered what Leibniz had frequently admitted he had himself not yet achieved - Godofredi Guilielmi Leibnitii Principia philosophiae more geometrico demonstrata. [Dut., II, 222-25] I have read your little work on Platonic enthusiasm with much pleasure, and I am convinced that what you are doing, along with others who are throwing light on the philosophies of the ancients, is most valuable. For such works both confirm and advance truths, whether merely revived or newly discovered. I should not care to quarrel with anyone as to whether Pythagoras and Plato learned anything from the Hebrews. So far I have not observed anything which would lead me to believe it. I recognize that the worship of one God, almost wiped out among mankind, was restored through the Hebrews. I am unwilling to believe that Homer and Hesiod visited the Egyptians. The author of Homer's life, who is held to be Herodotus, says nothing of the kind about him. But I willingly admit that the Greeks owe the beginnings of the sciences to the Egyptians and Phoenicians. Abraham, who came from the Chaldeans, is rightly thought to have taught some things to the Egyptians. The very old doctrine of the immortality of souls seems to have had metempsychosis added to it by the Indians, and we may believe that it came from them to the Magi and the Egyptians. Pythagoras then introduced it into the West, and Plato generally followed him. No ancient philosophy comes closer to Christianity, although wejustly censure those who think that Plato is everywhere reconcilable with Christ. But the ancients must be excused for denying the beginning of things, or creation, and the resurrection of the body, for these doctrines can be known only by revelation. Meanwhile many of the Platonic doctrines which you mention are most beautiful that all things have a single cause; that there is an intelligible world in the divine mind, which I also usually call the region of ideas; and that the object of wisdom is the really real [ra ovum; ovra] or simple substances, which I call monads and which, once existing, endure always; the first ground of life [np61m oiTmKa rfi!; (WIJ!;]1, that is, God and souls, and of the latter the most excellent ones, namely, minds, which are produced by God as images of divinity. The mathematical sciences, moreover, which deal with eternal truths rooted in the divine mind, prepare us for the knowledge of substances. Sensible things, however, and composite things in general, or the substantiated things, so to speak, are in flux and become rather than exist. Furthermore, as Plotinus has
HANOVER UNDER GEORGE LOUIS, 1698-1716 593 rightly said, every mind contains a kind of intelligible world within itself; indeed, in my opinion it also represents this sensible world to itself. But there is an infinite difference between our intellect and the divine, for God sees all things adequately and at once, while very few things are known distinctly by us; the rest lie hidden confusedly, as it were, in the chaos of our perceptions. Yet the seeds of the things we learn are within us - the ideas and the eternal truths which arise from them. Since we discover being, the one, substance, action, and the like within ourselves, and since we are conscious of ourselves 2, we need not wonder that their ideas are within us. The innate concepts of Plato, which he concealed by the term 'reminiscence', are therefore by far to be preferred to the blank tablets of Aristotle, Locke, and other recent exoteric philosophers. So I believe that to philosophize correctly, Plato must be combined usefully with Aristotle and Democritus, though a number of the principal doctrines would have to be stricken from each of them. The Platonists were not far wrong in recognizing four kinds of cognition in the mind - sense, opinion, knowledge (scientia), and understanding, or in other words, experience, conjecture, demonstration, and pure intellection, which looks into the connections of truth by a single act of the mind; this belongs to God in all things but is given to us in simple matters only. But the more we grasp in a shorter time, the closer we approach in our demonstrations to this pure intellection. Although our mind depends continuously on God in its existence and action, as does every other creature, I do not think that it needs his particular concourse over and above the laws of nature for its perceptions, but rather it deduces its later thoughts from its earlier ones by its internal force and in an order prescribed by God, as Roelius, whom you quote, rightly says. I extend this also to the perceptions of sensible things. For since they are not miraculously induced by God, and cannot be imparted naturally by the body, it follows that they arise within the soul by a definite law, as through a harmony divinely pre-established in the beginning. This is more worthy of the most wise Creator than the perpetual violation, by new impressions, of laws which he has given to the body or the soul. Meanwhile, it can be said that because of the divine concourse which continuously confers upon each creature whatever perfection there is in it, the external object of the soul is God alone, and that in this sense God is to the mind what light is to the eye. This is that divine truth which shines forth in us, about which Augustine says so much and on which Malebranche follows him. There is a sound sense in which we can understand that the soul is in this body as in a prison. But we must reject the opinion of the ancient philosophers that the body is a prison for punishing the understanding for its past sins. They were right in saying that the soul is attached to the body as to a post which it has no right to leave without the order of the supreme commander. It was It nice conception, too, that we are ruled by providence insofar as we follow reason; by fate and like a machine when we are carried away by our affections. For we have now seen, from the pre-established harmony, that God has ordered all things so wonderfully that corporeal machines serve minds and that what is providence in a mind is fate in a body. The ancient Platonists and Stoics also had excellent views about the virtues, and Augustine is too severe with them. For not content with having sought perpetual sins in their virtues, which is itself too much, he also considered the precepts of the philosophers as entirely evil, as if they had measured everything bearing the name of virtue by the vanity of praise and by pride. But we know they often rightly commended the For references see p. 595
594 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS wise man, not out of hope of reward or fear of punishment, but out of love of virtue, and there is no difference between this love of virtue and that devotion to justice which Augustine teaches and which he refers to the essential justice, that is, to God himself, in whom is the source of the good and the true. Nor was Plato entirely ignorant of this, for he always looked to the truth in itself. But Augustine objects that philosophers have always measured things by themselves, and so have placed the creature above the creator. I am afraid that this is oversubtIe 3 , as is the opinion of certain people who have recently commanded us to love God without any consideration of ourselves. For it is impossible, by the nature of things, for anyone to have no thought for his own happiness. But for those who love God, their own happiness arises from that love. Even before the controversy had arisen about the distinction between mercenary and true love, I had seen this difficulty and resolved it in the Preface of my Codex juris gentium4, giving a definition of love which intelligent men have received with applause and which seems to decide the dispute. For, as opposed to mercenary love, true love is that affection of the mind by which we are brought to find pleasure in the happiness of another. For what we take pleasure in, that we desire for itself. Furthermore, since the divine happiness is the confluence of all perfections, and pleasure is the feeling of perfection, it follows that the true happiness of a created mind is in its sense of the divine happiness. So those who seek the right, the true, the good, and the just because this delights them rather than because it is profitable - although it is in truth most profitable - are best prepared for the love of God, according to the opinion of Augustine himself, who brilliantly shows that the good desire to enjoy God, the bad to use him, and who proves, as the Platonists tried to do, that the exchange of the divine love for the ephemeral is the cause of the fall of souls. Therefore, too, our happiness cannot be separated from the love of God. Hence you may reject the quietists, false mystics, who deny individuality and action to the mind of the blessed, as if our highest perfection consisted in a kind of passive state, when on the contrary, love and knowledge are operations of the mind and will. Blessedness of the soul does indeed consist in union with God, but we must not think that the soul is absorbed in God, having lost its individuality and activity, which alone constitute its distinct substance, for this would be an evil enthusiasm [tvOOOUl(xuJlo,], an undesirable deification. Certain ancient and more recent thinkers have asserted, namely, that God is a spirit diffused throughout the whole universe, which animates organic bodies wherever it meets them, just as the wind produces music in organ pipes. The Stoics were probably not averse to this opinion, and the active intellect of the Averroists, and perhaps of Aristotle himself, reduce to it, being the same in all men. According to this view souls return to God in death, as streams to the ocean. I wish that Valentine Weigel, who, in an extraordinary book, not only explains the blessed life through deification, but frequently recommends a death and quiet of this sort, had not given us ground to suspect a similar opinion, along with other quietists. The chief to affirm this position is the man who calls himself John Angelus Silesius, the author of some beautiful sacred poems entitled Der cherubinische Wandersmann. 5 In another way Spinoza tends toward the same view. For him there is one substance, God. Creatures are his modifications, like figures in wax, continually arising and perishing through motion. So for him, just as for Almeric, the soul does not survive except through its ideal being in God, where it was from all eternity.
HANOVER UNDER GEORGE LOUIS, 1698-1716 595 But I observe nothing in Plato that would lead me to conclude that minds do not conserve their own substance. This, moreover, is beyond argument for those who philosophize carefully, for the contrary opinion cannot be understood unless you assume that God and the soul are corporeal, for in no other way can souls be tom as parts away from God. But such a notion of God and the soul is absurd on other grounds. The mind is not a part but an image of divinity, a being which represents the universe, a citizen of the divine kingdom. And for God neither substance in general simple substance, that is - nor person perishes in his kingdom. Souls which lack reason have substance incapable of happiness and misery. But I do not want to digress to them, since they are not pertinent to your discussion. In concluding this rather extended letter, I congratulate you on so well combining learning with wisdom and urge you to continue in this enlightened course. REFERENCES This term, which Leibniz commonly uses for substance in the last period of his thought, is drawn from Aristotle Physics vii. 4. 248b, 249a. 2 Reading simus for scimus. 3 Reading ne (Erd.) for nec. 4 See No. 44, I and II, and p. 430, note 3. 5 Seep.430,note9. 1
63 CORRESPONDENCE WITH DES BOSSES 1709-15 The correspondence between Leibniz and Bartholomew des Bosses, Jesuit teacher of theology at the seminary of his order in Hildesheim, and after 1711 professor of mathematics at Cologne, contains Leibniz's last and most extensive attempt to put his philosophy in acceptable Scholastic terms. Though Guhrauer found in it "the most complete and coherent explanations of the monadology ... preserved for us" (Guh. D., I, 373), many students have seen, in the central problem about which the later correspondence turned, an enigma which it is difficult to solve in terms of Leibniz's previous doctrine. This problem is the nature of composite corporeal beings, particularly their substantiality and unity. In 1703 Tournemine had criticized Leibniz (see No. 55, X, and p. 541, note 24) for failing to explain the nature of the unity of soul and body but, like Descartes, merely establishing a simple correspondence between them. From its beginning the discussion with Des Bosses was concerned in general with the consistency of the monadology with Aristotle's metaphysics. In 1709 it turned to Tournemine's criticism when Des Bosses raised the question of the origin of the dominant entelechy and its relation to the body. Not only the Council of Trent's pronouncement on the Eucharist but also realistic demands for the substantial nature of compound bodies led now to the discussion of a substantial reifying chain which binds together the monads constituting such a body, its relation to these monads, its role in contributing to (a) the unified nature and (b) the continuous extension of such bodies, and the issue of whether it is a substantial form in the Scholastic sense. 1 By 1712 Des Bosses and Leibniz agree upon the possibility of such a realitas unionalis, though the latter frequently emphasizes phenomenalism as an alternative. If composite bodies must be substantial, he insists that they are not original but secondary (or ortive) substances and that their reifying principle cannot itselfbe a mode or modification but must be a substantial form which is the source of modifications in the resulting bodily substance. Des Bosses argues, on the other hand, that the reifying chain cannot be considered as something absolute but must be a 'nonmodal' or 'categorial' accident, concepts which Leibniz is easily able to show contradictory in terms. The total effect ofthe correspondence was a greater realistic emphasis in Leibniz's thought about the apparent physical world, evidences of which will be found also in Nos. 66 and 67. The correspondence, which began after a visit by Des Bosses in 1706, covered a wide variety of topics from theology to Sinology andfrom problems ofpublication to ecclesiastical gossip. The selections given are largely restricted to the later philosophical argument. I. LEIBNIZ TO DES BOSSES 2 [G., II, 369-72] Hanover, April 30, 1709 3 Two things usually make publishers hesitate - one is their desire to profit; the other is
HANOVER UNDER GEORGE LOUIS, 1698-1716 597 ignorance. Thus they do not know what they should select. They do not trust scholars enough, because they believe that scholars have a better understanding of what is scholarly than of what will sell. I tried recently to publish a dissertation which I wrote some time ago and in which I examined some problems of the ninth century and became involved in chronological studies. I called it Flowers Scattered on the Grave o[ the Popess Joan; in it I explode the fable of the popess, partly by new arguments, and partly by confirming the old. I set the generally obscure chronology of the time in clear order, replying to the newest subterfuges of Frederick Spanheim, a Leyden theologian, which he put in a book published some years ago in Holland. I have also dealt with some matters that have been overlooked, for I discovered a book on magic ascribed to the popess which has not yet been published, and I drew some other things worthy of readers' interest from manuscripts. Perhaps this little book would please your printer in Liege better, but I would willingly give him either one - that in Latin about the popess as well as that in French against Bayle. 4 Now I come to your philosophical question. I do not determine whether the souls of beasts were not created until the fourth day; in any case innumerable entelechies must have been created at once, at the very beginning. I merely wanted to explain how new souls could exist even if no new part of matter were created. And if I am not mistaken, my recent letter showed this. By 'matter' I here mean mass or secondary matter, where there is extension with resistance. I do not recall having assigned matter proper (taken in this sense) to any soul; on the contrary, every part of an organic body contains other entelechies. It is true, of course, that a soul cannot pass over from one organic body into another but remains al ways in the same organic body, not even death violating this law. But it must be remembered that even this organic body remains the same in the way in which the ship of Theseus or a river does; that is, it is in perpetual flux. And perhaps no portion of matter can be designated which always remains the property of the same animal or soul. If you consider the question more carefully, perhaps you will try to say that a certain point can at least be assigned to the soul. But a point is not a definite part of matter, and even an infinity of points gathered into one will not make extension. This I prove as follows. Take a triangle ABC, with its side AC bisected at D, AD bisected at E, AE at F, AF at G, etc. (Figure 37). Assuming that this has been done to infinity, we will have an infinite number of triangles, BCD, BDE, BEF, BFG, etc. Anyone of these can exist separately (if we assign thickness to them so that they become bodies, or if we assume the triangle to have thickness from the beginning, that is, to be a pyramid). Thus each B Fig. 37. For references see p. 615 c
598 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS one has its own vertex. Now assume all these triangles put together so that they make the whole pyramid or triangle ABC; clearly all these infinite vertices compounded together in this way make up only the one common vertex B. If you do not wish to introduce an infinity of triangles, you will at least see that this is generally true of any number oftriangles. Extension arises from situation, but it adds continuity to situation. Points have situation, but they neither have nor compose continuity, nor can they stand by themselves. So there is nothing to prevent an infinity of points from coming into being and perishing (or at least coinciding or standing mutually outside of each other), without any increase or diminution of matter and extension, since they are only the modifications of matter and not its parts but its extremities. I do not consider it fitting, however, to think of souls as if they were in points. Perhaps someone would say that souls are not in a place except through an operation, speaking, that is, according to the old system of influence; or better, speaking according to the new system of pre-established harmony, that they are in a place only through correspondence and that they are thus in the whole organic body which they animate. However, I do not deny some real metaphysical union between the soul and the organic body, according to which it can be said that the soul is truly in the body; I have also said this in reply to Tournemine. But because such a thing cannot be explained by the phenomena and changes nothing in them, I cannot explain any more distinctly of what this union formally consists. It is enough that it is tied up with the correspondence. You will understand, moreover, that I have been speaking so far, not of the union of the entelechy or active principle with primary matter or passive power, but of the union of the soul or of the monad itself (which is the result of both of these principles) with the mass or with other monads. But what, you may ask, shall we say of this primary matter itself, which belongs to the soul? I reply that it is certainly created together with the soul or that the whole monad is created. Then does not primary matter increase and decrease? I acknowledge that it does, since it is only primitive passive power. Then mass also increases, you say. I agree that the number of monads increases, the result of which is the mass, but not the extension and resistance, nor the phenomena, any more than when new points arise. God could create an infinity of new monads without increasing the mass, if he merely added old monads to the organic body of the new monad. Mass is a real phenomenon, but with the exception of those which appear anew with the new monad itself, phenomena are not at all changed through the creation of a new monad, except perhaps by a miracle. For we must hold that the old monads have been so ordered from the beginning by God when he created them that their phenomena would correspond to the monad to be created sometime later, unless we prefer the view that God changes all other monads by a miracle when he creates a new one to adapt them to the neW one; this is less likely. In conclusion, all this tends to show that it is possible for God to create new monads. Yet I do not assert definitely that new monads are created by God. On the contrary, I think the view that the opposite is more probable can be defended and that monads pre-exist. In place of the absolute creation of a rational soul, the transcreation of a nonrational into a rational soul could be defended; this would happen if an essential degree of perfection were miraculously added to it. I maintain this view also in my dissertation against Bayle, as it seems to me more probable than complete creation and more true than traduction ....
HANOVER UNDER GEORGE LOUIS, 1698-1716 599 P.S. 5 Many years ago, when my philosophy was still too immature, I located souls in points and thus thought that the multiplication of souls could be explained through traduction, since many points can be made out of a single point, as the vertices of many triangles can be made through division from the vertex of one. 6 But having grown more circumspect, I grasped that we were not only led into innumerable difficulties in this way but also that this contains a certain confusion of classes, so to speak. Properties pertaining to extension are not to be assigned to souls, and their unity and multitude are not to be derived from the category of quantity but from the category of substance, that is, not from points but from the primitive force of action. But the action proper to the soul is perception, and the nexus of perceptions, according to which subsequent ones are derived from preceding ones, makes up the unity of the percipient. II. LEIBNIZ TO DES BOSSES [G., II, 409] Hanover, August 4,1710 ... In my earlier letter I had not noticed the objection which your last letter contained against the pre-established harmony; otherwise I should have answered at once, since it is one of those criticisms which I find most pleasing because they give opportunity to illumine the matter more fully. The very fact, namely, that the world, matter, and mind cannot be understood perfectly by finite minds is the argument which I use, among others, to prove that matter is not composed of atoms but is actually subdivided into infinity, so that there is in any particle of matter whatever a world of creatures infinite in number. If, on the contrary, the world were an aggregate of atoms, it could be known completely by a finite mind of sufficient excellence. Moreover, since no part of matter can be known perfectly by a created being, it appears from this that no soul can be known perfectly by a creature either, since the soul represents matter exactly through this very pre-established harmony. What you see as an objection can therefore be viewed as an argument for my position .... III. LEIBNIZ TO DES BOSSES [G., II, 412] Hanover, November 7,1710 ... I am pleased that my reply to your objection has satisfied you and especially that it was not entirely unforeseen. Whoever admits the pre-established harmony cannot fail also to accept the doctrine of the actual division of matter into infinite parts. But the same conclusion follows from elsewhere, namely, from the nature of the motion of fluids and from the fact that all bodies have a degree of fluidity. Would that the attribute of incomprehensibility did belong to God alone; our hope of knowing nature would then be greater. But it is all too true that there is no part of nature which we can understand perfectly; the very interdependence [neplxcbp1fO'I~] of things proves this. No creature, however excellent, can at once distinctly perceive or comprehend the infinite; on the contrary, indeed, whoever were to understand a single part of matter would understand the whole universe, by virtue of this same neplxcbp1fO'IV of which I spoke. My principles are such that they can hardly be torn apart from each other. He who knows one well, knows them all .... For references see p. 615
600 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS IV. LEIBNIZ TO DES BOSSES 7 [G., II, 435-37] Hanover, February 5, 1712 If a corporeal substance is something real in addition to monads, as a line is known to be something more than points, it will have to be said that corporeal substance consists in a kind of union or rather, in a real unifier [uniente reali] superadded to the monads by God and that out of the union of the passive power of the monads there arises primary matter or the impulsion [exigentia] to extension and antitypy or to diffusion and resistance. From the union of the monadic entelechies, however, there arises a substantial form. But whatever can arise and be extinguished in this way is also destroyed by the cessation of the union, unless it is conserved miraculously by God. Such a form, moreover, will then not be a soul, which is a simple and indivisible substance. This form, too, is in perpetual flux, just as is matter, since no point can truly be designated in matter which preserves the same position beyond a moment and which does not recede from its neighbors, however many they may be. But the soul remains the same in all its changes, and the same subject persists; in corporeal substance this is not so. We must therefore say one of two things: either bodies are mere phenomena, in which case extension too will be only a phenomenon and only monads will be real, but the union will be supplied in the phenomenon by the action of the perceiving soul; or if faith urges us to assert corporeal substances B, substance consists in that unifying reality [realitate unionali] which adds something absolute and hence substantial, even though fluid, to the things to be united. It is in the change of this being that your transubstantiation would have to be located, for monads are not truly ingredients of this added being but requisites, even if they may be needed for it not by an absolute metaphysical necessity, but by exigency only. Thus the substance of a body may change, but the monads be saved, and sensible phenomena based upon them. A nonmodal accident seems to be hard to explain, and I do not hold extension to be one. It can be said that even though monads are not accidents, it nevertheless happens [accidere] to a unifying substance that it may have them by physical necessity, just as it happens to a body that it may be struck by another body, even though a body is not an accident. The extension of a body seems to be nothing but the continuation of matter through parts external to each other, or diffusion. But where this 'externality' ends supernaturally, the extension which happens to the body itself also ends, and extension will remain only phenomenal, based in the monads along with the other properties which arise from them and which alone would exist if there were no unifying substance. If this substantial chain of monads [monadum substantiate vinculum] were absent, all bodies along with all their qualities would be nothing but well-founded phenomena, like the rainbow or an image in a mirror - in a word, continued dreams in perfect agreement with each other - and the reality of these phenomena would consist in this one fact. For we cannot say that monads are parts of bodies which touch each other, any more than we can say this of points or of souls. A monad, like the soul, is as a world by itself, having no intercourse of a dependent nature except with God. Therefore, if a body is a substance, it is the actualization [realisatioj9 of phenomena proceeding beyond their mere congruence. But if you do not want to consider these occurrences in the Eucharist to be merely phenomenal, they can be said to be grounded in a certain primary occurrence - not in
HANOVER UNDER GEORGE LOUIS, 1698-1716 601 extension, which cannot be permanent, but in the points of this extension which correspond to monads, the union which constitutes the continuum out of these points being removed, and thus continuous lines and figures being dropped, but qualities and other real accidents kept with the aid of the accidental points which remain, without the continuity which depended upon the unifying reality or the substantial chain. When the diffusion of this chain through parts external to each other ceased, it too would cease. These accidental points could thus be considered as primary accidents, and this would be the basis for the rest, and in a sense which is nonmodal, which cannot be said of extension or of the continuous diffusion of matter. In fact, when I weight the matter more carefully, I see that extension can itself be saved and that your opinion explaining the position of your society can thus be granted, even of one is opposed to phenomena. For since accidental points can be admitted, we could - indeed, we perhaps should - also admit their union. Then we have an absolute accidental extension. But such extension would formally involve a diffusion of parts beyond parts, though that which is diffused will not be matter or corporeal substance formally but only exigently [exigentialiter]. That which is diffused formally will be locality or that which constitutes situs; it will be necessary to conceive this itself as something absolute. So I believe that we will not quarrel now, provided that the monads are not involved in this supernatural change of the substance of a body, which would be entirely unnecessary, since, as I said, they are not parts of it - especially since the soul of Christ does not, according to your own views, change in transubstantiation, nor does it take a position in the substance 10 of the bread. I should say the same also of the monads of the most holy body. To speak candidly, however, I should prefer to explain the accidents of the Eucharist through phenomena; then we shall not need nonmodal accidents, for which I care very little .... '" Unless you decide otherwise, I think the title Tentamina theodicaeae can be kept. For theodicy is, as it were, a kind of science, namely, the doctrine of the justice of God - that is, of his wisdom together with his goodness. 11 ••• Y. DES BOSSES TO LEIBNIZ [G., II, 441-42] Paderborn, May 20, 1712 I finally reply to your letter sent to me in February, which was the more welcome for its greater length. I begin with the question about bodies, which I read through in your letter with the greatest satisfaction, and I have thought about it no less attentively. You say that we must say one thing or another: either bodies are mere phenomena, and then extension will be only a phenomenon; or there is superadded to the monads a certain unifying reality which is something absolute (and therefore substantial) even though it adds a flux unifying the (monads). This disjunction I accept with respect to the matter itself, but I now argue that the former is not true and therefore that the latter is. If bodies were mere phenomena, indeed, the paradox of Zeno would be true, who denies all true, proper motion, for if there are no things to touch each other, nothing will be moved. To deny this member of the disjunction the principles of all the philosophers seem to suffice, joined with the naive prejudice, both of which show no doubt that there is in any body something more than phenomena, that is, something more than continuous dreams, no matter how perfectly these may fit each other...• For references see p. 615
602 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS So it remains for us to accept something absolute in which the reification of phenomena consists. This you call a substance, I an accident; but I believe we are not in disagreement about the matter itself. I call an accident whatever in itself presupposes a complete substance, so that it cannot naturally exist without this substance. And this absolute unifier presupposes complete substance or the monads, without which it cannot exist naturally. For according to you, "monads are in fact ingredients of this added being, and yet not requisite to it in the sense of an absolute and metaphysical necessity but only exigently". This I interpret as meaning that monads are required by this added being as something prior in nature to it. If you do not reject this interpretation (and it does not seem that you can reject it, for whatever does not contain a principle of unity within itself must presuppose one from elsewhere), it is now obvious that this added thing is not a substance in the sense of the Peripatetics, who understand by substance nothing but a primary being, a substratum and presupposition for the rest. Therefore we will now have in bodies something absolute, distinct from the monads, which is not a substance; and so, since the body adds nothing to the monads except this absolute being, only an accident is superadded to them. Furthermore, I should not wish to ground this absolute solely in the accidental points corresponding to the monads, for the same difficulty seems to remain about these points as about the monads themselves. By what compact, namely, can they make an extended being when they are not themselves extended? So it seems further necessary to resort to something unifying which can be called absolute accidental extension. For the rest, I admit that, if the natural organization of bodies could be explained by phenomena alone, there would be no philosophical ground for resorting to nonmodal accidents in explaining the accidents of the Eucharist. But as I have said above, the common sense of men seems to understand that there is something more in sensible bodies than phenomena consisting in the operation of the perceiving mind. And speaking only of natural events, there ought to correspond to this perception some object distinct from the perception itself; otherwise there would be no harmony.... VI. LEIBNIZ TO DES BOSSES [G., II, 444] Hanover, May 26, 1712 If you deny that what is superadded to the monads to make a union is of the nature of a substance, you cannot say that a body is a substance, for it will then be a mere aggregate of monads; and I fear that you will fall back upon the mere phenomenality of body. For in themselves monads have no situation [situs] with respect to each other, that is, no real order which reaches beyond the order of phenomena. Each is as it were a separate world, and they correspond to each other through their own phenomena and not by any other intercourse and connection. If you call an accident whatever presupposes a complete substance in such a way that it cannot naturally be without it, you do not explain the essential mark of an accident by which it must be distinguished from substance itself, even in a supernatural state. The Peripatetics as a whole recognize something substantial besides monads; otherwise they would have no substances besides monads. Monads do not constitute a complete composite substance, since they do not make up a unity per se but merely an aggregate, unless some substantial chain is added.
HANOVER UNDER GEORGE LOUIS, 1698-1716 603 It cannot be proved from the principle of harmony that there is anything in bodies besides phenomena. For we know on other grounds that the harmony of phenomena in souls does not arise from the influence of bodies but is pre-established. This would suffice if there were only souls or monads; in this case all real extension would also disappear, not to speak of real motion, whose reality would be reduced to mere changes in phenomena. I wish someone would present the entire system of Jansen in a compendium; without this it is difficult to judge his position correctly in a matter so involved. 12 It seems to be possible to carve contrary opinions out of Augustine by separating his words from their context; it is possible that the same thing has happened to Jansen. But the connection of his thoughts can remove this doubt. In reading Augustine, one must be very well at home in his works, and know the time, the scope, and the outline of his different books, if one does not want to be deceived by passages taken from them. I noticed this long ago after examining some of his passages more carefully, and I have become more cautious with him .... VII. DES BOSSES TO LEIBNIZ [G., II, 446-47] Paderborn, June 12, 1712 ... I come now to the philosophical sections of your letter. You say, "If you deny that what is superadded to the monads in order to make a union is substantial, then a body cannot be called a substance, for it will then be a mere aggregate of monads." I reply that the Peripatetics establish a twofold meaning of body, one which is placed in the category of substance, and this is a substance in the way which I shall explain a little later; the other is mathematical, and this consists in the dimensional quantity which I acknowledge to be a mere accident. It was only with this meaning that I was dealing in my last letter. For I admit that the body, taken in the former meaning, would be a mere aggregate of monads if there were no substantial unity between the monads. This unity I further conceive of as follows, and I explain it in Peripatetic terms, by which I shall try to adapt your system in some way or other to the usage of the School. Forms, and thus monads themselves (I except the rational soul), are always, with regard to their essence or with regard to metaphysical actuality, not with regard to existence or to physical actuality, somewhat of the nature by which, according to some Peripatetics, parts are said to be in the whole potentially, or as Averroes and Zabarella think, elements remain in mixtures, namely 'refracted'. In an animal, for example a horse, only the dominant form, namely the soul of the horse, has existence or physical actuality. Since being and one are convertible, a thing is made one through the very thing by which it is made to exist, and so, since the whole animal has existence by virtue of an existent being which emanates from the soul, the body of the animal is constituted a unity through this existence. Furthermore, this existence is a kind of substantial mode emanating from the soul or the total and dominant form and affecting the other partial monads and subordinating them to itself, with the result that from these subordinate monads and this dominant monad, there exists one corporeal substance which is called a horse. It follows from this that the monads, viewed with respect to their essence and disregarding all existence or physical actuality, are indeed substances and primary comFor references see p. 615
604 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS plete beings in a metaphysical sense, because they have metaphysical actuality or an entelechy, yet they are not complete in the sense of physical substance, except insofar as and when a dominant entelechy bestows existence and therefore unity to the whole organic mass, for example, to the body of the horse, so that this itself will be subordinate to no other entelechy. 14 ••• VIII. LEIBNIZ TO DES BOSSES [G., II, 450-52] Hanover, June 16,1712 ... You .. , confer a benefit when you note the opinions of scholars from your holy order which agree with any whatsoever of mine. This is worth much, both in confirming and in understanding them. Of the Reverend Father Sebastian Izquierdo, I do not recall having seen anything but a book entitledPharus scientiarum, which I saw as a youth but whose idea has almost escaped me. Certain phrases of Izquierdo in the passages which you have excerpted diverge somewhat from mine, but we seem to agree in the essence. For example, when he says that in creating the world, God was necessitated morally but not physically, I should prefer to say morally, not metaphysically, for in my book I explain physical necessity as the consequence of moral. I consider the explanation of all phenomena solely through the perceptions of monads functioning in harmony with each other, with corporeal substances rejected, to be useful for a fundamental investigation of things. In this way of explaining things, space is the order of coexisting phenomena, as time is the order of successive phenomena, and there is no spatial or absolute nearness or distance between monads. And to say that they are crowded together in a point or disseminated in space is to use certain fictions of our mind when we seek to visualize freely what can only be understood. In this conception, also, there is involved no extension or composition of the continuum, and all difficulties about points disappear. It is this that I tried to say somewhere in my Theodicy - that the difficulties in the composition of a continuum ought to warn us that we must think far differently of things. 1s We must see then what must be superadded to monads if we add a substantial union or assume that there is a corporeal, and therefore a material, substance; whether it be necessary in that case to return to a mathematical body. Certainly monads cannot properly be in an absolute space, since they are not really ingredients but merely requisities of matter. It wiII not be necessary on this ground, therefore, to set up certain indivisible localities, which throw us into such difficulties. It is enough that corpereal substance is something that reifies [realizans] phenomena outside of souls, but I should not wish to conceive actual parts in it except those made by actual division, nor indivisible parts, except as an extreme measure. I believe that monads always have full existence and that we cannot conceive of parts being said to be potentially in the whole. Nor do I see what a dominant monad would detract from the existence of other monads, since there is really no intercourse between them but merely an agreement. The unity of corporeal substance in a horse does not arise from any 'refraction' of monads but from a superadded substantial chain through which nothing else is changed in the monads themselves. Some worm can be a part of my body and subject to my dominant monad, and the same worm can have other animalcules in its body subject to its dominant monads. But considered
HANOVER UNDER GEORGE LOUIS, 1698-1716 605 in the monads themselves, domination and subordination consist only in degrees of perfection. If an accident is defined as that which strives [exigo] to exist in a substance, I fear that in order to explain its formal reason, we must find a reason 16 why it strives. For certainly a substance also often demands [exigo] another substance; it would have to be explained what this 'existing in' [inesse] is in which the nature of an accident is usually located. My own answer to this would be that it is the modification of something entirely other. It is true that things which happen in the soul must agree with those which happen outside of it. But for this it is enough for the things taking place in one soul to correspond with each other as well as with those happening in any other soul, and it is not necessary to assume anything outside of all souls or monads. According to this hypothesis, we mean nothing else when we say that Socrates is sitting down than that what we understand by 'Socrates' and by 'sitting down' is appearing to us and to others who are concerned .... IX. LEIBNIZ TO DES BOSSES [G., II, 457-61] Wolfenbiittel, September 20,1712 17 ... Your version is beautiful and will throw light on the work. But on my part I am taking advantage of the freedom you have allowed me, and while you have limited yourself more narrowly to the original and so interpret all the more faithfully, I am explaining some things more clearly than they are in the French. Occasionally I am formulating matters more fully, as I should have done if I had written in Latin. When I return to Hanover - for I am now at work in Wolfenbiittel - I shall send the work back to you. is I come now to your philosophical points. If we accept substantial beings in addition to the monads, or admit some kind of real union, I feel that a union which makes an animal or any organic body of nature a substantial unity with one dominant monad is far different from a union which makes it a simple aggregate such as a pile of stones. The latter consists in a mere union of presence or of place, the former in a union constituting a new substantiation; the Scholastics call it a one per se, while they call the former a one per accidens. I nowhere said that monads otherwise unchanged would now constitute a horse and now not constitute one, for since a monad always expresses within itself its relations to all others, it will perceive far different things when it is in a horse than in a dog. That it depends upon a substance does not suffice to define the nature of an accident, for a composite substance also depends on simple substances or monads; we must add that an accident depends on a substance as a subject and, indeed, as ultimate subject. For an accident can be the affection of another accident; for example, the magnitude of heat or of impetus, so that the impetus is the subject and the magnitude is in it as an abstraction from the predicate, when we say that the impetus is great or is so much. Yet heat or impetus is in the body as in a subject, and the ultimate subject is always the substance. Every accident is a kind of abstraction; only substance is concrete. Accidents can also have concrete predicates, as when an impetus is called great, but they themselves are not concrete but abstracted from the predicates of substances. For references see p. 615
606 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Furthermore, since the composite substance or the thing which the chain of monads makes is not a mere modification of the monads and does not exist in them as subjects for of course, the same modification cannot be in many subjects at the same time I should hold that this substance depends on the monads, not in a logical dependence, that is, in such a way that it cannot be separated from them even supernaturally but merely in a natural dependence or in such a way that it strives to unite in a composite substance unless God wills otherwise. For God can use the same substance to unite other monads, so that it stops uniting the former ones; he can also remove it entirely and substitute for it another one, uniting other monads, and this either in such a way that it stops uniting the other monads and is transferred from one set of monads to another or in such a way that it retains its own monads, which it unites naturally, but now also unites new ones supernaturally. And according to your views, it seems this is what must be said of the change of the whole substance of a corporeal body into the whole substance of another body which at the same time retains its former nature. Let us come now to the real accidents which are in this unifying thing as their subject. You will agree, I believe, that some of them are only its modifications, which disappear when it is removed. But you ask whether there are not certain accidents which are more than modifications. Such accidents seem, however, to be entirely superfluous, and whatever is in such a substance other than a modification seems to pertain to the substantial thing itself. I do not see how we can distinguish an abstraction from the concrete, or from the subject in which it is; or how we can explain intelligibly what it is to be in or to inhere in a subject, except by considering inherence as a mode or state of a subject - a mode which may be either essential, so that it cannot change unless the nature of the substance changes, and differs from the substance only relatively, or which may be accidental, in which case it is called a modification and can come into being and perish while the subject remains. If you know another way of explaining inherence, I ask you to suggest it, for the issue hangs upon it. If this cannot be done, it must be feared that by saying that real accidents are conserved, you are truly conserving the substance, and thus the whole substance will not be transmuted. Hence, if I remember rightly, the Greeks also deny that real accidents are conserved, for they fear that then both nature and substance will be conserved together. . You say that it seems there can be no middle being between a substance and a modification. I should think that this middle being is the substantiated unity per se, or the composite substance, for it is the mean between a simple substance - or that which primarily deserves the name substance - and the modification. The simple substance 19 is perpetual; the substantiated can come into being and perish or can change. An accident is that which arises and ceases, while the substance is changed but itself remains. Besides, an accident is incapable of a new modification per se, that is, it is capable of it only per accidens or insofar as it is in a substance modified through another which is also accidental. For example, the same impetus or heat that is in the body A is now present in body B, now absent from it, because of the presence or absence from it of body A. But the same impetus cannot be greater or less, for while the former remains the same, a new degree is added as well, and the consequent total is different from the preceding total. Likewise, the same impetus cannot be sent first in this direction, then in that, for a new impetus added to the former will also have
HANOVER UNDER GEORGE LOUIS, 1698-1716 607 another direction and will thus determine a new total direction, both of the partial ones remaining. But the total impetus, itself composed of the others, will also provide a new total. Granting these things, I should think that your theory of transubstantiation can be explained by retaining the monads, which seem to fit the reason and order of the universe perfectly, but with a substantial chain added by God to unite the body of Christ to the monads of bread and wine, and the former substantial chain destroyed, and its modifications and accidents with it. Thus there would remain only the phenomena of the monads of bread and wine, which would have been there if no substantial chain had been added by God to these monads. But even if the bread or the wine is not a substantiated being constituting a unity per se and hence is not unified by a substantial chain, it is still an aggregate of organic bodies or substances constituting a unity per se, whose substantial chains would be destroyed and replaced by the substantial chain of the body of Christ. ... ... You ask why, if real extension is not necessary, primary matter is necessary and why the entelechy alone does not make up the monad. I reply that if there are only monads with their perceptions, primary matter will be nothing but the passive power of the monads, and entelechy will be their active power. But when you add composite substances, I must say that there must be added to these a principle ofresistance to the active principle or motive force. You ask further: Why actually an infinity of monads? I reply that the mere possibility of an infinity is enough to establish this, since it is manifest how very rich are the works of God. But the order of things also demands it, for otherwise phenomena would not correspond to all assignable percipients. Indeed, we know some confusedness in our perceptions, however distinct they may be, and so there are monads corresponding to these confused ones as there are monads corresponding to the greater and more distinct ones. Finally, you ask why fruit appears round rather than square if it is not really extended. I reply that fruit is itself only a phenomenon, since it is a being by aggregation. x. LEIBNIZ TO DES BOSSES [G., II, 473-75] Vienna, Austria, January 24,1713 You ask how the opinion of your order about transubstantiation [llspi TOO jJ8TOVGIaGlloO] can be explained, both according to the hypothesis of mere monads and according to the hypothesis of compound substances. Following the former hypothesis, you ask in what the substance of a composite body consists, whether in monads or even in the phenomena themselves. That is, you ask, for example, whether the soul of a worm existing in the body of a man is a substantial part of the human body, or whether it is rather a bare requisite, and that not by metaphysical necessity but only because it is required in the course 20 of nature; this is the view which I should prefer. But if you assert the former, then we must say that the monads of bread and wine are destroyed and the monads of the body of Christ put in their place. If monads are not substantial parts of bodies, however, and composite beings are mere phenomena, it would have to be said that the substances of bodies consist in true phenomena - phenomena, namely, which God himself perceives in them through intuition [scientia visionis], as do also angels and the blessed, to whom it is given to see things truly. So For references see p. 615
608 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS God and the blessed would perceive the body of Christ where only bread and wine appear to us. But if we should follow the popular hypothesis about corporeal or composite substances, I should say, as I have already expressed my opinion in my preceding letter, that a substantial chain or a substantial addition to the monads, which formally constitutes the compound substance and reifies the phenomena, can be changed while the monads themselves remain, because, as I have said, the soul of the little worm is not of the substance of the body which contains the worm, and we ought not to multiply miracles beyond necessity. A substantial chain superadded to the monads is in my opinion something absolute, such that although it corresponds accurately, in the course of nature, to the affections of the monads, that is, to their perceptions and appetites, and can therefore be taken to be within the monad in whose body its body is, it can nevertheless be independent of the monads in a supernatural sense and can be removed and adapted to other monads while its former monads remain. Thus the monads of bread and wine would then be without any substantial chain, the matter being reduced, as far as they are concerned, to the state of the hypothesis of mere monads. The accidents of bread and wine, or the phenomena, would remain, moreover, but not in the body of Christ as subject .... In your fifth point and elsewhere in your letter 21 you seem to have taken substantial chains in a different sense than I have, as if I think of them as having existed from the beginning of creation when I treat them as absolute entities. But if corporeal substances or substantial chains are admitted, my opinion must be taken to be that they are subject to generation and corruption. I have also adopted no new modification of monads, whether substantial or accidental, which will constitute composite substance, as you seem to interpret me in your Item 6, and I recognize nothing in the monads except perceptions and appetitions. I should be unwilling to call the chain which makes up a compound substance an absolute accident, because I hold every absolute to be substantial. If you wish to make it an accident, however, we shall be quarreling over a name, although there wiIl be some incongruity in saying that a compound substance is constituted through accidents. When Smiglecius follows Aristotle in saying that no accident is without a subject, he shows that he does not admit an absolute being. I should also prefer not to distinguish, as you seem to do in Item 7, between a being that reifies phenomena and a substantial chain. These two things are truly the same for me, and we must say that they come into being and perish. If compound substances are assumed, therefore, it seems to me incomparably easier and more convenient to destroy the being which actualizes phenomena, while saving the monads, than to do the contrary, as you seem to prefer in Item 8. The modifications of one monad are the ideal causes of the modifications of other monads (with this you deal in Item 17), insofar as there appear in one monad reasons which moved God from the beginning of things to establish modifications in another monad. In the hypothesis of mere monads, the infinitude of the physical continuum would depend not so much on the principle of the best as on the principle of sufficient reason, because there is no reason for limiting or ending, or stopping anywhere. The mathematical continuum consists in mere possibility, as do numbers; hence infinity is necessarily implied in its very concept. For the rest, you will be surprised to see these letters from Vienna, Austria. I
HANOVER UNDER GEORGE LOUIS, 1698-1716 609 decided to continue my journey here after I recently answered a summons to Karlsbad from the great monarch of Russia, for I had already finished half of the journey. I shall remain here until the season becomes moderate; then I hope by the goodness of God to return home. 22 XI. LEIBNIZ TO DES BOSSES [G., II, 485-86] Vienna, April 21, 1714 .,. It is worth inquiring into what can be contrived that will be appropriate to justify the reality of a phenomenon outside of the percipient being, or what constitutes a composite substance. So far as I can judge, it will have to consist of the primitive active and passive power of the composite being, and this will be what is called primary matter and substantial form. And it will be necessary for the accidents of the composite being to be its modifications; these will be transitory, but it itself will remain a composite substance, as much as will the dominant monad. But it will not be a composite substance, or a true being constituting a unity per se, unless there is a dominant monad with a living organic body. What you say about this substantial chain supervening upon a composite being already constituted through modal chains, I interpret in the sense that, cut away from the composite substance, the monads constitute a unity only per accidens; but if I am not mistaken, this unity per accidens will be a mere phenomenon. For since no modification can subsist by itself but essentially entails a substantial subject, these chains will have what reality they possess in the modification of each monad and in the harmony or agreement of the monads with each other. I do not believe that you will admit an accident that is in two subjects at the same time. My judgment about relations is that paternity in David is one thing, sonship in Solomon another, but that the relation common to both is a merely mental thing whose basis is the modifications of the individuals .... XII. LEIBNIZ TO DES BOSSES [G., II, 492] Hanover, March 15,1715 This winter I have experienced a rather severe case of gout, from which I have not yet fully recovered, and so I have painfully carried out only necessary labors which permitted no delay. But since there always remains a hope at bottom, I do not despair of recovering my health. I fear that the man who wrote in favor of physical predetermination in the action of God on creatures will complicate notions rather than bring light to them. 23 That acts are not absolute things but modifications of an entelechy or primitive conatus, I believe to be obvious, and this must be said not only of the will but also of every faculty of action. We rightly regard bodies as things, for phenomena too are real. But anyone who tries to consider bodies as substances will, I believe, need some new principle of real union. The Irishman who attacks the reality of bodies seems neither to offer suitable reasons nor to explain his position sufficiently. I suspect that he belongs to the class of men who want to be known for their paradoxes. 24 ••• For references see p. 615
610 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS XIII. DES BOSSES TO LEIBNIZ [G., II, 493] Cologne, April 6, 1715 ... You seem not to have noticed a small objection made in one of my earlier letters, the answer to which I should like from you. It is this. In the hypothesis that there is something reifying phenomena which is distinct from the monads and their perceptions, I asked what brings about the change of the phenomena within the body itself. If God, this will be a perpetual miracle; if the monads, then the body will in some way depend upon monads, etc. I add another objection about the pre-established harmony. If the monads of the universe get their perceptions out of their own store, so to speak, and without any physical influence of one upon the other; if, furthermore, the perceptions of each monad correspond exactly to the rest of the monads which God has already created, and to the perceptions of these monads, and are harmonized so as to represent them; it follows that God could not create anyone of these monads which thus exist without constructing all the others which equally exist now, for God can by no means bring it about that the natural perception and representation of the monads should be in error; their perception would be in error, however, if it were applied to nonexistent monads as if they existed. But if it is true that God could not do this, I do not see why we should so greatly praise the divine wisdom in the selection and organization of things with each other. For once any monad whatever, even the smallest which he produced, was chosen, God was necessitated to produce all the rest, just as he was necessitated not to deceive rational creatures or not to put error into them, or just as he was necessitated to attune the outcome to his promises .... XIV. LEIBNIZ TO DES BOSSES [G., II, 495-96] Hanover, April 29, 1715 ... Your objections are usually shrewd, and I am always grateful for them. Assuming that there is a real union, reifying, or better, substantializing phenomena, you ask what brings about changes in the body itself. I reply that since the body, if it is held to be a substance, can only be that which results from the real union of monads, there will result from the union also the modifications which it will have, corresponding to the changes in the monads; and to this extent they will take place as is popularly taught. The monads influence this reifler, but it itself will change nothing in their laws, for whatever modifications it will receive from them it will have as an echo, as it were, but naturally and not formally or essentially, since God can ascribe to it what the monads do not give, and take away from it what they do give. The arguments which can be advanced against this will all be valid against the common doctrine of corporeal substance, or against everything substantial which can be superadded to the monads. Doubtless if there is something substantial besides monads, this ought to be capable of its own modifications, and it will have these naturally in dependence upon the monads which it unites, supernaturally from God, who can separate it from these monads. So while you say that it must have its modifications either from God by a perpetual miracle, or from the monads, I say it has them naturally and for the
HANOVER UNDER GEORGE LOUIS, 1698-1716 611 most part from the monads, but miraculously and rarely from God, who is able to make it respond to monads which were not formerly its own. If any real chain is possible, an influence of the units upon it is necessarily possible; otherwise there will be no reason for calling it a chain of these units. For the rest, it will not be necessary to assume a chain except in bodies which have a dominant monad, or which are unities per se like organic bodies, and this chain will always adhere to this monad. Your other objection is the following: If all monads get their perceptions out of their own store, so to speak, and without any physical influence of one upon another; if, furthermore, the perceptions of each monad correspond exactly to the rest of the monads which God has now created, and to their perceptions; then God cannot have created anyone of these monads which now exist without having constituted all of the rest, etc. My reply is easy and has already been given. He can do it absolutely; he cannot do it hypothetically, because he has decreed that all things should function most wisely and harmoniously. There would be no deception of rational creatures, however, even if everything outside of them did not correspond exactly to their experiences, or indeed if nothing did, just as if there were only one mind; because everything would happen just as if all other things existed, and this mind, acting with reason, would not charge itself with any fault. For this is not to err. That the probable judgment which this mind formed of the existence of other creatures should be true, however, would no more be necessary than it was necessary that the earth should stand still because, with few exceptions, the whole human race once held this to be right. Not from necessity, therefore, but by the wisdom of God does it happen that judgments formed upon the best appearances, and after full discussion, are true.... XV. DES BOSSES TO LEIBNIZ [G., II, 500-502] Cologne, July 20,1715 ... To reply to your last letter. I think with you that if there is some real chain in bodies, more distinct from the monads than a mode, and if this is possible, there must necessarily be, or be possible, an influence of the units upon it. Otherwise, as you say, there would be no ground for calling it their chain. I also think it is not necessary to assume this chain except in bodies which have a dominant monad, or which are unities per se, like organisms, to whose monad or whole there should always adhere a chain. The monads therefore influence the reifying being; this latter, however, will bring about no change in the laws of the monads, since, whatever modifications it has, it will have from them as if an echo, as you have so carefully explained. Yet from these things it seems we can conclude, in fact, that this chain, however real, cannot be substantial. For you hold that the substantial (or at least the nonmodal) is a power or principle of action, and this does not seem applicable to this real chain whose modifications are like echoes. Furthermore, once it is established that this chain is not substantial, the matter is settled and the way is wide open for explaining the Eucharist. Nor do I see why it should not be possible for something to be real which is not substantial; if this is possible, however, it has certainly not been overlooked by God in the production of the world, unless we accept what is called a vacuum of forms. For references see p. 615
612 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS To your answer to my other argument, which was not unexpected, I answer in two ways. In the first place, even apart from the existence and wisdom of God, we seem able to conclude that, more than probably, there exist other creatures than ourselves. For will you deny that even an atheist has a knowledge of the existence of his own body? I remember that I once sent to you certain propositions prohibited in our schools by Michaelangelo Tambourino, who is today the head of our Society. Let me repeat here several of them which bear upon the present issue. 1. That the human mind can and should doubt everything except that it thinks. 2. That all other things can be known and examined by us only when we have acknowledged that God exists and is supremely good and not a deceiver who tries to lead our mind into error. 3. That, before the certain knowledge of the divine existence, one can and should always doubt whether he has not been so constituted by nature as to err in all his judgments, even in those which seem to be most certain and evident. 5. That it is only through faith in God that anyone can know with certainty that there exist other bodies, even his own. My second point bears on the divine wisdom, about which I made a suggestion in my argument which you have not noticed or at least have left untouched. To expound this, I ask whether or not there be possible any system similar to the present world with respect to all phenomena but in which substances act upon each other. If you deny this, show me why; if you admit it, then I argue as follows. It seems in greater conformity with the divine wisdom to choose a system of this kind in preference to another composed of mere monads which do not influence each other. Therefore God has really established the former, not the latter, system. The consequent holds by your principles; the antecedent I argue for as follows. In the system of pre-established harmony, the whole reason for the divine architectonic wisdom (at least if we stay within natural events) consists in the choice of working materials. In the common system, however, it turns also about the form of the work and its composition, apart from the choice of material itself, so that it can be said that the work excels over the material, and this last seems preferable and more worthy of infinite wisdom. To illustrate this by an example, I ask further which architect will deserve credit for greater wisdom in his art, one whose entire craftsmanship consists in his choosing stones that are not only already exactly square but also so fitted to each other by their nature that a most magnificent palace is put together out of them because of the mere fact that they have been brought together in one place, without the further labor of architect or craftsman, just as the poets narrate that the Theban walls sprang up to the lyre of Amphion. Or is that architect rather to be preferred who constructs an equally beautiful palace from stones unfinished by nature and not corresponding to each other in such harmony, but which must be fitted by craftsmanship and adjusted in time and place? ... I add one point to the account. It seems gratuitous to assume these monads which draw all their modifications out of their own store, and without a physical influence of one upon another, just as the assumption proved gratuitous that there was a certain Scholastic quality whose nature it was to be produced and to produce all the effects of heat, for example, independently of any mechanism or of the concourse of the remaining bodies which surrounded it, etc. The more recent philosophers usually hiss such a quality from the stage....
HANOVER UNDER GEORGE LOUIS, 1698-1716 613 XVI. LEIBNIZ TO DES BOSSES [G., II, 502-5] Hanover, August 19,1715 Your observations are keen, and I reply to them with pleasure, for they instruct me and throw light on the problem. I shall begin with the latter part. We conclude with the highest probability that we are not the only existents, not only from the principle of the divine wisdom, but also from that common principle which I have frequently urged - that nothing happens without a reason; for there appears to be no reason why we alone should be preferred above all other possible beings. But whether bodies are substances is another question. For it is possible that bodies are not substances, yet that all men are prone to consider that they are, just as everyone is prone to consider that the earth is standing still, even though it is really moving. I do not recall that you sent me the propositions prohibited by your general president, Tambourino. Those which you now send me seem to be in opposition to Descartes, and I agree fully with them. You give the fifth but omit the fourth. I should be glad to get them all. Honoratus Fabri, in certain published letters, recounted the prohibitions in effect when he was active. I do not believe a system is possible in which the monads act upon each other mutually, for there seems to be no possible way to explain such action. I add that influence is superfluous, for why should one monad give another what it already possesses? It is the very nature of substance that the present is great with the future and that everything can be understood out of one, at least if God does not intervene with a miracle. In reply to your analogy, I admit that the architect who rightly fits stones together acts with greater art than one who has found the stones already so prepared by someone else that they fall into order when merely brought together. But on the other hand, I believe you will admit that the craftsmanship of the architect who can so prepare stones in advance will be infinitely greater still. As an addition you say that it is gratuitous to assume monads which receive their modifications from their own resources, just as it is gratuitous to say that heat acts without a mechanism. But your point here is not merely an addition; it is primary. If you think this, we must go back to the beginning, as if I had written nothing. Besides, monads draw everything from their own resources, not mysteriously, as heat in the Scholastic sense produces its effect, but by a certain eminent mechanism, so to speak, which is the foundation and the concentration of the bodily mechanism; thus the way in which the one follows from the other can be explained. I was right in presupposing this, for if there are no monads such as I think of them, it is vain to discuss a chain of them. I come now to the question of whether this chain, if there is one, is something substantial. It seems so to me, and I consider it useless otherwise, for how could it otherwise make up a composite substance, this being the very reason for which it was introduced? But you object, first, that it is not a principle of action, since it is like an echo. I also reply that a body which returns an echo is a principle of action. This chain will be the principle of action of composite substance, and whoever admits such substance - as does the entire School, if I am not mistaken will also admit this chain. Have not the Scholastics until now acknowledged substantial principles in compounds which constitute a unity per se? Why then deny it to us? For references see p. 615
614 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS You say that you cannot see why something cannot be real without being substantial. Here we may be arguing about terms. Whatever is not a modification can be called a substance. But a modification is connected essentially to that whose modification it is. So there can be no modification without a subject; for example, no sitting without a sitter. But substantial can also be defined in another way, as the source of modifications. Assuming this, we may ask whether there can be a thing which is neither a modification nor a source of modifications - such as the Scholastics think of as accidents, which, they say, are in a subject naturally but not essentially, since they can be without a subject by the absolute power of God. But I do not yet see how such a thing can be explained if it is different from my substantial chain, which is truly in the subject, though not as an accident but as what the Scholastics call a substantial form, or as a source of modifications - if you like, after the manner of an echo. So I do not know whether there may be a categorial accident [accidens praedicamentale] really distinct from the subject, which is not a categorial accident, or whether there is a categorial accident which is not a modification; since I have already questioned that there is a categorial accident distinct from a subject, which is not a modification. Unless perhaps someone should hold that an accident makes up such a composite substantial being because it is not a primary source but an echo. But in this way I do not see how we can maintain the substance of a composite being, unless we want to regard substance as the result of accidents. In that case, however, I do not see how you explain participation. Therefore I should prefer to say that there are no substances over and above monads, but only appearances, but that these are not illusory, like a dream, or like a sword pointing at us out of a concave mirror, or like Doctor Faust eating up a cartful of hay, but that they are true phenomena, that is, in the sense that a rainbow or parhelion is an appearance, and, in fact, in the sense that colors are appearances according to the Cartesians and in reality. It can be said that composite beings which are not a unity per se or are not held together by a substantial chain or (as the jurisconsult Alfenus, following the Stoics, said in his Digests) by one spirit are semientities. Aggregates of simple substances such as an army or a pile of stones are semientities; colors, odors, tastes, etc., are semiaccidents. All these things would be mere phenomena, though real, if there were only monads without substantial chains. Furthermore, to have monads, or to have such monads, is itself natural, though not essential but only accidental, to composite substance. For it could happen that the absolute power of God should cause the echo to cease, and the monads would be separated from the composite substance. If then, according to your hypotheses, the substantial chains of organic bodies, or of the unities per se included in the bread and wine, were destroyed by God, while the monads and phenomena remained, the accidents of bread and wine would be left, but only as mere phenomena, not by some illusion but in such a way as would happen everywhere if there were no substantial chains in nature. For certainly everything will continue in the same way with respect to these monads of bread and wine as if there had never been any substantial chain between them. But the substantial chains of the monads of the body of Christ will have an influence upon the substantial chains of the monads of our body, which they would otherwise have had on the substantial chains of bread and wine, with the result that we perceive the substance of the body and blood of Christ. For the substantial chains of the former monads will have been removed, and after the phenomena of bread and wine have ceased or their appearances are destroyed, they cannot be restored
HANOVER UNDER GEORGE LOUIS, 1698-1716 615 such as they previously were but only as they would have developed if no destruction had taken place. 25 ••• REFERENCES For the origins of this doctrine among Jesuit Scholastics see J. Boehm, Le "Vinculum substantiale" chez Leibniz: Ses origines historiques, Paris 1938. It had arisen in answer to an alleged 1 ambiguity in Aristotle's analysis of substance as a combination of form and matter. Taking the totality of a corporeal being in the double sense of a unified essential nature and of continuous extension, that is, of the totum essentiale and the totum integrale, these thinkers set up a unifying principle which adheres to, but does not inhere in, matter and which is to be regarded as substantial form determining both composite essence and extension. Needless to say, this principle does not conform to Leibniz's previous application of the doctrine of substantial forms, and the theory is extraneous to his monadism and imposed upon it only with difficulty. 2 In preceding letters (February 14 and April 22, 1709) Des Bosses had raised questions resting in part upon a failure to distinguish between primary and secondary matter in Leibniz's thought. His argument was as follows: (1) Leibniz has said that matter has existed from the beginning of creation; therefore, the entelechies which are inseparable from matter must also have existed from the beginning of creation. (2) Leibniz has also admitted, in De natura ipse (No. 53), that the souls of animals may not have been created until the fourth day, and therefore the matter essential to their nature could not have existed earlier. (3) As a result, the original primary matter will belong to two entelechies and therefore not to the soul alone, or one entelechy will have to be destroyed, contrary to Leibniz's principles. (4) And would not the new monads, with their matter, increase the total amount of mass in the world? And if so, how can mass be dependent only upon the relati ve location of the matter inhering in individual monads? 3 This is the date in Dut., but G. gives April 24, only two days after Des Bosses's letter to which it replies. 4 The book against Bayle is the Theodi cy, for which Leibniz was seeking a publisher and which appeared the next year. He had written Des Bosses about this project on September 3, 1708, saying that he had intended to give it to him to read before his departure. Des Bosses later prepared the Latin translation, a project supervised by Leibniz to the point of submitting revisions appropriate to the Latin-reading public. This translation was not published until 1719. On the Popess Joan, alleged to have occupied the chair of St. Peter in the obscure period between Leo IV (d. 855) and Benedict III (d. 858), see the extensive article of that title in Bayle's Dictionary. The story was still common in Protestant circles, and Leibniz's study, though not published, was a conclusive refutation. 5 This note was added in Leibniz's copy but probably not sent in the letter. 6 This was in the writings on physics in 1670-71 (see No.8, I). 7 In the intervening correspondence the problem of the individual nature of composite bodies came to a head when Des Bosses proposed (January 28,1712 [G.,II, 433]) that, though extension does not constitute the essence of a body, it is a real, not a modal, accident and that this presupposes a substantial or constitutive being different from either matter or entelechy. "If you were to grant me this one real accident, I should not fear to consign what remains to modes." 8 On September 8, 1709, Leibniz had written: "To your question about my method of explaining the Eucharist, I reply that there is no place in our opinion, either for transubstantiation or for consubstantiation of the bread; but only for the view that when the bread is received, the body of Christ is perceived, and thus that only the presence of the body of Christ is to be explained. I have already explained to Tournemine that a presence is something metaphysical, like a union, which is not to be explained through phenomena" (G., 11,390). 9 The late Scholastic verb realizo and its derivatives, which are so important in defining the substantial chain, Leibniz had called a barbarism in No. 51. 10 Reading substantia (Dut., Erd.) for substantiae (G.). a
616 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS See note 4, above. The interpretation of St. Augustine by Cornelius Jansen (1585-1638), whose Augustinus was published posthumously at Louvain in 1640 and became the rallying point of the Jansenist movement, remained controversial in spite of the suppression of the Port Royal group. In his last letter Des Bosses had discussed the condemnation of Jansen's work by the church (G., 11,442). 14 In developing his reply further, Des Bosses quotes at some length the Jesuits Perez (De incarnatione disputatio) on the analysis of body and Sebastian Izquierdo on the problem of the Theodicy. 15 Cf. Theodicy, Preface (G., VI, 29), and Secs. 348-49 and 384 (G., VI, 321, 343). 16 Reading ratio for fatio (G.). 17 This letter is a reply to one by Des Bosses written August 28, 1712 (G., II, 452-56), in which he argues (1) for a real union which actuates the monads constituting a horse, for example, and further (2) that this unifying being is a nonmodal accident. His specific arguments are clearly restated by Leibniz. 18 This is another reference to the Latin version of the Theodicy. 19 Leibniz's marginal note: "The concrete can be distinguished into the accidental (as warm, warm man) and the substantial. The substantial I divide further into simple substances, such as God, angel, soul, and substantiated beings. Substantiated beings are divided into unities per se or composite substances, and unities per accidens or aggregates." 20 Reading cursu (Dut.) for ursu (G.). 21 Of December 12, 1712(G., II, 462ff.). 22 As the following letter shows, Leibniz did not at once return home from Vienna. On August 23, 1713, he wrote to Des Bosses: "I am preparing for the journey to Hanover, but I do not know by what detours, for Vienna is quarantined for fear of contagion. However I have so far seen no one dying or dead; the plague is raging among the common people where it is fed by terror and squalor. Unless the evil should grow worse, the Emperor refuses to leave, whatever is urged by those who serve this great ruler. But so a supreme ruler acts; he has more than once discussed with me how a society of sciences can be established with its seat in Vienna, but in such a way that it will have members from elsewhere." 23 In his letter of January 19, 1715 (G., II, 491), Des Bosses had reported on a work published in HolIand in 1714 entitled De raction de dieu sur les creatures, which contained a new way of defending physical predeterminism on the ground that voluntary acts are not modifications but things. 24 The only known reference in Leibniz's writings to George Berkeley. Kabitz has published a few critical marginal notes from Leibniz's copy of the Treatise concerning the Principles of Human Know/edge in the Sitzungsberichte d. Preuss. Akad. d. Wis., 1932. 25 The correspondence continued until Leibniz's death, but the essential issues and arguments have appeared at this point. 11 12
minds, souls, which are subject to no influence by other creatures. monad,lik~ Simple, a or r--A Modification Passive, resistance through magnitudeand figure; in other words, throughout its determinate te"t.ure. Primary or united; i. e., derivative power Active impetus Semiaccident; appearance or collection of the 'modifications of substances A unity by aggregation, a semi being: ' or phenomenon Semisubstance, Composite (like Of composite Ofamonad. a collection of animals or other substance, which arises substances, such organic beings) from its own which arises as the choir of outofthis which always reresources and angels, an army mutual jnflu~ mains unchanged consists exof men, a herd and adheres (0 a ence and conclusively of of animals, a fish~ sists of derivative dominant monad perception pond, a house, a but is subject and appetite. active and pas.rock, a cadaver. to the influence sivepowers Hence they are: of other composwhen bodies ite substances. collide aecorIt consists of acding to the Devoid of or Possessed tive and passive Jaws of motion, cohesion ofcohesion that is, in power originally. (pond, (herd, or consists of primary forces and rehouse) "group) sistances throughout matter, i.e., the printheir magnitudes ciple of resistance, Both are and figures. and of substantial form, i.e,. the princiNatural Artificial ple of impetus. For we (heap of (army, must recognize that new force is not given to sand. rock, house) bodies but that the tree trunk) force inherent in them is merely determined or modified by others. When one body collides with another, it impels that body by determining the inherent elastic force which arises from internal motion, in a way that can be seen when two equal inflated balls, colliding with equal velocity, are restored to rest through the collision and then resume motion through their inherent elastic force. The same thing happens in every collision, for nature never acts through a leap, nor does any body ever make a sudden transition from rest to motion or from faster to slower motion, or the opposite; it changes by intermediate steps, and this happens through elastic force or the motion of a fluid permeating it. Substance .A unity per se: a full being A permanent absolutecrea.ture:,which therefore is neither activity-passivity nor relation. is: Supplement 10 Letter XK Immediately,-as warmth, gravity, hardness By its effect, such as magnetic and elastic force, vo1atility Passive, such as firmness, fluidity, roughness. malleability; and perceptible Active. as he4t,cold. gravity. elasticity """' or physical. Secondary whose reason depends on an occult mechanism. a sensible accident. as it were: color, odor, taste; also sympathy. antipathy. etc, Such a quality is in tum -...I ~ 0- -...I I \0 00 0- ..'" -- S o t"' tTl Cl :<l o tTl Cl :<l tTl " Z c: :<l tTl <: ;I; > Z o
64 CONVERSATION OF PHI LA RETE AND ARISTE, FOLLOWING A CONVERSATION OF ARISTE AND THEODORE Ca. 1711 It is significant that at the same time at which he was defining his thought in Scholastic forms in the correspondence with Des Bosses, Leibniz had not abandoned the more popular exposition of his views in relation to Cartesian thought. This dialogue is the most successful of several criticisms of Malebranche; in form it is a continuation of that thinker's Entretiens sur la metaphysique et sur la religion. published in 1688. 1 In this work Malebranche himself appears as Theodore, who had expounded his opinions to Ariste; Leibniz's views are presented by Philarete. The exact date of the dialogue is not known. though it seems to have been written shortly after the Theodicy.In 1715 Leibniz sent it to Remond (see the letter of July 29. 1715 [G., III. 645]) as "a little dialogue on some opinions of the Reverend Faiher Malebranche". Des Maizeau, who received it from Remond. published it in 1720 with the title Examen des Principes du R. P. Malebranche; Leibniz's own manuscript bears the title translated above. [G., VI, 579-94] After Theodore had left, Ariste received a visit from his old friend Philarete, a highly esteemed doctor of the Sorbonne who had once taught philosophy and theology in the Scholastic manner but who nonetheless did not scorn the discoveries of the moderns but approached them with much caution and accuracy. He had entered into a kind of retreat in order the better to give himself to the exercises of piety, and at the same time he was at work putting the truths of religion in their true light, seeking to correct and to perfect their proofs. This led him to a rigorous examination of the proofs which were developed, to determine how they needed to be strengthened. Ariste, seeing him, cried out: What an appropriate time for you to call, my dear Philarete, after so long an interruption of our acquaintance. I have just ended a charming discussion at which I wish you might have been present. That profound philosopher, that excellent theologian, Theodore, has completely carried me away. He has taken me out of this corporeal and corruptible world into one intelligible and eternal. Yet, when I think without him, I fall back easily into myoId prejudices, and sometimes I do not know where I stand. No one is more able than you to fix me and to enable me to decide surely and with coolness, so to speak. For I must confess that the great and beautiful expressions of Theodore stir and elevate me but that after he leaves me, I no longer know why I was lifted so high, and I feel a kind of dizziness which confuses me. Philarete. I am well acquainted with Theodore's worth through his works, which contain great and beautiful thoughts; many of them have been well verified, but there
HANOVER UNDER GEORGE LOUIS, 1698-1716 619 are also some, and these among the most fundamental, which still need further clarification. I have no doubt that he has told you a thousand things fitted to help you in the excellent plan which I hear you have formed of leaving the vanities of the world, the deafening noise of people, and the vain and often evil conversations of the worldly, to give yourself up to such sound meditations as bind us to virtue and lead us to happiness. What I have heard of this happy change of yours has led me to pay you this visit to renew our old ties, and you could not have given me a better opportunity to begin and to show you my devotion than by speaking at once of the very things which have been the object of my own thinking for a long time and which should be one of the most interesting objects of yours. If you could recall the substance of Theodore's conversation, perhaps I could help you develop some of the concepts which he has given you, and he will himself finish by clarifying and grounding afterward whatever still seems obscure or doubtful to you. A. I am delighted with your help, and I shall try to summarize in substance what Theodore has told me. But do not expect from me the charm attached to everything which he said. He undertook first to show me that the I who thinks is not a body, since thoughts are not in any sense modifications of extension, and it is in extension that the essence of the body consists. I asked him to prove to me that my body is nothing but extension; when I heard him, it seemed to me that he did prove it, but his proof has somehow escaped me. It will return bit by bit, however. Extension, he told me, is all that is needed in order to form the body. He added also that if God were to destroy extension, the body would be destroyed as well. Ph. Philosophers who are not Cartesians will not agree that extension is enough to form a body; they will demand something more which the ancients called antitypy, that, namely, which makes one body impenetrable to another. According to them, bare extension is only the place, or the space, which the body occupies. It seems to me, in fact, that when Descartes and his followers try to refute this opinion, they merely make assumptions - or, to call the thing by its name, they beg the question. A. But don't you find that, since the assumption of the destruction of space involves that of body, it proves that body consists only of extension? Ph. It proves only that extension enters into the essence or nature of a body but not that it is its whole essence; just so, magnitude enters into the essence of extension but does not suffice for extension, since number, time, and motion also have magnitude yet are different from extension. If God were to destroy all actual magnitude, he would destroy extension, but in producing magnitude, he might produce only time, without producing extension. Likewise with extension and body - in destroying extension, God would destroy body, but in producing only extension, he might perhaps produce only space without body, at least according to men whom the Cartesians have not yet well refuted. A. I am sorry not to have noticed this difficulty at once, but I shall make a note to suggest it to Theodore. However, if I remember rightly, he gave me yet another argument tending toward the same conclusion, but this one seemed very subtle to me, since it was taken from the nature of substance. Theodore proved to me that extension is a substance and, I believe, tried to infer that body could be only extension, since otherwise it would consist of more than one substance. But I should not guarantee that this was Theodore's argument. I can be deceiving myself into giving his words a context different from what was in his mind; I shall find out about this. For references see p. 627
620 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Ph. I find some difficulty, once more, in this conclusion which you attribute to Theodore, even if only with some misgiving. For you know that the Peripatetics regard a body as composed of two substantial principles, matter and form. So we should have to prove that it is impossible for a body to be composed at once of two substances, that is, of extension - if we agree that extension is a substance - and of some other substance as well. But let us see how Theodore proved that extension is a substance; this is a very important point. A. I shall try to remember. Whatever one can conceive by itself, without thinking of anything else, or without using the idea which represents something else, or better, whatever one can conceive by itself as existing independently of anything else, is a substance. And whatever one cannot conceive alone, or without thinking of some other being, is a mode of being, or a modification of substance. This is what we mean when we say that a substance is a being which subsists in itself. We have no other way to distinguish substances from modifications. Now Theodore showed me that I could think of extension without thinking of anything else. Ph. This definition of substance is not free from difficulty. In the end only God can be thought of as independent of any other being. Shall we say then, as does a certain innovator who is only too well known, that God is the only substance and that created beings are only his modifications? 2 But if you restrict your definition by adding that substance is that which can be conceived independently of every other creature, we may perhaps find things which have as much independence as extension and yet are not substances. For example, active force, life, and antitypy are something essential and at the same time primitive, and one can conceive of them independently of other concepts, even of their subjects, by means of abstractions. Subjects, on the contrary, are conceived by means of such attributes. Yet these attributes are different from the substances of which they are attributes. So there is something which is not at all substance, yet which cannot be conceived as any more dependent than substance itself. Hence this independence on the part of its concept is not at all the mark of substance, since it must apply also to what is essential to substance. A. I believe that abstractions ought not to be thought of as independent of something, at least in their subject which should be concrete even though it is incomplete, and which, when joined to a sufficient essential primitive attribute, would make up the complete subject. But to get ourselves out of these thorns, let us say that the definition ought to apply only to concretes; thus substance would be a concrete being independent of every other created concrete being. Ph. Then you place another restriction on your definition; but it still contains great difficulties. For (1) perhaps the explanation of what 'only concrete' means presupposes substance itself, so that you will be reasoning in a circle in your definition. (2) I deny that extension is a concrete term, since it is an abstraction from what is extended. (3) It follows that the exact and incomplete subject, or the simple, primitive concrete term which, joined to an essential attribute, constitutes a complete substance, would itself alone deserve the name of substance, since neither the abstractions nor the complete concretes could be conceived or could exist without it. (4) I shall not insist, for the present, on the doctrine of those theologians who maintain that accidents can exist without their subject in the sacrament of the Eucharist, for they are essentially independent of it, and your definition therefore covers them. A. We are being plunged into plenty of subtleties, and it is a good thing that I was
HANOVER UNDER GEORGE LOUIS, 1698-1716 621 once in the College and have retained some of the Scholastic terms. But I admit that these subtleties are unavoidable here and that you put them in a very intelligible way so that I find it possible to reply to you. I answer, then, to the first point, that the definition of the concrete does not require that of substance, since accidents too can be concrete. 3 For example, heat can be great or have magnitude, but great is a concrete entity. A number can be called great, or proportional, or commensurable, etc. As for the second point, I should say that since extension, space, and body are one and the same thing for Theodore, he will say that extension is a concrete being. I reply to the third point that the extended being, or the body, is exactly this primary subject conceived as the matter which is formed by shapes and motions into a complete subject. Finally, I say to the fourth point that Theodore may not agree with the possibility of the existence of accidents without a subject. Others who may wish to maintain the definition will say that substance is a concrete being which is naturally independent of every other created concrete being. Ph. I find your reply to the first point good. Yet you must explain the concept of concrete and abstract more distinctly. But on the second point, I cannot agree with you that the extended and extension are the same thing. There is no example in created beings of the identity of the abstract and the concrete. Your reply to the third point can pass, and also that which you gave to the fourth, according to those who deny that accidents subsist outside of a subject. But those who would correct the definition of substance by limiting it to what occurs naturally will make it resemble the definition of man which is ascribed to Plato. It is said that he had defined man as a two-legged animal without feathers; whereupon Diogenes plucked a cock and threw it into Plato's lecture hall, saying, 'Here is a Platonic man.' A Platonist could have replied that the definition meant an animal as it is naturally. But we require that definitions be drawn from the essence of things. It is true that definitions may also be useful which are drawn from that which occurs naturally, and that one can distinguish three levels of predicates: the essential, the natural, and what is simply accidental. 4 In metaphysics, however, one seeks essential attributes or those drawn from what we call a formal reason. A. So far as I see, the only question at issue between us is whether extension is an abstract or a concrete being. Ph. I could also object to your definition that bodies are not at all independent of each other and that they need, for instance, to be acted upon or stimulated by their surroundings. But you could make use of my own answer in replying to me, namely, that the essence is all that is needed for a definition, since God can cause bodies to be independent and conserve them in their state when every other body has been destroyed. So I merely insist on my earlier remark - that extension is nothing but an abstraction and demands something which is extended. It needs a subject; it is something relative to this subject, like duration. In this subject it even presupposes something prior to it. It implies some quality, some attribute, some nature in the subject which is extended, which is expanded with the subject, which is continued. Extension is the diffusion of that quality or nature. For example, there is in milk an extension or diffusion of whiteness, in the diamond an extension or diffusion of hardness, in body in general an extension or diffusion of antitypy or of materiality. You will thus see at once that there is something in body prior to extension. One may say that in some way extension is to space as duration is to time. Duration and extension are attributes of things, but time For references see p. 627
622 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS and space are taken by us to be something outside of things and serve to measure them. 5 A. Those who admit a space distinct from body think of it as a substance which constitutes position. But the Cartesians and Theodore think of matter itself as you think of space, except that they give it a mobility along with extension. Ph. Then they tacitly admit that extension is not sufficient to constitute matter or body, since they have to add mobility, which is a result of antitypy or of resistance; otherwise one body could not be pushed or moved by another. A. They will say that mobility is a result of extension, since all extension is divisible in such a way that its parts are therefore separable from each other. Ph. Those who assume that there is vacuum, or at least a real space distinct from the matter which fills it, will not grant you this conclusion. They will say that one can note the different parts in space but that one cannot separate them. As for my own view, though I distinguish the notion of extension from that of body, I still believe that there is no vacuum and even that there is no substance which can be called space, i.e., that there is no subject having only the attribute of extension. Even if I were to admit such a substance 6, I should always distinguish between the extended or extension, and the attribute to which being extended, or diffusion, a relative concept, is referred. This would be situation or locality. Thus the diffusion of place forms space, which would be the first ground [npcmov 08KT1KovF or the primary subject of extension, and by which it would also apply to other things in space. Thus extension, when it is an attribute of space, is the diffusion or continuation of situation or locality, just as the extension of a body is the diffusion of antitypy or materiality. For there is position in a point as well as in space, and as a result there can be position without extension or diffusion, but diffusion in simple length constitutes a localized line endowed with extension. The same thing is true of matter; it is in a point as well as in a body, and its diffusion in simple length makes a material line. Other continuations or diffusions in breadth and depth form the surface and the solid of geometry - in a word, space in relations of position, and body in material relations. A. These relations of proportion between position and matter, space and body, please me. They help one speak with exactness. It is good to make these distinctions, and similarly that between duration and time, extension and space, as well. I shall have to ask Theodore about this. Ph. Finally, to go further still, I hold the opinion that not only extension but body as well cannot be thought of independently of other things. Thus we should have to say either that bodies are not substances at all· or that it is not a property of all substances to be thought of as independent, even though it may be of some single substances. For being a whole, the body depends essentially 8 upon other bodies of which it is composed and which constitute its parts. Only the monad$, that is, simple or indivisible substances, are truly independent of every concrete created thing. A. Then I shall say that substance is a concrete being independent of every concrete created thing outside of itself. Thus the dependence of a substance upon its own attributes and parts will be no obstacle at all to our arguments. Ph. But that makes the third restriction upon your definition. It is permissible for you to do this, of course, but to tell the truth, some things which are permissible are not expedient; non omne quod licet expedit. What does it matter if the worm which gnaws at me is within me or outside of me? Am I any the less dependent upon him?
HANOVER UNDER GEORGE LOUIS, 1698-1716 623 Only incorporeal substances are independent of every other created substance. So it seems that in philosophical strictness the body does not deserve the name of substance, a view which seems to have been Plato's, who says that there are transient beings which never subsist longer than a moment. But this point needs a fuller discussion, and I have still other important reasons for refusing to bodies the title and name of substances in a metaphysical sense. For to say a word about this, a body is not a true unity; it is only an aggregate, which the Scholastics call a being per accidens 9 , a collection like a herd. Its unity comes from our perception. It is a being of reason or rather, of imagination, a phenomenon. 1 0 A. I hope that Theodore will satisfy you on all these difficulties. Meanwhile let us assume that body and extension are not so very different, since you do not recognize a vacuum; or at least let us lay the point aside for a fuller discussion and go on to the rest of Theodore's demonstration. It reduces to this. Everything which has modifications which we are unable to explain by extension is distinct from a body, assuming that bodies and extension are the same thing or at least that they differ only as space and that which has only to fill it - that which has some resistance and mobility in addition to extension, as you seem to grant. Now the soul has modifications which are not modifications of extension or if you please, of antitypy or of simple spacefilling. Theodore even proves this; for my pleasure, my desire, and all my thoughts are not at all relations of distance, and one cannot measure them by feet or inches, like space or that which fills it. Ph. I share Theodore's opinion when he maintains that the modifications of the soul are not at all modifications of matter and that as a result the soul is immaterial. Yet his proof stilI contains some difficulty. He holds that no thoughts are relations of distance, since we cannot measure them; but a follower of Epicurus would say that this is due to our faulty knowledge of them and that if we knew the corpuscles which form thought and the movements necessary for it, we would see that thoughts are measurable and are the workings of certain subtle machines. Just so, the nature of color does not seem to consist, internally, of some measurable thing. Yet if it is true that the reason for such qualities in objects is to be found in certain configurations and movements - as the whiteness of foam, for instance, comes from little bubbles which are hollow and polished like many little mirrors - then these qualities may at last be reducible to something measurable, material, and mechanical. A. In this way you abandon to your opponents all the proofs which can be given for the distinction of soul and body. Ph. Not at all. I intend merely to perfect them. To give you a little sample now, I consider that matter includes only what is passive. It seems to me that the Democriteans as well as other philosophers who think mechanistically must agree with this. For not only extension but also the antitypy attributed to bodies are purely passive things, and as a result the origin of action cannot be a modification of matter. Hence movement as well as thought must come from another source. A. Permit me to point out the fault I find in your argument, for you teach me to be exact to the point of rigor. I shall say, then, that your argument is of no value except ad hominem, that is, for those who philosophize like Democritus and Descartes. But Platonists and Aristotelians, and some of the recent defenders of an archeus, as well as the latest sympathists who maintain the attraction of bodies at a distance 11, put qualities in the body which cannot be explained mechanically; they will therefore not For references see p. 627
624 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS agree that bodies are purely passive. I recall that a certain author, one of your friends, favors the purely mechanical explanation of bodily phenomena but has undertaken in some essays published in the Acta eruditorum of Leipzig to show that bodies are endowed with a certain active force and that bodies are thus composed of two natures a primitive active force (called first entelechy by Aristotle) and matter or primitive passive force, which seems to be antitypy. He holds, for this reason, that everything can be explained mechanically about material things except the principles of mechanism themselves, which cannot be derived from the consideration of matter alone. Ph. I am corresponding with this author and am fairly familiar with his opinions. This primitive active force, which could be called life, is precisely what is contained, he holds, in what we call a soul or in simple substance. It is an immaterial, indivisible, and indestructible reality; he locates it everywhere in the body, believing that there is no part of matter where there is not an organized body endowed with some perception or with a kind of soul. Thus this thinking leads us straight to the distinction of soul and matter. If one calls body what I should prefer, as does he, to call corporeal substance, which is composed of soul and matter, this is merely a question of terminology. This active force is exactly that which best shows the difference between soul and matter, and that in a sensible way, because the principles of mechanism, of which the laws of motion are the result, cannot be derived from what is purely passive, geometrical, or material, or proved by the axioms of mathematics alone. For this author has pointed out in more than one article in the Paris Journal des savants, the Leipzig Acta eruditorum, and elsewhere when speaking of his dynamics, and even recently in his Theodicy, that to justify the laws of dynamics, one must have recourse to a real metaphysics and to the principles of harmony which pertain to souls and which are no less exact than those of geometry. In the letters which he has exchanged with Mr. Hartsoeker and which are published in the Memoires de Trevoux, you will also find how he abolished the void and atoms through higher considerations, even making use in this of a part of dynamics. 12 Those who instead merely restrict their considerations to matter cannot reach a decision on this question. This is why the new philosophers, being usually too materialistic and not inclined to ally metaphysics with mathematics, have been in no position to decide whether there are atoms and a void or not. Many have even been led to believe that there are, that is to say that there exist, either a void and atoms or at least atoms swimming about in a perfect fluid, thus excluding the void. 13 But he shows that the void, the atoms, or perfect hardness, and a perfect fluid are all alike opposed to harmony and order. A. There is something in what you say, and with your assistance I want to think more about it, especially about dynamics, since it is so important for the knowledge of immaterial substances, and about the inconsistency of the void and atoms as well. But I have. still another objection. This is that God could himself have done immediately everything that you attribute to souls. Thus the modifications and the operations which go beyond matter would not lead you to souls distinct from matter, since they would be the acts of God himself. It is true that this objection applies also against Theodore himself, and perhaps more than against the others, for as you know he considers secondary causes as only occasional. Ph. Even if the operations in question were acts of God, the modifications which are attributed to souls and which we feel in our own soul could not be modifications of God. And as concerns operations too, it cannot be denied that we ourselves have
HANOVER UNDER GEORGE LOUIS, 1698-1716 625 internal actions, and this would be all that is necessary here, since matter, being passive, is incapable of such activity. But the viewpoint which ascribes all external actions to God alone has recourse to miracles, and even to unreasonable miracles, hardly worthy of the divine wisdom. By the same right by which we set up such fictions which only a miraculous omnipotence of God could make possible, it would be permissible to maintain that I am alone in the world and that God produces all the phenomena in my soul as if there were other things outside of me, without there actually being any. Yet even if our present argument, which proves the distinction between soul and matter insofar as this is supported by external operations or in dynamics, were valid only on the assumption that things take place in the ordinary course of nature by natural forces, without God acting upon them except to conserve them even this would be a great gain. For it would prove either the distinction between the soul and the body or the existence of God. We can go even further and show more distincly how dynamics verifies both of these two great doctrines, but that would demand a more extended discussion in which we need not now get involved. A. We must talk of this again some other time at your convenience. However, I find that we have already achieved much, since the opponents of religion cannot refute what you have just said in favor of the immortality of souls without recourse to God, that is, to the doctrine which they most abhor. But once convince them of the existence of God, or of a spirit infinitely powerful and wise, and it will not be hard to infer that he has also made finite spirits immaterial like himself and further, that God would not be just if our souls perished with their bodies. Ph. There is even good ground for doubting whether God has made any other things than monads, or substances without extension, and whether bodies are anything but the phenomena resulting from these substances. My friend, whose opinions I have detailed to you, gives evidence enough of leaning to this view, since he reduces everything to monads or to simple substances and their modifications, along with the phenomena which result from them and whose reality is established by their relations, which distinguish them from dreams. I have already touched somewhat on this; but now I must hear the rest of your estimable Theodore's conclusions. A. After having established the distinction between soul and body as the basis of the chief doctrines of philosophy, and also of the immortality of the soul, he drew my attention to the ideas perceived by the soul; he maintains that these ideas are realities. He goes even further and holds that the ideas have an eternal and necessary existence and that they are the archetype of the visible world, whereas the things which we think we see outside of us are often imaginary and always transitory. He even advanced the following argument. Suppose that God should annihilate every being he has created except you and me; suppose further that God gives our spirit the same ideas which now present themselves through the presence of objects; we should then see the same beauties which we see now. Hence the beauties which we see are not material but intelligible beauties. Ph. I fully agree that material things are not the immediate objects of our perception, yet I find some difficulty in the proof and in the way in which he explains the matter, and I wish it might be developed a little better. The hypothetical major premise of the argument: does it contain inevitable consequence? If we should see everything in an intelligible world in case external things were destroyed, it follows that we see everything in an intelligible world at present too. Is this conclusion, I say, certain? Is it not For references see p. 627
626 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS at all possible that our present ordinary perception is of a different kind from this extraordinary perception? The minor premise is that in the case of this destruction, we should see everything in an intelligible world. But to many people this minor premise would also seem doubtful. Would not the opponent who believes that bodies have an influence on souls say that in case our bodies were destroyed, God would supply their lack and would produce in our souls the qualities which the bodies would have produced, without any need of eternal ideas or an intelligible world? But even granting that everything takes place in us ordinarily just as it would in the case of bodily annihilation, that is, admitting that we ourselves always produce within us (as I in fact believe) or that God produces in us (as Theodore believes) internal phenomena without the body having any influence over us, must this necessarily involve external ideas? Is it not sufficient to hold that phenomena are simply new transitory modifications of our souls? 14 A. I cannot recall that Theodore ever proved to me in general that the ideas which we see are eternal realities. He undertook this only with regard to the idea of space and by a particular line of reasoning. But this itself always predisposes me to conclude the same thing about the ideas of other things, since space is very often a part of them. He also gave excellent answers to the arguments with which I opposed his view. I objected that the earth offers resistance to me and that there is something solid in this. He replied that this resistance could be imaginary, as in a vivid dream, whereas the ideas do not deceive. He also showed me, very fittingly, that ifresistance is a mark of reality, there is also resistance in the ideas, when one tries to ascribe to them that which they cannot endure. 1 5 But as I have already said, he proved to me that the idea of space is necessary, eternal, immutable, and the same in all minds. Ph. One may agree with you, Sir, that there are eternal truths, but not everyone will agree that there are eternal realities which are presented to our soul when it sees these truths. It will be said that it is enough that our thoughts have a relationship in this with those of God, in whom alone the eternal truths are realized. A. Yet this is the argument which Theodore offered to prove his thesis. When we have the idea of space, we have the idea of infinity; but the idea of infinity is infinite, and an infinite thing cannot be the modification of our soul, which is finite 16; hence there are ideas which we see but which are not modifications of our souls. Ph. This argument seems to me worth considering, and it ought to be developed more thoroughly. I agree that we have the idea of an infinite in perfection; for that we need only to think of the absolute, by setting aside all limitations. And we have a perception of that absolute because we participate in it, inasmuch as we have some share of perfection. But one can doubt with reason if we have an idea of an infinite whole or of an infinity composed of parts, for a compound being cannot be an absolute. It may be said, for example, that every straight line can be thought of as prolonged, or better, that there is always a straight line greater than the given one, yet we do not have the idea of an infinite straight line or of one greater than all others which can be given. A. It is Theodore's opinion that the idea we have of extension is infinite but that the thought which we have of it, which is a modification of our soul, is not. Ph. But how prove that we must have anything more than our thoughts and their objects within us and that an infinite idea existing in God is needed for our purpose, in order to have only a finite thought? Would it not be enough, if we must have ideas
HANOVER UNDER GEORGE LOUIS, 1698-1716 627 distinct from thoughts, for the ideas to be proportional to the thoughts? We must say, then, that there is no way of understanding such ideas. A. This is the way which Theodore provided for me. The mind does not see the infinite in the sense that it measures it by its thought. But neither is it enough for the mind not to see the end to its thought, for it could still hope to find such an end; but it understands that there is no such end. Thus the geometricians see that subdivision, though continued as far as you please, will never reveal any part of the side of a square, however small, which can also be some part of the diagonal or commensurate with it. Similarly, these geometricians see asymptotic lines which they know can never intersect the hyperbola, though they approach it without end. Ph. This method of knowing the infinite is certain and incontestable. It proves, too, that objects have no limits. But though we can conclude from it that there is no ultimate finite whole, it does not follow that we see an infinite whole. There is no infinite straight line, but every straight line can always be prolonged or surpassed by another longer one. Thus the example of space does not at all prove in particular that we need the presence of certain subsisting ideas different from the passing modes of our thought. It seems at once that our thoughts are themselves sufficient for this. A. It is not myself that I see when I see space and figures; therefore, it is something outside of myself. Ph. Why should I not see these things in myself? It is true that I see their possibility even when I am in no way aware of their existence and that even when I do not see them, these possibilities always subsist as eternal truths whose whole reality must, however, be founded in something actual, that is to say, in God. But the question is whether we have ground to say that we see them in God. Yet since I myself must applaud Theodore's beautiful thoughts, I think one can justify his opinion on this problem in the following way, though it appears highly paradoxical to those who have not lifted their minds above sense perception. I am convinced that God is the only immediate external object of souls, since there is nothing except him outside of the soul which acts immediately upon it. Our thoughts with all that is in us, insofar as it includes some perfection, are produced without interruption by his continuous operation. So, inasmuch as we receive our finite perfections from his which are infinite, we are immediately affected by them. And it is thus that our mind is affected immediately by the eternal ideas which are in God, since our mind has thoughts which are in correspondence with them and participate in them. It is in this sense that we can say that our mind sees all things in God. A. Far from displeasing Theodore, I hope that your criticisms and interpretations will please him. He delights to communicate with others, and the account which I shall bring him will give him an opportunity to share more and more of his insights with us. I even flatter myself that I can oblige both of you by bringing you together and that I myself would derive the most profit from this. REFERENCES 1 An English translation of Malebranche's work, with the title Dialogues on Metaphysics and Religion, was edited by Morris Ginsberg in 1923. As the correspondence with De Voider had shown, Leibniz differed from Descartes and Spinoza (who is here alluded to) in conceiving substance, not as static and incapable of change, 2
628 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS definable by internal attributes, and unaffected by its modifications, but as functional in both mathematical and dynamic senses of that term and therefore logically compound and analyzable. 3 This parallels the discussion with Des Bosses, at the time when Des Bosses sought to defend nonmodal and real accidents (see particularly p. 616, note 19). 4 Compare Leibniz's distinction between formal and exigent necessity in the correspondence with Des Bosses. The relation of the distinction to that between truths of reason and of fact is obvious. 5 See p. 540, note 7. This distinction corresponds to that between internal properties or accidents and the external relations (sometimes determined by the perceiving mind and sometimes by the related monad), which Leibniz made in the correspondence with De VoIder, Des Bosses, and elsewhere (cf. p. 540, note 15). 6 The passage beginning with "that there is no subject ... " is omitted in G.; this reading follows the collated text in Schmalenbach (Sch.). 7 See p. 595, note 1. S Following Dut. and Erd.; G. omits essentiellement. 9 With Dut. and Erd.; G.haspuraccident. 10 Thus Leibniz reaffirms his phenomenalism at the very time of his discussion of the vinculum substantiale and the real nature of bodies with Des Bosses. 11 Sympathism refers to the Newtonians, who interpret gravity as action at a distance, following the first edition of the Principia. Leibniz here includes them with the 'neovitalists', as his term nouveaux archealistes might be rendered (see p. 508, note 2). 12 Nicolas Hartsoeker, in the service of the Elector Palatine at Diisseldorf, had corresponded with Leibniz since 1706. His Eclaircissemens sur les conjectures physiques appeared in 1710, reviving the old controversy about atoms. Leibniz had recently written him (October 30, 1710), arguing that atoms are fictions (G., III, 504-10). 13 The latter view was that of Huygens in the correspondence of 1692-94 (cf. No. 43). 14 Like Malebranche, Leibniz believed that our perceptions are based in eternal ideas; but, far from conceiving these ideas as objects (save in reflection), he viewed them as the possibilities or forms of perception. 15 This sentence did not appear in the published version, and therefore not in Dut. and Erd.; G. gives itfrom the manuscript. 16 G. has infinie.
65 REMARKS ON THE THREE VOLUMES ENTITLED CHARACTERISTICS OF MEN, MANNERS, OPINIONS, TIMES, ... 1711 1712 Upon its appearance in 1711, Shaftesbury's Characteristics was sent to Leibniz by Pierre Coste, who had been given a number of copies to distribute to scholars for criticism (Coste to Leibniz, April 14, 1712 [G., III, 420]). Leibniz's favorable reaction to the witty and penetrating observations of this English intuitionalist throws interesting light upon the relation of his own thought to the gospel offeeling of succeeding decades. Leibniz himsel/wrote to Thomas Burnet on August 23,1713: The Count ofShaftesbury, who died recently in Naples, presented me with his three octavo volumes, which were full of beautiful things, and asked for my criticism. I was surprised to find a great number of thoughts which agree with my own principles. Yet I did add some slight criticisms, and he had the sincerity and moderation to tell me that my small corrections did not displease him. The loss ofso excellent and sublime a mind is no small one [G., III, 327J. Leibniz sent his comments to Coste, who passed them on to Masson. They were published in the latter's Histoire critique de la republique des lettres in 1715. [G., III, 423-31] The Letter on Enthusiasm contains a thousand beautiful thoughts. I believe that raillery is a good protection against this vice, but I do not find it suitable for curing people of it. On the contrary, the contempt which is clothed in raillery will be taken by them as affliction and persecution. I have observed, that when one rails at errors and absurdities in religious matters, one infinitely irritates the people at whom the raillery is directed and that this is the true way to pass for an atheist in their minds. Also, I am not sure that the use of ridicule is a good touchstone of error, since the best and most important matters can be turned to ridicule, and it is not always certain that truth will have those who laugh on its side, since it is most often hidden from vulgar eyes. I have already said that all raillery includes a little contempt, and it is not just to try to make contemptible what does not deserve it. But it is good always to be in good humor, so that joy will be apparent rather than irritation in our conversation and writing. The Essay on Free Manners, on Spirit, and on Good Humor seems to have the same purpose of bringing our contemporaries to humanize themselves and to brighten things; by its arguments and its example this work is wonderfully suited to the purpose. Though ironical, the remarks at the beginning in support of those who hold men to be wolves to each other, and against those who believe in their natural goodness, are pleasantly turned. But it can be said that ordinarily men are neither very malicious nor For references see p. 634
630 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS very good, and Machiavelli has well remarked that the two extremes are equally rare, with the result that great actions are rare also. The Iroquois and Hurons, uncivilized neighbors of New France and New England, have upset the too universal political maxims of Aristotle and Hobbes. By their surprising conduct they have shown that entire peoples can live without magistrates and without quarrels and as a result that men are neither carried far enough by their natural goodness nor forced by their malice to provide themselves with a government and so to renounce their freedom. Yet the roughness of these savages shows that it is not so much necessity as the inclination to advance to a better state and to arrive at happiness through mutual assistance which is the foundation of societies and states. But is must be admitted that security is the most essential point in this.1 I find good the remark on page 98 that true virtue should be disinterested, that is, as I interpret it, that one should come to find pleasure in the practice of virtue, and disgust and repugnance in the exercise of vice, and that this should be the goal of education. 2 The remark on page 99 is also good - that individual friendships are little recommended in our religion, which points us to charity or to general benevolence. It can also be said that a tested friendship is very rare and that it must be the effect of a great and beautiful passion or of a great virtue found in two persons at the same time. It is true that true friends who are very virtuous would be capable of going far. Our illustrious author is right in refuting those (on p. 109) who believe that there is no obligation in a state of nature or outside of government. For according to the authors of these principles, obligations by compact should form the right of government itself; so it is obvious that the obligation is prior to the government which it must form. It is a common saying that interest governs the world, but there is truth in the remark on page 115 that it is rather the passions that do so. The Duke de Rohan begins his book on politics with this sentence: The princes command peoples, and interest commands the princes. 3 It would be desirable for this to be true, for then we should listen the better to reason. But reason demands also that we be concerned with our satisfaction beyond merely mercenary interest; it orders us to strive for happiness, which is nothing but a state of enduring joy. And whatever achieves this is our true interest. As for those of whom he speaks on page 118, who refer everything to themselves and who seem to be in opposition to men who love their friends, parents, country, state, and even mankind in general, I believe that, rightly understood, we can reconcile the two positions provided that both sides listen to reason. Our own good is without doubt the basis of our motives, but very often we find that not only our own advantage but even our pleasure is in the good of someone else; in the latter case we should properly call this disinterested love, as I have shown in explaining the principles of justice in the Preface to my Diplomatic Codex on the Right of Nations. So the happiness of someone else often becomes a part of our own. We shall find that virtue, or the habit of acting reasonably, is that which achieves the most that one could promise himself - a lasting pleasure. I most heartily applaud what is said on pages 123ff., where it is shown that true honor [honnetete] does not depend essentially upon the opinion of others. It is true that this word has degenerated somewhat today, as have the sentiments as well; when we call a man 'honorable', we mean that he has the ability to make himself esteemed,
HANOVER UNDER GEORGE LOUIS, 1698-1716 631 that he makes a good appearance - a 'speciously proper outside' [spe~iosum pelle decor4 4 ••• The remark is good, on pages 130--31, that the truly honorable man would not even be capable of contemplating an evil act. Mr. Bayle has said something like this, which I strongly approved in the Theodicy, Section 318, having pointed out (in Sec. 75) that those who said of Cato that it was impossible for him to fail to do his duty meant only to praise him the more. The less we can be tempted by vice, the more strengthened we are in virtue. But there remains the important question of which of the two is better, whether to be irresolute or to be confirmed in vice. Our illustrious author seems to agree with this passage in Horace, Book ii, satire 7: Quanto constantior idem In vitiis, tanto levius miser, ac prior ilIo Qui iam contento, jam laxo fune laborat. s One suffers less, in fact, when a resolution has been taken than when one is in a state of embarrassing irresolution. The authors of the philosophical sin have gone still further, for according to them, those who sin with less remorse are more innocent. But Aristotle is for the half-wicked, whom he calls incontinent, and it can be said that their disease is more curable. The completely vicious are like people with gangrene who do not feel their illness. The unsatisfactory reasoning of certain modem philosophers leads him to say, on page 132, that as things stand today, honor and good morals do not appear to gain much from philosophy and profound speculation and that we should tum to common sense. He adds that usually men's first judgments on these matters are worth more than their reflections and afterthoughts. This may be true when one reasons according to the principles of Mr. Hobbes and perhaps even of Mr. Locke. But I should be sorry if it were true according to the true philosophy, which I flatter myself I have outlined in my Theodicy. I find myself surprised by the abundance of excellent things which I discover in the Soliloquy and by the beautiful tum which is given them. What he says there about destiny paralleling liberty and about the sciences of the Romans (pp. 219-20) seems to me very important. It is to be hoped that Great Britain will maintain the glorious title given her with so much justice on page 223. 6 But above all, literature is under obligation to our illustrious author for the recommendation with which he honors it in relation to great men (p. 224), and these will also benefit if they show a regard for that recommendation. I doubt that the sublime style is the easiest to achieve, as he seems to say on page 242. There are few who have attained it, even among the ancients, who are otherwise so successful. I do not think that this characteristic is found with much uniformity among the Latins outside of Virgil and Tacitus. The advice is excellent which is given to authors (pp. 264, 271) not to be guided solely by the prejudices of their country and their century and to labor to correct the vulgar rather than to flatter them. But it is only authors who resemble this one himself, that is, those having a higher talent, who can profit from this advice; the general run of authors are like the man who has written a play and is quite satisfied if he sees the stalls well filled. I believe that there is a reference on page 287 to the late Mr. van Helmont, the For references see p. 634
632 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS younger, who was a prisoner of the Inquisition at Rome and who took it into his head, in his solitude, to examine the function of the organs in pronouncing letters and thought he had found how these characters are formed. I have known this same person unusually well, and I must do him the justice of saying that he was not as ignorant in the moral field as he seems here to be represented as being. It was he who had the Lycurgas of Ottavio Pisani reprinted and who gave advice to the public on ways to abridge legal procedure. His conduct was without reproach, his actions were full of charity and disinterestedness. Except for certain chimeras which remained with him from the impressions of his youth like a hereditary illness, he was an excellent man whose conversation was very instructive to all who could benefit from it. His works reveal only that part of him which was least praiseworthy. 7 The remark on page 293 is good - that the physiological understanding of the passions, to which Descartes was attached, is inadequate for morals, though it has its usefulness in medicine. The Stoics were wrong, perhaps, in defining the passions by general opinion as by their popular classification, but they were right in examining the opinions which contributed toward forming and maintaining these. It is right to scorn a sterile philosophy (p. 299), but I believe that if the author had true ideas of space, of matter, and above all, of substance (ideas which he speaks of as quite useless but which are not so common or so well known as may be thought), he would find in them the self-knowledge which he here advises. One would also find there what he seeks on page 300, namely, a means of being certain about one's ideas and of bringing present opinions into accord with future ones. The question of whether or not there is a vacuum (p. 301) is more remote from morals, but whoever would establish the true principles even of ethics, and be demonstratively sure of them, will not disdain this question. The agreement and disagreement of ideas are not known through a simple comparison of our perceptions; we must come to an analysis. Able man that he was, Mr. Locke did not adequately recognize this. On the knowledge of substance, and therefore of the soul, depend the notions of virtue and of justice, as well as the question asked on page 302 - whether it is reasonable to risk one's life for the good of another. Our author excels here; his charms and exhortations reveal the advantages of this Calliope, this Clio, and this Urania of whom he speaks so well on pages 316 ff. Would God that a way might be found to reconcile learning with the education of a gentleman, as he recommends on page 335, and to direct both toward virtue. If our illustrious author had many companions in quality and merit, this could soon be achieved. He is also right in condemning the love of vain and extravagant tales which prevails (p. 349) and even more, the opinions, so unworthy of the enlightenment of our century, which represent virtue and vice as indifferent by nature (p. 352). I come to the second volume, in which the treatise entitled An Inquiry concerning Virtue and Merit is most systematic and contains sound opinions on the nature of virtue and happiness, showing that the affections which nature has given us lead us not merely to seek our own good but also to achieve that of those related to us, and even of society in general, and that we are happy when we act according to our natural affections. It seems to me that I could reconcile this very easily with my own language and opinions. Our natural affections do indeed make up our contentment, and the more natural we are, the more we are led to find our pleasure in the good of another. This is the basis of universal benevolence, charity, and justice. As I have said
HANOVER UNDER GEORGE LOUIS, 1698-1716 633 in the Preface to my Codex, cited above, justice is at bottom only charity which conforms to wisdom. It is only reluctantly, and for a greater good, that justice sometimes obligates us to do evil. Wisdom orders that this benevolence should have degrees, just as the air, though it extends all around our globe to a great height, has greater weight and density near us than it has in the higher atmospheric regions. In the same way, one can say that the charity which bears upon those who touch us most nearly should have the greater intensity and force. This work begins with the Divinity and distinguishes elegantly among true theism, which conceives of only one perfectly good substance governing the world; polytheism, which distributes this power; demonism, which ascribes government to some evil power; and atheism, which makes everything depend on chance or on a concourse of unintelligent causes. It seems to me that he does not make enough use, throughout the work, of the Divinity which he affirms at the beginning. Yet I see that the author wished to show that even atheists are obligated to follow virtue but that it is nevertheless true that nature leads us to admit a beneficent deity, since our natural affections conform to what such a power would order. It can be said that a certain degree of moral goodness exists independently of deity but that a consideration of the providence of God and the immortality of the soul brings morality to its height, so that in the wise man moral qualities are completely realized and honor and utility become entirely identified, without any exception or evasion. I thought I had penetrated deeply into the opinions of our illustrious author, until I came to the treatise which is unjustly called a Rhapsody. Then I perceived that I had been in the forechamber only and was now entirely surprised to find myself in the chamber itself, or to use a more suitable figure, in the sanctuary of the most sublime philosophy, where I was as enchanted as was his Philocles before Theocles and Palemono The turn of the discourse, its style, the dialogue, the new Platonism, the method of arguing through questions, but above all, the grandeur and beauty of the ideas, their luminous enthusiasm, the apostrophe to deity, ravished me and brought me to a state of ecstasy. At the end of the book I finally returned to myself and found leisure to think about it. From the first I found in it almost all of my Theodicy before it saw the light of day. The universe all of one piece, its beauty, its universal harmony, the disappearance of real evil, especially in relation to the whole, the unity of true substances, and the great unity of the supreme substance of which all other things are merely emanations and imitations are here put in the most beautiful daylight. It lacks almost nothing but my pre-established harmony, my elimination of death, and my reduction of matter or of plurality to unities or simple substances. I had expected merely to find a philosophy like Mr. Locke's but was led beyond Plato and Descartes. If I had seen this work before my Theodicy was published, I should have profited as I ought and should have borrowed its great passages. I find nothing to change but the title, which promises so little, and I am only sorry that the book does not fill an entire volume. I wish also that these great and beautiful meditations had been postponed until the third volume, at the end of the whole collection. For I find it hard to descend from this ublime part and to enjoy at once the more commonplace reading offered in the V1iscellanies which follow it and comprise the third volume. I should have received greater pleasure from this ifI had known that it ought to be read earlier. But I adjusted myself gradually and by degrees put myself in a state to judge it as it deserves. I even For references see p. 634
634 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS came to see that I should have been wrong in trying to change the order of the volumes, since this last contains the supplement to the other two and gives us comments on the five treatises which preceded, thus leaving a good taste in our mouths. I strongly approve the praise bestowed upon the Emperor Julian (p. 81), who has always seemed to me more unfortunate than evil. As for the story of the meeting between the great Attila and Pope Leo I (p. 91), there are historians worthy of faith (like Priscus and, later, Jomandes in De rebus geticis, chap. 42) who note that his fear of dying after such a visit helped greatly to tum Attila away from his purpose to go to Rome; this opinion had been spread abroad because Alaric, king of the Visigoths, had died shortly after the capture of Rome, and it was believed that the gods had punished his boldness, so great was the respect in which tqis capital of our world was held at that time. 8 The discourse on taste (MisCellany 3, chap. 2) seems to me to be important. Taste as distinguished from understanding consists of confused perceptions for which one cannot give an adequate reason. It is something like an instinct. Tastes are formed by nature and by habits. To have good taste, one must practice enjoying the good things which reason and experience have already authorized. Young people need guidance in this. He is right (p. 211) in comparing those who seek demonstrations everywhere, and are incapable of seeing anything in everyday light, to people who are called moon-blind because they can see only by moonlight. For there are many probabilities which one is obliged to follow in life. However, it is safest to satisfy such people too if possible. Excellent things are said about the natural inclinations (pp. 214ff.), and nothing is as plausible as the examples which are given of animals. Because of their artificial way of life, men have unfortunately largely lost their natural instinct for adjustment to the physical. Perhaps the savages surpass us in this. But we have maintained superiority in morals, and fortunately reason and feeling concur here. Our author is a sane judge of things. Instead of being contemptuous of ancient languages, the humanities, and criticism, as are persons of thought and those of good taste [beaux esprits] as well - two nearly opposite talents which he combines - he recognizes the importance of these fields, even in relation to religion (pp. 267-68). I shan not comment on the passages which consider the state and the church in England, of which I have not enough knowledge. But I am sure that the wise men of that nation are thinking effectively about establishing its security, which is also that of free Europe. In conclusion, I should strongly hope that everything in these three volumes will be translated into French as were the first pieces, so that foreigners may also profit by it. There are few works in which soundness and elegance are so wen combined. REFERENCES Many of his notions about the North-American Indians, Leibniz had gleaned from the Baron Louis Armand de la Hontan (1666-1715), author of the Dialogues curieux entre l'auteur et un sauvage de bon sense qui a voyage, et memoires de l'Amerique septentrionale, a work which did much to fix the Romantic notions of the next century. From Leibniz's letters to Bierling (G., VII, 491, 492) it is clear that the Baron, with whom he held conversations in 1710 and 1711, was already becoming a legendary figure. 1
HANOVER UNDER GEORGE LOUIS, 1698-1716 635 2 As becomes clearer in the more explicit references which follow, Leibniz still repudiates any concept of disinterested virtue in which the role of individual pleasure is denied - such a view as was defended by Fenelon in the famous debate with Bossuet, on which Leibniz had long since taken a position (see No. 44, I and II, and p. 430, notes 3 and 9). 3 Henri, Duc de Rohan, De !'interet des princes et etats de la chretiente (163S). 4 The quotation is from Horace Epist. i.16.15. 5 "The more content he is in his vices, the less miserable;/Better than the man who struggles, with his rope now taut, now loose" (from n. IS-20 of the indicated satire). e G. gives 225, which is incorrect. 7 On Franciscus Mercurius van Helmont see p. 50S, note 11, and p. 591, note 5. 8 Gibbon examines the story in chapter xxxiv of The Decline and Fall of the Roman Empire.
66 THE PRINCIPLES OF NATURE AND OF GRACE, BASED ON REASON 1714 The popular reception of Leibniz's Theodicy had the effect of establishing his reputation in even wider circles than before, and much of his last philosophical writing was done for this wider audience rather than for his scholarly correspondents and the readers of scientific journals. The circumstances and motives in writing the two best known of these works, Nos. 66 and 67 (the so-called 'Monadology'), are not clear. Both were written in Vienna in 1714. The Principles of Nature and of Grace was a popular introduction to his philosophy of nature and his metaphysics, written for Prince Eugene of Savoy, a copy of which was also sent, however, to Nicolas Remond and his circle in Paris; both facts are established in the correspondence with Remond in the same and the following year (G., Ill, 624, 629, 631, 633-34). The purpose of the Monadology is less clear; according to one careful study, it was begun for Remond somewhat earlier than the Principles, but finished later, and aimed to be a more careful clarification of Leibniz's principles for his followers. l In any case, though the Monadology is the more complete, the papers have much in common, both in what they include and in what they omit. [G., VI, 598-606] 1. Substance is a being capable of action. It is simple or compound. Simple substance is that which has no parts. Compound substance is a collection of simple substances, or monads. 2 Monas is a Greek word signifying unity or that which is one. Compounds, or bodies, are pluralities, and simple substances - lives, souls, and spirits - are unities. There must of necessity be simple substances everywhere, for without simple substances there would be no compounds. As a result, the whole of nature is full of life. 2. Monads, having no parts, can neither be formed nor unmade. They can neither begin nor end naturally, and therefore they last as long as the universe, which will change but will not be destroyed. They cannot have shapes, for then they would have parts. It follows that one monad by itself and at a single moment cannot be distinguished from another except by its internal qualities and actions, and these can only be its perceptions - that is to say, the representations of the compound, or of that which is without, in the simple - and its appetitions - that is to say, its tendencies from one perception to another - which are the principles of change. For the simplicity of a substance does not prevent the plurality of modifications which must necessarily be found together in the same simple substance; and these modifications must consist of the variety of relations of correspondence which the substance has with things outside. In the same way there may be found, in one center or point, though it is perfectly simple, an infinity of angles formed by the lines which meet in it. 3. Everything is a plenum in nature. Everywhere there are simple substances actually
HANOVER UNDER GEORGE LOUIS, 1698-1716 637 separate<t from each other by their own actions, which continually change their relations. And each outstanding simple substance or monad which forms the center of a compound substance (such as an animal, for example), and is the principle of its uniqueness, is surrounded by a mass composed of an infinity of other monads which constitute the body belonging to this central monad, corresponding to the affections by which it represents, as in a kind of center, the things which are outside of it. This body is organic when it forms a kind of automaton or natural machine, which is a machine not only as a whole but also in its smallest observable parts. And since everything is connected because of the plenitude of the world, and each body acts on every other one more or less, depending on the distance, and is affected by its reaction; it follows that each monad is a living mirror, or a mirror endowed with an internal action, and that it represents the universe according to its point of view and is regulated as completely as is the universe itself. The perceptions in the monad arise from each other according to the laws of the appetites or of the final causes of good and of evil, which consist in observable perceptions, whether regulated or unregulated, in the same way that bodily changes and external phenomena arise from each other according to the laws of efficient causality, that is, of motions. Thus there is a perfect harmony between the perceptions of the monad and the motions of the body, pre-established from the beginning between the system of efficient causes and that of final causes. It is in this that the accord and the physical union of soul and body consist, without either one being able to change the laws of the other. 4. Together with a particular body, each monad makes a living substance. 3 Thus not only is there life everywhere, joined to members or organs, but there are also infinite degrees of it in the monads, some of which dominate more or less over others. But when the monad has organs so adjusted that by means of them the impressions which are received, and consequently also the perceptions which represent these impressions, are heightened and distinguished (as, for example, when rays of light are concentrated by means of the shape of the humors of the eye and act with greater force), then this may amount to sentiment, that is to say, to a perception accompanied by memory - a perception of which there remains a kind of echo for a long time, which makes itself heard on occasion. Such a living being is called an animal, as its monad is called a soul. When this soul is raised to the level of reason, it is something more sublime and is counted among the spirits, as will be explained presently. It is true that animals are sometimes in the condition of simple living beings, and their souls in the condition of simple monads, namely, when their perceptions are not distinct enough so that they can be remembered. This happens in a deep sleep without dreams or in a swoon. But perceptions which have become completely confused must be developed again in animals, for reasons which I shall give below in Section 12. So it is well to make a distinction between perception, which is the inner state of the monad representing external things, and apperception, which is consciousness or the reflective knowledge of this inner state itself and which is not given to all souls or to any soul all the time. 4 It is for lack of this distinction that the Cartesians have made the mistake of disregarding perceptions which are not themselves perceived, just as people commonly disregard imperceptible bodies. It it this too which has made these same Cartesians think that only spirits are monads and that there is no soul in beasts, still less other principles of life. And after having defied the everyday opinion of men too much in denying that beasts have feeling, they adjusted their views too far For references see p. 641
638 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS to popular prejudices, on the other hand, when they confused a long stupor coming from a great confusion of perceptions with death in the rigorous sense, in which all perception would cease. This has confirmed the poorly grounded opinion that certain souls are destroyed and has supported the pernicious view of certain so-called freethinkers who have denied the immortality of our souls. 5. There is a connection between the perceptions of animals which has some resemblance to reason, but it is grounded only on the memory of facts or effects and not on the knowledge of causes. Thus a dog runs away from the stick with which he has been beaten, because his memory represents to him the pain which the stick had caused him. Men too, insofar as they are empiricists, that is to say, in three-fourths of their actions, act only like beasts. For example, we expect day to dawn tomorrow because we have always experienced this to be SO; only the astronomer predicts it with reason, and even his prediction will ultimately fail when the cause of daylight, which is by no means eternal, stops. But reasoning in the true sense depends on necessary or eternal truths, as are those oflogic, number, and geometry, which make the connection of ideas indubitable and their conclusions infallible. Animals in which such consequences cannot be observed are called beasts, but those who know these necessary truths are the ones properly called rational animals, and their souls are called spirits. These souls are capable of performing acts of reflection and of considering what is called 'I', 'substance', 'soul', 'spirit' - in a word, things and truths which are immaterial. It is this which makes us capable of the sciences or of demonstrative knowledge. 6. The investigations of the moderns have taught us, and reason confirms them, that the living beings whose organs are known to us, that is, plants and animals, do not come from putrefaction or chaos, as the ancients believed, but from preformed seeds, and therefore from the transformation of living beings existing prior to them. There are little animals in the seeds of large animals, which assume a new vesture in conception, which they appropriate and which provides them with a method of nourishment and growth, so that they may emerge into a greater stage and propagate the large animal. It is true that the souls of human spermatic animals are not rational and become so only when conception determines them for human nature. Just as animals in general are not completely born in conception or generation, moreover, neither do they completely perish in what we call death, for it is reasonable that what has no natural beginning also has no end within the order of nature. Thus, abandoning their masks or their rags, they merely return, but to a finer stage, on which, however, they can be as sensitive and as well ordered as on the larger one. And what has been said about grosser animals takes place also in the generation and death of spermatic animals themselves, that is, they are the enlargements of other smaller spermatic animals, in proportion to which they may be considered large, for everything in nature proceeds to infinity. Not only souls, therefore, but animals as well, cannot be generated or perish; they are only developed, enveloped, reclothed, stripped, transformed. Souls never leave the whole of their bodies and do not pass from one body to another entirely new to them. Thus there is no metempsychosis, though there is metamorphosis. Animals change, take on, and put off, only parts; in nutrition this taks place little by little and through minute, insensible particles, but continually, while in conception or in death, where much is acquired or lost all at once, it occurs suddenly and noticeably but infrequently. 7. So far we have been speaking simply as natural scientists; now we must rise to
HANOVER UNDER GEORGE LOUIS, 1698-1716 639 metaphysics and make use of the great, but not commonly used, principle that nothing takes place without a sufficient reason; in other words, that nothing occurs for which it would be impossible for someone who has enough knowledge of things to give a reason adequate to determine why the thing is as it is and not otherwise. This principle having been stated, the first question which we have a right to ask will be, 'Why is there something rather than nothing?' For nothing is simpler and easier than something. 5 Further, assuming that things must exist, it must be possible to give a reason why they should exist as they do and not otherwise. 8. Now this sufficient reason for the existence of the universe 'cannot be found in the series of contingent things, that is to say, of bodies and their representations in souls. For since matter is in itself indifferent to motion or rest, and to one motion rather than to another, one cannot find in it a reason for motion and still less for some particular motion. Although the present motion in matter arises from preceding motion, and that in turn from motion which preceded it, we do not get further howe\er far we may 'go, for the same question always remains. The sufficient reason, therefore, which needs no further reason; must qe outside of this series qf contingent things and is found in substance which is the cause of thIs series' or which is a necessary being bearing the reason 'for its existence within itself; otherwise we should not yet have a sufficient reason with which to stop. This final reason for things is called God. 9. This simple primary substance must include eminentIy 6 the perfections contained' in the derivative substances which are its effects. Thus it will have perfect power, knowledge, and will; that is to say, it will have omnipotence, omniscience, and sovereign goodness. And since justice, taken in its most general sense, is nothing but goodness conforming with wisdom, there is also necessarily a sovereign justice in God. The reason which has made things exist through him has also made them depend on him for their existence and operation, and they are continually receiving from him that which causes them to have some perfection. But whatever imperfection remains with them comes from the essential and original limitation of the created beings. 10. It follows from the supreme perfection of God that he has chosen the best possible plan in producing the universe, a plan which combines the greatest variety together with the greatest order; with situation, place, and time arranged in the best way possible; with the greatest effect produced by the simplest means; with the most power, the most knowledge, the greatest happiness and goodness in created things which the universe could allow. For as all possible things have a claim to existence in God's understanding in proportion to their perfections, the result of all these claims must be the most perfect actual world which is possible. Without this it would be impossible to give a reason why things have gone as they have rather than otherwise. 11. The supreme wisdom of God has made him choose especially those laws of motion which are best adjusted and most fitted to abstract or metaphysical reasons. There is conserved the same quantity of total and absolute force or of action, also the same quantity of relative force or of reaction, and finally, the same quantity of directive force. 7 Furthermore, action is always equal to reaction, and the entire effect is always equal to its full cause. It is surprising that no reason can be given for the laws of motion which have been discovered in our own time, and part of which I myself have discovered, by a consideration of efficient causes or of matter alone. For I have found that we must have recourse to final causes and that these laws do not depend upon the principle of necessity, as do the truths of logic, arithmetic, and geometry, but a For references see p. 641
640 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS upon the principle offitness, that is to say, upon the choice of wisdom. This is one of the most effective and obvious proofs of the existence of God for those who can probe into these matters thoroughly. 12. It follows also from the perfection of the supreme Author, not only that the order of the entire universe is the most perfect possible, but also that each living mirror which represents the universe according to its own point of view, that is, each monad or each substantial center, must have its perceptions and its appetites regulated in the best way compatible with all the rest. From this it also follows that souls, that is to say, the most dominant monads, or rather animals themselves, cannot fail to awake from the state of stupor into which death or some other accident may place them. 13. For everything has been regulated in things, once for all, with as much order and agreement as possible; the supreme wisdom and goodness cannot act except with perfect harmony. The present is great with the future; the future could be read in the past; the distant is expressed in the near. One could learn the beauty of the universe in each soul if one could unravel all that is rolled up in it but that develops perceptibly only with time. But since each distinct perception of the soul includes an infinity of confused perceptions which envelop the entire universe, the soul itself does not know the things which it perceives until it has perceptions which are distinct and heightened. 8 And it has perfection in proportion to the distinctness of its perceptions. Each soul knows the infinite, knows everything, but confusedly. Thus when I walk along the seashore and hear the great noise of the sea, I hear the separate sounds of each wave but do not distinguish them; our confused perceptions are the result of the impressions made on us by the whole universe. It is the same with each monad. Only God has a distinct knowledge of everything, for he is the source of everything. It has been very well said that he is everywhere as a center but that his circumference is nowhere, since everything is immediately present to him without being withdrawn at all from this center. 9 14. As for the reasonable soul or spirit, there is something more in it than in monads or even in simple souls. It is not only a mirror of the universe of creatures but also an image of divinity. The spirit not only has a perception of the works of God but is even capable of producing something which resembles them, though in miniature. For not to mention the wonders of dreams in which we invent, without effort but also without will, things which we should have to think a long time to discover when awake, our soul is architectonic also in its voluntary actions and in discovering the sciences according to which God has regulated things (by weight, measure, number, etc.). In its own realm and in the small world in which it is allowed to act, the soul imitates what God performs in the great world. 15. For this reason all spirits, whether of men or of higher beings [genies], enter by virtue of reason and the eternal truths into a kind of society with God and are members of the City of God, that is to say, the most perfect state, formed and governed by the greatest and best of monarchs. Here there is no crime without punishment, no good action without a proportionate reward, and finally, as much virtue and happiness as is possible. And this takes place, not by a dislocation of nature, as if what God has planned for souls could disturb the laws of bodies, but by the very order of natural things itself, by virtue of the harmony pre-established from all time between the realms of nature and of grace, between God as architect and God as monarch, in such a way that nature leads to grace, and grace perfects nature by using it.
HANOVER UNDER GEORGE LOUIS, 1698-1716 641 16. Thus, though reason cannot teach us the details of the great future, these being reserved for revelation, we can be assured by this same reason that things are arranged in a way which surpasses our desires. God being also the most perfect, the happiest, and therefore the most lovable of substances, and true pure love consisting in the state which causes pleasure to be taken in the perfections and the felicity of the beloved, this love must give us the greatest pleasure of which one is capable, since God is its object. 17. And it is easy to love him as we ought if we know him as I have said. For though God is not visible to our external senses, he is nonetheless most love-worthy and gives very great pleasure. We see how much pleasure honors give to men, although they do not consist of qualities which appear to the external senses. Martyrs and fanatics, though the affection of the latter is not well ordered, show what power the pleasure of the spirit has. What is more, even the pleasures of sense are reducible to intellectual pleasures, known confusedly. Music charms us, although its beauty consists only in the agreement of numbers and in the counting, which we do not perceive but which the soul nevertheless continues to carry out, of the beats or vibrations of sounding bodies which coincide at certain intervals. The pleasures which the eye finds in proportions are of the same nature, and those caused by other senses amount to something similar, although we may not be able to explain them so distinctly. 18. It may even be said that the love of God already gives us, here and now, a foretaste of future felicity. And although it is disinterested, by itself it constitutes our greatest good and interest, even when we do not seek these in it and when we consider only the pleasure it gives and disregard the utility it produces. For it gives us a perfect confidence in the goodness of our Author and Master, and this produces a true tranquillity of spirit, not such as the Stoics have who resolutely force themselves to be patient, but by a present contentment which itself assures us of future happiness. And apart from the present pleasure, nothing could be more useful for the future, for the love of God also fulfils our hopes and leads us in the way of supreme happiness, since, by virtue of the perfect order established in the universe, everything is done in the best possible way, as much for the general good as for the greatest particular good of those who are convinced of it and are satisfied by the divine government. This cannot fail to be true of those who know how to love the source of all good. It is true that the supreme happiness (with whatever beatific vision or knowledge of God it may be accompanied) cannot ever be full, because God, being infinite, cannot ever be known entirely. Thus our happiness will never consist, and ought never to consist, in complete joy, which leaves nothing to be desired and which would stupefy our spirit, but in a perpetual progress to new pleasures and new perfections. REFERENCES On the relation between the two works see C. Strack, Ursprung und sachliches Verhiiftnis von Leibnizens sogenannter Monadologie und der Principes de fa nature et de fa grace, Berlin 1915. 1 See also Kabitz in Fischer, p. 772. 2 It is noteworthy that Leibniz here refers to compound substances. Prior to the correspondence with Des Bosses he had generally affirmed the phenomenal nature of bodies, and even in it he ascribed to them only a substantiated and semisubstantial nature. It will be noted that his phenomenalism is not made explicit in Nos. 66 and 67. 3 Leibniz's frequent statement that all nature is alive and no monad without a body is not
642 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS without ambiguity, but his clearest statements, particularly to De Voider and Des Bosses, apply only to the individual monads but not to all composite bodies. Thus every monad is a vital center, but not all composite bodies have a dominant monad; only bodies endowed with life have. 4 On the origin of the distinction between perception and apperception see also p. 353, note 4. In the New Essays (II, 9,4, and 27, 23), where it first appears, the new term is synonymous with consciousness itself, as it is in the Monadology, Sec. 14. Here it is also identified with reflection, or consciousness of the perceptions themselves. This difference has perplexed many interpreters and entered into W. Wundt's attempt to deny the unconscious in Leibniz. 5 That is, analyzable into fewer simple concepts. Something seems to combine being and one. S 'Eminently' is opposed in Scholastic usage to 'formally'. Any quality or agency ascribed to God applies to him in a more exalted sense than the analogous quality or agency as known in man, since God's agency is on another level which our experience cannot reach and is therefore not univocal with its human analogue. 7 See No. 46, the Specimen dynamicum, PartI, and p. 451, note 9. 8 Reading relevees with Erd.; this agrees with the Monadology, Sec. 25. G. has revelies. 9 For the long history of the figure of the infinite sphere, which Leibniz may have learned from Pascal, or from the German Rosicrucians and theosophists, see D. Mahnke, Unendliche Sphiire und Allmittelpunkt, Halle 1937.
67 "THE MONADOLOGY"· 1714 [G., VI, 607-23] 1. The monad which we are to discuss here is nothing but a simple substance which enters into compounds. Simple means without parts. (Theodicy, Sec. to). 2. There must be simple substances, since there are compounds, for the compounded is but a collection or. an aggregate of simples. . 3. But where there are no parts, it is impossible to have either extension, or figure, or divisibility. The monads are the true atoms of nature ; in a word, they 'are the elements of things. 4. We need fear no dissolution in them, and there is no conceivable way in which a simple substance can be destroyed naturally. (Ibid., Sec. 89.) 5. For the same reason there is no way in which a simple substance can have a natural beginning, since it cannot be formed by composition. 6. So one can say that monads can only begin or end all at once, that is, they cannot begin except by creation or end except by annihilation. That which is compounded, instead, begins and ends in parts. 7. There is likewise no way of explaining how a monad can be altered or changed internally by any other creature, since nothing can be transposed in it, and we cannot conceive in it, as we can in composite things among whose parts there may be changes, that any internal motion can be excited, directed, increased, or diminished from without. Monads have no windows through which anything could enter or depart. Accidents cannot be detached from substances and march about outside of substances, as the sensible species of the Scholastics once did. 1 So neither substance nor attribute can enter a monad from without. 8. Yet it is necessary for monads to have some qualities; otherwise they would not even be beings. And if simple substances did not differ by their qualities, there would be no way of perceiving any change in things, since what is in the composite can come only from its simple ingredients; and monads, if they were without qualities, could not be distinguished from each other, especially since they do not differ in quantity. Consequently, assuming a plenum, each place would always receive in any motion the equivalent of what it had already had, and one state of things could not be distinguished from another. 9. It is even necessary for each monad to be different from every other. For there are never two things in nature which are perfectly alike and in which it is impossible to find a difference that is internal or founded on an intrinsic denomination. 2 10. I also take it as agreed that every created being is subject to change, and therefore the created monad also, and further that this change is continuous in each one. 11. It follows from what I have said that the natural changes in monads come from For references see p. 652
644 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS an internal principle, since an external cause could not influence [in/luer dans] their interior. (Ibid., Secs. 396 and 400.) 12. But besides the principle of change there must be some distinguishing detail in that which changes, which constitutes the specific nature and the variety, so to speak, of simple substances. 3 13. This detail must enfold a multitude in the unity or the simple. For every natural change takes place by degrees - something changes and something remains - and as a result there must be a plurality of affections and of relations in the simple substance, even though it has no parts. 14. The passing state which enfolds and represents a multitude in unity or in the simple substance is merely what is called perception. This must be distinguished from apperception or from consciousness, as what follows will make clear. It is in this that the Cartesians made a great riristake, for they disregarded perceptions which are not perceived. It is this, too, which led them to believe that only spirits are monads and that there are no souls in beasts or other entelechies. It led them into the popular confusion of a long stupor with death in a rigorous sense, which made them support the Scholastic prejudice that souls are entirely separate, and even confirmed some ill-balanced minds in a belief in the mortality of the soul. 15. The action of the internal principle which brings about change or the passage from one perception to another can be called appetition. It is true that appetite need not always fully attain the whole perception to which it tends, but it always attains some of it and reaches new perceptions. 16. We ourselves experience a multitude in a simple substance when we find that the slightest thought which we perceive enfolds a variety in its object. Hence everyone who recognizes that the soul is a simple substance should also recognize this multitude in the monad, and Mr. Bayle ought not to find the difficulty in it which he does in his Dictionary, in the article on Rorarius. 4 17. It must be confessed, moreover, that perception and what depends on it are inexplicable by mechanical reasons, that is, by figures and motions. If we pretend that there is a machine whose structure enables it to think, feel, and have perception, one could think of it as enlarged yet preserving its same proportions, so that one could enter it as one does a mill. If we did this, we should find nothing within but parts which push upon each other; we should never see anything which would explain a perception. So it is in the simple substance, and not in the composite substance or machine, that perception must be sought. Furthermore, this is the only thing - namely, perceptions and their changes - that can be found in simple substance. It is in this alone that the internal actions of simple substances can consist. (Ibid., Preface. 5) 18. All simple substances or created monads might be given the name of entelechies, for they have in them a certain perfection (exovUl 7:0 8V7:B'U~). There is in them a certain sufficiency (aimipKBla) which makes them the sources of their internal actions and so to speak, incorporeal automata. (Ibid., Sec. 87.) 19. If we wish to designate by soul everything which has perceptions and appetites in the general sense which I have just explained, all simple substances or created monads could be called souls. But since sentiment is something more than a simple perception, I agree that the general name of monads or entelechies is enough for simple substances which have only perception and that only those should be called souls in which perception is more distinct and accompanied by memory. 6
HANOVER UNDER GEORGE LOUIS, 1698-1716 645 20. For we experience within ourselves a state in which we remember nothing and have no distinguishable perception, as when we fall into a swoon or are overcome by a deep and dreamless sleep. In this condition the soul does not differ sensibly from a simple monad. But since this condition does not last, and the soul emerges from it, the soul is something more. (Ibid., Sec. 64.) 21. It does not follow that during this state the simple substance is without any perception. For the reasons already given, that is not even possible, for it cannot perish and it cannot subsist without some affection, which is nothing but its perception. But when there is a large multitude of small perceptions with nothing to distinguish them, we are stupefied, as when we turn continuously in the same direction several times, so that a dizziness overcomes us and we grow faint and can distinguish nothing. Death can produce this state in animals for a time. 22. Since every present state of a simple substance is a natural consequence of its preceding state, in such a way that the present is great with the future (ibid., Sec. 360), 23. and since we perceive our perceptions when awaking from a stupor, it follows necessarily that we have had these perceptions immediately before, even though we did not then perceive them, for a perception can come naturally only from another perception, just as one motion can come naturally only from another motion (Ibid., Sees. 401-3). 24. From this we can see that if we had nothing distinctive in our perceptions, and nothing lifted out, so to speak, and of a higher flavor, we should always be in a state of stupor. This is the state of the naked monads. 25. We see too that nature has given heightened perceptions to animals by the care she has taken to provide them with organs which gather numerous light rays, or many air waves, so as to give them greater effectiveness through their union. There is something approaching this in smell, taste, and touch and perhaps in many other senses which we do not know. I will explain presently how what occurs in the soul represents what happens in the organs. 26. Memory provides a kind of consecutiveness to souls which simulates reason but which must be distinguished from it. Thus we see that when animals have a perception of something which strikes them and of which they have had a similar perception previously, they are led by the representation of their memory to expect whatever was connected with it in this earlier perception and so come to have feelings like those which they had before. When one shows a stick to dogs, for example, they remember the pain it has caused them and whine or run away. (Ibid., Prelim., Sec. 65.) 27. The strong imagination which strikes and moves them comes either from the magnitude or from the number of the perceptions which preceded it. For often one single strong impression produces at once the effect of a long-formed habit or of many frequently repeated ordinary perceptions. 28. Men act like beasts insofar as the sequences of their perceptions are based only on the principle of memory, like empirical physicians who have a simple practice without theory. We are all mere empirics in three-fourths of our actions. For example, when we expect daylight tomorrow, we act as empiricists, because this has always happened up to the present. Only an astronomer concludes it by reason. 29. But it is the knowledge of necessary and eternal truths which distinguishes us from simple animals and gives us reason and the sciences, lifting us to the knowledge of ourselves and of God. It is this within us which we call the rational soul or spirit. For references see p. 652
646 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 30. It is also by the knowledge of necessary truths and by their abstractions that we rise to reflective acts, which enable us to think of what is called I and to consider this or that to be in us; it is thus, as we think of ourselves, that we think of being, of substance, of the simple and the compound, of the immaterial, and of God himself, conceiving of that which is limited in us as being without limits in him. These reflective acts provide us with the principal objects of our reasonings (Ibid., Preface, 4a). 31. Our reasonings are based upon two great principles: the first the principle of contradiction, by virtue of which we judge that false which involves a contradiction, and that true which is opposed or contradictory to the false (Ibid., Secs. 44 and 196); 32. and the second the principle of sufficient reason, by virtue of which we observe that there can be found no fact that is true or existent, or any true proposition, without there being a sufficient reason for its being so and not otherwise, although we cannot know these reasons in most cases (Ibid., Secs. 44 and 196). 33. There are also two kinds of truths, truths of reasoning and truths of fact. Truths of reasoning are necessary, and their opposite is impossible. Truths of fact are contingent, and their opposite is possible. When a truth is necessary, the reason for it can be found by analysis, resolving it into more simple ideas and truths until we reach the primitive (Ibid., Secs. 170, 174, 189,280-82, and 367; Abr. obj. 3). 34. It is thus that speculative theorems and rules of practice in mathematics are reduced by analysis to definitions, axioms, and postulates. 35. There are, finally, simple ideas which cannot be defined, and there are also axioms and postulates, or in brief, primitive principles, which cannot be proved and need no proof. And these are identical propositions whose opposites contain an explicit contradiction. 36. But a sufficient reason must also be found in contingent truths or truths of fact, that is to say, in the sequence of things distributed through the universe of creatures, whose analysis into particular reasons could proceed into unlimited detail because of the immense variety of things in nature and the division of bodies into the infinite. There is an infinity of shapes and motions, present and past, which enter into the efficient cause of my present writing, and there is an infinity of small inclinations and dispositions of my soul, present and past, which enter into its final cause. (Ibid., Secs. 36,37,44,45,49,52,121,122,337,340, and 344.) \ 37. As all this detail includes other earlier or more detailed contingent factors, each\ of which in tum needs a similar analysis to give its reason, one makes no progress, and the sufficient or final reason will have to be outside the sequence or series of these detailed contingent factors, however infinite they may be. 38. Thus the final reason of things must be in a necessary substance in which the detail of the changes can be contained only eminently, as in their source. It is this substance that we call God. (Ibid., Sec. 7.) 39. Now since this substance is a sufficient reason for all this detail, and the detail . is interconnected throughout, there is only one God, and this God is enough. 40. We may conclude, too, that this supreme substance, being unique, universal, and necessary, and having nothing outside of it which is independent of it, and being a simple consequence of possible being, must be incapable of limits and must contain as much reality as is possible. 41. It follows from this that God is absolutely perfect; perfection being nothing but
HANOVER UNDER GEORGE LOUIS, 1698-1716 647 the quantity of positive reality taken strictly, when we put aside the limits or bounds in the things which are limited. But where there are no bounds, that is, in God, perfection is absolutely infinite. (Ibid., Sec. 22; Preface, 4a.) 42. It also follows that creatures receive their perfections from the influence of God but that their imperfections are due to their own nature, which is incapable of being limitless. For it is in this that they differ from God. (Ibid., Secs. 20,27-31, 153, 167, and 377ff.) This original imperfection of creatures is noticeable in the natural inertia ofthe body. (Ibid., Secs. 30 and 380; Abr. obj. 5. 7 ) 43. It is also true that the source not only of existences but also of essences is in God, insofar as these e~sences are real or insofar as there is something real in possibility. This is because the understanding of God is the region of eternal truths or of the ideas upon which they depend and because without him there would be no reality in possibilities - not only nothing existent but also nothing possible. (Ibid., Sec. 20.) 44. For if there is a reality in the essences or possibilities, or in the eternal truths as well, this reality must be founded on something existent and actual, and therefore in the existence of a necessary being, in whom essence includes existence or in whom it is enough to be possible in order to be actual. (Ibid., Sees. 184, 189, and 335.) 45. Thus God alone, or the necessary being, has the privilege of necessarily existing if he is possible. And since nothing can prevent the possibility of that which is without any limits, without any negation, and consequently without any contradiction, this fact alone suffices to know the existence of God a priori. So we have proved it through the reality of eternal truths.8 But we have also proved it a posteriori, since contingent beings exist, and their final or sufficient reason can be discovered only in a necessary being which has its reason for its existence in itself. 46. We must not imagine as do some, however, that since the eternal truths are dependent upon God, they are arbitrary and dependent on his will, as Descartes and later Mr. Poiret seem to have held. 9 This is true only of contingent truths, whose principle is fitness or the choice of the best; necessary truths, however, depend solely on his understanding and are its internal object. (Ibid., Secs. 180, 184, 185, 335, 351, and 380.) 47. So only God is the primary unity or the simple original substance of which all the created or derivative monads are products, and from whom they are born, so to speak, by continual fulgurations of the divinity from moment to moment, but limited by the receptivity of the created being, for whom it is essential to have limits. (Ibid., Secs. 3~2-91, 398, and 395.) 48. There is in God the power which is the source of everything, there is also the knowledge which contains the variety of the ideas, and finally, there is the will which makes changes or products in accordance with the principle of the best. This corresponds to what is in created monads the subject or basis, the perceptive faculty, and the appetitive faculty. But in God these attributes are absolutely infinite or perfect, and in created monads or entelechies - or perfectihabies, as Hermolaus Barbarus translated this word - they are nothing but imitations in the degree to which the monad has perfection. (Ibid., Secs. 7, 149, 150, and 87.) 49. The created being is said to act outwardly insofar as it has perfection and to suffer from another insofar as it is imperfect. Thus action is attributed to a monad insofar as it has distinct perceptions, and passion insofar as it has confused ones. (Ibid., Secs. 32,66, and 386.) For references see p. 652
648 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 50. One created being is more perfect than another if one finds in it that which will supply a reason a priori for what happens in the other. And it is because of this that it is said to act upon the other. 51. But in simple substances there is only an ideal influence of one monad upon another. This can have its effect only by the intervention of God, insofar as one monad may with reason demand, in the ideas of God, that God should have a concern for it in regulating the rest from the beginning of things. For since a created monad can have no physical influence on the interior of another, it is only in this way that one can be dependent on the other. (Ibid., Sees. 9, 54, 65, 66, and 201; Abr. obj. 3.) 52. It is in this way that actions and passions are mutual among creatures. For God, comparing two simple substances,finds the reasons in each which oblige him to adapt the other to it, with the result that whatever is active in certain respects is passive considered from another point - active insofar as what we distinctly know in it serves as a reason for what happens in another, but passive insofar as the reason for what happens in it is found in what we know distinctly in another. (Ibid., Sec. 66.) 53. Now since there is an infinity of possible universes in the ideas of God, but only one can exist, there must be a sufficient reason for God's choice which determines him to one rather than another. (Ibid., Secs. 8, 10,44,173,196-97,225, and 414--16.) 54. This reason can be found only in the fitness or in the degrees of perfection which these worlds contain, each possible one having a right to claim existence in the measure of the perfection which it enfolds. (Ibid., Secs. 74, 167, 350, 201, 130, 352, 345-46, and 354.) 55. And this is the cause for the existence of the best, which his wisdom causes God to know, his goodness makes him choose, and his power makes him produce. (Ibid., Secs. 8, 78, 80, 84,119,204,206, and 208; Abr. obj. 1,8.) 56. Now this mutual connection or accommodation of all created things to each other and of each to all the rest causes each simple substance to have relations which express all the others and consequently to be a perpetual living mirror of the universe. (Ibid., Secs. 130 and 360.) 57. Just as the same city viewed from different sides appears to be different and to be, as it were, multiplied in perspectives, so the infinite multitude of simple substances, which seem to be so many different universes, are nevertheless only the perspectives of a single universe according to the different points of view of each monad. (Ibid., Sec. 147.) 58. This is the means of obtaining the greatest variety possible, but with tIte great~st possible order; that is to say, this is the means of attaining as much perfectioll as po~sible. (Ibid., Secs. 120,124,241-42,215,243, and 275.) 1 59. It is only this hypothesis, moreover, which I dare say is demonstrated, ~hat exalts the greatness of God as one ought. Mr. Bayle recognized this when he raised objections to it in his Dictionary (article Rorarius), where he was even inclined to believe that I ascribed too much to God, more than is possible. Yet he was unable to set forth any reason why this universal harmony, which results in every substance expressing exactly all the others by means of the relations which it has with them, should be impossible. 60. From what I have been saying, furthermore, we may see the a priori reasons why things could not be otherwise than they are. This is because God has had regard for each part in regulating the whole and in particular for each monad. The nature of
HANOVER UNDER GEORGE LOUIS, 1698-1716 649 the monad being to represent, nothing can keep it from representing only a part of things, though it is true that its representation is merely confused as to the details of the whole universe and can be distinct for a small part of things only, that is, for those which are the nearest or the greatest in relation to each individual monad. 1 0 Otherwise each monad would be a divinity. It is not in the object but in the modification of their knowledge of the object that the monads are limited. They all move confusedly toward the infinite, toward the whole, but they are limited and distinguished from each other by the degrees of their distinct perceptions. 61. In this respect compound beings are in symbolic agreement with the simple. For everything is a plenum, so that all matter is bound together, and every motion in this plenum has some effect upon distant bodies in proportion to their distance, in such a way that every body not only is affected by those which touch it and somehow feels whatever happens to them but is also, by means of them, sensitive to others which adjoin those by which it is immediately touched. It follows that this communication extends to any distance whatever. As a result, every body responds to everything which happens in the universe, so that he who sees all could read in each everything that happens everywhere, and, indeed, even what has happened and will happen, observing in the present all that is removed from it, whether in space or in time. "All things are conspirant", as Hippocrates said. l l But a soul can read within itself only what it represents distinctly; it cannot all at once develop all that is enfolded within it, for this reaches to infinity. 62. Thus, although each created monad represents the whole universe, it represents more distinctly the body which is particularly affected by it and of which it is the entelechy. And as this body expresses the whole universe by the connection between all matter in the plenum, the soul also represents the whole universe in representing the body which belongs to it in a particular way. (Ibid., Sec. 400.) 63. The body belonging to a monad which is its entelechy or soul constitutes what may be called a living being with that entelechy; with a soul it constitutes an animal. Now the body of a living being or an animal is always organic for since every monad is a mirror of the universe in its own way, and the universe is regulated in perfect order, there must also be an order in the being which represents it, that is to say, in the perceptions of the soul and therefore 'also in the body, according to which the universe is represented in it. (Ibid., Sec. 403.)1 64. So each organic body belonging to a living being is a kind of divine machine or natural automaton infinitely surpassing all artificial automata. For a machine made by human art is not a machine in each of its parts; for example, the tooth of a brass wheel has parts or fragments which are not artificial so far as we are concerned, and which do not have the character of a machine, in that they fit the use for which the wheel was intended. But the machines of nature, living bodies, are still machines in their smallest parts, into infinity. It is this that makes the difference between nature and art, that is, between the divine art and ours. (Ibid., Sees. 134, 146, 194, and 403. 12) 65. And the author of nature has been able to practice this divine and infinitely wonderful artisanship because each part of matter not only is infinitely divisible, as the ancients recognized, but also is actually subdivided without end, each part into parts, each of which has its own distinct movement. Otherwise it would be impossible that each part of matter could express the whole universe. (Ibid" Prelim., Sec. 70; Sec. 195.) For references see p, 652
650 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 66. It is clear from this that there is a world of creatures, living beings, animals, entelechies, souls, in the smallest particle of matter. 67. Each part of matter can be thought of as a garden full of plants or as a pond full of fish. But each branch of the plant, each member of the animal, each drop of its humors, is also such a garden or such a pond. 68. And although the earth and the air interspersed between the plants of the garden, and the water interspersed between the fish in the pond, are not themselves plants or fish, they also contain them, though most frequently of a fineness imperceptible to us. 69. Thus there is nothing fallow, sterile, or dead in the universe; no chaos, no confusions, save in appearance. This would be comparable, perhaps, to a pond seen from a distance, in which we should see the confused swarming movements of the fish, so to speak, without seeing the fish themselves. (Ibid., Preface, 5b_6. 13 ) 70. Hence we see that each living body has a dominant entelechy which is the soul in the case of an animal; but the members of this living body are full of other living beings, plants, and animals, each one of which also has its dominant entelechy or soul. 71. But we must not imagine, as some have done who have mi~understood my thought, that each soul' has its own mass or quantity of matter belonging to it or affected by it forever, and that it consequently possesses other inferior living beings forever destined to serve it. For all bodies are in a perpetual flux, like rivers, and parts are passing in and out from them continually. 72. Thus the soul only changes its body little by little and by degrees, so that it is never deprived of all its organs at once; there is often metamorphosis in animals but never metempsychosis or transmigration of souls. Neither are there entirely separated souls or higher spirits [genies] without bodies. God alone is entirely detached from body. (Ibid., Sees. 90 and 124.) 73. It is because of this, too, that there is never complete generation or, strictly speaking, perfect death, consisting in the separation of the soul. What we call generation is a development and an increase, just as what we call death is an envelopment and a diminution. 74. Philosophers have been greatly embarrassed over the origin offorms, entelechies, or souls. Today, however, when exact investigations made on plants, insects, and animals have shown that the organic bodies of nature are never produced from chaos or from putrefaction, but always through seeds in which there is undoubtedly some preformation, it has been concluded not only that the organic body was already there before conception but also that there was a soul in this body and, in a word, that the animal itself was there, so that conception is merely the means by which the animal is prepared for a great transformation by which it becomes an animal of another kind. Something approaching this may even be seen apart from generation, as when worms become flies and caterpillars become butterflies. (Ibid., Sees. 86, 89; Preface; Secs. 90, 187,188,403,86, and 397.) 75. The animals, some of which are raised by means of conception to the level of greater animals, can be called spermatic. But those among them which remain in their own kind - and this is most of them- are born, multiply, and perish like large animals; there is only a small number of chosen ones which pass into a greater theater. 76. This is but half of the truth, however. So I have concluded that if an animal never has a beginning naturally, neither does it end naturally, and that there will be not only no generation but also, rigorously speaking, no total destruction or death.
HANOVER UNDER GEORGE LOUIS, 1698-1716 651 And this a posteriori reasoning, drawn from experience, agrees perfectly with the principles which I have deduced a priori above. (Ibid., Sec. 90.) 77. So it can be said that not only the soul, as mirror of an indestructible universe, is itself indestructible but also the animal itself, although its machine may often perish in part and cast off or take on particular organic coverings. 78. These principles have given me a method for explaining naturally the union or better, the conformity of the soul and the organic body. The soul follows its own laws, and the body its own likewise, and they agree with each other by virtue of the harmony pre-established between all substances, since they are all representations of one and the same universe. (Ibid., Preface; Secs. 340, 352, 353, and 358.) 79. Souls act according to the laws of final causes through their appetitions, ends, and means. Bodies act according to the laws of efficient causes or the laws of motion. And the two kingdoms, that of efficient and that of final causes, are in harmony with each other. 80. Descartes recognized that souls cannot give force to bodies because the same quantity of force is always conserved in matter. He believed, however, that the soul could change the direction of the body. But this was because the law of nature was still unknown in his day, according to which matter conserves also the same total direction. If he had noticed this, he would have fallen upon my system of pre-established harmony. (Ibid., Preface; Secs. 22, 59, 60, 61, 63, 66, 346-47, 354, and 355.) 81. In this system bodies act as if there were no souls (to assume an impossibility), and souls act as if there were no bodies, and both act as if each influenced the other. 82. As for spirits or rational souls, although I find that what I have just been saying is true at bottom of all living beings and animals (that is, that the soul and the animal begin only with the world and come to an end only with the world), yet there is this peculiar thing about rational animals, that their little spermatic animals, as long as they are only this, have only ordinary or sensitive souls, but as soon as the elect among these, so to speak, arrive at human nature through actual conception, their sensitive souls are raised to the level of reason and to the prerogative of spirits. (Ibid., Secs. 91 and 397.) 83. Among other differences which exist between ordinary souls and spirits, some of which I have already pointed out, there is still this: souls in general are living mirrors or images of the universe of created beings, while spirits are also images of divinity itself or of the author of nature, capable of knowing the system of the universe and of imitating it to some extent by means of architectonic samples, each spirit being like a little divinity within its own sphere. (Ibid., Sec. 147.) 84. It is this which renders spirits capable of entering into a kind of society with God and makes his relation to them not merely that of an inventor to his machine (as God is related to other creatures) but also that of a prince to his subjects and even a father to his children. 85. It is easy to conclude from this that the assemblage of all spirits must make up the city of God, that is to say, the most perfect state which is possible under the most perfect of monarchs. (Ibid., Sec. 146; Abr. obj. 2.) 86. This city of God, this truly universal monarchy, is a moral world within the natural world and is the most exalted and the most divine of all of God's works. In it the true glory of God consists, for he would have no glory if his greatness and goodness were not known and admired by spirits. It is also in relation to this divine city For references see p. 652
652 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS that his distinctive goodness is found, whereas his wisdom and power are shown everywhere. 87. As we have established above a perfect harmony between two natural kingdoms, that of efficient and that of final causes, we must also point out here another harmony between the physical kingdom of nature and the moral kingdom of grace, that is to say, between God considered as architect of the machine of the universe and God considered as monarch of the divine city of spirits. (Ibid., Secs. 62, 74, 118, 248, 112, 130, and 247.) 88. The result of this harmony is that things lead to grace by means of the very ways of nature and that this globe, for example, must be destroyed and repaired by natural ways at those times which the government of spirits demands for the punishment of some and the reward of others. (Ibid., Secs.18-19, 110,244,245, and 340.) 89. It can also be said that God as architect satisfies God as lawgiver in everything and that sins must therefore carry their punishment with them by the order of nature, and even by virtue of the mechanical structure of things; and that noble actions, similarly, attain their rewards through ways that are mechanical in relation to bodies, although this cannot and should not always happen at once. 90. Finally, under this most perfect government there will be no good action without reward and no evil action without punishment, and everything must tum out for the well-being of those who are good, that is to say, those who are not dissatisfied in this great state, who trust in Providence after they have done their own duty, who love and imitate the Author of all good as they ought, taking pleasure in the contemplation of his perfections after the nature of the true pure love 14, which makes us find our pleasure in the happiness of the beloved. This it is which makes the wise and virtuous work for all that seems to conform to the divine will, presumptive or antecedent, and yet content themselves with what God causes to happen to them by his will, secret, consequent, and decisive 15; recognizing as they do that if we could sufficiently understand the order of the universe, we should find that it surpasses the desires of the most wise and that it is impossible to make it better than it is, not only for the whole in general, but also for ourselves in particular, if we are attached as we should be to the Author of the whole, not only as to the architect and efficient cause of our being, but also as to our master and final cause, who must be the whole end of our will and can alone make our happiness. (Ibid., Sec. 134 end; Preface, 4; Sec. 278.) * REFERENCES Leibniz's own manuscripts of this work bear no title, but it has been known by this title since Erdmann adopted it in his edition, following the designation of the first published version, a German translation, in 1720. For further considerations see the introduction to No. 66. The references to the Theodicy were added by Leibniz in the first revision. 1 See p. 329, note 30, and p. 461, note 9. 2 See p. 271, note 4, and the reference there to the Introduction. 'Denomination' implies more than 'quality' (in Sec. 8, preceding), for it is a logical term and points to an essence or sufficient reason for changing qualities. 3 The internal principle in Sec. 11 is clearly the law of the individual series, or the individual concept; the detail in that which changes is the particular value of this law or concept which contitutes the changing qualities of the monad. The dynamic parallels to the two concepts are primary and secondary force. Leibniz now proceeds further to divide the details (or secondary
HANOVER UNDER GEORGE LOUIS, 1698-1716 653 force) into aspects of activity and passivity and, from another point of view, into perceptions and the appetites which impel them. Thus he offers a more popular derivation of the organic structure of the monad than in the more critical Scholastic discussions with such men as De Vol der and Des Bosses. 4 See Nos. 52 and 60 above. 5 G., VI, 41ff. 6 Memory is thus still considered by Leibniz as a condition necessary for conscious perceptions (cf. p. 553, note 4). Leibniz has held to this point since 1670, when memory was used to distinguish between matter and mind (No.8, I, Sec. 17). 7 The last sentence appears in the first revision; G. has it in a footnote. S Since the ontological argument here depends upon the principle (in Sec. 44) that the reality of essences or possibilities must be founded upon existence, this can hardly be regarded as the ontological argument in its purity. Thus the emphasis in the argument has shifted since Leibniz's early period (see Nos. 14 and 20) from a consideration of the possibility of the existence of a perfect being to the existence of possibilities. 9 Pierre Poiret (1646-1719) moved from Cartesianism to a theosophic interpretation inspired by Antoinette Bourignon. 10 The relations between monads are not spatial, of course, and therefore do not differ in distance in the phenomenal sense. As Sec. 61 shows, spatial relations are merely symbolic analogies to the ultimate relations of perception. Distance is here a matter of the number of middle terms intervening in the analysis of perceptions. 11 Leibniz writes (Jvp7tvOIa mivm; he makes the same citation in the New Essays, Introduction (G., V., 48). 12 G. omits the references to the Theodicy. 13 G., VI, 40, 44. 14 See p. 430, notes 3 and 9. 15 St. Thomas distinguished (De veritate, Q. XXIII, a, 3c; Summa theologica, I, Q. XIX, a, 6) between the antecedent and consequent will of God. Leibniz's definitions, which modify Thomas', are found in Theodicy, Part I, Sec. 23. God's antecedent will is for the good, absolutely; his consequent will is for the best possible in existing conditions.
68 LETTERS TO NICOLAS REMOND 1714-15 Nicolas Remond, chief counselor ofthe Duke ofOrleans and brother ofthe mathematician Remond de Monmort, was a courtier of wide interests and attainments, whose correspondence with Leibniz, opened through the mediation of Pierre Coste in 1713, constitutes a critical and philosophical miscellany of considerable interest for the closing years of Leibniz's life. He seems to have looked to Remond in Paris, as to Eugene of Savoy in Vienna, for the propagation of his ideas in the circles of the powerful and influential. The correspondence begins with Remond's account ofhis interest in Plato. [G., III, 605-7] Vienna, January 10,1714 ... I find it natural that you have enjoyed some of my thoughts after having penetrated into Plato's, an author who has meant much to me and who deserves to be systematized. I believe that I can carry out the demonstration of truths which he has merely advanced. Having followed his steps and those of certain other great men, I flatter myself to have profited by them and to have penetrated, at least to a point, the bright temples of wisdom: Edita doctrina, sapien tum templa serena. 1 This relates to general truths which do not depend upon facts but which are nonetheless, in my opinion, the key to the knowledge which judges facts. I should venture to add that if I had been less distracted, or if I were younger or had talented young men to help me, I should still hope to create a kind of universal symbolistic [specieuse generale] in which all truths of reason would be reduced to a kind of calculus. At the same time this could be a kind of universal language or writing, though infinitely different from all such languages which have thus far been proposed, for the characters and the words themselves would give directions to reason, and the errors - except those of fact - would be only mistakes in calculation. It would be very difficult to form or invent this language or characteristic but very easy to learn it without any dictionaries. When we lack sufficient data to ar,rive at certainty in our truths, it would also serve to estimate degrees of probability and to see what is needed to provide this certainty. Such an estimate would be most important for the problems of life and for practical considerations, where our errors in estimating probabilities often amount to more than a half.... ... Besides always taking care to direct my study toward edification, I have tried to uncover and unite the truth buried and scattered under the opinions of all the different philosophical sects, and I believe I have added something of my own which takes a few steps forward. The circumstances under which my studies proceeded from my earliest youth have given me some facility in this. I discovered Aristotle as a lad, and even the
HANOVER UNDER GEORGE LOUIS, 1698-1716 655 Scholastics did not repel me; even now I do not regret this. But then Plato too, and Plotinus, gave me some satisfaction, not to mention other ancient thinkers whom I consulted later. After having finished the trivial schools 2, I fell upon the modems, and I recall walking in a grove on the outskirts of Leipzig called the Rosental, at the age of fifteen, and deliberating whether to preserve substantial forms or not. Mechanism finally prevailed and led me to apply myself to mathematics. It is true that I did not penetrate into its depths until after some conversations with Mr. Huygens in Paris. But when I looked for the ultimate reasons for mechanism, and even for the laws of motion, I was greatly surprised to see that they could not be found in mathematics but t~at I should have to return to metaphysics. This led me back to entelechies, and from the material to the formal, and at last brought me to understand, after many corrections and forward steps in my thinking, that monads or simple substances are the only true substances and that material things are only phenomena, though well founded and well connected. Of this, Plato, and even the later Academics and the skeptics too, had caught some glimpses, but these successors of Plato did not make as good use of it as did he himself. I have found that most of the sects are right in a good part of what they propose, but not so much in what they deny. The formalists, Platonists and Aristotelians, for example, are right in seeking the source of things in final and formal causes. But they are wrong in neglecting efficient and material causes and in inferring from this, as did Henry More in England and certain other Platonists, that there are phenomena which cannot be explained mechanically. The materialists, on the other hand, or those who accept only a mechanical philosophy, are wrong in rejecting metaphysical considerations and trying to explain everything in terms of sense experience. I flatter myself to have penetrated into the harmony of these different realms and to have seen that both sides are right provided that they do not clash with each other; that everything in nature happens mechanically and at the same time metaphysically but that the source of mechanics is in metaphysics. It was not easy to uncover this mystery, because there are few men who take the pains to combine both types of study. Descartes did it, but not thoroughly enough. He went too fast in setting up most of his doctrines; one may say that his philosophy is the entrance hall to the truth. What held him back most was that he did not know the true laws of mechanics or of motion; these could have put him back on the track. Mr. Huygens was the first to see them, though imperfectly, but he had no taste for metaphysics, any more than did other capable men who have followed him in investigating this subject. I have observed in my book that if Descartes had seen that nature conserves not only the same force but also the same total directiqn in the laws of motion, he would not have held that the soul can change the direction 9f the body more easily than its force, and he would have gone straightway to the system. of pre-established harmony, which is a necessary conclusion from the conservation of both force and direction. 3 ••• II [G., III, 611-13] Vienna, March 14, 1714 ... If I have succeeded in arousing men of excellence to cultivate the infinitesimal calculus, this is because I have been able to give some important examples of its For references see p. 660
656 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS usefulness. When I first told Mr. Huygens something about it in my letters, he scorned it; he did not think there was anything mysterious in it until he saw its surprising applications, which led him to study it just before his death - this man whose preeminent merit almost gave him the right to distrust everything which he himself did not know. I have spoken to the Marquis de I'Hospital and others about my universal symbolistic, but they have paid no more attention to it than if I had told them about a dream I had dreamed. I should have to support it too by some obvious application, but to achieve this it would be necessary to work out at least a part of my characteristic - a task which is not easy, especially in my present condition and without the advantage of discussions with men who could stimulate me and help me in work of this nature. The source of our difficulties with the composition of the continuum comes from the fact that we think of matter and space as substances, whereas in themselves material things are merely well-regulated phenomena, and space is exactly the same as the order of coexistence, as time is the order of existence which is not simultaneous. 4 Insofar as they are not designated in extension by factual phenomena, parts consist only in possibility; there are no parts in a line except as there are fractions in unity. But if we assume that all possible points actually exist in the whole - as we should have to say if this whole were a substantial thing composed of all its parts - we should be lost in an inextricable labyrinth. I once said something about this to Mr. Hugony, who writes me that he has the honor of your acquaintance. He has also seen my rather extensive thoughts on Locke's work on the human understanding. I have a repugnance against publishing refutations of dead authors, however, for such refutations should appear during their lives and be sent to the authors themselves. Some slight comments escaped me, I do not know how, and were carried to England by a relative of the late Mr. Burnet, Bishop of Salisbury. Mr. Locke saw them and spoke of them with disdain in a letter to Mr. Molyneux, which is found with others in Locke's posthumous letters. I did not know of his opinion until after this letter was published, but I am not surprised, for our principles differed a little too widely, and those which I advanced must have seemed paradoxical to him. But a friend who is inclined to favor me rather than Locke tells me that what was insetted of my reflections seemed to him the best in the collection. s Since I have not seen it, I cannot confirm his judgment. Mr. Locke had subtlety and skill and a kind of superficial :metaphysics for which he was able to secure acclaim, but he was ignorant of the math~matical method. It is too bad that Pascal, a mind at once outstanding in mathematics and metaphysics, grew, weak too soon, as Mr. Huygens once told me, because of too persistent labors and t~p much pre-occupation with theological works with which he might have secured the ~rplause of a large party if he had been able to finish them. He even gave himself up tq austerities which could not have helped profound thinking, and even less his healthl His nephew, Mr. Perier, once gave me an excellent work by his uncle on conic section~ to read and arrange; I hoped that it would be published at once. It would have conserve~ for him the honor of originality in matters which deserve such pains.. ,. III [G., III, 618-21] Vienna, July, 1714 ... It is true that my Theodicy does not suffice to present my system as a whole. But if
HANOVER UNDER GEORGE LOUIS, 1698-1716 657 it is joined with what I have published in various journals, those of Leipzig, Paris, and those of Mr. Bayle and Mr. Basnage, it will not fall far short of doing so, at least for the principles .... Mr. Wolff has adopted some of my opinions, but since he is very busy with teaching, especially in mathematics, and we have not had much correspondence together on philosophy, he can know very little about my opinions beyond those which I have published. I have seen some of the things which young men have written under him; I found much that is good in them, yet there were points with which I did not agree. So if he has written something in the soul, whether in German or some other language, I shall try to see it and tell you about it .... When I was young, I found some pleasure in the Lullian art, yet I thought also that I found some defects in it, and I said something about these in a little schoolboyish essay called On the Art o/Combinations, published in 1666, and later reprinted without my permission. But I do not readily disdain anything - except the arts of divination, which are nothing but pure cheating - and I have found something valuable, too, in the art of Lully and in the Digestum sapientiae of the Capuchin, Father Ives, which pleased me greatly because he found a way to apply Lully's generalities to useful particular problems. But it seems to me that Descartes had a profundity of an entirely different level. In spite of the advancement which much of our knowledge has received from it, however, his philosophy also has its defects, of which you cannot be unaware by this time. As for Gassendi, of whom you ask my opinion, I find that he has great and wide knowledge and is well versed in his reading of the ancients and in both secular and ecclesiastical history and all classes of learning. But his thoughts satisfy me less now than they did when I first began to drop Scholastic views in my own schoolboy days. Since the atomic theory satisfies the perceptual imagination, I gave myself to it, and it seemed to me that the void of Democritus or Epicurus, together with their incorruptible atoms, would remove all difficulties. It is true that this hypothesis can satisfy mere physical scientists, and assuming that there are such atoms and giving them suitable motions and figures, there are few material qualities which they could not explain if we knew enough of the details of things. So the philosophy of Gassendi could be used to introduce young students to the knowledge of nature, if they were told that the void and the atoms were used merely as a hypothesis and that they might someday fill this void with a fluid so subtle that it could hardly affect phenomena and also that the permanent rigidity of the atoms must not be taken too rigorously. Having pushed my own thinking further, however, I have found that the void and the atoms cannot subsist at all. Some letters which I exchanged with Mr. Hartsoeker have been published in the Memoires de Trevoux, in which I propose certain general reasons drawn from higher principles, which refute atoms. 6 I could offer still others, for my whole system is opposed to them. As concerns the disputes between Gassendi and Descartes, I find that Gassendi was right in rejecting some alleged demonstrations of Descartes about God and the soul. Fundamentally, however, I believe that the opinions of Descartes are the better, even though they have not been sufficiently demonstrated. Gassendi, instead, seems to me to waver too much on the nature of the soul and, in a word, on natural theology. It appears from a letter of Mr. Locke to Molyneux which is printed in Locke's posthumous correspondence that this able Englishman could not willingly endure For references see p. 660
658 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS criticism. Since his reply to my criticisms had not been communicated to me, he did not make it possible to answer him. I do not know whether my comments are found in this collection in their entirety. In my Theodicy I have expressed my opinion on the question of the action of God and creatures, which is being so actively discussed now. If I am to examine the matter more deeply, it seems to me that I shall have to hold to what I have said there. But I should not be unwilling, some day, to examine the criticisms against Malebranche and his replies to them. These questions lack clarity because we do not have good definitions .... IV [G., III, 634-40] Hanover, February 11,1715 Your letters always reveal your kindness and intelligence alike; I should like to deserve the former and to satisfy the latter. The lack of confidence which I feel about my health has prevented me from accompanying Her Highness, the Princess of Wales. Indeed, the gout has since seized me; it is not so very painful, but it prevents me from working outside my study, where I always find time too short, and am therefore never bored. This is a joy in my misfortune. I come to your difficulties, and I thank you for stating them, Sir, for I ask for nothing more than to receive objections from people of your sincerity and penetration. 1. As for metempsychosis, I believe that the universal order does not permit it; it demands that everything should be explicable distinctly and that nothing should take place in a leap. But the passage of the soul from one body to another would be a strange and inexplicable leap. What happens in an animal at present happens in it always; that is, the body is in continuous change like a river, and what we call generation or death is only a greater or quicker change than ordinary, as would be a waterfall or cataract in a river. But these leaps are not absolute and of the kind which I reject, as would be that of a body which went from one position to another without passing through the intervening space. Such leaps are prohibited not only in motion but also in the whole order of things or of truths. This is why I have shown, in the letters to Mr. Hartsoeker recently printed in the Memoires de Trevoux, that the assumption of a void and atoms would lead us to such leaps. But just as there are certain outstanding points in a geometric curve which are called summits, bend points, points of return, or some other thing, and as there are curves which contain an infinity of them, even so there must be conceived in the life of an animal or a person times of extraordinary change which still fall within the general rule - as the distinctive points of a curve can be determined by its general nature or its equation. We can always say of an animal that everything is just as it is now; the difference is only that of more or less. 2. Since it is possible to conceive that by a development and change of matter the machine which constitutes the body of a spermatic animal can become such a machine as is necessary to form the organic body of man, it is also necessary for a soul which is only sensitive to become a reasonable soul, because of the perfect harmony between the soul and the machine. But since this harmony is pre-established, the future state will already be contained in the present, and a perfect intelligence would recognize the future man far in advance in the present animal, as much in its soul alone as in its body alone. Thus a mere animal will never become a man, and the human spermatic animals
HANOVER UNDER GEORGE LOUIS, 1698-1716 659 which do not pass into this great transformation through conception are mere animals. 3. There are undoubtedly a thousand derangements, a thousand disorders, in particular. But it is impossible that there should be any in the whole, even in each monad, since each monad is a living mirror of the universe according to its point of view. It is impossible that the universe as a whole should not be well regulated, since the superiority of its perfections is the reason for the existence of this system of things in preference to any other possible system. Thus the disorders must exist only in the parts. Just so there are geometric curves the parts of which are irregular, but, when the entire curve is considered, one finds it to be perfectly regulated according to its equation or general nature. So all these particular disorders are redressed with benefit in the whole, even in each monad. 4. As for the inertia of matter, since matter itself is nothing but a phenomenon though well founded - which results from the monads, this is also true of inertia, which is a property of this phenomenon. It is necessary that matter should seem to be something which resists motion and that a small body in motion or with force could not impart it to a great body at rest without losing its own; otherwise the effect would exceed the cause, that is, there would be more force in the succeeding state than in the preceding one. Thus it would appear that matter is something which resists the motion which one tries to impart to it. But in the interior of things, since absolute reality rests only in the monads and their perceptions, these perceptions must be well regulated; that is, the rules of fitness must be observed, one of which orders that the effect must not exceed its cause. If matter were a substance, as it is commonly thought to be, it could not (without a miracle) observe the rules of fitness, and left to itself, it would observe certain brute laws depending upon a mathematical necessity and absolutely separated from experience. I said something about this some years ago in one of the Paris journals, in reply to the Abbe Catelan, I believe, and I regret not being able now to give you the year and the number. 7 Furthermore, since all monads (except the primitive one) are subject to passions, they are not pure forces; they are the foundation not only of actions but of resistance and passivity, and their passions are found in their confused perceptions. It is in this that matter or the numerically infinite is involved. You see, Sir, that I make an effort always to satisfy you, and as you see, by using the same principles. But I do not know if I have succeeded. If there remain difficulties for you, the more you explain them, the more I shall be in a position to enter into them and either give up my view or satisfy you. I have always been most satisfied, from my very youth, with the ethics of Plato and in some ways with his metaphysics as well; these two sciences demand each other's company, as do mathematics and physics. If someone were to reduce Plato to a system, he would render a great service to mankind, and it would then be clear that my own views approach his somewhat. The late Mr. Boileau spoke a little too much like a Jansenist when he called the ancients "these damned ancients". The Jesuits are more reasonable in this matter. But I believe that Boileau was trying to jeer. When I was a young boy, the students of my day sang: "Summus Aristoteles, Plato, et Euripides, ceciderunt in profundum." 8 When I made my comments on the little work on the uses of raillery, I did not know that Lord Shaftesbury was its author. Nor did I give my notes to anyone, contenting myself with reading them to Madame the Electress. I found afterward that Lord For references see p. 660
660 LE'IBNIZ: PHILOSOPHICAL PAPERS AND LETTERS Shaftesbury had corrected himself remarkably as his thought progressed and that from a Lucian he had become a Plato - certainly an unusual metamorphosis, and one which made me regret his loss greatly. Also, I spoke in an entirely different tone in commenting on his Characteristics. 9 I shall send you a copy of my first comments, however. But here are some slight reflections of an entirely different nature which I take the liberty of sending you, Sir, and I beg you, after having read them and even having them copied, if you wish, to put them in the letter by quick post addressed to the Abbe de St.-Pierre; I pray you to have this sealed and sent thus to the Abbe Varignon along with the letter for him. For it is he who sent me the letter of the Abbe de St.-Pierre, along with his work on the Project for Perpetual Peace, about which the author had asked my opinion. This project shows excellent intentions and contains sound reasoning. 10 It is very certain that, if men wished, they could free themselves of these three scourges - war, pestilence, and famine. As for the last two, every sovereign wants this, but against war this accord of sovereigns is still lacking and is difficult to obtain. This interesting subject could receive very great elaboration, particularly through historical studies .... REFERENCES Lucretius De rerum natura ii. That is, the Latin schools preparatory to the university. The curriculum of the Nicolai School in Leipzig, while not conforming completely to the medieval trivium, still consisted of Latin and Greek, rhetoric, and logic, together with Scholastic theology. Kabitz has shown that Leibniz's memory was at fault in setting his decision at so early an age; he was probably 17. 3 Theodicy, Part I, Sec. 61 ; cf. Monadology, Sec. 80. 4 The sentence underscored by Leibniz is in Latin. 5 The reference is to Some Familiar Letters between Mr. Locke and Several of His Friends, which appeared in London in 1708. It contained Re/lexions de M. L. sur /' Essai de /' entendement humain de M. Locke, written in 1696 and sent to Thomas Burnet (G., V., 14-19). 6 See p. 628, note 12. 7 The reply to Catelan was made, not in a Paris journal, but in Bayle's Nouvelles de fa republique des fettres, in 1687 (G., III, 407-17). 8 "Aristotle, Plato, and Euripides, all together, have fallen into the depths." 9 See No. 65 for Leibniz's notes on the Characteristics. His earlier comments on Shaftesbury's Letter on Enthusiasm (including the Uses of Raillery) are found in G., III, 407-17. 10 Leibniz's Observations sur Ie projet d'une paix perpetuelle de M. l' Abbe de Saint-Pierre was published by Des Maizeaux in 1720. 1 2
69 LETTERS TO LOUIS BOURGUET 1714-15 An early supporter of Leibniz's views, with a keen interest in their applications to natural science, Louis Bourgu,;{ (1678-1742) was a merchant and scholar of broad interests who lived in Venice from 1711 to 1715. The correspondence of the two men began in 1709 on matters relating to the origin of the alphabet, proceeded to problems of the Theodicy, and later raised important questions about Leibniz's consistency in matters of physics, biology, and historical change. [G., III, 572-76] Hanover, December ... , 1714 I have at last received the letter which you sent by Mr. Hermann, and I am pleased to see your comments on my Theodicy. I quite agree that the idea of possibles necessarily implies the idea of the existence of a being who could produce the possible. But the idea of possibles does not at all imply the existence itself of this being, as you seem to hold when you say, "If there were no such being, nothing would be possible." In order for the thing to be possible, it suffices that a being should be possible capable of producing the thing. Generally speaking, if a thing is to be possible, it suffices that its efficient cause should be possible; I make an exception of the supreme efficient cause, which must exist in fact. But this belongs to another chapter - that nothing would be possible if the necessary being did not exist. This is because the reality of possibles and of eternal truths must be founded upon something real and existent. I do not agree that "in order to know of the romance if 'Astrea' is possible, it is necessary to know its connections with the rest of the universe". It would indeed be necessary to know this if it is to be compossible with the universe, and as a consequence to know if this romance has taken place, is taking place, or will take place in some corner of the world, for surely there would be no place for it without such connections. And it is very true that what is not, never has been, and never will be is not possible, if we take the possible in the sense of the compossible, as I have just said. It may be that Diodorus, Abelard, Wycliffe, and Hobbes had this idea in their heads without completely untangling it. But whether the 'Astrea' is possible in an absolute sense is another question, to which I answer 'Yes', because it does not imply any contradiction. Yet in order for this novel to exist in fact, it would be necessary for the rest of the universe also to be entirely different from what it is - and it is possible that it should be otherwise. I am in no greater agreement, Sir, with your added remark that, "in order to be sure that there is an infinity of possible worlds, we should have to think of them as ended and determined". This comes from the same confusion of possibles for compossibles. When you say that "one world that is infinite (in every respect) must in a sense include all possible worlds", I agree - in the sense which I have given, taking possibles to mean compossibles. For references see p. 665
662 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS You also say that "one infinite series contains all possible numbers". I cannot agree with this either, for the series of square numbers is infinite, yet it does not contain all possible numbers. You add to this the words: "If one considers the universe as a collection, one cannot say that there could be many worlds in it." This would be true if the universe were a collection of all possibles, but it is not, since all possibles are not compossible. Thus the universe is a collection of a certain order of compossibles only, and the actual universe is a collection of all the possibles which exist, that is to say, those which form the richest composite. And since there are different combinations of possibilities, some of them better than others, there are many possible universes, each collection of compossibles making up one of them. I can see no reason why "one cannot say in a rigorous sense that our intellects conceive of possibilities which will never exist". Perhaps there are figures of geometry and of surd numbers which have never existed and never will. Are they any the less possible, that is to say, less knowable? "Everything which comes from God (you say) necessarily bears the characteristics of order, and consequently is admitted to existence as the product of his perfections." These are your words, with which I agree. They prove that only the best exists but not that only the best is possible - unless you change the meaning of terms. I call possible anything which is perfectly conceivable and which, as a result, has an essence or an idea, without raising the question of whether the rest of the world permits it to become existent. So far I have given an exact analysis of your objections, after which there is no need to run through what you say about the actions of God and of intelligent creatures, about a private man becoming king, about the journey of someone like Bacchus or Hercules to India, about the possibility of sin, etc. It seems to me that these objections are the aftereffects of reading Mr. Poiret. But when you say that "to hold that a world without evil, preferable in order to ours is impossible, is to let Mr. Bayle win", I do not rightly understand the reasons which you offer, for what you say contains no 'becauses' or 'therefores'. So I do not consider it an objection. You add that "evil counts for nothing in the decisions of God". If this is understood as you seem to explain it a little later, that "the consideration of evil is not great enough to counterbalance the good", I agree with it. In this way the striving for the greatest good still involves the admission of moral evil, though it seems that you would prefer to agree to this only for metaphysical evil, or at most for some physical evil, though you add no reason for this limitation. "As for metaphysical evil (you say) I do not consider it as evil." But if you admit that there is metaphysical good, Sir, the privation of this good will be metaphysical evil. When an intelligent being loses his understanding without any pain and without sin - and therefore without any physical or moral evil - do you not consider this as an evil? In any case you would merely be changing. the meaning of terms. So I find, Sir, that you could have satisfied all your doubts if you had taken the pains to think carefully about what I have already said. Yet I am glad that I have been able to show you this. What you say about the development of life seems to me well taken. Those human seminal animals which never attain a development of reason do not have this reason enveloped within them. In the way in which I define perception and appetite, all monads must necessarily be endowed with them. I hold perception to be the representation of plurality in the
HANOVER UNDER GEORGE LOUIS, 1698-1716 663 simple, and appetite to be the striving from one perception to another. But these two things occur in all monads, for otherwise a monad would have no relation to the rest of the world. I do not see how you can deduce any Spinozism from this; to do so is to jump at conclusions. On the contlary, it is through these very monads that Spinozism is destroyed, for there are just as many true substances, as many living mirrors of the universe which subsist always, or as many concentrated universes, as there are monads; according to Spinoza, on the contrary, there is only one substance. He would be right if there were no monads; then everything except God would be of a passing nature and would vanish into simple accidents or modifications, since there would be no substantial foundation in things, such as consists in the existence of monads .... II [G., III, 580-83] Hanover, August 5,1715 ... You are right, Sir, in taking offense at the none too courteous remarks of the author of the Preface to Mr. Newton's second edition 1, and I am astonished that Mr. Newton let it pass. They should have spoken of Mr. Descartes with more respect, and with more moderation of his followers. As far as I and my friends are concerned, whom they also had in mind, they are angry because their alleged 'attractive force' was criticized in the Leipzig Acts, though with much restraint, as being merely a revival of chimeras which had already been banned. They commit a shrewd sophism to give themselves an air of reasonableness and to make us appear in the wrong, as if we were opposing those who assume gravity, without giving a reason for it. This is not at all true; we rather disapprove of the method of those who assume irrational qualities, as the Scholastics once did, that is, primary qualities which have no natural reason, to be explained by the nature of the subject to which the equality must belong. We agree and maintain with them, and have maintained even before they published their view, that the great globes of our system, having a certain magnitude, attract each other. But since we hold that this can happen only in a way that has an explanation, namely, by the impact of more subtle bodies, we cannot admit that attraction is a primary property essential to matter, as these gentlemen claim. It is this opinion which is false, based on a hasty judgement, and incapable of being proved by phenomena. This error has produced their second one, namely, that there must necessarily be a vacuum. They see rightly that their pretended mutual attraction between all the parts of matter would be useless and without effect if everything were full. I will not reply to men who attack me in a crude and unkind manner. According to these authors, substances would not only be unknown to us, as you well remark, Sir; it would even be impossible for anyone, whoever he might be, to know them. God himself could not know them if their nature is such as these men say. The only thing they can reply to this with any appearance of reason will be that God makes them act in this way by a miracle or better, that he acts for them. So we should have to return to the Mosaic philosophy of Robert Fludd, which Gassendi gave its fitting treatment in a special work. 2 Similarly, when Roberval said, in his Aristarque, that the planets attract each other - a remark which he may have understood in its right sense - Descartes, taking it in the sense of our new philosophers, made himself merry over it in a letter to Father Mersenne. 3 You would oblige me by telling me where Mr. Clarke, Mr. Ditton, and others make For references see p. 665
664 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS use of the principle which I have put forward - that God has chosen the best possible plan. I am too busy to be able to do enough reading. Of what the perception of plants consists, we cannot say; indeed, we do not even have any good conception of that of animals. But it is enough to say that the plant has a variety in unity and therefore has a perception; and it is enough that it has a tendency toward new perceptions and therefore appetite, in the general sense in which I use these terms. Mr. Swammerdam has supplied observations which show that insects are close to plants with respect to their organs of respiration and that there is a definite order of descent in nature from animals to plants. But perhaps there are other beings between these two. As for the nature of succession, where you seem to hold that we must think of a first, fundamental instant, just as unity is the foundation of numbers and the point is the foundation of extension, I could reply to this that the instant is indeed the foundation of time but that since there is no one point whatsoever in nature which is fundamental with respect to all other points and which is therefore the seat of God, so to speak, I likewise see no necessity whatever of conceiving a primary instant. I admit, however, that there is this difference between instants and points - one point of the universe has no advantage of priority over another, while a preceding instant always has the advantage of priority, not merely in time but in nature, over following instants. 4 But this does not make it necessary for there to be a first instant. There is involved here the difference between the analysis of necessities and the analysis of contingents. The analysis of necessities, which is that of essences, proceeds from the posterior by nature to the prior by nature, and it is in this sense that numbers are analyzed into unities. But in contingents or existents, this analysis from the posterior by nature to the prior by nature proceeds to infinity without ever being reduced to primitive elements. Thus the analogy of numbers to instants does not at all apply here. It is true that the concept of numbers is finally resolvable into the concept of unity, which is not further analyzable and can be considered the primitive number. But it does not follow that the concepts of different instants can be resolved finally into a primitive instant. Yet I do not venture to deny that there may be a first instant. Two hypotheses can be formed one that nature is always equally perfect, the other that it always increases in perfection. If it is always equally perfect, though in variable ways, it is more probable that it had no beginning. But if it always increases in perfection (assuming that it is impossible to give it its whole perfection at once), there would still be two ways of explaining the matter, namely, by the ordinates of the hyperbola B or by that of the triangle C (Figure 38). According to the hypothesis of the hyperbola, there would be no beginning, and the instants or states of the world would have been increasing in perfection from all eternity. But, according to the hypothesis of the triangle, there would have been a beginning. The hypothesis of equal perfection would be that of rectangle A. I do not yet see any way of demonstrating by pure reason which of these we should choose. But though the state of the world could never be absolutely perfect at any particular instant whatever according to the hypothesis of increase, nevertheless the whole actual sequence would always be the most perfect of all possible sequences, because God always chooses the best possible. When I say that unity is not further analyzable, I mean that it cannot have parts whose concept is simpler than it. Unity is divisible but not resolvable, for fractions, which are parts of unity, have less simple concepts than whole numbers, which are
HANOVER UNDER GEORGE LOUIS, B ! I I I A I 1698-1716 665 c I ~ I I I I I I Fig. 38. less simple than unity, since whole numbers always enter into the concepts offractions. Many who have philosophized about the point and about unity in mathematics have become confused by failing to distinguish between analysis into concepts and division into parts. Parts are not always simpler than wholes, though they are always less than the whole .... REFERENCES The second edition of the Principia appeared in 1713. It was edited by Roger Cotes, one of the ablest and most careful of England's younger mathematicians. The bitterness ofthecontroversy over the founding of the calculus was shown in the Preface and is reflected in this letter. 2 On Fludd see p. 412, note 37. Fludd's views were attacked, and a mathematical theory of physical method defended, by both Kepler and Gassendi, the latter in his Epistolica exercitatio 1 in qua praecipua principia philosophiae Roberti Fluddi reteguntur (1630). 3 Descartes to Mersenne, Apri120, 1646 (Correspondence, ed. Adam and Tannery, IV, 392-94, 397-403). 4 The irreversibility of temporal series is thus implicit in Leibniz's logic of existence.
70 THE METAPHYSICAL FOUNDATIONS OF MATHEMATICS After 1714 In spite of the distractions of which he complained in the last years of his life, especially the burdensome history of the House of Brunswick of which he was never free, Leibniz had occasion to return to his earlier studies in mathematics and logic. This paper, first published from the Hanover manuscripts by Gerhardt, continues and pushes to a higher degree of generality the geometrical studies of 1679 (No. 27). It is part of an effort to base a universal mathematical doctrine of quantity and quality, space and time, upon the relations and processes of the universal characteristic. The relations of similarity and congruence used in the earlier studies are combined in those of homogeneity, and the principle of continuity is generalized into homogony. Specifically, algebra and analytic geometry on the one hand, and Leibniz's own geometry of situation on the other, are presented as special determinations of his science of characters, the former based on quantity, the latter on quality. [OM., VII, 17-29] In his Latin course in mathematics (see the Acta eruditorum for 1714), the distinguished mathematician Christian Wolff has recently mentioned certain ideas of mine about the analysis of axioms and the mathematical nature of similarity and has explained them in terms of his method. 1 I should like therefore to present here, lest they be lost, certain views which I worked out some time ago, from which it will be clear that there is an art of analysis more inclusive than mathematics, from which mathematical science derives its most beautiful methods. To do this I shall have to introduce a somewhat higher order of principles. If a plurality of states of things is assumed to exist which involve no opposition to each other, they are said to exist simultaneously. Thus we deny that what occurred last year and this year are simultaneous, for they involve incompatible states of the same thing. If one of two states which are not simultaneous involves a reason for the other, the former is held to be prior, the latter posterior. My earlier state involves a reason for the existence of my later state. And since my prior state, by reason of the connection between all things, involves the prior state of other things as well, it also involves a reason for the later state of these other things and is thus prior to them. Therefore whatever exists is either simultaneous with other existences or prior or posterior. Time is the order of existence of those things which are not simultaneous. Thus time is the universal order of changes when we do not take into consideration the particular kinds of change. Duration is magnitude of time. If the magnitude of time is diminished uniformly and continuously, time disappears into a moment, whose magnitude is zero. Space is the order of coexisting things, or the order of existence for things which are simultaneous. In each of the two orders - that of time and that of space - we can judge
HANOVER UNDER GEORGE LOUIS, 1698-1716 667 relations of nearer to and farther from between its terms, according as more or less middle terms are required to understand the order between them. Thus two points are nearer if the maximally determined intervening forms arising from them produce a simpler configuration. Such an interval of maximum determination, that is, the minimum and at once the most conformal figure made by the intervening terms is the simplest path from one to the other; in the case of points this is the straight line, which is shorter between nearer points. 2 Extension is magnitude of space. It is wrong to confuse extension with what is extended, as is commonly done, and so to consider it as a substance. If the magnitude of space is decreased continuously and uniformly, it disappears in a point which has no magnitude. Situs is a mode ofcoexistence. Therefore it involves not only quantity but also quality. Quantity or magnitude is that in things which can be known only through their simultaneous compresence - or by their simultaneous perception. Thus it is impossible for us to know what a foot or a yard is unless we actually have something to serve as a measure which can be applied to successive objects after each other. A foot or a yard can therefore not be explained adequately by a definition; that is, by one which does not include something similar to the thing defined. For though we may say that a foot is twelve inches, the same question arises concerning the inch, and we gain no greater insight, for we cannot say whether the notion of the inch or of the foot is prior in nature, since it is entirely arbitrary which we wish to assume as basic. Quality, on the other hand, is what can be known in things when they are observed singly, without requiring any compresence. Such are the attributes which can be explained by a definition or through the various modes which they involve. 3 Equals are things having the same quantity. Similars are things having the same quality. Hence, if two similar things are different, they can be distinguished only when they are co-present. From this it is clear, for example, that two equiangular triangles have their sides proportional, and the converse. For if the sides are proportional, the triangles are similar, since they may be determined in a similar way. Furthermore, the sum of the angles in all triangles is the same, since it is equal to two right angles; therefore the ratio of each angle in one triangle to the sum must necessarily correspond to the ratio of the corresponding angle in the other triangle to the sum, for otherwise one triangle could be distinguished from the other by this fact itself, that is, without further comparison and in itself. In this way we can easily demonstrate what otherwise would require many devious detours. 4 Two entities are homogeneous to which two other entities can be assigned which are equal to them and similar to each other. Given A and B; if L is taken equal to A, and M equal to B, and Land M are similar, we call A and B homogeneous. Hence I usually say also that homogeneous entities are those which can be made similar to each other by means of transformations, like curves and straight lines. That is, if A is transformed into its equal L, it can be made similar to B, or to its equal M into which B is assumed to have been transformed. We say that an entity is in [inesse] some locus, or is an ingredient of something, if, when we posit the'latter, we must also be understood, by this very fact and immediately, without the necessity of any inference, to have posited the entity as well. Thus when we posit any finite line, we also posit its end points as belonging to it. For references see p. 673
668 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS An entity which is in something and is also homogeneous to it is called a part, and that which it is in is called a whole; or a part is a homogeneous ingredient of a whole. 5 A common boundary of two things is an entity which is in them when they do not have a part in common. Insofar as these two things are understood to be parts of a single whole, their common boundary is called a section of the whole. It is clear from this that a boundary is not homogeneous with what it bounds, nor a section with what it cuts. Although they are not homogeneous, time and a moment, space and a point, boundary and the bounded, are nevertheless homogonous, because one can disappear into the other by a process of continuous change. If one locus is said to be in another locus, we understand it to be homogonous to it; if it is also a part, or equal to a {lart of the other locus, it will be not merely homogonous but also homogeneous. Although an angle is at a point, it is not in a point; otherwise a point would be understood to have magnitude. If a part of one thing is equal to the whole of another, the former is called greater, the latter less. Hence the whole is greater than a part. For let the whole be A, the part B. Then A is greater than B, because a part of A (namely, B) is equal to the whole of B. This can be expressed in a syllogism whose major proposition is a definition, its minor an identity: Whatever is equal to a part of A is less than A, by definition. But B is equal to a part of A (namely, to B), by hypothesis. Therefore B is less than A. Here we see that demonstrations are finally resolvable into two kinds of indemonstrables: definitions or ideas, and primitive propositions or identities, such as B is B, anything whatever is equal to itself, and a great many others ofthis kind. Motion is change of situs. We say that a thing is moved if there is in it a change of situs and at the same time a reason for this change. The mobile is homogonous to the extended, for even a point is thought of as movable. A path is the continuous and successive locus of a movable thing. A trace [vestigium] is the locus of a movable thing, which it occupies at some moment. Thus the trace of the boundary of a moving thing is a section of the path which the boundary describes, assuming, namely, that the movable thing does not move within its own trace. A movable thing is said to move within its own trace when each of its points, with the exception of its boundary, continuously and successively moves into the position of another point of the same thing. But assuming that the movable thing does not move in this way, then a line is the path of a point. A surface is the path of a line. A filled space [amp/um] or what is commonly called a solid is the path of a surface. The magnitudes of the paths in which points describe lines, lines surfaces, and surfaces solids are called length, breadth, and depth. These are called dimensions, and in geometry it is shown that there are only three. An entity has breadth if its section has extension or if its boundary is extended. An entity has depth of it does not terminate anything extended or if it cannot be a section of the extended; clearly there is something more in depth than what can be a boundary. A line is the ultimate extended terminating entity. A solid is the ultimate extended terminated entity. Similarity or dissimilarity in solids or in space is recognized on the basis of their
HANOVER UNDER GEORGE LOUIS, 1698-1716 669 boundaries; thus, since a solid is something more than what can be a boundary, it is internally everywhere similar. Solids whose boundaries completely coincide and are congruent and assimilated, themselves coincide, are congruent and similar. The same thing is true in a plane, which is a surface internally uniform or similar to itself, and in a straight line, which is a line internally similar to itself. The complete boundary of an extended thing having breadth can be called its perimeter [ambitus]. Thus the perimeter of a circle is its circumference; that of a sphere is the spherical surface. A point (i.e., of space) is the simplest locus, or the locus of no other locus. Absolute space is the fullest locus, or the locus of all loci. Nothing results [prosultare] from a single point. From two points something new results, namely, the locus of all the points which are uniquely determined by their situation in relation to the two given points, that is, the straight line which passes through the two points. From three points there results a plane, that is, the locus of all points whose situation is uniquely determined in relation to three points not falling in the same straight line. From four points not falling in the same plane there results absolute space. For every point whatsoever is uniquely determined by its situation in relation to four points not falling in the same plane. I use the word 'to result' to indicate the determination of a new idea; that is, when on the basis of certain assumed data, something else is uniquely determined by a specific relation to these data. In the present case the relationship involved is that 01 situs. Time can be continued to infinity. For since a whole of time is similar to a part, it will be related to another whole of time as its part is to it. Thus it must always be understood as capable of being continued into another greater time. Similarly, solid space or amplitude can also be continued to infinity, since any of its parts can also be taken as similar to the whole. In the same way a plane and a straight line can also be continued to infinity. The same argument can be used to show that space, as well as a straight line and time, or in general, any continuum, can be subdivided to infinity. For in a straight line as in time, a part is similar to the whole and can therefore itself be cut in the same ratio as the whole. Though there are extended things in which the part is not similar to the whole, they can nevertheless be transformed into entities in which this is true and can thus be cut in the same ratio as that into which they are transformed. From these considerations it follows also that for every given motion we can posit another that is faster or slower in a given ratio, for if a rigid ray be moved about one of its points as center, the motions of its points are proportional to their distance from the center, so that the velocities will vary as the distances. The estimation of magnitude is of two kinds, imperfect and perfect. It is imperfect when we say something is greater or less than another, although they are not homogeneous and have no ratio between them; as, for instance, when it is said that a line is greater than a point, or a surface than a line. It was in this sense that Euclid said that the angle of contact [of a tangent to a circle] is less than any straight-lined angle, though there is no true comparison between these two entirely distinct types, since they are not homogeneous, nor can one pass into the other by continuous change. In perfect estimations of the quantity of homogeneous entities, the rule must hold that all intermediate states can be passed through in moving continuously from one extreme For references see p. 673
670 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS to another. This rule does not hold in imperfect estimations, because what we here call intermediate states are heterogeneous. Thus, in passing over from a given acute angle to a right angle, one does not pass through the angle which a diameter or radius makes with the circumference of a circle, although this angle is said to be less than a right angle and greater than any acute angle. Here 'greater' is incorrectly taken to mean that one thing falls entirely within the boundaries of another. There are many relations according to quantity; thus two straight lines can have the relation to each other that their sum is equal to a constant straight line. There can be an infinite number of pairs of straight lines, x and y, which have the relation, x + y = a. So, for example, if a is 10, x and y can be 1 and 9,2 and 8, 3 and 7, 4 and 6, 5 and 5, 6 and 4, 7 and 3, 8 and 2, 9 and 1. But there can also be an infinite number of fractions within 10 which satisfy the condition. We can also have a relation between two straight lines such that the sum of their squares equals the square of a given straight line a, or that x 2 + y2 = a 2 , and of these, there could also be an infinite number of pairs. In the circle this is the relation between the sine of any angle and the sine of its complementary angle, or the opposite, if either one is x, the other is y, and the radius is a. An infinite number of such relations can be devised, as many as there are kinds of curves which one can describe in a plane. For instance, if the x's are taken as abscissas on a horizontal line, the y's are ordinates parallel to each other applied vertically to the abscissas, whose ends form a curve. The simplest of all relations is that called ratio or proportion, and this is the relation between two homogeneous quantities which arises from themselves alone without assuming a third homogeneous quantity. So if y is to x as any number is to unity, or y = nx, x being taken as abscissa, and y as ordinate, the locus, or the line in which the ordinates end, is a straight line. It is also clear from this that if there be an equation of any degree for the locus, such as Ix 3 + my3 + nx 2y + pxy2 = 0, where I, m, n, and pare specific numbers, the locus to which the equation will apply will be a ratio between these same x's and y's . ... 6 ... It is also to be noted that the whole of algebra is an application to quantities of the art o[ combinations, or of the science of abstracted forms, which is the universal characteristic and belongs to metaphysics. So the product of the multiplication of a + b + c + etc. by 1+ m + n + etc. is nothing but the sum of alI the binary combinations which can be built out of the letters of the two series, and the product of the three series a+b+ c + etc., I+m +n + etc., and s + t+v + etc. is the sum of all the ternary combinations which can be built from the three series ofletters. Other forms will be produced from other operations. Thus our calculation usefully obeys not only the law of homogeneous entities but also the law of justice [lex justitiae] 7, according to which the relations between entities in our conclusions or results must correspond to the similar relations in the data, and must therefore be treated in the same way in mathematical operations, insofar as this is practical. The proposition is true in general that when the data proceed in a certain order, the conclusions proceed in a corresponding order. From this arises also the law o[ continuity which I was the first to formulate, according to which the law of bodies at rest is, as it were, a special case of the law of bodies in motion; the law of equals, as it were, a special case of the law of unequals; the law of curves, as it were, a special case of the law for straight lines. This is always true when a transition is possible from a genus to its limit in a special case which is its apparent opposite. Here belongs
HANOVER UNDER GEORGE LOUIS, 1698-1716 671 also tl}e method of reasoning which geometricians have long admired, in which they make use of an initial hypothesis to prove its opposite, by first treating it as a special case and then finding it to be disparate and opposite from the original problem. 8 This is the advantage of the continuous. But continuity is found in time, extension, qualities, and movement - in fact, in all natural changes, for these never take place by leaps. Situs is a certain relationship of coexistence between a plurality of entities; it is known by going back to other coexisting things which serve as intermediaries, that is, which have a simpler relation of coexistence to the original entities. But we know as coexisting, not merely those things which we perceive together, but also those which we perceive successively, provided only that, during the transition from the perception of one to that of the other, the former is not destroyed and the latter generated. From the latter requirement it follows that both coexist now, at the present moment in which we attain the latter perception; from the former it follows that both existed when we experienced the former thing. There is, moreover, a definite order in the transition of our perceptions when we pass from one to the other through intervening ones. This order, too, we can call a path. But since it can vary in infinite ways, we must necessarily conceive of one that is most simple, in which the order of proceeding through determinate intermediate states follows from the nature of the thing itself, that is, the intermediate stages are related in the simplest way to both extremes. If this were not the case, there would be no order and no reason for distinguishing among coexisting things, since one could pass from one given thing to another by any path whatever. It is this minimal path from one thing to another whose magnitude is called distance. 9 To make this more understandable, we shall now leave out of consideration all that we see in the particular things in which distance is involved and consider them as if they contained no plurality of properties; that is, we shall consider them as points. For that is a point in which nothing else can be assumed to coexist, so that whatever is in it is it. Then the path of a point will be a line, and this cannot have breadth, since its section, a point, can have no length. Nothing further is determined by one given point. But two points determine the simplest path from one to the other, which we designate as a straight line. 1. From this it follows, in the first place, that a straight line is the shortest distance between two points or that its magnitude is the distance between the points. 2. Second, the straight line is uniform between its extremities. For there is no determining factor given from which we can infer a reason for variation. 3. It follows necessarily, therefore, that one locus of a point moving along it can be distinguished from another only in relation to its extremities. Hence any part of a straight line is also straight, and a line is everywhere internally similar to itself, nor can two parts be distinguished from each other if they cannot be distinguished by means of their extremities. 4. It follows also that if the extremities of two lines are taken to be similar, congruent, or coincident, the lines themselves will be similar, congruent, or coincident. But extremities are always similar; therefore two str~ight lines are always similar, as is every part to its whole. 5. In the third place, it follows from the definition that a straight line passes through those points which have a unique relation to the two given points, this relation being For references see p. 673
672 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS that of maximal determination. There must necessarily be such points, otherwise no further determinations whatever could result from two points. If there were any other point related in the same way to A and B together as are the proposed points, there would be no reason why that simplest path should be determined by these given points rather than by that other one. This is also clear from what has preceded, where we showed that a straight line is determined if its extremities are given or that lines coincide when their extremities coincide. 6. Fourth, it follows that a straight line is uniform in all directions; it is neither concave nor convex as is a curve, since no reason for such diversity can be derived from two given points. 7. Hence it follows that if any two points, Land M, are taken outside of the line in such a way as to be related in the same way to two points on the line, or in such a way that the relation of L to A and B is identical with that of M to A and B, they will also have an identical relationship to the entire line, or L will be related to the line AB in exactly the same way as M is related to it. S. It is also clear that a rigid straight line, or one whose points do not change their situs with respect to each other, cannot move if two points in it are fixed. Otherwise there would be many points having the same relations to the two fixed points - namely, the situation in which the moving point was before it moved, and that to which it moved. 9. It follows conversely that all other points which do not fall on a straight line AB or which do not lie in the direction AB can be moved without changing their situs in relation to A and B, if A and B remain fixed. For the straight line is the locus of all points having a unique relation to A and B; therefore all other points can be varied, and in any direction, since the straight line has the same relations in all directions. 10. Therefore if a rigid solid is moved in such a way that two points remain fixed, all its points which remain at rest will fall on a straight line passing through the fixed points; any moving point will describe a circle about that same straight line as axis. Given three points which do not fall in the same straight line, the figure uniquely determined by them is a plane. Let A, B, and C be three points not falling in the same straight line; then the points A and B determine a straight line AB, and points Band C determine the straight line BC. But any point on the line AB, together with any point on the line BC, determines a new straight line, and hence, given three points A, B, and C, an infinite number of straight lines is determined whose locus is called the plane. 1. Hence, in the first place, a plane is the smallest surface within a given boundary. Its perimeter does not consist in a straight line, because a straight line does not inclose space; otherwise a part of the straight line would be dissimilar to the whole. If the perimeter is given, therefore three points not falling in the same straight line are also given, and so the given perimeter determines only the plane which it bounds, and this plane must be a minimum. 2. Second, a plane is uniform within its boundaries, since no reason can be found in its origin for any variation. 3. Hence it follows that a plane is everywhere internally similar to itself, so that the momentary locus of any point moving within it cannot be distinguished from any other locus except in relation to the boundaries of the plane. Nor can one part of a plane be distinguished from another part except through their boundaries.
HANOVER UNDER GEORGE LOUIS, 1698-1716 673 4. It follows further that planes whose perimeters are similar or congruent or coincident are themselves similar, or congruent, or coincident. 5. Third, it is clear from the definition of a plane that it is the locus of all points uniquely determined in relation to three given points. 6. Fourth, it follows that a plane is related in the same way to both sides of it, and so is neither concave nor convex. 7. If a point has a definite relation to A, E, and C at the same time, or to the plane determined by them, then there is another point which has the same relation to these three points and to their plane, since no reason can be given for a difference. 8. The plane possesses breadth, for it can be cut by a straight line passing through any two given points on it. Hence its section possesses length. But a figure whose section has length itself has breadth. Given four points not in the same plane, the result is depth, or a figure in which there is something which cannot serve as a boundary, or which cannot be common to itself and to some other figure unless the latter is included in it as a part. 10 ••. REFERENCES The reference is to an anonymous review of Christian Wolff, Elementa matheseos universae, Vol. I (Halle, 1713), in which are pointed out Wolff's use of Leibniz's definition ofsimilars and his syllogistic proof of the axiom that the whole is greater than any of its parts. Leibniz here puts both ideas into a context of more general principles. 2 See p. 247, note 5; p. 258, notes 8 and 10; and p. 410, note 1. Though Leibniz does not here make clear the conditions imposing a maximal determination upon points constituting a straight line, they involve conformality in the sense that any part of the line is similar to the whole, and this conformality includes the property of minimal distance between points. Considered as a definition of a straight line, therefore, his account does not free itself from Archimedes' definition, though it uses a much broader basis - the principle of the extremum. 3 These logical and intensional analyses of Leibniz illustrate the distinction between logical and empirical analysis which he made at the close of the second letter to Bourguet (No. 68, II). This distinction is essential, too, in understanding the point of view of his logic, which moves from perceptual grasp of qualities to the analysis and combination of essences. Quality, as contrasted with quantity, is intrinsically determinable (cf. No. 27, III). It must not be confused with sense qualities, however, but must be understood to mean the intrinsic relations between the elements of single mathematical figures or 'formulas'. 4 For the calculus of similarity see No. 27, III, where these theorems are developed more fully. 5 See p. 144, note 7. The relation of part-whole is thus more determinate than that of contained-container, adding to it the requirement of homogeneity (see New Essays, Book IV, 17,8 [G., V, 469], and Couto L., pp. 305-6). 6 The omitted paragraphs describe more complex functions, those involving infinite series and incommensurables, as well as linear, quadratic, and cubic functions. The whole thus constitutes an analytic derivation of the notion of functionality, in which the homogeneity of all real numbers with one is involved. 7 Or the law of correspondence or of equipollence. S An example which Leibniz frequently uses is Euclid's derivation of the area of a circle from that of a circumscribed regular polygon (Elements xii. 2), not directly but by proving the absurdity of alternate assumptions. 9 This paragraph, treating a monadic series as a specially determined case of more general mathematical principles, is valuable for studying the relations between logical analysis and 1
674 HANOVER UNDER GEORGE LOUIS, 1698-1716 phenomenological interpretation in Leibniz. In the case of our perceptions the maximally determined movement is determined by the law of the series; thus the paragraph also identifies the mathematical principle of the extremum or maximum with the axiological principle of the best possible. 10 There follows a more detailed analysis of the solid determined by four points.
71 THE CONTROVERSY BETWEEN LEIBNIZ AND CLARKE 1715-16 The sharp issues raised between Leibniz's physics and metaphysics and the conceptions of his English rival, Sir Isaac Newton, were clearly and bitterly drawn in the correspondence with Newton's English follower, the theologian Samuel Clarke (1675-1729). The correspondence was mediated by Leibniz's former pupil at Hanover, Caroline, Princess of Wales; and it is clear that Newton himself supplied Clarke with his critical questions and answers. There was not merely objective concern for truth in the letters but animus as well, for Clarke had set out to discredit Leibniz's philosophical and theological pretensions, as the Royal Society had apparently succeeded in discrediting his mathematical originality in the Commercium epistolicum D. Joh. Collinsii et aliorum de analysi promota, which it published in 1712. As Leibniz himself explains in writing to Christian Wolff on December 23,1715, a note which he wrote to the Princess of Wales gave the occasion for Clarke's first reply. Leibniz's death, after nine letters had passed between the correspondents, gave Clarke the last word; though he published his fifth letter!, it has not been found among Leibniz's papers. The historical importance of the controversy is shown in its effects upon later discussions of the problems of physical relativity, causality, and method. The texts are taken, though with modernized spelling, capitalization, and punctuation, from Clarke's edition of the correspondence, and his translation of Leibniz's letters is used (cj. G., VII, 345-440). I. LEIBNIZ'S FIRST PAPER, BEING AN EXTRACT OF A LETTER WRITTEN IN NOVEMBER 1715 1. Natural religion itself seems to decay [in England] very much. Many will have human souls to be material; others make God himself a corporeal being. 2. Mr. Locke and his followers are uncertain at least whether the soul be not material and naturally perishable. 3. Sir Isaac Newton says that space is an organ which God makes use of to perceive things by. But if God stands in need of an organ to perceive things by, it will follow that they do not depend altogether on him, nor were produced by him. 4. Sir Isaac Newton and his followers have also a very odd opinion concerning the work of God. According to their doctrine, God Almighty 2 wants [Le., needs] to wind up his watch from time to time; otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion. Nay, the machine of God's making is so imperfect according to these gentlemen that he is obliged to clean it now and then by an extraordinary concourse, and even to mend it as a clockmaker mends his work, who must consequently be so much the more unskilful a workman, as he is oftener obliged to mend his work and to set it right. According to my opinion, the For references see p. 717
676 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS same force and vigor remains always in the world and only passes from one part of matter to another, agreeably to the laws of nature and the beautiful pre-established order. And I hold that when God works miracles, he does not do it in order to supply the wants of nature but those of grace. Whoever thinks otherwise must needs have a very mean notion of the wisdom and power of God. II. CLARKE'S FIRST REPLY That there are some in England as well as in other countries who deny or very much corrupt even natural religion itself is very true and much to be lamented. But (next to the vicious affections of men) this is to be principally ascribed to the false philosophy v; the materialists, to which the Mathematical Principles of Philosophy are the most directly repugnant. That some make the souls of men, and others even God himself, to be a corporeal being is also very true; but those who do so are the great enemies of the Mathematical Principles of Philosophy, which principles, and which alone, prove matter or body to be the smallest and most inconsiderable part of the universe. That Mr. Locke doubted whether the soul was immaterial or no may justly be suspected from some parts of his writings. But herein he has been followed only by some materialists, enemies to the Mathematical Principles of Philosophy, and who approve little or nothing in Mr. Locke's writings but his errors. Sir Isaac Newton doth not say that space is the organ which God makes use of to perceive things by, nor that he has need of any medium at all whereby to perceive things; but on the contrary, that he, being omnipresent, perceives all things by his immediate presence to them, in all space wherever they are, without the intervention or assistance of any organ or medium whatsoever. In order to make this more intelligible, he illustrates it by a similitude: that as the mind of man, by its immediate presence to the pictures or images of things formed in the brain by means of the organs of sensations, sees these pictures as if they were the things themselves, so God sees all things by his immediate presence to them, he being actually present to the things themselves, to all things in the universe, as the mind of man is present to all the pictures of things formed in his brain. Sir Isaac Newton considers the brain and organs of sensation as the means by which those pictures are formed but not as the means by which the mind sees or perceives those pictures when they are so formed. And in the universe he doth not consider things as if they were pictures formed by certain means or organs but as real things formed by God himself and seen by him in all places wherever they are without the intervention of any medium at all. And this similitude is all that he means when he supposes infinite space to be (as it were) the sensorium of the omnipresent being. 3 The reason why, among men, an artificer is justly esteemed so much the more skilful, as the machine of his composing will continue longer to move regularly without any further interposition of the workman, is because the skill of all human artificers consists only in composing, adjusting, or putting together certain movements, the principles of whose motion are altogether independent upon the artificer. Such are weights and springs and the like, whose forces are not made but only adjusted by the workman. But with regard to God the case is quite different, because he not only composes or puts things together but is himself the author and continual preserver of their original forces or moving powers. And consequently 'tis not a diminution but the true
HANOVER UNDER GEORGE LOUIS, 1698-1716 677 glory of his workmanship that nothing is done without his continual government and inspection. The notion of the world's being a great machine, going on without the interposition of God as a clock continues to go without the assistance of a clockmaker, is the notion of materialism and fate and tends (under pretense of making God a supramundane intelligence) 4 to exclude providence and God's government in reality out of the world. And by the same reason that a philosopher can represent all things going on from the beginning of the creation without any government or interposition of providence, a skeptic will easily argue still further backward and suppose that things have from eternity gone on (as they now do) without any true creation or original author at all but only what such arguers call all-wise and eternal nature. If a king had a kingdom wherein all things would continually go on without his government or interposition, or without his attending to and ordering what is done therein, it would be to him merely a nominal kingdom, nor would he in reality deserve at all the title of king or governor. And as those men who pretend that in an earthly government things may go on perfectly well without the king himself ordering or disposing of anything may reasonably be suspected that they would like very well to set the king aside, so whosoever contends that the course of the world can go on without the continual direction of God, the supreme governor, his doctrine does in effect tend to exclude God out of the world. III. LEIBNIZ'S SECOND LETTER 1. It is rightly observed in the paper delivered to the Princess of Wales, which Her Royal Highness has been pleased to communicate to me 5, that next to corruption of manners, the principles of the materialists do very much contribute to keep up impiety. But I believe the author has no reason to add that the mathematical principles of philosophy are opposite to those of the materialists. On the contrary, they are the same, only with this difference - that the materialists, in imitation of Democritus, Epicurus, and Hobbes, confine themselves altogether to mathematical principles and admit only bodies, whereas the Christian mathematicians admit also immaterial substances. Wherefore not mathematical principles (according to the usual sense of that word) but metaphysical principles ought to be opposed to those of the materialists. Pythagoras, Plato, and Aristotle in some measure had a knowledge of these principles, but I pretend to have established them demonstratively in my Theodicy, though I have done it in a popular manner. The great foundation of mathematics is the principle of contradiction or identity, that is, that a proposition cannot be true and false at the same time and that therefore A is A and cannot be non-A. This single principle is sufficient to demonstrate every part of arithmetic and geometry, that is, all mathematical principles. But in order to proceed from mathematics to natural philosophy, another principle is requisite, as I have observed in my Theodicy; I mean the principle of a sufficient reason, viz., that nothing happens without a reason why it should be so rather than otherwise. And therefore Archimedes, being desirous to proceed from mathematics to natural philosophy, in his book De aequilibrio, was obliged to make use of a particular case of the great principle of a sufficient reason. He takes it for granted that if there be a balance in which everything is alike on both sides, and if equal weights are hung on the two ends of that balance, the whole will be at rest. 'Tis because no reason can be given why one side should weigh down rather than the other. Now by that For references see p. 717
678 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS single principle, viz., that there ought to be a sufficient reason why things should be so and not otherwise, one may demonstrate the being of a God and all the other parts of metaphysics or natural theology and even, in some measure, those principles of natural philosophy that are independent upon mathematics; I mean the dynamic principles or the principles offorce. 2. The author proceeds and says that according to the mathematical principles, that is, according to Sir Isaac Newton's philosophy (for mathematical principles determine nothing in the present case), matter is the most inconsiderable part of the universe. The reason is because he admits empty space besides matter and because, according to his notions, matter fills up a very small part of space. But Democritus and Epicurus maintained the same thing; they differed from Sir Isaac Newton only as to the quantity of matter, and perhaps they believed there was more matter in the world than Sir Isaac Newton will allow; wherein I think their opinion ought to be preferred, for the more matter there is, the more God has occasion to exercise his wisdom and power. Which is one reason, among others, why I maintain that there is no vacuum at all. 3. I find, in express words in the Appendix to Sir Isaac Newton's Optics, that space is the sensorium of God. But the word 'sensorium' hath always signified the organ of sensation. He and his friends may now, if they think fit, explain themselves quite otherwise; I shall not be against it. 4. The author supposes that the presence of the soul is sufficient to make it perceive what passes in the brain. But this is the very thing which Father Malebranche and all the Cartesians deny; and they rightly deny it. More is requisite besides bare presence to enable one thing to perceive what passes in another. Some communication that may be explained, some sort of influence, is requisite for this purpose. Space, according to Sir Isaac Newton, is intimately present to the body contained in it and commensurate with it. Does it follow from thence that space perceives what passes in a body and remembers it when that body is gone away? Besides, the soul being indivisible, its immediate presence, which may be imagined in the body, would only be in one point. How then could it perceive what happens out of that point? I pretend to be the first who has shown how the soul perceives what passes in the body. 5. The reason why God perceives everything is not his bare presence but also his operation. 'Tis because he preserves things by an action which continually produces whatever is good and perfect in them. But the soul having no immediate influence over the body, nor the body over the soul, their mutual correspondence'cannot be explained by their being present to each other. 6. The true and principal reason why we commend a machine is rather grounded upon the effects of the machine than upon its cause. We don't inquire so much about the power of the artist as we do about his skill in his workmanship. And therefore the reason alleged by the author for extolling the machine of God's making, grounded upon his having made it entirely, without wanting any materials to make it of - that reason, I say, is not sufficient. 'Tis a mere shift the author has been forced to have recourse to, and the reason why God exceeds any other artist is not only because he makes the whole, whereas other artists must have matter to work upon. This excellency in God would be only on the account of power. But God's excellency arises also from another cause, viz., wisdom, whereby his machine lasts longer and moves more regularly than those of any other artist whatsoever. He who buys a watch does not mind whether the workman made every part of it himself, or whether he got the several parts made by
HANOVER UNDER GEORGE LOUIS, 1698-1716 679 others and did only put them together - provided the watch goes right. And if the workman had received from God even the gift of creating the matter of the wheels, yet the buyer of the watch would not be satisfied unless the workman had also received the gift of putting them well together. In like manner, he who will be pleased with God's workmanship cannot be so without some other reason than that which the author has here alleged. 7. Thus the skill of God must not be inferior to that of a workman; nay, it must go infinitely beyond it. The bare production of everything would indeed show the power of God, but it would not sufficiently show his wisdom. They who maintain the contrary will fall exactly into the error of the materialists and of Spinoza, from whom they profess to differ. They would, in such case, acknowledge power, but not sufficient wisdom, in the principle or cause of all things. 8. I do not say the material world is a machine or watch that goes without God's interposition, and I have sufficiently insisted that the creation wants to be continually influenced by its creator. 6 But I maintain it to be a watch that goes without wanting to be mended by him; otherwise we must say that God bethinks himself again. No, God has foreseen everything. He has provided a remedy for everything beforehand. There is in his works a harmony, a beauty, already pre-established. 9. This opinion does not exclude God's providence or his government of the world; on the contrary, it makes it perfect. A true providence of God requires a perfect foresight. But then it requires, moreover, not only that he should have foreseen everything but also that he should have provided for everything beforehand with proper remedies; otherwise he must want either wisdom to foresee things or power to provide against them. He will be like the God of the Socinians who lives from day to day, as Mr. Jurieu says. Indeed, God, according to the Socinians, does not so much as foresee inconveniences, whereas the gentlemen I am arguing with, who put him upon mending his work, say only that he does not provide against them. But this seems to me to be still a very great imperfection. According to this doctrine, God must want either power or good will. 10. I don't think I can be rightly blamed for saying that God is intelligentia supramundana. Will they say that he is intelligentia mundana, that is, the soul of the world? 7 I hope not. However, they will do well to take care not to fall into that notion unawares. 11. The comparison of a king, under whose reign everything should go on without his interposition, is by no means to the present purpose, since God preserves everything continually and nothing can subsist without him. His kingdom therefore is not a nominal one. 'Tis just as if one should say that a king who should originally have taken care to have his subjects so well educated, and should, by his care in providing for their substance, preserve them so well in their fitness for their several stations and in their good affection toward him 8, as that he should have no occasion ever to be amending anything among them, would be only a nominal king. 12. To conclude. If God is obliged to mend the course of nature from time to time, it must be done either supernaturally or naturally. If it be done supernaturally, we must have recourse to miracles in order to explain natural things, which is reducing a hypothesis ad absurdum, for everything may easily be accounted for by miracles. But if it be done naturally, then God will not be intelligentia supramundana; he will be comprehended under the nature of things, that is, he will be the soul of the world. For references see p. 717
680 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS IV. CLARKE'S SECOND REPLY When I said that the MathematicalPrinciples o/Philosophy are opposite to those of the materialists, the meaning was that, whereas materialists suppose the frame of nature to be such as could have arisen from mere mechanical principles of matter and motion, of necessity and fate, the Mathematical Principles 0/ Philosophy show on the contrary that the state of things (the constitution of the sun and planets) is such as could not arise from anything but an intelligent and free cause. As to the propriety of the name, so far as metaphysical consequences follow demonstratively from mathematical principles, so far the mathematical principles may (if it be thought fit) be called metaphysical principles. 'Tis very true that nothing is without a sufficient reason why it is and why it is thus rather than otherwise. And therefore, where there is no cause, there can be no effect. But this sufficient reason is ofttimes no other than the mere will of God. For instance, why this particular system of matter should be created in one particular place, when (all place being absolutely indifferent to all matter) it would have been exactly the same thing vice versa, supposing the two systems (or the particles) of matter to be alike; there can be no other reason but the mere will of God. Which if it could in no case act without a predetermining cause, any more than a balance can move without a preponderating weight 9 , this would tend to take away all power of choosing and to introduce fatality. 2. Many ancient Greeks, who had their philosophy from the Phoenicians and whose philosophy was corrupted by Epicurus, held indeed in general matter and vacuum, but they knew not how to apply these principles by mathematics to the explication of the phenomena of nature. How small soever the quantity of matter be, God has not all the less subject to exercise his wisdom and power upon, for other things, as well as matter, are equally subjects on which God exercises his power and wisdom. By the same argument it might just as well have been proved that men, or any other particular species of beings, must be infinite in number, lest God should want subjects on which to exercise his power and wisdom. 3. The word 'sensory' does not properly signify the organ but the place of sensation. The eye, the ear, etc., are organs but not sensoria. Besides, Sir Isaac Newton does not say that space is the sensory but that it is, by way of similitude only, as it were, the sensory, etc. 4. It was never supposed that the presence of the soul was sufficient but only that it is necessary in order to perception. Without being present to the images of the things perceived, it could not possibly perceive them. But being present is not sufficient, without it be also a living substance. Any inanimate substance, tho' present, perceives nothing, and a living substance can only there perceive where it is present either to the things themselves (as the omnipresent God is to the whole universe) or the images of things (as the soul of man is in its proper sensory). Nothing can any more act or be acted upon where it is not present than it can be where it is not. The soul's being indivisible does not prove it to be present only in a mere point. Space, finite or infinite, is absolutely indivisible, even so much as in thought (to imagine its parts moved from each other is to imagine them moved out of themselves) 1 0, and yet space is not a mere point. 5. God perceives things, not indeed by his simple presence to them, nor yet by his
HANOVER UNDER GEORGE LOUIS, 1698-1716 681 operation upon them, but by his being a living and intelligent, as well as an omnipresent, substance. The soul likewise (within its narrow sphere), not only by its simple presence, but by its being a living substance, perceives the images to which it is present and which, without being present to them, it could not perceive. 6 and 7. 'Tis very true that the excellency of God's workmanship does not consist in its showing the power only but in its showing the wisdom also of its author. But then this wisdom of God appears not in making nature (as an artificer makes a clock) capable of going on without him (for that's impossible, there being no powers of nature independent upon God, as the powers of weights and springs are independent upon men). But the wisdom of God consists in framing originally the perfect and complete idea of a work which began and continues according to that original perfect idea by the continual uninterrupted exercise of his power and government. 8. The word 'correction' or 'amendment' is to be understood, not with regard to God, but to us only. The present frame of the solar system, for instance, according to the present laws of motion, will in time fall into confusion and perhaps, after that, will be amended or put into a new form. But this amendment is only relative with regard to our conceptions. In reality and with regard to God, the present frame, and the consequent disorder, and the following renovation are all equally parts of the design framed in God's original perfect idea. 'Tis in the frame of the world, as in the frame of man's body; the wisdom of God does not consist in making the present frame of either of them eternal but to last so long as he thought fit. 9. The wisdom and foresight of God do not consist in providing originally remedies which shall of themselves cure the disorders of nature. For in truth and strictness, with regard to God there are no disorders, and consequently no remedies, and, indeed, no powers of nature at all, that can do anything of themselves (as weights and springs work of themselves with regard to men). But the wisdom and foresight of God consist, as has been said, in contriving at once what his power and government is continually putting in actual execution. 10. God is neither a mundane intelligence nor a supramundane intelligence but an omnipresent intelligence, both in and without the world. He is in all, and through all, as well as above all. 11. If God's conserving all things means his actual operation and government in preserving and continuing the beings, powers, orders, dispositions, and motions of all things, this is all that is contended for. But if his conserving things means no more than a king's creating such subjects as shall be able to act well enough without his intermeddling or ordering anything among them ever after, this is making him, indeed, a real creator, but a governor only nominal. 12. The argument of this paragraph supposes that whatsoever God does is supernatural or miraculous, and consequently it tends to exclude all operation of God in the governing and ordering of the natural world. But the truth is, natural and supernatural are nothing at all different with regard to God but distinctions merely in our conceptions of things. To cause the sun (or earth) to move regularly is a thing we call natural; to stop its motion for a day, we call supernatural. But the one is the effect of no greater power than the other, nor is the one, with respect to God, more or less natural or supernatural than the other. God's being present in or to the world does not make him to be the soul of the world. l l A soul is part of a compound whereof the body is the other part, and they mutually affect each other as parts of the same whole. For references see p. 717
682 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS But God is present in the world, not as a part, but as a governor, acting upon all things, himself acted upon by nothing. He is not far from every one of us, for in him we (and all things) live and move and have our beings. v. MR. LEIBNIZ'S THIRD PAPER 12 1. According to the usual way of speaking, mathematical principles concern only mere mathematics, viz., numbers, figures, arithmetic, geometry. But metaphysical principles concern more general notions, such as are cause and eifect. 13 2. The author grants me this important principle, that nothing happens without a sufficient reason why it should be so rather than otherwise. But he grants it only in words and in reality denies it. Which shows that he does not fully perceive the strength of it. And therefore he makes use of an instance which exactly falls in with one of my demonstrations against real absolute space, which is an idol of some modern Englishmen. I call it an idol, not in a theological sense, but in a philosophical one, as ChanceIl or Bacon says that there are idola tribus, idola specus. 3. These gentlemen maintain, therefore, that space is a real absolute being. But this involves them in great difficulties, for such a being must needs be eternal and infinite. Hence some have believed it to be God himself, or one of his attributes, his immensity. But since space consists of parts, it is not a thing which can belong to God. 4. As for my own opinion, I have said more than once that I hold space to be something merely relative, as time is: that I hold it to be an order of co-existences as time is an order of successions. For space denotes, in terms of possibility, an order of things which exist at the same time, considered as existing together, without inquiring into their particular manner of existing. And when many things are seen together, one perceives that order of things among themselves. 5. I have many demonstrations to confute the fancy of those who take space to be a substance or at least an absolute being. But I shall only use, at the present, one demonstration, which the author here gives me occasion to insist upon. I say, then, that if space was an absolute being, there would something happen for which it would be impossible there should be a sufficient reason. Which is against my axiom. And I can prove it thus. Space is something absolutely uniform, and, without the things placed in it, one point of space does not absolutely differ in any respect whatsoever from another point of space. Now from hence it follows (supposing space to be something in itself, besides the order of bodies among themselves) that 'tis impossible there should be a reason why God, preserving the same situations of bodies among themselves, should have placed them in space after one certain particular manner and not otherwise; why everything was not placed the quite contrary way, for instance, by changing east into west. But if space is nothing else but that order or relation, and is nothing at all without bodies but the possibility of placing them, then those two states, the one such as it now is, the other supposed to be the quite contrary way, would not at all differ from one another. Their difference therefore is only to be found in our chimerical supposition of the reality of space in itself. But in truth the one would exactly be the same thing as the other, they being absolutely indiscernible, and consequently there is no room to inquire after a reason of the preference of the one to the other. 6. The case is the same with respect to time. Supposing anyone should ask why God
HANOVER UNDER GEORGE LOUIS, 1698-1716 683 did not create everything a year sooner, and the same person should infer from thence that God has done something concerning which 'tis not possible there should be a reason why he did it so and not otherwise; the answer is that his inference would be right if time was anything distinct from things existing in time. For it would be impossible there should be any reason why things should be applied to such particular instants rather than to others, their succession continuing the same. But then the same argument proves that instants, considered without the things, are nothing at all and that they consist only in the successive order of things, which order remaining the same, one of the two states, viz., that of a supposed anticipation, would not at all differ, nor could be discerned from the other which now is. 7. It appears from what I have said that my axiom has not been well understood and that the author denies it though he seems to grant it. 'Tis true, says he, that there is nothing without a sufficient reason why it is, and why it is thus rather than otherwise, but he adds that this sufficient reason is often the simple or mere will of God - as when it is asked why matter was not placed otherwise in space, the same situations of bodies among themselves being preserved. But this is plainly maintaining that God wills something without any sufficient reason for his will, against the axiom or the general rule of whatever happens. This is falling back into the loose indifference which I have confuted at large and showed to be absolutely chimerical even in creatures and contrary to the wisdom of God, as if he could operate without acting by reason. 8. The author objects against me that, if we don't admit this simple and mere will, we take away from God the power of choosing and bring in a fatality. But the quite contrary is true. I maintain that God has the power of choosing, since I ground that power upon the reason of a choice agreeable to his wisdom. And 'tis not this fatality (which is only the wisest order of providence) but a blind fatality or necessity void of all wisdom and choice which we ought to avoid. 9. I had observed that by lessening the quantity of matter, the quantity of objects upon which God may exercise his goodness will be lessened. The author answers that instead of matter there are other things in the void space on which God may exercise his goodness. Be it so, though I don't grant it, for I hold that every created substance is attended with matter. However, let it be so; I answer that more matter was consistent with those same things, and consequently the said objects will be still lessened. The instance of a greater number of men or animals is not to the purpose, for they would fill up place in exclusion of other things. 10. It will be difficult to make me believe that sensorium does not, in its usual meaning, signify an organ of sensation. See the words of Rudolphus Goclenius in his Dictionarium philosophicum under sensiterium. "Barbarum Scholasticorum", says he, "qui interdum sunt simae Graecorum. Hi dicunt (UfJ'17:ljpIOV. Ex quo illi facerunt sensiterium pro sensorio, id est, organo sensationis." 14 11. The mere presence of a substance, even an animated one, is not sufficient for perception. A blind man, and even a man whose thoughts are wandering, does not see. The author must explain how the soul perceives what is without itself. 12. God is not present to things by situation but by essence; his presence is manifest by his immediate operation. The presence of the soul is quite of another nature. To say that it is diffused all over the body is to make it extended and divisible. To say it is, the whole of it, in every part of the body is to make it divided from itself. To fix it to a point, to diffuse it all over many points, are only abusive expressions, idola tribus. For references see p. 717
684 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 13. If active force should diminish in the universe by the natural laws which God has established, so that there should be need for him to give a new impression in order to restore that force, like an artist's mending the imperfections of his machine, the disorder would not only be with respect to us but also with respect to God himself. He might have prevented it and taken better measures to avoid such an inconvenience, and therefore, indeed, he has actually done it. 14. When I said that God has provided remedies beforehand against such disorders, I did not say that God suffers disorders to happen and then finds remedies for them but that he has found a way beforehand to prevent any disorders happening. 15. The author strives in vain to criticize my expression that God is intelligentia supramundana. To say that God is above the world is not denying that he is in the world. 16. I never gave any occasion to doubt but that God's conservation is an actual preservation and continuation of the beings, powers, orders, dispositions, and motions of all things, and I think I have perhaps explained it better than many others. But, says the author, this is all I contended for. To this I answer, your humble servant for that, Sir. Our dispute consists in many other things. The question is whether God does not act in the most regular and most perfect manner; whether his machine is liable to disorder, which he is obliged to mend by extraordinary means; whether the will of God can act without reason; whether space is an absolute being; also concerning the nature of miracles; and many such things, which make a wide difference between us. 17. Divines will not grant the author's position against me, viz., that there is no difference, with respect to God, between natural and supernatural; and it will be still less approved by most philosophers. There is a vast difference between these two things, but it plainly appears it has not been duly considered. That which is supernatural exceeds all the powers of creatures. I shall give an instance which I have often made use of with good success. If God would cause a body to move free in the ether round about a certain fixed center, without any other creature acting upon it, I say it could not be done without a miracle, since it cannot be explained by the nature of bodies. For a free body does naturally recede from a curve in the tangent. And therefore I maintain that the attraction of bodies, properly so called, is a miraculous thing, since it cannot be explained by the nature of bodies. VI. CLARKE'S THIRD REPLY 1. This relates only to the signification of words. The definitions here given may well be allowed, and yet mathematical reasonings may be applied to physical and metaphysical subjects. 2. Undoubtedly nothing is without a sufficient reason why it is rather than not and why it is thus rather than otherwise. But in things in their own nature indifferent, mere will without anything external to influence it is alone that sufficient reason, as in the instance of God's creating or placing any particle of matter in one place rather than in another, when all places are originally alike. And the case is the same even though space were nothing real but only the mere order of bodies. For still it would be absolutely indifferent, and there could be no other reason but mere will why three equal particles should be placed or ranged in the order 1, 2, 3, rather than in the contrary order.l ~ And therefore no argument can be drawn from this indifferency of all places to prove that no space is real. For different spaces are really different or distinct one
HANOVER UNDER GEORGE LOUIS, 1698-1716 685 from aQother, though they be perfectly alike. And there is this evident absurdity in supposing space not to be real but to be merely the order of bodies - that, according to that notion, if the earth and sun and moon had been placed where the remotest fixed stars now are, provided they were placed in the same order and distance they now are with regard one to another, it would not only have been (as this learned author rightly says) fa meme chose, the same thing in effect, which is very true; but it would also follow that they would then have been in the same place too as they are now, which is an express contradiction. The 16 ancients did not call all space which is void of bodies, but only extramundane space, by the name of imaginary space. The meaning of which is not that such space is not real but only that we are wholly ignorant what kinds of things are in that space. Those writers who by the word 'imaginary' meant at any time to affirm that space was not real did not thereby prove that it was not real. 3. Space is not a being, an eternal and infinite being, but a property, or the consequence of the existence of a being infinite and eternal. Infinite space is immensity, but immensity is not God, and therefore infinite space is not God. Nor is there any difficulty in what is here alleged about space having parts. For infinite space is one, absolutely and essentially indivisible. And to suppose it parted is a contradiction in terms, because there must be space in the partition itself, which is to suppose it parted and yet not parted at the same time. The immensity or omnipresence of God is no more a dividing of his substance into parts than his duration or continuance of existing is a dividing of his existence into parts.17 There is no difficulty here but what arises from the figurative abuse of the word 'parts'. 4. If space was nothing but the order of things coexisting, it would follow that if God should remove in a straight line the whole material world entire, with any swiftness whatsoever, yet it would always continue in the same place, and that nothing would receive any shock upon the most sudden stopping of that motion. And if time was nothing but the order of succession of created things, it would follow that if God had created the world millions of ages sooner than he did, yet it would not have been created at all the sooner. Further, space and time are quantities, which situation and order are not. 5. The argument in this paragraph is that, because space is uniform or alike, and one part does not differ from another, therefore the bodies created in one place, if they had been created in another place (supposing them to keep the same situation with regard to each other), would still have been created in the same place as before, which is a manifest contradiction. The uniformity of space does indeed prove that there could be no (external) reason why God should create things in one place rather than in another. But does that hinder his own will from being to itself a sufficient reason of acting in any place, when all places are indifferent or alike, and there be good reason to act in some place? 6. The same reasoning takes place here as in the foregoing. 7 and 8. Where there is any difference in the nature of things, there the consideration of that difference always determines an intelligent and perfectly wise agent. But when two ways of acting are equally and alike good (as in the instances before mentioned), to affirm in such case that God cannot act at all, or that 'tis no perfection in him to be able to act, because he can have no external reason to move him to act in one way rather than the other, seems to be a denying God to have in himself any original For references see p. 717
686 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS principle or power of beginning to act, but that he must needs (as it were mechanically) be always determined by things extrinsic. 9. I suppose that determinate quantity of matter that is now in the world is the most convenient for the present frame of nature, or the present state of things, and that a greater (as well as a less) quantity of matter would have made the present frame of the world less convenient and consequently would not have been a greater object for God to have exercised his goodness upon. 10. The question is not what Goclenius, but what Sir Isaac Newton, means by the word 'sensorium', when the debate is about the sense of Sir Isaac Newton's and not about the sense of Goclenius' book. If Goclenius takes the eye or ear or any other organ of sensation to be the sensorium, he is certainly mistaken. But when any writer expressly explains what he means by any term of art, of what use is it, in this case, to inquire in what different senses perhaps some other writers have sometimes used the same word? Scapula explains it by domicilium, the place where the mind resides. 11. The soul of a blind man does for this reason not see, because no images are conveyed (there being some obstruction in the way) to the sensorium where the soul is present. How the soul of a seeing man sees the images to which it is present, we know not. But we are sure it cannot perceive what it is not present to, because nothing can act or be acted upon where it is not. 12. God, being omnipresent, is really present to everything, essentially and substantially.18 His presence manifests itself indeed by its operation, but it could not operate if it was not there. The soul is not omnipresent to every part of the body and therefore does not and cannot itself actually operate upon every part of the body but only upon the brain or certain nerves and spirits, which, by laws and communications of God's appointing, influence the whole body. 13 and 14. The active forces 19 which are in the universe diminishing themselves so as to stand in need of new impressions is no inconvenience, no disorder, no imperfection in the workmanship of the universe, but is the consequence of the nature of dependent things. Which dependency of things is not a matter that wants to be rectified. The case of a human workman making a machine is quite another thing, because the powers or forces by which the machine continues to move are altogether independent on the artificer. 15. The phrase intelligentia supramundana may well be allowed as it is here explained. But, without this explication, the expression is very apt to lead to a wrong notion, as if God was not really and substantially present everywhere. 16. To the questions here proposed, the answer is that God does always act in the most regular and perfect manner, that there are no disorders in the workmanship of God, and that there is nothing more extraordinary in the alterations he is pleased to make in the frame of things than in his continuation of it; that in things in their own nature absolutely equal and indifferent the will of God can freely choose and determine itself without any external cause to impel it, and that 'tis a perfection in God to be able to do so; that space does not at all depend on the existence or order or situation of bodies. And as to the notion of miracles: 17. The question is not what [it] is that divines or philosophers usually allow or not allow but what reasons men allege for their opinions. If a miracle be that only which surpasses the power of all created beings, then for a man to walk on the water, or for the motion of the sun or the earth to be stopped, is no miracle, since none of these
HANOVER UNDER GEORGE LOUIS, 1698-1716 687 things r,equire infinite power to effect them. For a body to move in a circle round a center in vacuo, if it be usual (as the planets moving about the sun), 'tis no miracle, whether it be effected immediately by God himself or mediately by any created power. But if it be unusual (as for a heavy body to be suspended and move so in the air), 'tis equally a miracle, whether it be effected immediately by God himself or mediately by any invisible created power. Lastly, if whatever arises not from, and is not explicable by, the natural powers of body be a miracle, then every animal motion whatsoever is a miracle. Which seems demonstrably to show that this learned author's notion of a miracle is erroneous. VII. LEIBNIZ'S FOURTH LETTER 1. In things absolutely indifferent there is no (foundation for) choice, and consequently no election or will, since choice must be founded on some reason or principle. 2. A mere will without any motive is a fiction, not only contrary to God's perfection but also chimerical and contradictory, inconsistent with the definition of the will, and sufficiently confuted in my Theodicy. 3. 'Tis a thing indifferent to place three bodies, equal and perfectly alike, in any order whatsoever, and consequently they will never be placed in any order by him who does nothing without wisdom. But then, he being the author of things, no such things will be produced by him at all, and consequently there are no such things in nature. 4. There is no such thing as two individuals indiscernible from each other. An ingenious gentleman of my acquaintance, discoursing with me in the presence of Her Electoral Highness, the Princess Sophia, in the garden of Herrenhausen, thought he could find two leaves perfectly alike. The princess defied him to do it, and he ran all over the garden a long time to look for some; but it was to no purpose. Two drops of water or milk, viewed with a microscope, will appear distinguishable from each other. This is an argument against atoms, which are confuted, as well as a vacuum, by the principles of true metaphysics. 5. These great principles of sufficient reason and of the identity of indiscernibles change the state of metaphysics. That science becomes real and demonstrative by means of these principles, whereas before it did generally consist in empty words. 6. To suppose two things indiscernible is to suppose the same thing under two names. And therefore to suppose that the universe could have had at first another position of time and place than that which it actually had, and yet that all the parts of the universe should have had the same situation among themselves as that which they actually had - such a supposition, I say, is an impossible fiction. 7. The same reason which shows that extramundane space is imaginary proves that all empty space is an imaginary thing, for they differ only as greater and less. 8. If space is a property or attribute, it must be the property of some substance. But what substance will that bounded empty space be an affection or property of, which the persons I am arguing with suppose to be between two bodies? 9. If infinite space is immensity, finite space will be the opposite to immensity, that is, 'twill be mensurability, or limited extension. Now extension must be the affection of something extended. But if that space be empty, it will be an attribute without a subject, an extension without anything extended. Wherefore, by making space a property, the author falls in with my opinion, which makes it an order of things and not anything absolute. For references see p. 717
688 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 10. If space is an absolute reality, far from being a property or an accident opposed to substance, it will have a greater reality than substances themselves. God cannot destroy it, nor even change it in any respect. It will be not only immense in the whole but also immutable and eternal in every part. There will be an infinite number of eternal things besides God. 11. To say that infinite space has no parts is to say that it does not consist of finite spaces and that infinite space might subsist though all finite space should be reduced to nothing. It would be as if one should say, in the Cartesian supposition of a material extended unlimited world, that such a world might subsist, though all the bodies of which it consists should be reduced to nothing. 12. The author attributes parts to space, on page 9 of the third edition of his Defense of the Argument against Mr. Dodwell, and makes them inseparable one from another. But on page 30 of his Second Defense he says they are parts improperly so called - which may be understood in a good sense. 13. To say that God can cause the whole universe to move forward in a right line or in any other line, without making otherwise any alteration in it, is another chimerical supposition. For two states indiscernible from each other are the same state, and consequently 'tis a change without any change. Besides, there is neither rhyme nor reason in it. But God does nothing without reason, and 'tis impossible that there should be any here. Besides, it would be agendo nihil agere, as I have just now said, because of the indiscernibility. 14. These are idola tribus, mere chimeras, and superficial imaginations. All this is only grounded upon the supposition that imaginary space is real. 15. It is a like fiction (that is), an impossible one, to suppose that God might have created the world some millions of years sooner. They who run into such kind offictions can give no answer to one that should argue for the eternity of the world. For since God does nothing without reason, and no reason can be given why he did not create the world sooner, it will follow either that he has created nothing at all or that he created the world before any assignable time, that is, that the world is eternal. But when once it has been shown that the beginning, whenever it was, is always the same thing, the question why it was not otherwise ordered becomes needless and insignificant. 16. If space and time were anything absolute, that is, if they were anything else besides certain orders of things, then indeed my assertion would be a contradiction. But since it is not so, the hypothesis (that space and time are anything absolute) is contradictory, that is, 'tis an impossible fiction. 17. And the case is the same as in geometry, where by the very supposition that a figure is greater than it really is, we sometimes prove that it is not greater. This indeed is a contradiction, but it lies in the hypothesis, which appears to be false for that very reason. 18. Space being uniform, there can be neither any external nor internal reason by which to distinguish its parts and to make any choice among them. For any external reason to discern between them can only be grounded upon some internal one. Otherwise we should discern what is indiscernible or choose without discerning. A will without reason would be the chance of the Epicureans. A God who should act by such a will would be a God only in name. The cause of these errors proceeds from want of care to avoid what derogates from the divine perfections. 19. When two things which cannot both be together are equally good, and neither
HANOVER UNDER GEORGE LOUIS, 1698-1716 689 in themselves nor by their combination with other things has one the advantage over the other, God will produce neither of them. 20. God is never determined by external things but always by what is in himself, that is, by his knowledge of things before anything exists without himself. 21. There is no possible reason that can limit the quantity of matter, and therefore such limitation can have no place. 22. And supposing an arbitrary limitation of the quantity of matter, one could always add something without detracting from the perfection of the things which are already there, and consequently something must always be added in order to act according to the principle of the perfection of the divine operations. 23. And therefore it cannot be said that the present quantity of matter is the fittest for the present constitution of things. And supposing it were, it would follow that this present constitution of things would not be the fittest absolutely if it hinders God from using more matter. It were therefore better to choose another constitution of things, capable of something more. 24. I should be glad to see a passage of any philosopher who takes sensorium in any other sense than Goc1enius does. 20 25. If Scapula says that sensorium is the place in which the understanding resides, he means by it the organ of internal sensation. And therefore he does not differ from Goc1enius. 26. Sensorium has always signified the organ of sensation. The pineal gland would be, according to Descartes, the sensorium in the above-mentioned sense of Scapula. 27. There is hardly any expression less proper upon this subject than that which makes God to have a sensorium. It seems to make God the soul of the world. And it will be a hard matter to put a justifiable sense upon this word, according to the use Sir Isaac Newton makes of it. 28. Though the question be about the sense put upon that word by Sir Isaac Newton, and not by Goc1enius, yet I am not to blame for quoting the philosophical dictionary of that author, because the design of dictionaries is to show the use of words. 29. God perceives things in himself. Space is the place of things and not the place of God's ideas, unless we look upon space as something that makes a union between God and things in imitation of the imagined union between the soul and the body, which would still make God the soul of the world. 30. And indeed the author is much in the wrong when he compares God's knowledge and operation with the knowledge and operation of souls. The soul knows things because God has put into it a principle representative of things without. But God knows things because he produces them continually. 31. The soul does not act upon things, according to my opinion, any otherwise than because the body adapts itself to the desires of the soul, by virtue of the harmony which God has pre-established between them. 32. But they who fancy that the soul can give a new force to the body, and that God does the same in the world in order to mend the imperfections of his machine, make God too much like the soul by ascribing too much to the soul and too little to God. 33. For none but God can give a new force to nature, and he does it only supernaturally. If there was need for him to do it in the natural course of things, he would have made a very imperfect work. At that rate, he would be with respect to the world what the soul, in the vulgar notion, is with respect to the body. For references see p. 717
690 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 34. Those who undertake to defend the vulgar opinion concerning the soul's influence over the body, by instancing in God's operating on things external, make God still too much like a soul of the world. To which I add that the author's affecting to find fault with the words intelligentia supramundana seems also to incline that way. 35. The images with which the soul is immediately affected are within itself, but they correspond to those of the body. The presence of the soul is imperfect and can only be explained by that correspondence. But the presence of God is perfect and manifested by his operation. 36. The author wrongly supposes against me that the presence of the soul is connected with its influence over the body, for he knows I reject that influence. 37. The soul's being diffused through the brain is no less inexplicable than its being diffused through the whole boc!y. The difference is only in more and less. 38. They who fancy that active force lessens of itself in the world do not well understand the principal laws of nature and the beauty of the works of God. 39. How will they be able to prove that this defect is a consequence of the dependence of things? 40. The imperfection of our machines, which is the reason why they want to be mended, proceeds from this very thing, that they do not sufficiently depend upon the workman. And therefore the dependence of nature upon God, far from being the cause of such an imperfection, is rather the reason why there is no such imperfection in nature, because it depends so much upon an artist who is too perfect to make a work that wants to be mended. 'Tis true that every particular machine of nature is in some measure liable to be disordered, but not the entire universe, which cannot diminish in perfection. 41. The author contends that space does not depend upon the situation of bodies. I answer: 'Tis true, it does not depend upon such or such a situation of bodies, but it is that order which renders bodies capable of being situated, and by which they have a situation among themselves when they exist together, as time is that order with respect to their successive position. But if there were no creatures, space and time would be only in the ideas of God. 42. The author seems to acknowledge here that his notion of a miracle is not the same with that which divines and philosophers usually have. It is therefore sufficient for my purpose that my adversaries are obliged to have recourse to what is commonly called a miracle. 21 43. I am afraid the author, by altering the sense commonly put upon the word 'miracle', will fall into an inconvenient opinion. The nature of a miracle does not at all consist in usefulness or unusefulness, for then monsters would be miracles. 44. There are miracles of an inferior sort which an angel can work. He can, for instance, make a man walk upon the water without sinking. But there are miracles which none but God can work, they exceeding all natural powers. Of which kind are creating and annihilating. 45. 'Tis also a supernatural thing that bodies should attract one another at a distance without any intermediate means and that a body should move around without receding in the tangent, though nothing hinder it from so receding. For these effects cannot be explained by the nature of things. 46. Why should it be impossible to explain the motion of animals by natural forces? Though, indeed, the beginning of animals is no less inexplicable by natural forces than the beginning of the world.
HANOVER UNDER GEORGE LOUIS, 1698-1716 691 P.S. All those who maintain a vacuum are more influenced by imagination than by reason. When I was a young man, I also gave in to the notion of a vacuum and atoms, but reason brought me into the right way. It was a pleasing imagination. Men carry their inquiries no further than those two things: they (as it were) nail down their thoughts to them; they fancy they have found out the first elements of things, a non plus ultra. We would have nature to go no further and to be finite as our minds are; but this is being ignorant of the greatness and majesty of the author of things. The least corpuscle is actually subdivided in infinitum and contains a world of other creatures which would be wanting in the universe if that corpuscle was an atom, that is, a body of one entire piece without subdivision. In like manner, to admit a vacuum in nature is ascribing to God a very imperfect work; 'tis violating the grand principle of the necessity of a sufficient reason, which many have talked of without understanding its true meaning; as I have lately shown in proving, by that principle, that space is only an order of things, as time also is, and not at all an absolute being. To omit many other arguments against a vacuum and atoms, I shall here mention those which I ground upon God's perfection and upon the necessity of a sufficient reason. I lay it down as a principle that every perfection which God could impart to things without derogating from their other perfections has actually been imparted to them. Now let us fancy a space wholly empty. God could have placed some matter in it without derogating in any respect from all other things; therefore he hath actually placed some matter in that space; therefore there is no space wholly empty; therefore all is full. The same argument proves that there is no corpuscle but what is subdivided. I shall add another argument grounded upon the necessity of a sufficient reason. 'Tis impossible there should be any principle to determine what proportion of matter there ought to be, out of all the possible degrees from a plenum to a vacuum, or from a vacuum to a plenum. Perhaps it will be said that the one should be equal to the other, but, because matter is more perfect than a vacuum, reason requires that a geometrical proportion should be observed and that there should be as much more matter than vacuum, as the former deserves to have the preference before the latter. But then there must be no vacuum at all, for the perfection of matter is to that of a vacuum as something to nothing. And the case is the same with atoms: What reason can anyone assign for confining nature in the progression of subdivision? These are fictions merely arbitrary and unworthy of true philosophy. The reasons alleged for a vacuum are mere sophisms. VIII. CLARKE'S FOURTH REPLY 1 and 2. This notion leads to universal necessity and fate, by supposing that motives have the same relation to the will of an intelligent agent as weights have to a balance, so that, of two things absolutely indifferent, an intelligent agent can no more choose either than a balance can move itself when the weights on both sides are equal. But the difference lies here. A balance is no agent but is merely passive and acted upon by the weights, so that, when the weights are equal, there is nothing to move it. But intelligent beings are agents - not passive, in being moved by motives as a balance is by weights, but they have active powers and do move themselves, sometimes upon the view of strong motives, sometimes upon weak ones, and sometimes where things are absolutely indifferent. In which latter case, there may be very good reason to act, though two or more ways of acting may be absolutely indifferent. This learned writer always For references see p. 717
692 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS supposes the contrary as a principle but gives no proof of it either from the nature of things or the perfections of God. 3 and 4. This argument, if it was true, would prove that God neither has created nor can possibly create any matter at all. For the perfectly solid parts of all matter, if you take them of equal figure and dimensions (which is always possible in supposition), are exactly alike, and therefore it would be perfectly indifferent if they were transposed in place; and consequently it was impossible (according to this learned author's argument) for God to place them in those places wherein he did actually place them at the creation, because he might as easily have transposed their situation. 'Tis very true that no two leaves, and perhaps no two drops of water, are exactly alike, because they are bodies very much compounded. But the case is very different in the parts of simple solid matter. And even in compounds, there is no impossibility for God to make two drops of water exactly alike. And if he should make them exactly alike, yet they would never the more become one and the same drop of water because they were alike. Nor would the place of the one be the place of the other, though it was absolutely indifferent which was placed in which place. The same reasoning holds likewise concerning the original determination of motion, this way or the contrary way. Sand 6. Two things by being exactly alike do not cease to be two. The parts of time are as exactly alike to each other as those of space; yet two points of time are not the same point of time, nor are they two names of only the same point of time. Had God created the world but this moment, it would not have been created at the time it was created. And if God has made (or can make) matter finite in dimensions, the material universe must consequently be by its nature movable, for nothing that is finite is immovable. To say therefore that God could not have altered the time or place of the existence of matter is making (this) to be necessarily infinite and eternal and reducing all things to necessity and fate. 7. Extramundane space (if the material world be finite in its dimensions) is not imaginary but real. Nor are void spaces in the world merely imaginary. In an exhausted receiver, though rays of light, and perhaps some other matter, be there in exceeding small quantity, yet the want of resistance plainly shows that the greatest part of that space is void of matter. For subtleness or fineness of matter cannot be the cause of want of resistance. Quicksilver is as subtle and consists of as fine parts and as fluid as water and yet makes more than ten times the resistance, which resistance arises therefore from the quantity and not from the grossness of the matter. 8. Space void of body is the property of an incorporeal substance. Space is not bounded by bodies but exists equally within and without bodies. Space is not inclosed between bodies, but bodies, existing in unbounded space, are themselves only terminated by their own dimensions. 9. Void space is not an attribute without a subject, because by void space we never mean space void of everything but void of body only. In all void space God is certainly present, and possibly many other substances which are not matter, being neither tangible nor objects of any of our senses. 10. Space is not a substance but a property. And if it be a property of that which is necessary, it will consequently (as all other properties of that which is necessary must do) exist more necessarily (though it be not itself a substance) than those substances themselves which are not necessary. Space is immense and immutable and eternal, and so also is duration. Yet it does not at all from hence follow that anything is eternal
HANOVER UNDER GEORGE LOUIS, 1698-1716 693 hors de dieu. For space and duration are not hors de dieu but are caused by and are immediate and necessary consequences of his existence. And without them his eternity and ubiquity (or omnispresence) would be taken away.zz 11 and 12. Infinites are composed of finites in no other sense than as finites are composed of infinitesimals. In what sense space has or has not parts has been explained before (Paper 3, Sec. 3). Parts in the corporeal sense of the word are separable, compounded, ununited, independent on and movable from each other. But infinite space, though it may by us be partially apprehended, that is, may in our imagination be conceived as composed of parts, yet those parts (improperly so called) being essentially indiscernible and immovable from each other, and not partable without an express contradiction in terms (see above, Paper 3, Sec. 3), space consequently is in itself essentially one and absolutely indivisible. 13. If the world be finite in dimensions, it is movable by the power of God, and therefore my argument drawn from that movableness is conclusive. Two places, though exactly alike, are not the same place. Nor is the motion or rest of the universe the same state, any more than the motion or rest of a ship is the same state, because a man shut up in the cabin cannot perceive whether the ship sails or not, so long as it moves uniformly. The motion of the ship, though the man perceives it not, is a real different state and has real different effects and upon a sudden stop would have other real effects; and so likewise would an indiscernible motion of the universe. To this argument no answer has ever been given. It is largely insisted on by Sir Isaac Newton in his Mathematical Principles, Definition 8, where, from the consideration of the properties, causes, and effects of motion, he shows the difference between real motion, or a body's being carried from one part of space to another, and relative motion, which is merely a change of the order or situation of bodies with respect to each other. This argument is a mathematical one, showing from real effects that there may be real motion where there is relative, and relative motion where there is none real, and is not to be answered by barely asserting the contrary. 14. The reality of space is not a supposition but is proved by the foregoing arguments, to which no answer has been given. Nor is any answer given to that other argument, that space and time are quantities, which situation and order are not. 15. It was no impossibility for God to make the world sooner or later than he did, nor is it all impossible for him to destroy it sooner or later than it shall actually be destroyed. As to the notion of the world's eternity, they who suppose matter and space to be the same must indeed suppose the world to be not only infinite and eternal but necessarily so; even as necessarily as space and duration, which depend not on the wiIl but on the existence of God. But they who believe that God created matter in what quantity, and at what particular time, and in what particular spaces he pleased are here under no difficulty. For the wisdom of God may have very good reasons for creating this world at that particular time he did and may have made other kinds of things before this material world began and may make other kinds of things after this world is destroyed. 16 and 17. That space and time are not the mere order of things but real quantities (which order and situation are not) has been proved above (see Paper 3, Sec. 4, and in this paper, Sec. 13), and no answer yet given to those proofs. And tiIl an answer be given to those proofs, this learned author's assertion is (by his own confession in this place) a contradiction. For references see p. 717
694 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 18. The uniformity of all the parts of space is no argument against God's acting in any part after what manner he pleases. God may have good reasons to create finite beings, and finite beings can be put in particular places. And, all things being originally alike, even though place were nothing else but the situation of bodies, God's placing one cube of matter behind another equal cube of matter rather than the other behind that is a choice in no wise unworthy of the perfections of God, though both these situations be perfectly equal, because there may be very good reasons why both the cubes should exist, and they cannot exist but in one or other of equally reasonable situations. The Epicurean chance is not a choice of will but a blind necessity of fate. 19. This argument (as I now observed, Sec. 3), if it proves anything, proves that God neither did nor can create any matter at all, because the situation of equal and similar parts of matter could not but be originally indifferent, as was also the original detennination of their motions, this way or the contrary way. 20. What this tends to prove with regard to the argument before us, I understand not. 21. That God cannot limit the quantity of matter is an assertion of too great consequence to be admitted without proof. If he cannot limit the duration of it neither, then the material world is both infinite and eternal, necessarily and independently upon God. 22 and 23. This argument (if it were good) would prove that whatever God can do he cannot but do, and consequently that he cannot but make everything infinite and everything eternal. Which is making him no governor at all but a merely necessary agent, that is, indeed, no agent at all but mere fate and nature and necessity. 24-28. Concerning the use of the word 'sensory' (though Sir Isaac Newton says only "as it were the sensory"), enough has been said in my third paper, Section 10, and second paper, Section 3, and first paper, Section 3. 29. Space is the place of all things and of all ideas, just as duration is the duration of all things and of all ideas. That this has no tendency to make God the soul of the world, see above in Paper 2, Section 12. There is no union between God and the world. The mind of man might with greater propriety be styled the soul of the images of things which it perceives than God can be styled the soul of the world, to which he is present throughout and acts upon it as he pleases, without being acted upon by it. Though this answer was given before (Paper 2, Sec. 12), yet the same objection is repeated again and again, without taking any notice of the answer. 30. What is meant by "a representative principle", I understand not. The soul discerns things by having the images of things conveyed to it through the organs of sense; God discerns things by being present to and in the substances of the things themselves. Not by producing them continually (for he rests now from his work of creation) but by being continually omnipresent to everything which he created at the beginning. 31. That the soul should not operate upon the body, and yet the body, by a mere mechanical impulse of matter, conform itself to the will of the soul in all the infinite variety of spontaneous animal motion, is a perpetual miracle. Pre-established harmony is a mere word or term of art and does nothing toward explaining the cause of so miraculous an effect. 32. To suppose that in spontaneous animal motion the soul gives no new motion or impression to matter but that all spontaneous animal motion is performed by me-
HANOVER UNDER GEORGE LOUIS, 1698-1716 695 chanical impulse of matter is reducing all things to mere fate and necessity. God's acting in the world upon everything after what manner he pleases, without any union and without being acted upon by anything, shows plainly the difference between an omnipresent governor and an imaginary soul of the world. 33. Every action is (in the nature of things) the giving of a new force to the thing acted upon. Otherwise 'tis not really action but mere passiveness, as in the case of all mechanical and inanimate communications of motion. If therefore the giving a new force be supernatural, then every action of God is supernatural, and he is quite excluded from the government of the natural world. And either every action of man is supernatural or else man is as mere a machine as a clock. 34 and 35. The difference between the true notion of God and that of a soul of the world has been before shown: Paper 2, Section 12, and in this paper, Sections 29 and 32. 36. This has been answered just above, Section 31. 37. The soul is not diffused through the brain but is present to that particular place, which is the sensorium. 38. This is a bare assertion without proof. Two bodies void of elasticity meeting together with equal contrary forces both lose their motion. And Sir Isaac Newton has given a mathematical instance (p. 341 of the Latin edition of his Optics) wherein motion is continually diminishing and increasing in quantity, without any communication thereof to other bodies. 23 39. This is no defect as is here supposed, but 'tis the just and proper nature of inert matter. 40. This argument (if it be good) proves that the material world must be infinite and that it must have been from eternity and must continue to eternity; and that God must always have created as many men and as many of all other things as 'twas possible for him to create and for as long a time also as it was possible for him to do it. 41. What the meaning of these words is: "an order (or situation) which renders bodies capable of being situated", I understand not. It seems to me to amount to this - that situation is the cause of situation. That space is not merely the order of bodies has been shown before, Paper 3, Sections 2 and 4. And that no answer has been given to the argument there offered has been shown in this paper, Sections 13 and 14. Also that time is not merely the order of things succeeding each other is evident because the quantity of time may be greater or less, and yet that order continue the same. The order of things succeeding each other in time is not time itself, for they may succeed each other faster or slower in the same order of succession but not in the same time. If no creatures existed, yet the ubiquity of God and the continuance of his existence would make space and duration to be exactly the same as they are now. 42. This is appealing from reason to vulgar opinion, which philosophers should not do, because it is not the rule of truth. 43. Unusualness is necessarily included in the notion of a miracle. For otherwise there is nothing more wonderful, nor that requires greater power to effect, than some of those things we call natural, such as the motions of the heavenly bodies, the generation and formation of plants and animals, etc. Yet these are for this only reason not miracles, because they are common. Nevertheless, it does not follow that everything which is unusual is therefore a miracle. For it may be only the irregular and more rare effect of usual causes, of which kind are eclipses, monstrous births, madness in men, and innumerable things which the vulgar call prodigies. For references see p. 717
696 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 44. This is a concession of what I alleged. And yet 'tis contrary to the common opinion of divines to suppose that an angel can work a miracle. 45. That one body should attract another sans aucun moyen is indeed not a miracle but a contradiction. For 'tis supposing something to act where it is not. But the moyen by which two bodies attract each other may be invisible and intangible, and of a different nature from mechanism, and yet, acting regularly and constantly, may well be called natural, being much less wonderful than animal motion, which yet is never called a miracle. 46. If the word 'natural forces' means here mechanical, then all animals, and even men, are as mere machines as a clock. But if the word does mean not mechanical forces, then gravitation may be effected by regular and natural powers, though they be not mechanical. 24 IX. LEIBNIZ'S FIFTH PAPER To Sections 1 and 2 ofthe Preceding Paper: 1. I shall at this time make a larger answer to clear the difficulties and to try whether the author be willing to hearken to reason and to show that he is a lover of truth, or whether he will only cavil without clearing anything. 2. He often endeavors to impute to me necessity and fatality, though perhaps no one had better and more fully explained than I have done in my Theodicy the true difference between liberty, contingency, spontaneity, on the one side, and absolute necessity, chance, coaction, on the other. 25 I know not yet whether the author does this because he will do it, whatever I may say, or whether he does it (supposing him sincere in those imputations) because he has not yet duly considered my opinions. I shall soon find what I am to think of it, and I shall take my measures accordingly. 3. It is true that reason in the mind of a wise being, and motives in any mind whatsoever, do that which answers to the effect produced by weights in a balance. The author objects that this notion leads to necessity and fatality. But he says so without proving it and without taking notice of the explications I have formerly given in order to remove the difficulties that may be raised upon that head. 4. He seems also to play with equivocal terms. There are necessities which ought to be admitted. For we must distinguish between an absolute and a hypothetical necessity. We must also distinguish between a necessity which takes place because the opposite implies a contradiction (which necessity is called logical, metaphysical, or mathematical) and a necessity which is moral, whereby a wise being chooses the best, and every mind follows the strongest inclination. 5. Hypothetical necessity is that which the supposition or hypotbesis of God's foresight and preordination lays upon future contingents. And this must needs be admitted, unless we deny, as the Socinians do, God's foreknowledge of future contingents and his providence which regulates and governs every particular thing. 6. But neither that foreknowledge nor that preordination derogate from liberty. For God, being moved by his supreme reason to choose, among many series of things or worlds possible, that in which free creatures should take such or such resolutions, though not without his concourse, has thereby rendered every event certain and determined once for all, without derogating thereby from the liberty of those creatures that simple decree of choice, not at all changing but only actualizing their free natures which he saw in his ideas. 26
HANOVER UNDER GEORGE LOUIS, 1698-1716 697 7. As for moral necessity, this also does not derogate from liberty. For when a wise being, and especially God who has supreme wisdom, chooses what is best, he is not the less free upon that account; on the contrary, it is the most perfect liberty not to be hindered from acting in the best manner. And when any other chooses according to the most apparent and the most strongly inclining good, he imitates therein the liberty of a truly wise being, in proportion to his disposition. Without this, the choice would be a blind chance. 8. But good, either true or apparent - in a word, the motive - inclines without necessitating, that is, without imposing an absolute necessity. For when God (for instance) chooses the best, what he does not choose, and is inferior in perfection, is nevertheless possible. But if what he chooses was absolutely necessary, any other way would be impossible, which is against the hypothesis. For God chooses among possibles, that is, among many ways none of which implies a contradiction. 9. But to say that God can only choose what is best, and to infer from thence that what he does not choose is impossible, this, J say, is confounding of terms; 'tis blending power and will, metaphysical necessity and moral necessity, essences and existences. For what is necessary is so by its essence, since the opposite implies a contradiction. But a contingent which exists owes its existence to the principle of what is best, which is a sufficient reason for the existence of things. And therefore I say that motives incline without necessitating and that there is a certainty and infallibility but not an absolute necessity in contingent things. Add to this what will be said hereafter, in Nos. 73 and 76. 10. And I have sufficiently shown in my Theodicy that this moral necessity is a good thing, agreeable to the divine perfection, agreeable to the great principle or ground of existences, which is that of the want of a sufficient reason, whereas absolute and metaphysical necessity depends upon the other great principle of our reasonings, viz., that of essences, that is, the principle of identity or contradiction. For what is absolutely necessary is the only possible way, and its contrary implies a contradiction. 11. I have also shown that our will does not always exactly follow the practical understanding, because it may have or find reasons to suspend its resolution till a further examination. 27 12. To impute to me after this the notion of an absolute necessity, without having anything to say against the reasons which I have just now alleged and which go to the bottom of things, perhaps beyond what is to be seen elsewhere - this, I say, will be an unreasonable obstinacy. 13. As to the notion of fatality which the author lays also to my charge, this is another ambiguity. There is a fatum Mahometanum, a fatum Stoicum, and a fatum Christianum. 28 The Turkish fate will have an effect to happen even though its cause should be avoided, as if there was an absolute necessity. The Stoical fate will have a man to be quiet because he must have patience whether he will or not, since 'tis impossible to resist the course of things. But 'tis agreed that there is a fatum Christianum, a certain destiny of everything, regulated by the foreknowledge and providence of God. Fatum is derived from fari, that is, 'to pronounce', 'to decree', and in its right sense it signifies the decree of providence. And those who submit to it through a knowledge of the divine perfections, whereof the love of God is a consequence, have not only patience, like the heathen philosophers, but are also contented with what is ordained by God, knowing he does everything for the best and not only for the For references see p. 717
698 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS greatest good in general but also for the greatest particular good of those who love him. 14. I have been obliged to enlarge in order to remove ill-grounded imputations once for all, as I hope I shall be able to do by these explications, so as to satisfy equitable persons. I shall now come to an objection raised here against my comparing the weights of a balance with the motives of the will. 'Tis objected that a balance is merely passive and moved by the weights, whereas agents intelligent, and endowed with will, are active. To this I answer that the principle of the want of a sufficient reason is common to both agents and patients - they want a sufficient reason of their action as well as of their passion. A balance not only does not act when it is equally pulled on bot sides, but the equal weights likewise do not act when they are in an equilibrium, so that one of them cannot go down without the other's rising up as much. 15. It must also be considered that, properly speaking, motives do not act upon the mind as weights do upon a balance, but 'tis rather the mind that acts by virtue of the motives, which are its dispositions to act. And therefore to pretend, as the author does here, that the mind prefers sometimes weak motives to strong ones, and even that it prefers that which is indifferent before motives; this, I say, is to divide the mind from the motives as if they were without the mind as the weight is distinct from the balance and as if the mind had, besides motives, other dispositions to act by virtue of which it could reject or accept the motives. Whereas, in truth, the motives comprehend all the dispositions which the mind can have to act voluntarily, for they include not only the reasons but also the inclinations arising from passions or other preceding impressions. Wherefore if the mind should prefer a weak inclination to a strong one, it would act against itself and otherwise than it is disposed to act. Which shows that the author's notions, contrary to mine, are superficial and appear to have no solidity in them when they are well considered. 16. To assert also that the mind may have good reasons to act when it has no motives and when things are absolutely indifferent, as the author explains himself here; this, I say, is a manifest contradiction. For if the mind has good reasons for taking the part it takes, then the things are not indifferent to the mind. 17. And to affirm that the mind will act when it has reasons to act, even though the ways of acting were absolutely indifferent; this, I say, is to speak again very superficially and in a manner that cannot be defended. For a man never has a sufficient reason to act when he has not also a sufficient reason to act in a certain particular manner, every action being individual and not general, nor abstract from its circumstances, but always needing some particular way of being put into execution. Wherefore when there is a sufficient reason to do any particular thing, there is also a sufficient reason to do it in a certain particular manner, and consequently several manners of doing it are not indifferent. As often as a man has sufficient reasons for a single action, he has also sufficient reasons for all its requisites. See also what I shall say below, No. 66. 18. These arguments are very obvious, and 'tis very strange to charge me with advancing my principle of the want of a sufficient reason without any proof drawn either from the nature of things or from the divine perfections. For the nature of things requires that every event should have beforehand its proper conditions, requisites, and dispositions, the existence whereof makes the sufficient reason of such event. 19. And God's perfection requires that all his actions should be agreeable to his
HANOVER UNDER GEORGE LOUIS, 1698-1716 699 wisdom and that it may not be said of him that he has acted without reason or even that he has preferred a weaker reason before a stronger. 20. But I shall speak more largely at the conclusion of this paper concerning the solidity and importance of this great principle of the want of a sufficient reason in order to every event, the overthrowing of which principle would overthrow the best part of all philosophy. 'Tis therefore very strange that the author should say I am herein guilty of a petitio principii, and it plainly appears he is desirous to maintain indefensible opinions, since he is reduced to deny that great principle which is one of the most essential principles of reason. To Sections 3 and 4: 21. It must be confessed that though this great principle has been acknowledged, yet it has not been sufficiently made use of. Which is in great measure the reason why the prima philosophia has not been hitherto so fruitful and demonstrative as it should have been. I infer from that principle, among other consequences, that there are not in nature two real, absolute beings, indiscernible from each other, because, if there were, God and nature would act without reason in ordering the one otherwise than the other; and that therefore God does not produce two pieces of matter perfectly equal and alike. The author answers this conclusion without confuting the reason of it, and he answers with a very weak objection. "That argument", says he, "if it was good, would prove that it would be impossible for God to create any matter at all. For the perfectly solid parts of matter, if we take them of equal figure and dimensions (which is always possible in supposition), would be exactly alike." But 'tis a manifest petitio principii to suppose that perfect likeness, which, according to me, cannot be admitted. This supposition of two indiscernibles, such as two pieces of matter perfectly alike, seems indeed to be possible in abstract terms, but it is not consistent with the order of things, nor with the divine wisdom by which nothing is admitted without reason. The vulgar fancy such things because they content themselves with incomplete notions. And this is one of the faults of the atomists. 22. Besides, I don't admit in matter parts perfectly solid, or that are the same throughout without any variety or particular motion in their parts, as the pretended atoms are imagined to be. To suppose such bodies is another popular opinion ill grounded. According to my demonstrations, every part of matter is actually subdivided into parts differently moved, and no one of them is perfectly like another. 23. I said that in sensible things two that are indiscernible can never be found; that, for instance, two leaves in a garden or two drops of water perfectly alike are not to be found. The author acknowledges it as to leaves and perhaps as to drops of water. But he might have admitted it without any hesitation, without a 'perhaps' (an Italian would say senza/orse), as to drops of water likewise. 24. I believe that these general observations in things sensible hold also in proportion in things insensible and that one may say in this respect what Harlequin says in the Emperor 0/ the Moon: 'tis there just as 'tis here. And 'tis a great objection against indiscernibles that no instance of them is to be found. 29 But the author opposes this consequence, because (says he) sensible bodies are compounded, whereas he maintains there are insensible bodies which are simple. I answer again that I don't admit simple bodies. There is nothing simple, in my opinion, but true monads, which have neither parts nor extension. Simple bodies, and even perfectly similar ones, are a conFor references see p. 717
700 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS sequence of the false hypothesis of a vacuum and of atoms, or of lazy philosophy, which does not sufficiently carryon the analysis of things and fancies it can attain to the first material elements of nature because our imagination would be therewith satisfied. 25. When I deny that there are two drops of water perfectly alike, or any two other bodies indiscernible from each other, I don't say 'tis absolutely impossible to suppose them but that 'tis a thing contrary to the divine wisdom, and which consequently does not exist. To Sections 5 and 6: 26. I own that if two things perfectly indiscernible from each other did exist they would be two, but that supposition is false and contrary to the grand principle of reason. The vulgar philosophers were mistaken when they believed that there are two things different solo numero, or only because they are two, and from this error have arisen their perplexities about what they called the principle of individuation. 30 Metaphysics have generally been handled like a science of mere words, like a philosophical dictionary, without entering into the discussion of things. Superficial philosophy, such as is that of the atomists and vacuists, forges things which superior reasons do not permit. I hope my demonstrations will change the face of philosophy, notwithstanding such weak objections as the author raises here against me. 27. The parts of time and place considered in themselves are ideal things, and therefore they perfectly resemble one another like two abstract units. But it is not so with two concrete ones, or with two real times, or two spaces filled up, that is, truly actual. 28. I don't say that two points of space are one and the same point, nor that two instants of time are one and the same instant, as the author seems to charge me with saying. But a man may fancy, for want of knowledge, that there are two different instants where there is but one; in like manner, as I observed in the seventeenth paragraph of the foregoing answer, that frequently in geometry we suppose two in order represent the error of a gainsayer, where there is really but one. If any man should suppose that a right line cuts another in two points, it will be found, after all, that these two pretended points must coincide and make but one point. 29. I have demonstrated that space is nothing else but an order of the existence of things observed as existing together, and therefore the fiction of a material finite universe moving forward in an infinite empty space cannot be admitted. It is altogether unreasonable and impracticable. For besides that, there is no real space out of the material universe, such an action would be without any design in it; it would be working without doing anything, agendo nihil agere. There would happen no change which could be observed by any person whatsoever.31 There are imaginations of philosophers who have incomplete notions, who make space an absolute reality. Mere mathematicians who are only taken up with the conceits of imagination are apt to forge such notions, but they are destroyed by superior reasons. 30. Absolutely speaking, it appears that God can make the material universe finite in extension, but the contrary appears more agreeable to his wisdom. 31. I don't grant that every finite is movable. According to the hypothesis of my adversaries themselves, a part of space, though finite, is not movable. What is movable must be capable of changing its situation with respect to something else and to be in
HANOVER UNDER GEORGE LOUIS, 1698-1716 701 a new state discernible from the first; otherwise the change is but a fiction. A movable finite Irtust therefore make part of another finite, that any change may happen which can be observed. 32. Cartesius maintains that matter is unlimited 32, and I don't think he has been sufficiently confuted. And though this be granted him, yet it does not follow that matter would be necessary, nor that it would have existed from eternity, since that unlimited diffusion of matter would only be an effect of God's choice judging that to be the better. To Section 7: 33. Since space in itself is an ideal thing like time, space out of the world must needs be imaginary, as the Schoolmen themselves have acknowledged. The case is the same with empty space within the world, which I take also to be imaginary, for the reasons before alleged. 34. The author objects against me the vacuum discovered by Mr. Guericke of Magdeburg, which is made by pumping the air out of a receiver, and he pretends that there is truly a perfect vacuum or a space without matter (at least in part) in that receiver.33 The Aristotelians and Cartesians, who do not admit a true vacuum, have said in answer to that experiment of Mr. Guericke, as well as to that of Torricelli of Florence (who emptied the air out of a glass tube by the help of quicksilver), that there is no vacuum at all in the tube or in the receiver, since glass has small pores which the beams of light, the effluvia of the loadstone, and other very thin fluids may go through. I am of their opinion, and I think the receiver may be compared to a box full of holes in the water having fish or other gross bodies shut up in it, which, being taken out, their place would nevertheless be filled up with water. There is only this difference that though water be fluid and more yielding than those gross bodies, yet it is as heavy and massive, if not more, than they, whereas the matter which gets into the receiver in the room of the air is much more subtle. The new sticklers for a vacuum allege in answer to this instance that it is not the grossness of matter but its mere quantity that makes resistance, and consequently that there is of necessity more vacuum where there is less resistance. They add that the subtleness of matter has nothing to do here and that the particles of quicksilver are as subtle and fine as those of water, and yet that quicksilver resists above ten times more. To this I reply that it is not so much the quantity of matter as its difficulty of giving place that makes resistance. For instance floating timber contains less of heavy matter than an equal bulk of water does, and yet it makes more resistance to a boat than the water does. 35. And as for quicksilver, 'tis true, it contains about fourteen times more of heavy matter than an equal bulk of water does, but it does not follow that it contains fourteen times more matter absolutely. On the contrary, water contains as much matter, if we inc1ude both its own matter, which is heavy, and the extraneous matter void of heaviness which passes through its pores. For both quicksilver and water are masses of heavy matter, full of pores, through which there passes a great deal of matter void of heaviness (and which does not sensibly resist), such as is probably that of the rays of light and other insensible fluids, and especially that which is itself the cause of the gravity of gross bodies, by receding from the center toward which it drives those bodies. For it is a strange imagination to make all matter gravitate, and that toward all other matter, as if each body did equally attract every other body according to their masses and For references see p. 717
702 LEIBNIZ: PHILOSOP HICAL PAPERS AND LETTERS distances - and this by an attraction properly so called, which is not derived from an occult impulse of bodies, whereas the gravity of sensible bodies toward the center of the earth ought to be produced by the motion of some fluid. And the case must be the same with other gravities such as is that of the planets toward the sun or toward each other. (A body is never moved naturally except by another body which impels it by touching it, and afterward it advances until it is stopped by another body which touches it. Every other operation on bodies is either miraculous or imaginary.)34 To Sections 8 and 9: 36. I objected that space, taken for something real and absolute without bodies, would be a thing eternal, impassible, and independent upon God. The author endeavors to elude this difficulty by saying that space is a property of God. In answer to this I have said, in my foregoing paper, that the property of God is immensity but that space (which is often commensurate with bodies) and God's immensity are not the same thing. 37. I objected further that if space be a property, and infinite space be the immensity of God, finite space will be the extension or mensurability of something finite. And therefore the space taken up by a body will be the extension of that body. Which is an absurdity, since a body can change space but cannot leave its extension. 35 38. I asked also, if space is a property, what thing will an empty limited space (such as that which my adversary imagines in an exhausted receiver) be the property of? It does not appear reasonable to say that this empty space, either round or square, is a property of God. Will it be then perhaps the property of some immaterial, extended, imaginary substances which the author seems to fancy in the imaginary spaces? 39. If space is the property or affection of the substance which is in space, the same space will be sometimes the affection of one body, sometimes of another body, sometimes of an immaterial substance, and sometimes perhaps of God himself, when it is void of all other substance, material or immaterial. But this is a strange property or affection, which passes from one subject to another. Thus subjects will leave off their accidents like clothes, that other subjects may put them on. At this rate how shall we distinguish accidents and substances? 36 40. And if limited spaces are the affections of limited substances which are in them, and infinite space be a property of God, a property of God must (which is very strange) be made up of the affections of creatures, for all finite spaces taken together make up infinite space. 41. But if the author denies that limited space is an affection of limited things, it will not be reasonable neither that infinite space should be the affection or property of an infinite thing. I have suggested all these difficulties in my foregoing paper, but it does not appear that the author has endeavored to answer them. 42. I have still other reasons against this strange imagination that space is a property of God. If it be so, space belongs to the essence of God. But space has parts; therefore there would be parts in the essence of God. Spectatum admissi ! 43. Moreover, spaces are sometimes empty and sometimes filled up. Therefore there will be in the essence of God parts sometimes empty and sometimes full and consequently liable to a perpetual change. Bodies filling up space would fill up part of God's essence and would be commensurate with it; and in the supposition of a vacuum, part of God's essence will be within the receiver. Such a God having parts will very much
HANOVER UNDER GEORGE LOUIS, 1698-1716 703 resemble the Stoic's god, which was the whole universe considered as a divine animal. 44. If infinite space is God's immensity, infinite time will be God's eternity; and therefore we must say that what is in space is in God's immensity and consequently in his essence and that what is in time is also in the essence of God. Strange expressions, which plainly show that the author makes a wrong use of terms. 45. I shall give another instance of this. God's immensity makes him actually present in all spaces. But now if God is in space, how can it be said that space is in God or that it is a property of God? We have often heard that a property is in its subject, but we never heard that a subject is in its property. In like manner, God exists in all time. How then can time be in God, and how can it be a property of God? These' are perpetual alloglossies. 46. It appears that the author confounds immensity, or the extension of things, with the space according to which that extension is taken. Infinite space is not the immensity of God; finite space is not the extension of bodies, as time is not their duration. Things keep their extension, but they do not always keep their space. Everything has its own extension, its own duration, but it has not its own time and does not keep its own space. 47. I will here show how men come to form to themselves the notion of space. They consider that many things exist at once, and they observe in them a certain order of coexistence, according to which the relation of one thing to another is more or less simple. This order is their situation or distance. When it happens that one of those coexistent things changes its relation to a multitude of others which do not change their relations among themselves, and that another thing, newly come, acquires the same relation to the others as the former had, we then say it is come into the place of the former; and this change we call a motion in that body wherein is the immediate cause of the change. And though many, or even all, the coexistent things should change according to certain known rules of direction and swiftness, yet one may always determine the relation of situation which every coexistent acquires with respect to every other coexistent, and even that relation which any other coexistent would have to this, or which this would have to any other, if it had not changed or if it had changed any otherwise. And supposing or feigning that among those coexistents there is a sufficient number of them which have undergone no change, then we may say that those which have such a relation to those fixed existents as others had to them before have now the same place which those others had. And that which comprehends all those places is called space. Which shows that in order to have an idea of place, and consequently of space, it is sufficient to consider these relations and the rules of their changes, without needing to fancy any absolute reality out of the things whose situation we consider; and to give a kind of definition, place is that which we say is the same to A and to B, when the relation of the coexistence of B, with C, E, F, G, etc., agrees perfectly with the relation of the coexistence which A had with the same C, E, F, G, etc., supposing there has been no cause of change in C, E, F, G, etc. It might be said also, without entering into any further particularity, that place is that which is the same in different moments to different existent things when their relations of coexistence with certain other existents which are supposed to continue fixed from one of those moments to the other agree entirely together. Andfixed existents are those in which there has been no cause of any change of the order of their coexistence with others, or (which is the same thing) in which there has been no motion. Lastly, space is that which results from places taken together. And here it may not be amiss to consider the difference between For references see p. 717
704 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS place and the relation of situation which is in the body that fills up the place. For the place of A and B is the same, whereas the relation of A to fixed bodies is not precisely and individually the same as the relation which B (that comes into its place) will have to the same fixed bodies; but these relations agree only. For two different subjects, as A and B, cannot have precisely the same individual affection, it being impossible that the same individual accident should be in two subjects or pass from one subject to another. But the mind, not contented with an agreement, looks for an identity, for something that should be truly the same, and conceives it as being extrinsic to the subject; and this is what we here call place and space. But this can only be an ideal thing, containing a certain order, wherein the mind conceives the application of relations. 37 In like manner as the mind can fancy to itself an order made up of geneological lines whose bigness would consist only in the number of generations wherein every person would have his place; and if to this one should add the fiction of a metempsychosis and bring in the same human souls again, the persons in those lines might change place; he who was a father or a grandfather might become a son or a grandson, etc. And yet those genealogical places, lines, and spaces, though they should express real truths, would only be ideal things. I shall allege another example to show how the mind uses, upon occasion of accidents which are in subjects, to fancy to itself something answerable to those accidents out of the subjects. The ratio or proportion between two lines Land M may be conceived three several ways: as a ratio of the greater L to the lesser M, as a ratio of the lesser M to the greater L, and, lastly, as something abstracted from both, that is, the ratio between Land M without considering which is the antecedent or which the consequent, which the subject and which the object. And thus it is that proportions are considered in music. In the first way of considering them, L the greater, in the second, M the lesser, is the subject of that accident which philosophers call 'relation'. But which of them will be the subject in the third way of considering them? It cannot be said that both of them, Land M together, are the subject of such an accident; for, if so, we should have an accident in two subjects, with one leg in one and the other in the other, which is contrary to the notion of accidents. Therefore we must say that this relation, in this third way of considering it, is indeed out of the subjects; but being neither a substance nor an accident, it must be a mere ideal thing, the consideration of which is nevertheless useful. To conclude, I have here done much like Euclid, who, not being able to make his readers well understand what ratio is absolutely in the sense of geometricians, defines what are the same ratios. Thus, in like manner, in order to explain what place is, I have been content to define what is the same place. Lastly, I observe that the traces of movable bodies, which they leave sometimes upon the immovable ones on which they are moved, have given men occasion to form in their imagination such an idea, as if some trace did still remain, even when there is nothing unmoved. But this is a mere ideal thing and imports only that if there was any unmoved thing there, the trace might be marked out upon it. And 'tis this analogy which makes men fancy places, traces, and spaces, though these things consist only in the truth of relations and not at all in any absolute reality. 48. To conclude, if the space (which the author fancies) void of all bodies is not altogether empty, what is it then full of? Is it full of extended spirits perhaps, or immaterial substances capable of extending and contracting themselves which move therein and penetrate each other without any inconveniency, as the shadows of two bodies penetrate one another upon the surface of a wall? Methinks I see the revival of
HANOVER UNDER GEORGE LOUIS, 1698-1716 705 the odd imaginations of Dr. Henry More, otherwise a learned and well-meaning man, and of some others who fancied that those spirits can make themselves impenetrable whenever they please. Nay, some have fancied that man in the state of innocency had also the gift of penetration and that he became solid, opaque, and impenetrable by his fall. Is it not overthrowing our notions of things to make God have parts, to make spirits have extension? The principle of the want of a sufficient reason does alone drive away all these specters of imagination. Men easily run into fictions for want of making a right use of that great principle. To Section 10: 49. It cannot be said that a certain duration is eternal but that things, which continue always, are eternal, by gaining always new duration. 38 Whatever exists of time and of duration, being successive, perishes continually, and how can a thing exist eternally which (to speak exactly) does not exist at all? For how can a thing exist whereof no part does ever exist? Nothing of time does ever exist but instants, and an instant is not even itself a part of time. Whoever considers these observations will easily apprehend that time can only be an ideal thing. And the analogy between time and space will easily make it appear that the one is as merely ideal as the other. (However, if by saying that the duration of a thing is eternal is merely understood that it lasts eternally, I have no objection. 39 ) 50. If the reality of space and time is necessary to the immensity and eternity of God, if God must be in space, if being in space is a property of God, he will in some measure depend upon time and space and stand in need of them. For I have already prevented that subterfuge - that space and time are in God and as it were properties of God. (Could the opinion which should affirm that bodies move about in the parts ofthe divine essence be maintained? 40) To Sections 11 and 12: 51. I objected that space cannot be in God because it has parts. Hereupon the author seeks another subterfuge by departing from the received sense of words, maintaining that space has no parts because its parts are not separable and cannot be removed from one another by discerption. But 'tis sufficient that space has parts, whether those parts be separable or not, and they may be assigned in space, either by the bodies that are in it or by lines and surfaces that may be drawn and described in it. To Section 13: 52. In order to prove that space without bodies is an absolute reality, the author objected that a finite material universe might move forward in space. I answered, it does not appear reasonable that the material universe should be finite, and though we should suppose it to be finite, yet 'tis unreasonable it should have motion any otherwise than as its parts change their situation among themselves, for then there is motion in space, but it consists in the order of relations which are changed. The author replies now that the reality of motion does not depend upon being observed and that a ship may go forward, and yet a man who is in the ship may not perceive it. I answer, motion does not indeed depend upon being observed, but it does depend upon being possible to be observed. There is no motion when there is no change that can be observed. And when there is no change that can be observed, there is no change at all. 41 The For references see p. 717
706 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS contrary opinion is grounded upon the supposition of a real absolute space, which I have demonstratively confuted by the principle of the want of a sufficient reason. 53. I find nothing in the eighth definition of the Mathematical Principles of Nature, nor in the scholium belonging to it, that proves or can prove the reality of space in itself.42 However, I grant there is a difference between an absolute true motion of a body and a mere relative change of its situation with respect to another body. For when the immediate cause of the change is in the body, that body is truly in motion, and then the situation of other bodies with respect to it will be changed consequently, though the cause of that change be not in them. 'Tis true that, exactly speaking, there is not anyone body that is perfectly and entirely at rest, but we will frame an abstract notion of rest by considering the thing mathematically. Thus have I left nothing unanswered of what has been alleged for the absolute reality of space. And I have demonstrated the falsehood of tha~ reality by a fundamental principle, one of the most certain both in reason and experience, against which no exception or instance can be alleged. Upon the whole, one may judge from what has been said that I ought not to admit a movable universe, nor any place out of the material universe. To Section 14: 54. I am not sensible of any objection but what I think I have sufficiently answered. As for the objection that space and time are quantities, or rather things endowed with quantity, and that situation and order are not so, I answer that order also has its quantity; there is in it that which goes before and that which follows; there is distance or interval. Relative things have their quantity as well as absolute ones. For instance, ratios or proportions in mathematics have their quantity and are measured by logarithms, and yet they are relations. 43 And therefore, though time and space consist in relations, yet they have their quantity. To Section 15: 55. As to the question whether God could have created the world sooner, 'tis necessary here to understand each other rightly. Since I have demonstrated that time, without things, is nothing else but a mere ideal possibility, 'tis manifest if anyone should say that this same world which has been actually created might have been created sooner without any other change, he would say nothing that is intelligible. For there R S ,..----------, !, iA .! 18 c I.l=E'--_ _ _ _ _~F Fig. 39.
HANOVER UNDER GEORGE LOUIS, 1698-1716 707 is no mark or difference whereby it would be possible to know that this world was created sooner. And, therefore (as I have already said), to suppose that God created the same world sooner is supposing a chimerical thing. 'Tis making time a thing absolute, independent upon God, whereas time must coexist with creatures and is only conceived by the order and quantity of their changes. 56. But yet, absolutely speaking, one may conceive that a universe began sooner than it actually did. Let us suppose our universe or any other to be represented by the figure AF and that the ordinate AB represents its first state and the ordinates CD and EF its following states; I say one may conceive that such a world began sooner by conceiving the figure prolonged backward and by adding to it SRABS (Figure 39). For thus, things being increased, time will be also increased. But whether such an augmentation be reasonable and agreeable to God's wisdom is another question, to which we answer in the negative; otherwise God would have made such an augmentation. 44 It would be like as Humano capiti cervicem pictor equinam Jungere si velit. 45 The case is the same with respect to the destruction 46 of the universe. As one might conceive something added to the beginning, so one might also conceive something taken off toward the end. But such a retrenching from it would be also unreasonable. 57. Thus it appears how we are to understand that God created things at what time he pleased, for this depends upon the things which he resolved to create. But things being once resolved upon, together with their relations, there remains no longer any choice about the time and the place, which of themselves have nothing in them real, nothing that can distinguish them, nothing that is at all discernible. 58. One cannot therefore say, as the author does here, that the wisdom of God may have good reasons to create this world at such or such a particular time, that particular time considered without the things being an impossible fiction, and good reasons for a choice being not to be found where everything is indiscernible. 59. When I speak of this world, I mean the whole universe of material and immaterial creatures taken together, from the beginning of things. But if anyone mean only the beginning of the material world, and suppose immaterial creatures before it, he would have somewhat more reason for his supposition. For time then being marked by things that existed already, it would be no longer indifferent, and there might be room for choice. And yet, indeed, this would be only putting off the difficulty. For supposing the whole universe of immaterial and material creatures together to have a beginning, there is no longer any choice about the time in which God would place that beginning. 60. And therefore one must not say, as the author does here, that God created things in what particular space and at what particular time he pleased. For all time and all spaces being in themselves perfectly uniform and indiscernible from each other, one of them cannot please more than another. 61. I shall not enlarge here upon my opinion explained elsewhere that there are no created substances wholly destitute of matter. For I hold with the ancients, and according to reason, that angels or intelligences, and souls separated from a gross body, have always subtle bodies, though they themselves be incorporeal. The vulgar philosophy easily admits all sorts of fictions; mine is more strict. For references see p. 717
708 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS 62. I don't say that matter and space are the same thing. I only say there is no space where there is no matter and that space in itself is not an absolute reality. Space and matter differ as time and motion. However, these things, though different, are inseparable. 63. But it does not at all follow that matter is eternal and necessary, unless we suppose space to be eternal and necessary - a supposition ill grounded in all respects. To Sections 16 and 17: 64. I think I have answered everything, and I have particularly replied to that objection that space and time have quantity and that order has none. See above, No. 54. 65. I have clearly shown that the contradiction lies in the hypothesis of the opposite opinion, which looks for a difference where there is none. And it would be a manifest iniquity to infer from thence that I have acknowledged a contradiction in my own opinion. To Section 18: 66. There I find again an argument which I have overthrown above, No. 17. The author says God may have good reasons to make two cubes perfectly equal and alike, and then (says he) God must needs assign them to their places, though every other respect be perfectly equal. But things ought not to be separated from their circumstances. This argument consists in incomplete notions. God's resolutions are never abstract and imperfect, as if God decreed first to create the two cubes and then made another decree where to place them. Men, being such limited creatures as they are, may act in this manner. They may resolve upon a thing and then find themselves perplexed about means, ways, places, and circumstances. But God never takes a resolution about the ends without resolving at the same time about the means and all the circumstances. Nay, I have shown in my Theodicy that, properly speaking, there is but one decree for the whole universe, whereby God resolved to bring it out of possibility into existence. And therefore God will not choose a cube without choosing its place at the same time, and he will never choose among indiscernibles. 67. The parts of space are not determined and distinguished but by the things which are in it, and the diversity of things in space determines God to act differently upon different parts of space. But space without things has nothing whereby it may be distinguished and, indeed, not anything actual. 68. If God is resolved to place a certain cube of matter at all, he is also resolved in which particular place to put it. But 'tis with respect to other parts of matter, and not with respect to bare space itself, in which there is nothing to distinguish it. 69. But wisdom does not allow God to place at the same time two cubes perfectly equal and alike, because there is no way to find any reason for assigning them different places. At this rate there would be a will without a motive. 70. A will without a motive, such as superficial reasoners suppose to be in God, I compared to Epicurus' chance. The author answers, Epicurus' chance is a blind necessity and not a choice of will. I reply that Epicurus' chance is not a necessity but something indifferent. Epicurus brought it in on purpose to avoid necessity. 'Tis true, chance is blind, but a will without motive would be no less blind and no less owing to mere chance.
HANOVER UNDER GEORGE LOUIS, 1698-1716 709 To Section 19: 71. The author repeats here what has been already confuted above, No. 21 - that matter cannot be created without God's choosing among indiscernibles. He would be in the right if matter consisted of atoms, similar particles, or other the like fictions of superficial philosophy. But that great principle which proves there is no choice among indiscernibles destroys also these ill-contrived fictions. To Section 20: 72. The author objected against me in his third paper (Nos. 7 and 8) that God would not have in himself a principle of acting if he was determined by things external. I answered that the ideas of external things are in him and that therefore he is determined by internal reasons, that is, by his wisdom. But the author here will not understand to what end I said it. To Section 21: 73. He frequently confounds in his objections against me what God will not do with what he cannot do. See above, No.9, and below, No. 76. For example, God can do everything that is possible, but he will do only what is best. And therefore I don't say, as the author here will have it, that God cannot limit the extension of matter; but 'tis likely he will not do it and that he has thought it better to set no bounds to matter. 74. From extension to duration, non valet consequentia. Though the extension of matter were unlimited, yet it would not follow that its duration would be also unlimited; nay, even a parte ante, it would not follow that it had no beginning. If it is the nature of things in the whole to grow uniformly in perfection, the universe of creatures must have had a beginning. 47 And therefore there will be reasons to limit the duration of things, even though there were none to limit their extension. Besides, the world's having a beginning does not derogate from the infinity of its duration a parte post, but bounds of the universe would derogate from the infinity of its extension. And therefore it is more reasonable to admit a beginning of the world than to admit any bounds of it, that the character of its infinite author may be in both respects preserved. 75. However, those who have admitted the eternity of the world, or at least (as some famous divines have done), the possibility of its eternity, did not for all that deny its dependence upon God, as the author here lays to their charge without any ground. To Sections 22 and 23: 76. He here further objects, without any reason, that according to my opinion, whatever God can do he must needs have done. As if he was ignorant that I have solidly confuted this notion in my Theodicy, and that I have overthrown the opinion of those who maintain that there is nothing possible but what really happens, as some ancient philosophers did, and among others, Diodorus in Cicero. 48 The author confounds moral necessity, which proceeds from the choice of what is best, with absolute necessity; he confounds the will of God with his power. God can produce everything that is possible or whatever does not imply a contradiction, but he wills only to produce what is the best among things possible. See what has been said above, Nos. 9 and 74. 77. God is not therefore a necessary agent in producing creatures, since he acts with For references see p. 717
710 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS choice. However, what the author adds here is ill grounded, viz., that a necessary agent would not be an agent at all. He frequently affirms things boldly and without any ground, advancing against me notions which cannot be proved. To Sections 24-28: 78. The author alleges it was not affirmed that space is God's sensorium but only, as it were, his sensorium. The latter seems to be as improper and as little intelligible as the former. To Section 29: 79. Space is not the place of all things, for it is not the place of God. Otherwise there would be a thing coetemal with God and independent upon him; nay, he himself would depend upon it ifhe has need of place. 80. Nor do I see how it can be said that space is the place of ideas, for ideas are in the understanding. 81. 'Tis also very strange to say that the soul of man is the soul of the images it perceives. The images, which are in the understanding, are in the mind, but if the mind was the soul of the images, they would then be extrinsic to it. And if the author means corporeal images, how then will he have a human mind to be the soul of those images, they being only transient impressions in a body belonging to that soul? 82. If 'tis by means of a sensorium that God perceives what passes in the world, it seems that things act upon him and that therefore he is what we mean by a soul of the world. The author charges me with repeating objections without taking notice of the answers, but I don't see that he has answered this difficulty. They had better wholly lay aside this pretended sensorium. To Section 30: 83. The author speaks as if he did not understand how, according to my opinion, the soul is a representative principle. Which is as if he had never heard of my preestablished harmony. 84. I don't assent to the vulgar notions that the images of things are conveyed by the organs of sense to the soul. For it is not conceivable by what passage, or by what means of conveyance, these images can be carried from the organ to the soul. This vulgar notion in philosophy is not intelligible, as the new Cartesians have sufficiently shown. It cannot be explained how immaterial substance is affected by matter, and to maintain an unintelligible notion thereupon is having recourse to the Scholastic chimerical notion of I know not what inexplicable species intentionales passing from the organs to the soul. Those Cartesians saw the difficulty, but they could not explain it. 49 They had recourse to a certain wholly special concourse of God, which would really be miraculous. But I think I have given the true solution of that enigma. 85. To say that God perceives what passes in the world because he is present to the things, and not by the dependence which the continuation of their existence has upon him and which may be said to involve a continual production of them, is saying something unintelligible. A mere presence or proximity of coexistence is not sufficient to make us understand how that which passes in one being should answer to what passes in another. 86. Besides, this is exactly falling into that opinion which makes God to be the soul
HANOVER UNDER GEORGE LOUIS, 1698-1716 711 of the world, seeing it supposes God to perceive things, not by their dependence upon him, that is, by a continual production of what is good and perfect in them, but by a kind of perception, such as that by which men fancy our soul perceives what passes in the body. This is a degrading of God's knowledge very much. 87. In truth and reality, this way of perception is wholly chimerical and has no place even in human souls. They perceive what passes without them by what passes within them, answering to the things without, in virtue of the harmony which God has preestablished by the most beautiful and the most admirable of all his productions, whereby every simple substance is by its nature (if one may so say) a concentration and a living mirror of the whole universe according to its point of view. Which is likewise one of the most beautiful and most undeniable proofs of the existence of God, since none but God, viz., the universal cause, can produce such a harmony of things. But God himself cannot perceive things by the same means whereby he makes other beings perceive them. He perceives them because he is able to produce that means. And other beings would not be caused to perceive them if he himself did not produce them all harmonious and had not therefore in himself a representation of them; not as if that representation came from the things, but because the things proceed from him and because he is the efficient and exemplary cause of them. He perceives them because they proceed from him - if one may be allowed to say that he perceives them, which ought not to be said unless we divest that word of its imperfection, for else it seems to signify that things act upon him. They exist and are known to him because he understands and wills them and because what he wills is the same as what exists. Which appears so much the more because he makes them to be perceived by one another and makes them perceive one another in consequence of the natures which he has given them once for all and which he keeps up only according to the laws of everyone of them severally, which, though different one from another, yet terminate in an exact correspondence of the results of the whole. This surpasses all the ideas which men have generally framed concerning the divine perfections and the works of God and raises (our notion of) so them to the highest degree, as Mr. Bayle has acknowledged, though he believed, without any ground, that it exceeded possibility. 51 88. To infer from that passage of Holy Scripture, wherein God is said to have rested from his works, that there is no longer a continual production of them would be to make a very ill use of that text. 'Tis true, there is no production of new simple substances, but it would be wrong to infer from thence that God is now in the world only as the soul is conceived to be in the body, governing it merely by his presence without any concourse being necessary to continue its existence. To Section 31,' 89. The harmony or correspondence between the soul and the body is not a perpetual miracle but the effect or conSf:quence of an original miracle worked at the creation of things, as all natural things are. Though indeed it is a perpetual wonder, as many natural things are. 90. The word 'pre-established harmony' is a term of art, I confess, but 'tis not a term that explains nothing, since it is made out very intelligibly; and the author alleges nothing that shows there is any difficulty in it. 91. The nature of every simple substance, soul, or true monad being such that its following state is a consequence of the preceding one, here now is the cause of the For references see p. 717
712 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS harmony found out. For God needs only to make a simple substance become once and from the beginning a representation of the universe according to its point of view, since from thence alone it follows that it will be so perpetually and that all simple substances will always have a harmony among themselves because they always represent the same universe. To Section 32: 92. 'Tis true that according to me the soul does not disturb the laws of the body, nor the body those of the soul, and that the soul and body do only agree together, the one acting freely according to the rules of final causes and the other acting mechanically according to the laws of efficient causes. But this does not derogate from the liberty of our souls, as the author here will have it. For every agent which acts 52 according to final causes is free, though it happens to agree with an agent acting only by efficient causes without knowledge, or mechanically, because God, foreseeing what the free cause would do, did from the beginning regulate the machine in such a manner that it cannot fail to agree with that free cause. Mr. Jaquelot has very well resolved this difficulty in one of his books against Mr. Bayle, and I have cited the passage in my Theodicy, Part I, Section 63. I shall speak ofit again below, No. 124. To Section 33. 93. I don't admit that every action gives a new force to the patient. It frequently happens in the concourse of bodies that each of them preserves its force, as when two equal hard bodies meet directly. Then the direction only is changed without any change in the force, each of the bodies receiving the direction of the other and going back with the same swiftness it came. 94. However, I am far from saying that it is supernatural to give a new force to a body, for I acknowledge that one body does frequently receive a new force from another, which loses as much of its own. But I say only 'tis supernatural that the whole universe of bodies should receive a new force, and consequently that one body should acquire any new force without the loss of as much in others. And therefore I say likewise, 'tis an indefensible opinion to suppose the soul gives force to the body, for then the whole universe of bodies would receive a new force. 95. The author's dilemma here is ill grounded, viz., that according to me, either a man must act supernaturally or be a mere machine like a watch. For man does not act supernaturally, and his body is truly a machine acting only mechanically, and yet his soul is a free cause. To Sections 34 and 35: 96. I here refer to what has been or shall be said in this paper, Nos. 82, 86, 88, and 111, concerning the comparison between God and a soul of the world, and how the opinion contrary to mine brings the one of these too near to the other. To Section 36: 97. I here also refer to what I have before said concerning the harmony between the soul and the body; No. 89, etc. To Section 37: 98. The author tells us that the soul is not in the brain but in the sensorium, without
HANOVER UNDER GEORGE LOUIS, 1698-1716 713 saying what that sensorium is. But supposing that sensorium to be extended, as I believe the author understands it, the same difficulty still remains, and the question returns whether the soul be diffused through that whole extension, be it great or small. For more or less in bigness is nothing to the purpose here. To Section 38: 99. I don't undertake here to establish my Dynamics or my doctrine of forces; this would not be a proper place for it. However, I can very well answer the objection here brought against me. I have affirmed that active forces are preserved in the world (without diminution).53 The author objects that two soft or unelastic bodies meeting together lose some of their force. I answer, 'No.' 'Tis true their wholes lose it with respect to their total motion, but their parts receive it, being shaken internally by the force of the concourse. And therefore that loss of force is only in appearance. The forces are not destroyed but scattered among the small parts. The bodies do not lose their forces, but the case here is the same as when men change great money into small. 54 However, I agree that the quantity of motion does not remain the same, and herein I approve what Sir Isaac Newton says, page 341 of his Optics, which the author here quotes. But I have shown elsewhere that there is a difference between the quantity of motion and the quantity of force. To Section 39: 100. The author maintained against me that force does naturally lessen in the material universe and that this arises from the dependence of things (third reply, Secs. 13 and 14). In my third answer, I desired him to prove that this imperfection is a consequence of the dependence of things. He avoids answering my demand by falling upon an incident and denying this to be an imperfection. But whether it be an imperfection or not, he should have proved that 'tis a consequence of the dependence of things. 101. However, that which would make the machine of the world as imperfect as that of an unskilful watchmaker surely must needs be an imperfection. 102. The author says now that it is a consequence of the inertia of matter. But this also he will not prove. That inertia alleged here by him, mentioned by Kepler, repeated by Cartesius in his letters, and made use of by me in my Theodicy in order to give a notion, and at the same time an example, of the natural imperfection of creatures has no other effect than to make the velocities diminish when the quantities of matter are increased, but this is without any diminution of the forces. 55 To Section 40: 103. I maintained that the dependence of the machine of the world upon its divine author is rather a reason why there can be no such imperfection in it, and that the work of God does not want to be set right again, that it is not liable to be disordered, and, lastly, that it cannot lessen in perfection. Let anyone guess now how the author can hence infer against me, as he does, that if this be the case, then the material world must be infinite and eternal, without any beginning, and that God must always have created as many men and other kinds of creatures as can possibly be created. To Section 41: 104. I don't say that space is an order or situation which makes things capable of For references see p. 717
714 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS being situated; this would be nonsense. Anyone needs only consider my own words, and add them to what I said above, No. 47, in order to show how the mind comes to form to itself an idea of space, and yet that there needs not be any real and absolute being answering to that idea distinct from the mind and from all relations. I don't say, therefore, that space is an order or situation, but an order of situations, or an order according to which situations are disposed, and that abstract space is that order of situations when they are conceived as being possible. Space is therefore something merely ideal. But it seems the author will not understand me. I have already, in this paper, No. 54, answered the objection that order is not capable of quantity. 105. The author objects here that time cannot be an order of successive things because the quantity of time may become greater or less, and yet the order of successions continue the same. I answer, this is not so. For if the time is greater, there will be more successive and like states interposed, and if it be less, there will be fewer, seeing there is no vacuum, nor condensation, nor penetration (if I may so speak) in times any more than in places. 106. 'Tis true, I maintain that the immensity and eternity of God would subsist though there were no creatures, but those attributes would have no dependence either on times or places. If there were no creatures, there would be neither time nor place, and consequently no actual space. The immensity of God is independent upon space, as his eternity is independent upon time. These attributes signify only, in respect to these two orders of things, that God would be present and coexistent with all the things that should exist. And therefore I don't admit what's here alleged, that if God existed alone there would be time and space as there is now, whereas then, in my opinion, they would be only in the ideas of God as mere possibilities. The immensity and eternity of God are things more transcendent than the duration and extension of creatures, not only with respect to the greatness, but also to the nature of the things. Those divine attributes do not imply the supposition of things extrinsic to God, such as are actual places and times. These truths have been sufficiently acknowledged by divines and philosophers. To Section 42: 107. I maintained that an operation of God by which he should mend the machine of the material world, tending in its nature, as this author pretends, to lose all its motion, would be a miracle. His answer was that it would not be a miraculous operation because it would be usual and must frequently happen. I replied that 'tis not usualness or unusualness that makes a miracle properly so called, or a miracle of the highest sort, but its surpassing the powers of creatures, and that this is the general opinion of divines and philosophers; and that therefore the author acknowledges at least that the thing he introduces and I disallow is, according to the received notion, a miracle of the highest sort, that is, one which surpasses all created powers, and that this is the very thing which all men endeavor to avoid in philosophy. He answers now that this is appealing from reason to vulgar opinion. But I reply again that this vulgar opinion, according to which we ought in philosophy to avoid as much as possible what surpasses the natures of creatures, is a very reasonable opinion. Otherwise nothing will be easier than to account for anything by bringing in the deity, deum ex machina, without minding the natures of things. lOS. Besides, the common opinion of divines ought not to be looked upon merely
HANOVER UNDER GEORGE LOUIS, 1698-1716 715 as vulgar opinion. A man should have weighty reasons before he ventures to contradict it, and I see no such reasons here. 109. The author seems to depart from his own notion, according to which miracle ought to be unusual, when in Section 31, he objects to me - though without any ground - that the pre-established harmony would be a perpetual miracle. Here, I say, he seems to depart from his own notion, unless he had a mind to argue against me ad hominem. To Section 43: 110. If a miracle differs from what is natural only in appearance and with respect to us, so that we call that only a miracle which we seldom see, there will be no internal real difference between a miracle and what is natural, and at the bottom everything will be either equally natural or equally miraculous. Will divines like the former, or philosophers the latter? 111. Will not this doctrine, moreover, tend to make God the soul of the world, if all his operations are natural like those of our souls upon our bodies? And so God will be a part of nature. 112. In good philosophy and sound theology we ought to distinguish between what is explicable by the natures and powers of creatures and what is explicable only by the powers of the infinite substance. We ought to make an infinite difference between the operation of God, which goes beyond the extent of natural powers, and the operations of things that follOW the law which God has given them, and which he has enabled them to follow by their natural powers, though not without his assistance. 113. This overthrows attractions, properly so called, and other operations inexplicable by the natural powers of creatures, which kinds of operations the assertors of them must suppose to be effected by miracle, or else have recourse to absurdities, that is, to the occult qualities of the Schools, which some men begin to revive under the specious name of forces, but they bring us back again into the kingdom of darkness. This is inventafruge, glandibus vescio 56 114. In the time of Mr. Boyle and other excellent men who flourished in England under Charles the Second, nobody would have ventured to publish such chimerical notions, I hope that happy time will return under so good a government as the present and that minds a little too much carried away by the misfortune of the times will betake themselves to the better cultivation of sound learning. Mr. Boyle made it his chief business to inculcate that everything was done mechanically in natural philosophy. 57 But it is men's misfortune to grow at last out of conceit with reason itself and to be weary of light. Chimeras begin to appear again, and they are pleasing because they have something in them that is wonderful. What has happened in poetry happens also in the philosophical world. People are grown weary of rational romances such as were the French CM/ie or the German Aramene, and they are become fond again of the tales offairies. 58 115. As for the motions of the celestial bodies and even the formation of plants and animals, there is nothing in them that looks like a miracle except their beginning. The organism of animals is a mechanism which supposes a divine preformation. What follows upon it is purely natural and entirely mechanical. 59 116. Whatever is performed in the body of man and of every animal is no less mechanical than what is performed in a watch. The difference is only such as ought For references see p. 717
716 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS to be between a machine of divine invention and the workmanship of such a limited artist as man is. To Section 44: 117. There is no difficulty among divines about the miracles of angels. The question is only about the use of that word. It may be said that angels work miracles, but less properly so called, or of an inferior order. To dispute about this would be a mere question about a word. It may be said that the angel who carried Habakkuk through the air, and he who troubled the water of the pool of Bethesda, worked a miracle. But it was not a miracle of the highest order, for it may be explained by the natural powers of angels, which surpass those of man. To Section 45: 118. I objected that an attraction, properly so called or in the Scholastic sense, would be an operation at a distance without any means intervening. The author answers here that an attration without any means intervening would be indeed a contradiction. Very well. But then what does he mean when he will have the sun to attract the globe of the earth through an empty space? Is it God himself that performs it? But this would be a miracle if ever there was any. This would surely exceed the powers of creatures. 119. Or are perhaps some immaterial substances or some spiritual rays, or some accidents without a substance, or some kind of species intentionalis, or some other 'I know not what', the means by which this is pretended to be performed? Of which sort of things the author seems to have still a good stock in his head, without explaining himself sufficiently. 120. That means of communication, says he, is invisible, intangible, not mechanical. He might as well have added inexplicable, unintelligible, precarious, groundless, and unexampled. 121. But it is regular, says the author; it is constant and consequently natural. I answer, it cannot be regular without being reasonable, nor natural unless it can be explained by the natures of creatures. 122. If the means which causes an attraction properly so called be constant and at the same time inexplicable by the powers of creatures, and yet be true, it must be a perpetual miracle, and if it is not miraculous it is false. 'Tis a chimerical thing, a Scholastic occult quality. 123. The case would be the same as in a body going round without receding in the tangent, though nothing that can be explained hindered it from receding. Which is an instance I have already alleged, and the author has not thought fit to answer it because it shows too clearly the difference between what is truly natural, on the one side, and a chimerical occult quality of the Schools, on the other. To Section 46: 124. All the natural forces of bodies are subject to mechanical laws, and all the natural powers of spirits are subject to moral laws. The former follow the order of efficient causes, and the latter follow the order of final causes. The former operate without liberty, like a watch; the latter operate with liberty, though they exactly agree
HANOVER UNDER GEORGE LOUIS, 1698-1716 717 with that machine which another cause, free and superior, has adapted to them beforehand. I have already spoken of this above, No. 92. 125. I shall conclude with what the author objected against me at the beginning of this fourth reply, to which I have already given an answer above, Nos. 18, 19,20. But I have deferred speaking more fully upon that head to the conclusion of this paper. He pretended that I have been guilty of a petitio principii. But of what principle, I beseech you? Would to God less clear principles had never been laid down. The principle in question is the principle of the want of a sufficient reason in order to anything's existing, in order to any event's happening, in order to any truth's taking place. Is this a principle that wants to be proved? The author granted it or pretended to grant it, No.2 of his third paper, possibly because the denial of it would have appeared too unreasonable. But either he has done it only in words or the contradicts himself or retracts his concession. 126. I dare say that without this great principle one cannot prove the existence of God, nor account for many other important truths. 127. Has not everybody made use of this principle upon a thousand occasions? 'Tis true, it has been neglected out of carelessness on many occasions, but that neglect has been the true cause of chimeras such as are, for instance, an absolute real time or space, a vacuum, atoms, attraction in the Scholastic sense, a physical influence of the soul over the body, and a thousand other fictions either derived from erroneous opinions of the ancients or lately invented by modern philosophers. 128. Was it not upon account of Epicurus' violating this great principle that the ancients derided his groundless declination of atoms? And I dare say the Scholastic attraction, revived in our days and no less derided about thirty years ago, is not at all more reasonable. 129. I have often defied people to allege an instance against that great principle, to bring anyone uncontested example wherein it fails. But they have never done it, nor ever will. 'Tis certain there is an infinite number of instances wherein it succeeds, or rather it succeeds in all the known cases in which it has been made use of. From whence one may reasonably judge that it will succeed also in unknown cases, or in such cases as can only by its means become known, according to the method of experimental philosophy which proceeds a posteriori, though the principle were not perhaps otherwise justified by bare reason, or a priori. 60 130. To deny this great principle is likewise to do as Epicurus did, who was reduced to deny that other great principle, viz., the principle of contradiction, which is that every intelligible enunciation must be either true or false. Chrysippus undertook to prove that principle against Epicurus, but I think I need not imitate him. I have already said what is sufficient to justify mine, and I might say something more upon it, but perhaps it would be too abstruse for this present dispute. And I believe reasonable and impartial men will grant me that having forced an adversary to deny that principle is reducing him ad absurdum. 61 REFERENCES In A Collection of Papers Which Passed between the Late Learned Mr. Leibnitz and Dr. Clarke, in the Years 1715 and 1716, Relating to the Principles of Natural Philosophy and Religion, London, printed for James Knapton, MDCCXVII. 2 Clarke supplies the reference to Newton's Optics, Question 31. Irregularities in cometal 1
718 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS motion led Newton to ascribe loss of energy to collision and to suggest the possibility of a time when "the present system of nature shall want to be anew put in order by its author". 8 The passage referred to is in Newton's Optics, Question 20. 4 Clarke's note refers to Theodicy, p. 396: "God, according to my opinion, is an extramundane intelligence, as Martianus Capella styles him, or rather, a supramundane intelligence." 5 The clause "In the paper ... communicate to me" is lacking in Leibniz's manuscript, as are the paragraph numbers, which were supplied by Clarke. 6 Leibniz: ont besoin de son influence continuelle. 7 Newton had already rejected the view that God is anima mundi in the famous scholium ending the second edition of the Principia. 8 Leibniz wrote merely: leur capacite et bonne volonte. S Clarke gives a reference to the Theodicv, pp.158 and 161. 10 the Principia, scholium to Def. 8, from which Clarke quotes (Opera omnia, ed. Horsley [1779], II, 8). Note the assumption that space is something really existent, which cannot be divided without being moved. 11 Oarke here quotes the closing scholium to the Principia on God. 12 Leibniz's copy has the note: "Duplicate. Sent to the Princess of Wales, Feb. 25, 1716." 18 Leibniz's notion of metaphysics is thus more inclusive than his monadology but close to Aristotle's science of first principles, including both essence and existence, and therefore the phenomenal principle of causality. At the same time it is more sharply distinguished from mathematics than in his first period, when he regarded number as a metaphysical ultimate. The steps in this separation were, first, the subordination of mathematics to the universal characteristic and, then, the separation of dynamics from geometry and phoronomy. 14 "A barbarism of the Scholastics, who sometimes ape the Greeks. The latter say i'1.I8'17:1jplOv, from which the former make sensiterium, for sensorium, that is, for the organ of sensation." Rudolf Goclenius (1547-1628) professor at Marburg, published the Lexicon philosophicum quo tanquam clave philosophiae fores aperiuntur in 1613. 15 Clarke's example, assuming an indifference of spatial arrangements of the same elements, runs counter, of course, to Leibniz's view that their spatial properties are intrinsic denominations of things and merely abstracted from their dynamic properties, a view which he had used in his theory of relative force and motion. The fundamental difference in the two men's approach, Clarke assuming the independence and ultimacy of spatial relations, Leibniz their abstract and dependent nature, is never resolved. 18 Clarke's note: "This was occasioned by a passage in the private letter wherein Mr. Leibnitz's third paper came enclosed." (G. did not find this letter among the Leibniz papers.) 17 Leibniz, too, recognized a distinction between space and situation but regarded both as subject to the same logical-phenomenological analysis and not as paralleling the distinction between space and matter (see p. 540, note 7; p. 541, note 20; and p. 628, note 5; and the definition of situs in No. 70). 18 Clarke notes: "God is omnipresent not only virtually but substantially, for powers cannot subsist without a substance. Newton's Principia, general scholium at end." 19 Clarke notes: "The word active force signifies here nothing but motion, and the impetus or relative impulsive force of bodies arising from and being proportional to their motion. For the occasion of what has passed upon this head was the following passage." (Here Clarke again quotes the passage from the last question of the Optics describing the diminution of motion.) 20 Sentence omitted by Clarke: "I was right in quoting the philosophical dictionary of this author to show the usual sense in which the word sensorium is taken; this is what dictionaries are for." 21 Leibniz's copy adds: "and which they try to avoid in philosophizing". 22 Clarke again quotes the general scholium of Newton's Principia on God. 88 The reference is to Newton's account of the loss of motion in the collision of inelastic and cr.
HANOVER UNDER GEORGE LOUIS, 1698-1716 719 imperfectly elastic bodies; he infers the necessity, therefore, of active principles affecting matter from without (somewhat in the tradition of Leibniz's own early arguments for mind) and suggests that gravity may be such a principle. Active force and passive matter are therefore mutually exclusive for Newton; for Leibniz they are two aspects offorce itself. 24 Clarke ends his letter with a note on Leibniz's postscript which G. omits: "N.B. The arguments alleged in the postscript to Mr. Leibnitz's fourth paper have been already answered in the foregoing replies. All that needs here to be observed is that his notion concerning theimpossibility of physical atoms (for the question is not about mathematical atoms) is a manifest absurdity. For either there are or there are not any perfectly solid particles of matter. If there are such, then the parts of such perfectly solid particles, taken of equal figure and dimensions (which is always possible in supposition), are physical atoms perfectly alike. But if there be no such perfectly solid particles, then there is no matter at all in the universe. For the farther the division and subdivision of the parts of any body is carried, before you arrive at parts perfectly solid and without pores, the greater is the proportion of pores to solid matter in that body. If therefore carrying on the division in infinitum, you never arrive at parts perfectly solid and without pores, it will follow that all bodies consist of pores only, without any matter at all; which is a manifest absurdity." 25 cr. Theodicy, Part III, Secs. 301-20. 26 The meaning of this paradoxical sentence is found in Leibniz's doctrine of freedom, according to which the spontaneous (i.e., self-determined) act of a rational monad is entirely consistent with the natural contingency (or temporal determinateness) of the world which God has chosen as the best of all possible ones. Freedom in this sense is therefore entirely consistent with God's election of each individual law as the best of all possible individuals within the conditions of the entire contingent system (see No. 29). 27 cr. Theodicy, Part III, Sec. 310. Note that Leibniz does not here, like Kant, identify will with practical reason. 28 These meanings offate are analyzed in the Preface to the Theodicy. 29 This is, of course, only an empirical consideration, not bearing directly on the principle as applied to monads. But phenomenal relations imperfectly represent an infinity of real ones. 30 Clarke's solution of the old issue is Thomistic in the sense that this principle is matter; Leibniz's, on the other hand, is an extension of Scotism in that individuality is the result of the combination of a number of logical possibilities, themselves indeterminate, into a determinate concept or notion. 31 The pragmatic way in which Leibniz uses the principle of sufficient reason, here and elsewhere, is noteworthy. A theory like Newton's conception of gravitational force is 'impracticable' when it does not provide a sufficient reason for observable differences in facts or if it provides a sufficient reason for supposed facts which contradict experience. 32 See Principia philosophiae, Part I, 26, 27. 33 Leibniz's correspondence with Guericke on vacuums and other problems is given in G., 1,93-112. 34 The sentences in parentheses are in Leibniz's copy of the letter but are printed by Clarke as footnotes. 35 Sections 36-48, particularly Sec. 47, give one of the clearest of Leibniz's analyses of the relations of situation, space, and body, in terms both of Scholastic categories and of Leibniz's own new relational analysis. In part it repeats, in part supplements, the logical analysis in the preceding work (No. 70). The relational and abstract nature of space finds clear expression, and the reader must not lose sight, not merely of the a priori nature of space, as formal possibility demanding empirical content in order to determine existence, but also of its basis in metaphysics and in the Leibnizian theory ofiogical form. 36 This reformulates, for spatial relations, Leibniz's doctrine of the intrinsic nature of all denominations. There are no freely floating qualities and relations such as neorealism held to.
720 LEIBNIZ: PHILOSOPHICAL PAPERS AND LETTERS For earlier analyses of the abstract nature of situation and space see Nos. 54, 62, and 63, p. 540, note 7, and p. 628, note 3. Leibniz's derivation of space perception here may be contrasted with Berkeley's in being, not psychological, but logical and existential, with an empirical or 'phenomenological' test for the truly existent as opposed to the fictional reification of abstractions with which he charges his opponents. The theory of space and situation is thus, on the one hand, a more empirical and determinate application of the universal characteristic and logic of relations and, on the other, an analysis of the forms constitutive of perception and of their limitations. The functional notation would have served Leibniz (as it would Euclid in the example mentioned) to universalize his theory of the pragmatic nature of relations. The three interpretations of the relation between Land M would then be L=f(M}; M=f(L); andf(L,M} =0. 88 New Essays, II, 14, Secs. 25-26. 89, 40 See note 34 above 41 This application of the principle of indiscernibility to phenomena brings Leibniz close to Kant's phenomenalism, since possible experience is the decisive mark of existence. But Leibniz would not have subordinated geometry and algebra to the forms of space and time, as did Kant (cf. Sees. 54 and 129 below). 42 See p. 628, note 4. 43 The logarithm of a ratio, for example, can be expressed as the difference between the logarithms of its two terms: log(a/b)=loga-Iogb. 44 Leibniz's fuller analysis of the possibilities regarding the beginning of the universe in time are found in the letter to Bourguet, August 5, 1715 (No. 69, 11). Here as elsewhere, however, merely logical considerations do not entirely determine existence (see note 47, below). 45 "As if a painter tried to join the neck of a horse to the head of a man." 46 O. has duratio for destructio. 47 Leibniz thus arrives at an assertion of a finite beginning.of creation on theological grounds (Clarke's and his own beliefin uniform growth in perfection), not on logical. 48 Cicero De fato chap. xvii. 49 Leibniz here interprets the occasionalists as developing their view in correction of the Scholastic doctrine of intentional species transmitted by the body to the soul. For the sources see Thomas, Contra Gentiles i. 46; ii. 59; Summa theologica i. 85. 2, etc. (see p. 329, note 30). 50 The phrase in parentheses inserted by Clarke has no support in Leibniz's original; his sense seems to have been: "and raises them to the highest level". 51 See the second reply to Bayle in 1702 (No. 60). 52 O.insertsavecchoix. 58 The words in parentheses are added by Clarke. 54 The transfer of energy from macromasses to their internal molecules is inferred by Leibniz as a result ofthe conservation of force (see No. 46, I, for a fuller exposition, in relation to the principle ofthe conservation of internal, relative force). 55 On the distinction between Leibniz's theory of inertia and Newton's see p. 539, note 3. 66 "To live on acorns when fruit has been discovered." Leibniz's criticism, here and in what follows, of Newton's theory of gravitational attraction overlooks entirely Newton's clarification in the closing scholium of his second edition and the sharp delineation which results between the methods of physics and of metaphysics. Throughout the controversy Leibniz seems to be conscious of the influence of Henry More upon Newton's earlier speculations. The view that space is indivisible is traceable to him. 57 For Leibniz's appreciation of Robert Boyle (1626-91) see No. 52 and the New Essays, IV, 12, 13, where he expresses approval of Boyle's mechanistic principles but denies that they can be established on the basis of experience alone (0., V, 437). 58 Cltflie (1656) waS written by Mile de Scudery; Aramena (1669), by Duke Anton Ulrich of Brunswick-Wolfenbiittel, as whose librarian Leibniz served. Leibniz's perception of the change of taste at the tum of the centuries was acute. 37 cr.
HANOVER UNDER GEORGE LOUIS, 1698-1716 721 For Leibniz's theory of preformation see Nos. 58 and 60, and Introduction, Sec. VIII. This empirical justification of the principle of sufficient reason, considered along with Leibniz's rejection of the possibility of any 'pure' empiricism, is an instance of Leibniz's twofold method, a posteriori and a priori. 61 Clarke's fifth reply, probably written after Leibniz's death, is here omitted. 59 60
INDEX Academy, 8-9, 151, 153-54, 582; see also Skepticism Accident, 246, 600, 601-3, 605-6, 609, 621 - absolute, 602 - categoriai, 614 - and modification, 600, 606, 609; 614,617 - nonmodal, 600--1 Action, 271, 502-4, 511-12, 609 - external, 503 - internal, 644 - and passion, 118-19, 269, 313, 448, 511-12,520,530--31,533-34,623-24, 647-48; see also Force Addition - logical, 380--81 - real and quantitative, 381 Aesthetics, 48-49, 425-26, 428, 489-91, 565-66; see also Beauty Affections, 76 - natural, 632-33, 634 Aggregates, 605, 614, 617 Agricola, Rudolf, 127 Agrippa von Nettesheim, 101 Albertus Magnus, 342, 454 Alchemy, 85, 124,249 Algebra, 76, 84, 166, 192, 193,233,248, 250,276,545-46 Anagogical principle, 45,477, 484-85; see also Mechanism, and teleology Analogy, 123, 284 Analysis situs, 248-258; see also Geometry, of situation Analysis and synthesis, 20--21, 80, 88, 151-52,173-76,184-85,186--88,191, 182-93,226,229-34,234,236,264-65, 282-86, 293, 540, 664, 673 - reductive, 233; see also Judgment Anaxagoras, 96--97 Ancient philosophy; see Philosophy, ancient and modem Andreae, Tobias, 94 Angelus Silesius, 47, 425, 554, 594 Animals; see Beasts Anselm, St., 231, 234, 386 Antitypy, 95, 101-102; see also Mass Aphthonius of Antioch, 469, 471 Apollonius of Perga, 187,254, 383 Apologetics, Christian, 109-20,259-62, 303-330 Apperception, 22, 62, 553, 637, 642, 644; see a/so Reflection; Self-consciousness Appetite, 38,101,504,537,636,644,662-63 Aquinas, St. Thomas, 117, 274, 293, 308, 309, 342, 386, 454, 461, 653 Archeus, 309, 328, 409, 412, 441, 555, 587 Archimedes, 180, 187, 227, 236, 268, 341, 393, 468, 543, 677 Architectonic, 479, 480, 484, 485; see also Optimum, principle of Aristotelians, 135, 188, 432, 436, 554-55, 586; see a/so Aristotle Aristotle, 25, 37, 48, 60, 81, 93-104, 117, 124,126,127, 161,186,188-89,190,223, 274,320--21,342,391,454,456,477.499. 554,571,593, 630, 631, 654-55, 677 - logic, 389, 465-66 Arithmetic, 90, 92 Arithmetical machine, 274-75,474 Arnauld, Antoine, 6, 19, 60, 148-50, 210, 211, 212, 259-260, 271, 276, 291, 294, 303, 331-350, 359--62, 453, 460, 474, 579 Art of characteristics; see Characteristic; Universal characteristic Art of combinations, 73-84, 84, 91, 173-75, 192-93, 222-23, 229-30, 657, 670, see also Logical calculus; Universal calculus Art of Thinking, The, 60, 294, 465 Assistance, way of; see Occasionalism Association, 40, 90, 638 - laws of, 86--87. Atheism, 50, 102, 109-10; 272-74, 633 Atomism, 112, 157-58,269-70,405-6, 415-16, 420, 506, 599, 657, 691, 719 Atoms; see Atomism Attention, 113, 384, 388 Attila, 634
INDEX Attributes, 160-61, 197-201,245,246, 284-87, 390, 411, 519, 526, 528, 620, 621 - simple, 205, 285, 525, 526; see also Concepts Augustine, St., 38, 147, 322, 342, 582, 593, 594,603 Authorship, 631 Averroes, 95, 117,321,425,554, 603 Averroists, 95, 321, 425, 560, 594; see also Averroes Avicenna, 499 Axioms, geometric, 383-84 Bacon, Francis, 89, 93, 94, 109, 110, 124, 152, 188,277,465,682 Bacon, John; see Baconthorpe, John Baconthorpe, John, 342, 454 Barbarism, 223 Barometer, 474 Barrow, Isaac, 419 Bartholin, Erasmus, 76. Basnage de Beauval, Henri, 383, 416, 453, 513,586 Basso, Sebastian, 93, 127 Bayle, Pierre, 12, 56,212,453,492-97,513, 527-28, 559, 574-85, 586, 590, 644, 648, 711 Beasts, 190,211,275-76, 342, 345-47, 455, 512-13, 557-58, 588-89, 638, 644, 645 Beatific vision, 109, 154, 559, 641 Beauty, 137, 425-26, 428, 479, 489-91, 552-53,565-66,641 Becher, Johann Joachim, 58, 249, 258 Bede, St. 115 Being, 89, 242, 363, 549; see also Substance - law of, 24 - most perfect; see Ontological argument - and nonbeing, 367-68 Berkeley, George, 609, 514, 616 Bernier, Nicolas, 472 Bernoulli, James, 417, 511, 542 Bernoulli, John, 383,417,477,511-14, 523, 538, 542 Best possible, principle of, 27, 45, 157, 209-10,217-19,304-6,328,333-34,513, 659,664; see also Optimum, principle of Biel, Gabriel, 128, 342 Bignon, Jean Paul, 475, 476 Billettes, Giles Fillieau des, 211, 472-76 Binary numbers, 59 Biology, 35-37, 186,282,316,317,345-46, 455, 557-58; see also Beasts 723 Bisterfeld, John Henry, 88, 91 Bodenhausen, Baron, 359, 435 Bodies - composite; see Substance, composite - as phenomenal, 330, 343, 600--1; see also Body; Phenomenalism - system of, 450 Bodin, Jean, 93, 102, 104 Body, 33-34, 75, 106, 109-12, 107, 116, 140-41, 142-45, 165, 173-76, 210, 270, 274,277-79,309-10,325-26,343-44, 360,365,392,440-42,444-45,503-4, 521-22,532-33,539,596-617,715 - mathematical, 100, 535-36 Body-soul relation, 39-40, 211, 269, 324-25,338-39,453-61,492-95,513-14, 517-18,556-57,574-81,593,649-50, 686,689-90,710-12 Body-soul unity, 269, 339, 360, 539, 598 Boehme, Jacob, 221 Boileau, Nicolas, 659 Boineburg, Baron von, 109, 121,259-60 Borelli, John Alphonso, 298, 439 Bosses, Bartholomew des, 597-617 Bossuet, Jacques Benigne, 6, 47, 259, 430 Boundary,95-96,141,668 Bourguet, Louis, 661-65 Boyle, Robert, 94, 110, 165, 166,277,290, 498,499,508,715,720 Brachistochrone, 477, 478, 485 Brain, 565 Brief Demonstration of a Notable Error of Descartes, etc., A, 296-302 Brunswick, House of, history of, 359 Burnet, Gilbert 656 Burnet, Thomas, 356, 629 Caesar, Gaius Julius, 569 Calculus - differential and integral, 59, 61, 191, 361, 417, 419, 420, 474, 475, 542-43, 655-56 - logical; see Logical calculus - mathematical, 191 Campanella, Tommaso, 93, 100-101, 104 Campensis, Claudius, 81 Cardan, Jerome, 75, 78-79, 93, 193, 466 Caroline, princess of Wales, 356, 658, 675, 677 Cartesians, 33, 34, 94, 177-81, 188, 190, 274,275,298,333,494-95,512,521,522, 526,527,532,536,578,588,619-20,637; see also Descartes, Rene
724 Cartesius, Renatus; see Descartes, Rene Casuistry, legal, 82 Casuists, 215 Categories, 229, 464-65 Catelan, Abbe, 210, 212, 296, 348, 351,542, 659 Catholic Demonstrations, 49-51, 109-20, 148, 173, 259--62, 277, 303 Causality, 26-27, 35, 75, 89, 129, 153, 173-76,201,208,268-69,279-87, 312-13, 321, 365, 588, 637, 680 Cause, see Causality Cavalieri, Francesco Bonaventura, 8, 140, 144, 584 Certainty, 122, 153-54,283-84, 383 - moral and metaphysical, 129-30, 364-65 Chance, 708; see also Indifference Change, 96-97, 519, 521, 531, 532-33, 538, 643-44 Character, 21, 164, 183-85, 192-93, 208 Characteristic, 21, 192-93,221-28,248-49, 249-50,261-62,273-74,371-82 - geometrical 248-58; see also Universal characteristic Characteristic numbers, 221-25, 235-36, 238-40 Charity; see Love Chemistry, 97, 173-76 Chevreuse, Due de, 249 Christina, queen of Sweden, 554 Church, 213-15, 260 - unification of, 259--62 Cicero, 99, 136, 570 City of God, 347-48, 458, 640, 651-52; see also Grace, kingdom of Claim, legal versus moral, 422-23 Clarity, 121-23; see also Clear and distinct Clarke, Samuel, 32, 94, 663, 675-721 Clauberg, Johann, 94 Clavius, Christopher, 79 Clear and distinct, 287, 291-92, 293-94, 318-19,389; see also Concepts; Ideas Clerselier, Claude de, 94 Cluver, Philipp, 544 Cocceius, John, 227 Codex juris gentium diplomaticus, Preface of, 421-24,567,594 Coherence, 363-64 Cohesion, 106-7, 112, 141, 148, 403-9 Coincident terms, 237, 371-72 Cointegrant terms, 379 Colbert, Jean Baptiste, 249 INDEX Colors, 484 Combinations; see Art of combinations Comenius, John Amos, 90, 389 Commercium epistolicum, 675 Common sense, 548, 602, 631 Complexions; see Art of combinations Component terms, 372 Composition and division, 243-44, 372 - of conatuses, 142 Compossibility, 169, 266, 661-62 Conatus, 16, 17, 32, 107, 108, 140-42, 144-45,149,279,299,435,437,473,609; see also Impetus Concepts, 318-21, 518-20, 522, 549; see also Ideas; Terms - complete versus partial, 24, 268-69, 307-8, 332-35, 348-49, 529, 708 - distinct and confused, 178-80, 230--31, 285-87,292,389,525 - obscure and clear, 291-92 - perfect; see Concepts, complete versus partial - primary and derivative, 91, 230--31, 292 - simple and complex; see Terms, simple and complex Concomitance, 269, 336-38, 340, 458 Concrete and abstract, 529, 620--21; see also Concepts, complete versus partial; Ideal and real c;on/ession 0/ Nature against Atheists, The, 50, 102, 109-13 Congregation for the Propagation of the Faith,262 Congruence, 135,251-53,258,363-64 Conring, Herman, 95, 96, 103, 186-91 Conscience, 135-36 Consciousness, 161, 671 Consensus; see Body-soul relation; Harmony Conservation - of force; see Force, conservation of - principle of, 27, 296-302, 314-15 - of quantity of motion; see Quantity, of motion, conservation of Considerations on Vital Principles and Plastic Natures (1705), 586-91 Consistency, 153-54, 351 Constance, Council of, 58 Contained-containing; see Inclusion Contarini, Casparo Cardinal, 554 Contingency, 203-4, 263-66, 268, 310--11, 328-29,487,697
INDEX Contingent truths, 263-66; see also Truths, of faltt; Truths, necessary and contingent Continuity, 315, 412, 447, 521, 544, 658, 671; see also Continuum - principle of, 30--31,271, 351-54, 354, 397-403, 446-48, 484, 515-16, 521, 539, 546, 573, 583, 670 Continuum, 96, 139-42, 158,264,270,608, 656 Contradiction, principle of, 225, 646 Conversation of Philarete and Ariste (ca. 1711),618-28 Cooper, Anthony Ashley; see Shaftesbury, third Earl of Copernicus, 419, 450 Cordemoi, Gerauld de, 270, 343, 456, 502 Corpuscular philosophy, 93-104, 110,290, 338,349, 353,451,478,496 Cosmography, 90 Cosmological argument, 50,73-74, 486-87, 565-66, 587 Coste, Pierre, 356, 629, 654 Couturat, Louis, 23, 267 Creation, 97, 331-36, 486-91, 500--1, 597, 598, 664, 691, 706-8, 720; see also Best possible, principle of Criterion of truth; see Truth, criterion of Cryptography, 188, 192, 283 Cudworth, Ralph, 586, 589, 590 Cycloid, 142 Dalesme, Andre, 472 De diaeta, 342, 456 De Witt, Jan, 584 Death, 345-46, 514, 557-58, 638; see also Immortality Deduction, 20 Deferent, 361, 415 Definition, 25, 122-23, 133, 183, 187, 194, 197, 230--32, 245, 246, 267, 292-93, 319, 511,519 Deism, 676 Democritus, 112, 188, 435, 558, 593, 623, 677 Demonstration, 133-34, 138, 177, 187,232, 383-84,465-67,668 Denominations, 268, 365, 464, 500, 526-27, 643,719 Denores, Jason, 95 Descartes, Rene, 36,42, 76, 88, 91, 93-94, 107, 110, 139, 152-54, 165, 188-90, 210--12, 223, 254, 261, 263, 264, 272-74, 725 291,292, 339-40, 342, 352, 432-33, 439, 447, 452, 468, 473, 522, 537, 613, 655, 657, 663, 701 - conservation of quantity of motion, 296-302, 352, 393-95, 443-44, 587, 655 - demonstration of existence of God, 143-45,154,168,180,211,231,292 - laws of motion, 274, 352, 396-403, 408, 448 - ontological argument, 143-45,211, 386-87 - optics, 480 - Principles of Philosophy, 383-412, 416, 419 - voluntarism, 181, 387-89, 647; see also Cartesians Deschales, Claude, 298, 439 Determinants, 258 Determinism, 146-47, 179-80, 322-23, 331-50; see also Necessity Digby, Kenelm, 93, 94, 97, 103, 110 Diophantus, 248 Dioptrics; see Optics Discourse on Metaphysics, 303-30 Discovery; see Invention Disparate terms, 238, 245, 372, 379-81 Disposition, 78, 95, 323, 698-99 Disputation, 224, 466-67 Distance, 666-67, 671 Ditton, Humphrey, 663 Diverse terms, 245, 371 Doubt, Cartesian, 383-84 Dreams, 113-15, 119, 153-54,557,640 Dreier, Christian, 95 Du Cange, Sieur, 359 Duns Scotus, John, 60, 120, 128 Durr, Johann Conrad, 95 Duty, 48 Dynamics, 139-45, 296-302, 359, 360, 413-20,435-452,459,625 Dynamism, 16, 19; see also Force Eckhard, Arnold, 177-81, 190 Education, 85-92 Ego, 39, 325, 335, 456, 549, 593, 619, 638, 646; see also Apperception; Reflection; Selfconsciousness Egoism, 47, 134,424-25 Elastic force, 279, 350, 397, 446-47, 448. 473, 506, 718-19 Election. 323-24
726 INDEX Elegance, 121-22 Elementa de mente, 37, 105, 107, 149, 165 Elementa physicae, 277-290 Elements, physical, 75, 81 Elements 0/ Calculus, 235-240 Elements 0/ Natural Law, 131-38, 150 Elements of Natural Science, On the; see Elementa physicae Elizabeth, Countess Palatine, 209 Eloquence, 132 Emanation, 311, 312, 324 Empiricism, 153-54, 547-551, 645 Encyclopedia, 221, 277 Entelechy, 522, 529, 576-77, 644; see also Force, primitive and derivative; Souls; Substantial form Enthusiasm, 592-95, 629 Epicurus, 99, 112, 577-78, 677, 680, 708, 717 Epistemology, 18, 41-44, 151-56, 161-62, 182-85,207-8, 291-95, 363-66, 547-51, 626-27 Equality, 667; see also Equipollence Equilibrium, 698 Equipollence, 205, 227, 279,296-301, 442-43,445 Equity, 422, 568-69 Equivalence; see Equipollence Erasmus, Desiderius, 469, 471 Ernest August, Duke of Hanover, 272 Ernest of Hesse-Rheinfels, Landgrave, 7, 259, 303, 331 Error, 44, 292, 384-86, 387-88, 391, 611; see also Truth, and falsity Essence and existence, 203-4, 664 Eternity, 705 Ethics, 46-49, 75-76, 89, 131-38, 150, 360, 421-31,561-73,593-94,630-35 Eucharist, 109,596,600-1,614-15; see also Transsubstantiation Euclid, 82, 142, 153, 187, 193,230,236,248, 254,258,294,383-84,391,410,486 Eugene of Savoy, Prince, 59, 356, 636, 654 Evil, 49, 51, 147,211,217-18,265,322-23, 489-91,513,582,659 - moral, 307, 567-68, 630-31, 662 Evolution, 37, 513 Exigence, 487, 600, 601 Existence, 91, 158, 163,205,363-64 - law of, 26 Experiment, 173-76,282-84 Expression, 198, 203, 207-8, 242, 269, 312, 327, 337-38, 339-41, 365, 457-58, 531; see also Perception; Representation Extension, 143-45, 270, 390, 392-93, 516, 518-19,525,527,601,607,619-22,667; see also Space Extremum, principle of; see Optimum, principle of Extrinsic denominations, 268, 271, 365, 432, 500, 505; see also Denominations Fabri, Honoratius, 298, 439, 613 Faith, 369 Fardella, Michelangelo, 359 Fate, 146, 697 Fatio de Duillier, 417, 420 Feeling, 38, 325,340-41,492-94 Felden, Johann von, 48, 95, 421, 428-30, 431 Fenelon, Francois, 47, 328, 425, 431 Fermat, Pierre de, 165, 248, 318, 479, 584 Fernel, Jean, 342 Fictions, 543, 552, 604 Figure, 95-96, 110,254,270,278,505 Filmer, Robert, 572, 573 Final causes, 477-79, 651; see also Mechanism, and teleology Firmness, 111,403-9,415-16,449 First philosophy; see Metaphysics First truths, 74, 225-27, 228, 234, 267-71, 385 Fitness, principle of, 76, 640, 647; see also Best possible, principle of Fludd, Robert, 409, 412, 441, 502, 663, 665 Fluidity; see Firmness; Fluids Fluids, 403-8 Fontenelle, Bernard de, 456 Force, 32, 33, 92, 155, 221, 276, 279, 301, 360,361,393,433,434,435,444-50,451, 501-2, 503-5, 516, 537, 624, 712 - active, 433, 436-37, 517, 528, 609, 686, 718 - conservation of, 33, 296-302,314-15, 393-95, 443-44, 499, 639, 676, 713 - dead and living, 299, 438-39, 512 - passive, 437; see also Force, active; Matter - primitive and derivative, 341, 436-37, 514, 529, 533-34 - violent and harmless, 442 Forge, Louis de la, 502, 508 Forms, 160--61, 162-63, 269, 271, 511-12; sf;e also Ideas; Substantial forms; Terms
INDEX - simple, 160; see also Qualities, primary Formulas, 193, 233 Foucher, Simon, 151-56,453,582 Fracastori, Girolamo, 93 Freedom,27-28,40-41,52-53,146-47,211, 214,263-66,280,321-22,324,384, 388-89,503,696-97,712,719 Fromond, Libertus, 60, 159 Function, mathematical, 29-31, 60, 579 Future, 310-11, 360, 513 Gabets, Dom Robert des, 151, 154-55 Galen, 81 - hynm of, 280, 479 Galilei, Galileo, 93,110,153,188,259,273, 301,302,393,439,469-70 Gallois, Abbe, 167, 542, 544 Games, 61,472,487,584 Gassendi, Pierre, 93, 94,110,112,152,290, 450, 579, 584, 657, 663 General Characteristic, On the; see Universal characteristic General science, 21-23, 60 Genus-species, 237, 246 Geometry,90,92,98-99,148-49,274,278, 383-84, 666-74; see also Characteristic, geometrical - of situation, 193, 248-58, 361 Geopolitics, 59 German language, 125 Geulincx, Arnold, 461 Gilbert, William, 94 Glanville, Joseph, 93, 103, 221 Goc1enius, Rudolph, 683, 686, 689 God,45, 50-52,138,158-60,163-64,197206, 280, 283, 294, 301-330,346-48, 360, 367-69, 488, 489, 507, 552-53, 561-73, 580, 639, 646-48, 678-79, 68384,702-3 - arguments for existence of, 50-52, 73-74, 109-12, 200-201, 211, 275, 341, 386-87, 486-87,587,711 - foreknowledge of, 322-23, 681, 696 - immensity and eternity of, 714 - vision of, 305, 627; see also Beatific vision - will of, 303-4, 305-6, 500-1, 561, 647-48, 683, 685-86, 709 Goeckel, Rudolf; see Goclenius, Rudolph, Goodness, 134,561-62,564 Grace, 305-6, 323-24, 368-69 - kingdom of, 46, 53,218, 327-28, 346-48, 409-10,442,478-79,588,590,641,651- 727 52, 679; see also Nature, kingdom of Gravity, 361, 414-15, 417-18, 473, 513, 663, 696, 701-2, 716 Great Britain, 631, 634 Gregory of Rimini, 128 Gregory of St. Vincent, 130 Grotius, Hugo, 6, 58, 59, 75-76, 84,469 Guericke, Otto von, 94, 103,701 Guyon, Mme, 328 Habit, 85-88, 645 Hamel, Jean Baptiste du, 94 Hansch, Michael Gottlieb, 592-97 Happiness, 131,219,306,327,424-25 Harmony,I4-17,76,112,138,141,146,15758,311-12,425-26,489-91,565-67,569, 640,648-49,652,658-59,711-12 - pre-established, 457, 460, 461, 492-95, 574-81, 586-88, 599, 610, 612, 637, 651, 679, 694-95, 710-12 Hartsoeker, Niklaas, 455, 461, 628, 657, 658 Harvey, William, 36 Hedonism, 46-47, 630 Heereboord, Adrian, 94 Hegel, G. W. F., 56-57 HeImont, Franciscus Mercurius von, 508, 589,591,631-32 Helmont, Jean Baptiste, 328 Hermann, Jacob, 542 Herrenhausen, 13-14 Heterogeneity, 238; see also Homogeneity Hippocrates, 342, 499 History, 88-89, 131,290,421,491,660,664 - of House of Brunswick, 359 Hobbes, Thomas, 37, 82, 85, 88, 93, 94, 105-8, 110, 114, 126, 128, 130, 161, 182, 183, 231, 258, 273, 397, 501, 562, 569, 571, 577, 588, 630, 631, 677 Hoghelande, Cornelius von, 94 Homme honnete; see Honor, man of Homogeneity, 278, 286, 443, 666, 668, 672; see also Heterogeneity - of bodies, 394 Homogony, 666, 668 Honor (honestas), 48, 136,423,570 - man of, 3, 9, 14, 58, 213, 426-28, 631 Hontan, Baron de la, 7 Hooke, Robert, 96 Hospital, Marquis de 1', 417, 435, 474, 542,584 Hudde, Jean, 249, 584 Huet, Pierre Daniel, 275, 276, 463, 471
728 INDEX Hugony, Charles, 656 Humanities, 464 Hume, David, 56 Humor, 629 Huygens, Christian, 139, 151,248-49,301, 413-20,419,439,452,459,465,542,655 - De ludo aleae, 472, 584 Hylarchic principle, 441, 499, 587 Hypotheses, equivalence of, 445, 459 Hypothesis, 73, 83, 100, 133, 188, 231, 283-84, 458, 493, 514, 515, 527 Iceland spar, 413, 485 Idea; see Ideas Ideal and real, 539, 543-44, 704-5 Idealism, 578 Ideas, 15-19,118-19, 120,154-55,163,204, 207-8,291-95,318-321,344,386-87, 517-18,520,625-27,646,710 - operative, 100 Identities; see Identity Identity, 23-24, 163, 187,225-26,677-78 - of indiscemibles, 268, 308, 505-6, 643, 687, 692, 699-700 - personal, 39, 162, 349; see also Selfawareness; Self-consciousness; Selfknowledge - principle of, 45,225-26,267, 677-78 Imaginary numbers, 511, 543 Imagination, 89, 91, 161,478,522,548-49, 553,645 Immensity, 159, 163, 164,685,702,703; see also Space Immortality, 53,113,162, 169,270,326-27, 337, 455, 556--57, 564-65, 588-89, 594, 638,650 Impact, 111-12,269,278,349-50 - laws of, 142,302, 352, 396-403, 411-12, 447-49 Impenetrability, 95, 100,517; see also Firmness Impetus, 299-301, 437, 450 Impossibility, 319 Inclination, 227, 696--97 Inclusion, 236--37, 372-74, 379-80,668; see also Subject-predicate inclusion Indians, American, 630, 634 Indifference, 322, 337, 687 Indiscernibles; see Identity, ofindiscemibles Individual - concept, 307-8, 309-10, 331-35 - law of, 17, 30, 39, 155, 309-11, 331-35, 360,535, 652; see also Individuation principle of - as series, 360, 533, 534, 577 Individuality, 17-19, 203, 268-69, 307-9, 331-35,360,530-31,534,554-60,581-82, 586--90 Individuation, principle of, 117, 120, 700, 719 Induction, 129-30, 234, 284, 550 Inertia, 437, 503-4, 516--17, 539, 647, 659, 713 Infallibility and contingency, 263-66; see also Contingency; Necessity Infinite, 30-31, 75, 159, 167--68, 264-65, 351, 387, 511-14, 541, 542-44, 555, 626--27,649,669,693 Infinitesimals, 511, 514, 542-46, 583-84 Infinity; see Infinite Influence, 75, 83, 126,269,453-60 Ingredience; see Inclusion; Subjectpredicate inclusion Initia et specimina scienfiae generalis, 221 Innate ideas, 593 Innocent XI, Pope, 259, 262 Instruments, scientific, 131, 174, 175 Intellect, 204, 549-50, 554, 556 Intension and extension, logical, 237-38, 247,379 Intensity, 86--87, 177 Intentional species, 320, 710, 716, 720; see also Species, sensible Interaction, 338,494,534,613,694-95,710; see also Influence Interest, 630 Internal sense, 548 Intuition, 120,292,593,607; see also Knowledge, intuitive or symbolic Invention, 88, 281-83, 463-65 - and judgment, 80, 88, 126--27, 229-34 Ives, Father, 657 Izquierdo, Sebastian, 604 Jagodinski, Ivan, 157 Jansen, Comelis, 603, 616 Jansenists, 148,214,474,603,659; see also Jansen, Comelis Jaquelot, Isaac, 712 Jesuits, 213-16, 261, 274, 359, 659 Jesus Christ, 214--16, 327 Joan, Popess, 597, 615 John Frederick, Duke of Brunswick, 259-62 Joy, 425, 492; see also Pleasure
INDBX Judgment, 465-67; see also Invention, and judgment Julian, Emperor, 634 Jung, Joachim, 95, 124, 130, 223, 227, 290, 468 Jurieu, Pierre, 679 Jurisprudence, 82, 85-92, 106, 131-38, 149-50,421-24,561-73 Justel, Henri, 195, 359 Justice, 47, 75-76, 106, 133-38, 149-50,360, 421-24, 561-73, 640 - principle of, 348, 490, 670; see also Harmony Kant, Immanuel, 56, 329, 410 Kepler, Johannes, 301, 393, 395, 473 Kircher, Athanasius, 230, 234 Knowledge, 18,41-44, 151-56,291-95, 318-19,363-66,689; see also Concepts; Epistemology; Truth - adequate or inadequate, 42, 291-92 - finite, 599 - intuitive or symbolic, 232, 291-92, 319 - of other minds, 365, 612, 613 La Chaise, Fran90is d'Aix de, 273-75, 276 Laboratories, 282 Labyrinths, 27, 159,264,309 Lami, Dom Francis, 453, 585 Language, 121-30, 193,221 - universal, 654 Lasser, Herman Andrew, 6, 85, 131 Lavintheta, Bernard, 82 Law, 6,47, 81,422-25, 564 - of the indefinite series; see Individual, as series - natural and moral, 423-24,716-17 positive divine, 424 Laws - of motion, Cartesian; see Descartes, laws of motion - of nature, 144, 306-7, 477-78, 494-95, 499-502 Le Clerc, Jean, 586 Learning, 87-88 Leeuwenhoek, Anton van, 36, 345, 350, 455, 560, 566 Leibniz, Gottfried Wilhelm von - autobiographical, 152-53, 222-23, 229, 259-60, 440-41, 453-57, 462-65, 654-55 - life and works, 4-13 - philosophical inconsistencies, 54-56 729 - philosophical infil.1ence, 56-58 Leucippus, 112 Liberty; see Freedom Life, 637; see also Organism; Vitalism Light,473 - inner, 367 - natural, 549-51; see also Intellect Line, 668 - straight, see Straight line Lipsius, Justus, 85, 90 Locality; see Situs Loci; see Locus Locke,John,12,56,547,554,593,631,632, 656, 657, 675, 676 Locus, 88,251-53,668-73 Logic, 23-28, 73-84, 126-27, 160-61, 221-28,229-47,260,371-82,389,404, 462-71 - and metaphysics, 23-28, 126-27,267-71 Logical calculus, 25-26, 235-47, 371-82, 463-64 Logistics, 254 Love, 135-37, 150,213-16,219,280, 305, 360,368,421-24,641.652 - disinterested, 133-34,424-25, 430, 594, 630, 632-33, 635 Lucretius, 112 LulIy, Raymond, 82, 88,91,230,657 LUlla Fixa, 237 Luther, Martin, 128 Mabillon, Jean, 359 Machines, natural and artificial, 456, 574-76,637,649, 677-79, 690; see also Mechanism Magnenus, John Chrysostum, 112 Magnetism, 75, 415, 473-74 Magnitude, 110,249,254 Malebranche, Nicolas, 151, 154-55,207, 209-12, 276, 291, 294, 295, 344, 351, 352-53, 448, 455, 457, 463, 502, 532, 555, 593, 618-28, 658, 678; see also Occasionalism Malpighi, MarceIlo, 344, 350, 455, 560 Mandates, 81 Manicheism, 583 Mantissa codicis juris gentium, 424-25 Marci, Marcus, 100-101, 104,439 Marinus of Neopolis, 254 Mariotte, Edmonde, 248, 439, 447 Masham, Lady, 356, 591 Mass, 95, 101, 103,296,451, 503, 598,
730 INDEX 701-2; see a/so Matter, primary and secondary Materia prima; see Matter, primary and secondary Materialism, 501-2, 551-53, 577, 587-88, 623-24,676,677,680; see a/so Atomism Mathematics, 28-31, 76-77, 89-90, 98-99, 189,261,273-74,535,542--46,584, 666-74, 677-78, 682 - and metaphysics, 28-31, 76-77, 98-99, 261, 289, 513, 529, 542--43, 583-84, 592, 666-74, 677-78, 682 Matter, 100, 158, 342--43, 350, 503--4, 517, 529, 597, 659, 701-2 - primary and secondary, 17, 33, 95-96, 350, 366, 437, 451, 504, 508, 511, 598, 615 Maxima and minima, 478-79, 487-88 Maximum, principle of, 477-85, 667; see a/so Optimum, principle of Measurement, 249, 256, 468, 667, 669-70 Mechanism, 109-10, 173, 189-90,217, 275-76,456,499,574-76,624, 655; see a/so Machines, natural and artificial - organic, 189-90,275-76,529-31 - and teleology, 35, 44-46, 189-90, 273, 288-89, 290, 315-18, 338, 347--48, 353, 409-10,441--42,472-73,477-85,588, 655,715-16 Medicine, 132, 191,274,282,417,474,632 Meditations on Knowledge, Truth, and Ideas, 291-95 Melissus, 342, 456 Memory, 113-15, 141, 155, 160-61,325-6, 337,384,637,645.653 Menochius, Jacob, 82 Mercenarius, Angelus, 117 Mere, Chevalier de, 475, 584 Mersenne, Marin, 282, 302, 433, 663 Metamorphosis; see Transformation Metaphysical Foundations 0/ Mathematics, The (after 1714), 666-74 Metaphysics, 13-19,44--46,76-77,260, 267-71,303-30,432-34,453-61,472-73, 492-97, 498-508, 511, 515--41, 554-55, 586-89, 596-617, 636--42, 643-53, 655, 661-65, 666-74, 675-721, 718; see also Logic, and metaphysics; Mathematics, and metaphysics Metempsychosis, 455, 658 Method, 19-23, 88, 133, 173-76, 186-91, 229-34, 277-90 Method/or Distinguishing Real/rom Imaginary Phenomena, On the, 363-66 Middle science, 27, 61, 266 Mind, 88, 107, 113, 116-18, 141, 149, 160, 161-62,210,454,535; see also Spirit Mind-body problem; see Body-soul relation Mind-body unity; see Body-soul unity Minds, other, 365 Miracle, 306-7, 313,494,497,578,625, 684, 686-8, 690, 695, 714-15 Mirandola, John Pico of; see Pico della Mirandola, Giovanni Missionaries, 225, 262 Mnemonics, 88 Modem philosophy; see Philosophy, ancient and modem Modes, 203, 390, 524-25, 528-29, 532-33, 608,617, 624 Modifications; see Modes Molanus, Gerhard, 177 Molina, Luis, 61 Molinos, Miguel de, 328, 425, 554 Molyneux, William, Dioptrics, 442, 479, 500, 656, 657 Momentum; see Quantity, of motion, conservation of Monadology, The (1714),60,643-53 Monads, 45, 62, 503, 504, 508, 521, 534, 539, 579, 603-5, 636-37, 643-53, 663 - dominant, 531, 580, 604-5, 617; see also Entelechy; Souls - as series; see Individual, as series Monism, 532, 554-55 Moral certainty; see Certainty More, Henry, 342,441,452, 499, 555, 655 Morland, Sir Samuel, 298 Motion, 32, 73-74, 96-104, 111-13, 139--42, 148-50, 278, 341, 445--46, 505, 533,668 -laws of, 144,274, 301-2, 352, 396--403, 412,459 - relativity or absoluteness of, 393, 418, 419,420,445--46,448-50,459,693 Motives, 570, 697, 698 Multiplication, logical, 235; see also Addition, logical Murcia, Francesco, 117 Music, 48--49, 425-26, 490, 641 Mysticism, 49, 367-70,424,593, 594 Napier, John, 275
INDEX Natural law, 106, 131-38,421-25,428-30, 630 Natural right; see Natural law Natural science, 173-76, 277-290, 296-302, 566,638 - utility, 131-32,273-75, 277-281 Naturalism, 49, 102; see also Nature Nature, 62, 142, 166, 198,498-508, 566, 621,630,632,634,664 - and art, 499 - kingdom of, 409-10, 442, 478-79, 588, 590, 651; see also Grace, kingdom of - laws of; see Laws, of nature Nature Itself, On (1698), 498-508 Naude, Gabriel, 102, 555 Necessary truths; see Truths, necessary and contingent Necessity, 152, 185, 187, 203, 205, 226-27, 331,664,691,696-97 - metaphysical, 488-89 - metaphysical versus moral, 696-97, 709-10 - physical or hypothetical, 488-89, 696 Negative truths; see Truths, negative New Method of Learning and Teaching Jurisprudence, A, 85-92, 186 New Physical Hypothesis, 139, 148,440, 516 New System of the Nature and the communication of Substances, A (1695), 453-61, 492, 574 Newton, Sir Isaac, 12, 355, 413, 415, 417, 418,419,473,513,663,675-721 Nicole, Pierre, 60, 474 Nieuwentijt, Bernard, 542, 544 Nijmegen, Treaty of, 259 Nizolius, Marius, 93, 121-30, 133 Nominalism, 127-30 Number, 76-77, 84, 92, 221, 664 Obedience - external and internal, 260 - passive and active, 59, 260 Obligation, 137,630 Occam, William of, 128 Occasionalism, 269,321-22,338,340, 444-45,450,457,460,494,506-7,532, 580, 587, 624, 720 Ocellus Lucanus, 81 Oldenburg, Henry, 165-66,419 Ontological argument, 52. 143-45, 157, 165-66,167-68,169,177-180,231, 292-93,385-86,647,653 731 Optics, 248,317-18,479-83 Optimism, 131-32, 147, 216-20, 322-28, 489-91; see also Pessimism Optimum, principle of, 61,217-19, 304-6, 308,477-79,487-88; see also Best possible, principle of Order, principle of, 77, 184-85,348, 351-52, 381, 495, 496, 515-16, 521, 557, 565 Organ, musical, 81-82 Organism, 35-36, 343-44, 347, 637, 638 Origenists, 583 Ovid,86 Papin, Denis, 296, 471, 474 Pappus, 254 Paracelsus, 328, 412 Parallelism; see Body-soul relation Pardies, Ignatius Baptista, 439 Paris Notes, 157-64 Parmenides, 342, 343, 456 Parsimony, principle of, 128 Part-whole, 73, 76-77, 83, 379, 534, 664-65, 668; see also Inclusion Pascal, Blaise, 165, 275, 276, 294, 298, 474, 476, 584, 656 Passions, 632 Passivity; see Action, and passion Path, mathematical, 668 Peirce, Charles S., 57 Pellisson-Fontanier, Paul, 6, 475 Penn, William, 369 Perception, 38-39, 41, 62, 91-92, 119, 160--61, 161-62,271,279,292,339-41, 344,456,496,513,537,552,580-81, 586, 610, 611, 625-26,636-37, 644, 662-63,671,678,680,683,710-11 - unconscious or petit, 557, 587, 644 Perfection, 45, 167-68, 177,218-20,303-6, 367,424-26,489-90,523,569-70,640, 646-47; see also Attributes Perier, Antoine Scipion, 474, 476, 656 Perier, Casimir Pierre, 474, 476, 656 Permutation; see Variation Personality, 39, 347, 552 Perspectives, 97, 103, 312, 468, 648 Pessimism, 216-217; see also Optimism Peter I, czar of Russia, 609 Phenomenalism, 142-45,232,270,343, 363-66,390-91,445-46,496,530,531, 600,601-2,604,623,659 Philipp, Christian, 272-73, 276
732 INDEX Philoponus, 342 Philosophy - ancient and modem, 93-104, 124-25, 188-90,261 - history of, 93, 496-97, 592-93, 680 - terminology of, 124-26 Phoronomy, 139-42, 145 Phosphorus, 176, 249, 277, 289-90 Physics, 31-35, 75, 90, 93-104, 139-45, 274, 296-302, 352-53, 360, 391-412, 435-52,450-51; see also Natural science Piccart, Michel, 95 Pico della Mirandola, Giovanni, 127 Piety, 214-16, 423, 570 Placcius, Vincent, 12-13, 465, 471 Place, 703-4; see also Locus Plane, 672-73 Plants, 344, 664 Plastic natures, 101, 586-91 Plato, 76, 118, 151, 155,272,316,320,343, 432, 436, 477, 562, 592-95, 654-55, 659, 677 - Phaedo, 272, 276, 316, 353, 549, 579 Platonism, 367,432,496, 549, 555, 592-95, 633 Pleasure, 136-37, 425, 569-70, 579 - and pain, 141, 177,492-94 Plenitude, 157-58, 347, 579, 636 Plenum, principle of; see Plenitude Plotinus, 592, 655 Plus ultra, 221, 229 Pneumatics, 89; see also Psychology Point, 140, 145, 253, 456, 669 - metaphysical, 456, 460, 461, 599; see also Monads Poiret, Pierre, 647, 662 Politics, 132, 260-61, 630 Pomponatius, Petrus, 554 Porphyry, 464-65 Possibility, 152, 159,231,263,324-25,329, 336-37,488-89,513 - and actuality, 177, 273, 333, 583-84, 661-62 - and existence 143-45, 147, 157-58, 168, 181, 204-5, 263, 336, 709 Power, 73, 177,204-5, 368-69,421, 426-27,479,564 - kingdom of, 442 Practical philosophy; see Ethics Predicables, 465, 621 ; see also Denominations Predicate, 621; see also Subject-predicate inclusion Preformation, 36-37, 455, 589, 638, 650, 715 Prestet, Jean, 210, 212 Primary matter; see Matter, primary Primary truths; see Truths, primary Primitive concepts; see Concepts, primary and derivative Principles of Nature and of Grace, The (1714), 59, 636-42 Probability, 61, 260, 283-85, 364-65, 389, 467, 584, 654; see also Certainty, moral and metaphysical Probity; see Piety Proclus, 383, 384 Progress, 37,436,491,664 Property, 245-46 Proportion, 265-66; see also Ratio Proposition, 24, 82, 88-89, 187-88,225-26, 235, 236-37, 240-42; see also Subjectpredicate inclusion - hypothetical, 151-52 - necessary and contingent, 74-75, 88-89, 152-53, 311; see also Truths, necessary and contingent - negative; see Truths, negative Protagaea, 37 Providence, 217-20, 565-66, 679 Prudence, 133-34; see also Justice Psychology, 37-41, 61, 62, 89, 159-62 - of learning, 85-88 Pythagoras, 221, 477, 496, 555, 589, 592, 677 Pythagoreans; see Pythagoras Qualities - intelligible and sensible, 89, 277 - primary, 75, 81, 110, 167-68 - sense, 89,101,110, 161, 189, 547-49,580 Quality, 233, 277, 287-88, 290, 667, 673 Quantity, 233, 667 - of motion, conservation of, 290,296-302, 314-15, 393-95,411,437, 499-500 - and quality, 76-77, 255, 667 Quietism, 305, 328, 430, 554, 559, 594 Radical Origination of Things, On the (1697), 786-91 Raey, Jean de, 94, 97, 103 Raillery, 629 Ramists; see Ramus, Petrus
INDBX Ramus, Petrus, 58, 464, 471 Ratio, 670, 704; see also Relation Rational souls; see Spirit Reading, 152-53 Realis de Vienna; see Wagner, Gabriel Realization, 491, 600, 602, 604 Reason, 547-53, 645; see also Sufficient reason, principle of - lazy, 305, 425 Reductive analysis; see Analysis, reductive Reflection, 39, 44, 113-14, 162, 360, 638,646, see a/so Apperception; Self-consciousness Reflections on the Common Concept of Justice (1702[?]), 561-73 Reflections on the Doctrine of a Single Universal Spirit (1702), 554-60 Refraction of light; see Optics Regis, Henry, 94 Regis, Pierre Sylvain, 455, 461 Relation, 28, 76, 247, 271, 337, 525, 540, 609,648,670,703-4,718 - oblique, 24 Religion, 213-20, 562, 633 - natural, 675, 676 Remond, Nicolas, 636, 654-60 Repetition, 86-87 Representation, 21, 62, 208, 339, 493, 517,639, 648-49, 694, 710--11; see also Expression; Perception Resistance, 162, 517, 520, 522, 532, 701 ; see also Force, passive Respiration, 186 Result (prosu/tare), 669 Rhetoric, 121-30 Right, 133-38, 421-24 - and justice, 421-31,561-73; see also Justice; Law Roanez, Duc de, 275, 472, 474 Roberval, Gilles Personne de, 153, 155, 165, 383, 584, 663 Rohan, Duc de, 630 Roi, Honore Ie, 586, 590--91 Rolle, Michel, 542, 544 Romanticism, 56-57 Rorarius, Jerome, 85, 90 Roscellin of Campeinge, 128 Rosental (Leipzig), 83, 655 RusselI, Bertrand, 23, 33, 59. Saint-Pierre, Abbe de, 58, 660 733 Sanchez, Francisco, 544 Scaliger, Julius Caesar, 94, 97, 101, 103, 122, 130, 470, 499, 589 Scapula, John, 686, 689 Schelhammer, Gunther Christopher, 488 Schonborn, John Phillip of, 85 Scholastics, 95, 102, 117, 124, 125, 127-28, 188-90, 259, 289, 321, 338, 432-33,454,538,596-617,655,710 Schooten, Francis, 76, 84, 472, 475 Schwenter, Daniel, 78, 84 Science, applied, 131-32,281 Sciences, hierarchy of, 43 Scripture, sacred, 82, 367, 369,424,561 Seckendorff, Veit Ludwig von, 275 Sectarianism, philosophical, 209, 496-97, 654-55 Self-awareness, 334-35 Self-consciousness, 113-14, 161-62,325, 593,638,645-46; see also Apperception; Ego; Reflection Self-knowledge, 349, 368, 549 Sennert, Daniel, 93 Sensation, 38, 107, 325, 344, 391-92 457,547-48; see also Qualities, intelligible and sensible - as resistance 162 Sense, 143-45, 547-51 - knowledge of, 161, 384 Sensible species, 320, 548-49 Sensorium; see Space, as sensorium Sentiment, 637, 644 Series, 265-6, 534, 536, 543-44 Sextus Empiricus, 544 Shaftesbury, third Earl of, 629-35, 659-60 Sign, 88,141,145; see also Character Similarity, 254-57, 258, 278, 667, 668-69; see a/so Homogeneity Simple ideas; see Terms, simple and complex Simultaneity, 666; see also Space, and time; Time Sin, 265, 322-23, 368-69, 652, 662 Situation, 254-57, 277-78, 598, 695 Situs, 77-78, 162, 184,249, 667, 671; see also Situation Skepticism, 102, 153-54, 384, 496, 655 Slavery, 428-29, 572-73 Snell, WiIlebrord, 317, 318, 329, 479 Societies, 48, 428-30 Socinians, 102, 679, 696
734 INDEX Socrates, 353, 579 Solicitation, 438, Soner, Ernst, 95 Sophia, electress of Hanover, 209, 272, 561,687 Sophia Charlotte, queen of Prussia, 365, 547,561 Souls, 36, 38, 62, 155,278-79,289,329, 342,349,360,454-56,495-96,503-4, 512, 520, 522, 551-52, 560, 578-80, 586-91, 644-45, 658 - origin of, 342, 555-56, 589, 597, 598-99 Space, 100, 139-42,278-79, 392-93,598, 622,678,682,684-85,690,692-93 - as sensorium, 676, 678, 680, 683, 686, 689, 694-95, 710 - and time, 16, 531, 536, 540, 583, 604, 656, 666-67, 690, 713-14, 719 - ideality of, 700-1 - relativity or absoluteness of, 328, 682-83,684-85,688-89,692-94, 700-706; see also Extension Spanheim, Frederick, 597 Species, 329, 332, 581 - sensible, 320, 578, 720; see also Intentional species Specimen dynamicum (1695),435-52,477 Spener, Phillip Jacob, 90, 102, 104. Sperling, Johann, 93 Spinola, Ambrozio di, 259 Spinoza, Baruch, 40, 46, 94, 120, 162,165, 167-69,194,195,207,263,273,496,502, 507, 526, 532, 533, 554, 555, 559, 582, 583,594,620,663,679 Ethics, notes on, 196-206 Spirit, 326-27, 346-47, 454-55, 551, 554-60,640,651-5; see also Mind Spitzel, Theophilus Gottlieb, 102, 104 Spontaneity, 99, 325, 457, 492-94, 496-97,577; see also Freedom State, 105-6,281-82 Steno, Nicolaus, 213, 220, 263, 581 Stoicism, 58, 136, 436, 463, 496, 582, 593, 594,632 Straight line, 236, 253, 667, 720, 671-72, 673 Strict right, 422,567-68,570-71 Sturm, John Christopher, 432, 498-508, 532 Suarez, Francisco, 10,40, 83, 126, 329 Subalternate terms, 372, 379 Subject, 160, 287, 540 Subject-predicate inclusion, 191, 236-37, 264,267-68,307-8,337 Sublime, 633-34 Subordinate regulations, 307, 314-15, 328-29; see also Laws, of nature Substance, 73, 97-99, 115-16, 117-19, 153,155,160,179,196-201,307-11, 325-27, 332, 335-36, 344, 365, 390, 432-34, 435-36, 445-46, 453-61, 515-41,551-53,596-617,620,627-28, 636-37,643-45,663; see also Bodies; Individual; Individuality; Souls - composite, 596-617 - corporeal, 270, 365, 600-1, 619-20, 624; see also Body - living, 637 - simple and compound, 617, 636-37, 641, 643 Substantial chain; see Vinculum substan- tiate Substantial form, 97-99, 104, 117-18, 189, 261, 271, 288-89, 309-10, 342-44, 345, 454,503-4; see also Entelechy; Monads; Souls Substantive, 246 Substitution, 241 Subtraction, logical, 380, 381 Succession; see Time Sufficient reason, 677, 680,684 - principle of, 24-25, 142,227,268, 337, 486-87,639,646,677,682,683,684,687, 698,717,719; see also Reason Supernatural, 679, 681, 684, 686-87, 690; see also Miracle Suppositum, 115, 117, 119-20,307,502 Surface, 668 Swarnmerdam, Jan, 345, 350, 455, 584, 585, 664 Syllogism, 75, 404, 465-67 Symbol, 649; see also Character Symbolistic, universal, 654, 655-56; see also Universal characteristic Sympathy, 288, 325, 339, 426, 527, 623, 628 Synthesis, 187-88,232-33; see also Analysis and synthesis Tambourino, Michelangelo, 612, 613 Tartalea, Nicolas, 79 Taste, 634, 715, 720 Teaching, 85-92
INDEX Teleology, 51, 486-91; see also Mechanism, and teleology Telesio, Bernardino, 93 Tentamen anagogicum (1696), 477-85 Term, 89, 123-24, 235; see also Concepts; Ideas Terms - collective, 128-29 - concrete and abstract, 126, 540 - disparate and diverse, 245, 371-72, 379-80 - simple and complex, 89,160-61, 169, 285, 295, 519 Theism, 486-87, 633 Theodicy, 56, 597, 601, 605, 615, 624, 633, 656-57,658,661,677,687,696,697,710, 712; see also Evil Theology, 49-53, 82, 109-20, 213-20, 259-60, 265, 303, 367-70; see also Catholic Demonstrations Theory of Abstract Motion, The, 139-42 Thing, 142 Thomasius, Christian, 462 Thomasius, Jacob, 37, 93-104 Thought, 89, 113, 160--61, 339, 579-80 Thrasymachus, 76, 562 Time, 141-42, 531, 534, 664, 669, 682-83, 693; see also Space and time Toland, John, 547 Torricelli, Evangelista, 584, 701 Tournemine, Rene Joseph, 538, 596 Trace, 155, 668 Traduction, 342, 598 Transcendentals, mathematical, 274 Transcreation, 515-16, 521; see also Occasionalism Transformation, 270, 325, 667, 669 - biological, 345-47, 557-58, 589 Transsubstantiation, 115-19, 600--1, 602, 607-8 Trent, Council of, 58, 117, 118,259,596 Trew, Abdias, 98 True Theologia mystica, On the, 367-70 Truth,121,182-85,239-40,291-95, 549-51 - criterion of, 43, 363-66, 517, 518, 550 - and falsity, 182-85; see also Error Truths - of fact, 43, 60, 226, 363-66, 646; see also Contingent truths - primary, 152, 153, 232, 385 - necessary and contingent, 133, 151-54, 735 226-27,232,263-66,268, 310--11, 550, 646 - negative, 163,237,247,381-82 - primary, 74-75, 226, 267-71 - primary and derivative; see Concepts, primary and derivative - of reason, 133, 138, 646, 654; see also Truths, of fact Tschirnhaus, Ehrenfried Walter von, 165, 166, 192-95, 275-76 Unconscious, 40, 180,557 Understanding; see Intellect Union, metaphysical, 596, 598, 600, 602, 604,605-6,610--11; see also Body-soul unity; Vinculum substantiale Unity, 76-77, 342-44,530,535, 559-60, 664-65 Universal calculus, 240--46; see also Logical calculus; Universal characteristic Universal characteristic, 166, 192-94, 221-28, 380, 654, 655-56, 670 Universals, 128-30 Vacuum, 96, 269, 347, 392, 414, 415, 622, 687, 691, 692, 701 Valerianus Magnus, 165 Valla, Lorentio, 127 Values, 18-19,48-49, 136-38,326,489-91, 565-67 Variation, 77-78 Varignon, Pierre, 542-44, 660 Vector, 439 Velocity, relative, 450; see also Motion Vergil,3 Vicinity, 77, 78; see also Distance Vieta, Fran\tois, 193, 248 Vinculum substantiale, 34, 600, 608, 610-11, 614, 615 Violence, 577, 585 Viotti, Bartholomeo, 95 Virtues, 135,569-70, 593-94, 630 Vitalism, 101, 329, 409,496,498-99,508, 555,586-91, 624 Vives, Ludovico, 127 Viviani, Vincent, 419 Vogel, Martin, 124, 130 Voider, Burcher de, 511, 515-41 Vorst, Conrad, 158 Vortex, 158, 162,413-15 Vossius, Gerhard, 94
736 Wagner, Gabriel, 25, 462-71 Wallis, John, 417, 419, 439 Wander, Guillaume, 212 War, 660 Ward, Seth, 75 Wedderkop~ ~agnus, 146-47 Weigel, Erhard, 98, 104 Weigel, Valentine, 47, 425, 430, 554, 594 What Is Independent of Sense and Matter, On, 547-53 White, Thomas, 94, 98,139 Whitehead, Alfred North, 57 Whole; see Part-whole Will, 91, 146,204,321-22, 332-33,384-85, INDEX 387-89, 687, 691, 697, 698, 708-9 - general and particular, 307, 310-11; see also God, will of William of Occam; see Occam, William of William of Saint-Amour, 321 Winds, 473 Wisdom, 425-28, 564 Wolff, Christian, 56, 657, 666,675 Words, 122-23, 182-85 World, beginning and end, 164,664, 693-94, 706-8; see also Creation Wren, Sir Christopher, 139, 439, 452 Zarabella, Jacob, 95, 117, 603