Leibniz (2001) 9781138711198, 9781315199887

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Leibniz

The International Library of Critical Essays in the History of Philosophy Series Editor: Tom Campbell Titles in the Series: Hume: Moral and Political Philosophy Rachel Cohon Adam Smith Knud Haakonssen Grotius, Pufendorf and Modern Natural Law Knud Haakonssen Immanuel Kant, Vols I & II Heiner F. Klemme and Manfred Kuehn Hegel, Vols I & II David Lamb Marx SCOII Meikle Locke's Moral, Political and Legal Philosophy J.R. Milton Hume: General Philosophy David WD. Owen Bentham: Moral, Political and Legal Philosophy, Vols I & II Gerald Postema The General Philosophy of John Stuart Mill Victor Sanchez-Valencia Hobbes Robert Shaver Descartes Tom Sorell Mill's Moral, Political and Legal Philosophy CL. Ten Locke Udo Thiel Nietzsche Richard White Leibniz Catherine Wilson Rousseau Robert Wokler Spinoza Yirmiyahu Yovel and Gideon Segal

Leibniz

Edited by

Catherine Wilson University of British Columbia, Canada

First published 2001 by Darthmouth Publishing Company and Ashgate Publishing Reissued 2018 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN 711 Third Avenue, New York, NY 10017, USA Routledge is an imprint of the Taylor & Francis Group, an informa business

Copyright © Catherine Wilson 2001. For copyright of individual articles please refer to the Acknowledgements All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Publisher's Note The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original copies may be apparent. Disclaimer The publisher has made every effort to trace copyright holders and welcomes correspondence from those they have been unable to contact. A Library of Congress record exists under LC control number: 00034843 ISBN 13: 978-1-138-71119-8 (hbk) ISBN 13: 978-1-315-19988-7 (ebk)

Contents AcknowLedgements Series Preface Introduction

PART I

4 5 6

3 41 61

LEIBNIZIAN SUBSTANCES

David S. Scarrow (1973), 'Reflections on the Idealist Interpretation of Leibniz's Philosophy', Studia Leibnitiana SuppLementa, 12, pp. 85-93. Donald P. Rutherford (1990), 'Leibniz's "Analysis of Multitude and Phenomena into Unities and Reality"', JournaL of the History of PhiLosophy, 28, pp. 525-52. John Kronen (1997), 'Substances are not Windowless: A Suarezian Critique of Monadism', American Catholic PhiLosophicaL Quarterly, 71, pp. 59-81.

PART III

XI

MATTER, SPACE AND RELATIONS

2 John W. Nason (1945), 'Leibniz's Attack on the Cartesian Doctrine of Extension', JournaL of the History of Ideas, 6, pp. 447-83. 2 John Earman (1977), 'Perceptions and Relations in the Monadology', Studia Leibnitiana, 9, pp. 212-30. 3 Richard Arthur (1994), 'Space and Relativity in Newton and Leibniz', British JournaLfor the Philosophy of Science, 45, pp. 219-40.

PART II

vii ix

85 95 123

LIFE, MIND AND ACTION

7

Samuel Scheffler (1976), 'Leibniz on Personal Identity and Moral Personality', Studia Leibnitiana, 8, pp. 219-40. 8 Mark Kulstad (1981), 'Leibniz, Animals, and Apperception' , Studia Leibnitiana, 13,pp.25-60. 9 Ezio Vailati (1990), 'Leibniz on Locke on Weakness of Will' , JournaL of the History of Philosophy, 28, pp. 213-28. 10 William Seager (1991), 'The Worm in the Cheese: Leibniz, Consciousness and Matter', Studia Leibnitiana, 23, pp. 79-91. II Catherine Wilson (1994), 'Leibniz and the Logic of Life' ,Revue InternationaLe de Philosophie, 48, pp. 237-53.

149 171 207 223 237

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PART IV 12 13 14

15 16 17

William E. May (1962), 'The God of Leibniz', New Scholasticism, 36, pp. 506-28. Raja Bahlul (1992), 'Leibniz, Aristotle, and the Problem of Individuation', Pacific Philosophical Quarterly, 73, pp. 185-99. Daniel Fouke (1994), 'Emanation and the Perfections of Being: Divine Causation and the Autonomy of Nature in Leibniz', Archiv Fuer Geschichte der Philosoph ie, 76, pp. 168-94. Steven Nadler (1994), 'Choosing a Theodicy: The Leibniz-Malebranche-Arnauld Connection', Journal of the History of Ideas, 50, pp. 573-89. David Scott (1997), 'Leibniz and the Two Clocks', Journal of the History of Ideas, 58, pp. 445-63. Jack Davidson (1998), 'Imitators of God: Leibniz on Human Freedom' , Journal of the History of Philosophy, 36, pp. 387-412.

PART V 18 19

20 21 22

METAPHYSICS

281

297 325 343 363

LEIBNIZ IN CONTEXT

Donald F. Lach (1945), 'Leibniz and China', Journal of the History of Ideas, 6, pp.436-55. Carolyn Merchant (1979), 'The Vitalism of Anne Conway: Its Impact on Leibniz's Concept of the Monad', Journal of the History of Philosophy, 17, pp.255-69. Nicholas Rescher (1981) , 'Leibniz and the Concept of a System', Studia Leibnitiana, 13, pp. 114-22. Michael Losonsky (1992), 'Leibniz's Adamic Language of Thought' ,Journal of the History of Philosophy , 30, pp. 523-43. Domenico Bertoloni Meli (1988), 'Leibniz on the Censorship of the Copernican System', Studia Leibnitiana, 20, pp. 19-42.

Name Index

257

391

411 427 437 459 483

Acknowledgements The editor and publishers wish to thank the following for pennission to use copyright material. American Catholic Philosophical Association for the essays: John Kronen (1997), 'Substances are not Windowless: A Suarezian Critique of Monadism', American Catholic Philosophical Quarterly, 71, pp. 59-81. Copyright © 1997 American Catholic Philosophical Association; William E. May (1962), 'The God of Leibniz', New Scholasticism, 36, pp. 506-28. Copyright © 1962 American Catholic Philosophical Association. Blackwell Publishers Limited for the essay: Raja Bahlul (1992), 'Leibniz, Aristotle, and the Problem ofIndividuation', Pacific Philosophical Quarterly, 73, pp. 185-99. Copyright © 1992 University of Southern California. Published by Blackwell Publishers. Copyright Clearance Center, Inc. for the essay: Catherine Wilson (1994), 'Leibniz and the Logic of Life', Revue Internationale de Philosophie, 48, pp. 237-53. John Eannan (1977), 'Perception and Relations in the Monadology', Studia Leibnitiana, 9, pp. 212-30. Copyright © 1977 John Earman. Daniel Fouke (1994), 'Emanation and the Perfections of Being: Divine Causation and the Autonomy of Nature in Leibniz', Archiv Fuer Geschichte der Philosophie, 76, pp. 168-94. Copyright © 1994 Daniel Fouke. Johns Hopkins University Press for the essays: John W. Nason (1945), 'Leibniz'sAttack on the Cartesian Doctrine of Extension' , Journal of the History of Ideas, 6, pp. 447-83. Copyright © 1945 Journal of the History of Ideas, Inc. Reprinted by permission of the Johns Hopkins University Press; Steven Nadler (1994), 'Choosing a Theodicy: The Leibniz-MalebrancheArnauld Connection', Journal of the History of Ideas, 50, pp. 573-89. Copyright © 1994 Journal of the History of Ideas, Inc. Reprinted by pennission of the Johns Hopkins University Press; David Scott (1997), 'Leibniz and the Two Clocks' , Journal of the History of Ideas, 58, pp. 445-63; Copyright © 1997 Journal of the History ofIdeas, Inc. Reprinted by permission of the Johns Hopkins University Press; Donald F. Lach (1945), 'Leibniz and China' , Journal of the History of Ideas, 6, pp. 436-55. Copyright © 1945 Journal of the History of Ideas, Inc. Reprinted by permission of the Johns Hopkins University Press. Journal of the History of Philosophy, Inc. for the essays: Donald P. Rutherford (1990), 'Leibniz's "Analysis of Multitude and Phenomena into Unities and Reality" , , Journal of the History of Philosophy, 28, pp. 525-52; Ezio Vailati (1990), 'Leibniz on Locke on Weakness of Will', Journal of the History of Philosophy, 28, pp. 213-28; Jack Davidson (1998), 'Imitators of God: Leibniz on Human Freedom', Journal of the History of Philosophy, 36, pp. 387-412;

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Carolyn Merchant (1979), 'The Vitalism of Anne Conway: Its Impact on Leibniz's Concept of the Monad', Journal of the History of Philosophy, 17, pp. 255-69; Michael Losonsky (1992), 'Leibniz's Adamic Language of Thought', Journal of the History of Philosophy, 30, pp.523-43. Mark Kulstad (1981), 'Leibniz, Animals, and Apperception', Studia Leibnitiana, 13, pp. 2560. Copyright © 1981 Mark Kulstad. Domenico Bertoloni Meli (1988), 'Leibniz on the Censorship of the Copernican System', Studia Leibnitiana, 20, pp. 19-42. Copyright © 1988 Domenico Bertoloni Meli. Oxford Uni versi ty Press forthe essay: Richard Arthur (1994), 'Space and Relati vity in Newton and Leibniz', British Journalfor the Philosophy of Science, 45, pp. 219-40. Nicholas Rescher (1981), 'Leibniz and the Concept of a System', Studia Leibnitiana, 13, pp. 114-22. Copyright © 1981 Nicholas Rescher. David S. Scarrow (1973), 'Reflections on the Idealist Interpretation of Leibniz's Philosophy', Studia Leibnitiana Supplementa, 12, pp. 85-93. Copyright © 1973 David Scarrow. Samuel Scheffler (1976), 'Leibniz on Personal Identity and Moral Personality', Studia Leibnitiana, 8, pp. 219-40. Copyright © 1976 Samuel Scheffler. William Seager (1991), 'The Worm in the Cheese: Leibniz, Consciousness and Matter' , Studia Leibnitiana, 23, pp. 79-91. Copyright © 1991 William Seager. Every effort has been made to trace all the copyright holders, but if any have been inadvertently overlooked the publishers will be pleased to make the necessary arrangement at the first opportunity.

Series Preface The International Library of Critical Essays in the History of Philosophy is designed to bring together, in an accessible fonn, the best journal essays in English on the history ofphilosophy. The series makes readily available, in a systematic manner, the most important essays in the history of philosophy, selected and presented by volume editors who are highly respected in their fields. The original essays are reproduced in full which helps to make the series an invaluable reference tool for all scholars interested in the history of philosophy. It is of particular assistance to advanced undergraduate and graduate students in the history of philosophy as well as those who research in this area. The series focuses primarily on the philosophical traditions of Gennany, France, Britain and the United States. The dominant approach of the series is philosophical in that the essays are primarily accounts and critiques from the perspective on the philosophical issues of the time. Some essays trace philosophical influences and elucidate the context of the major philosophical writings. Other essays offer commentary on the texts in the light of current theories of interpretation and historical understanding. The overriding criteria for the selection of essays are their quality and importance. The essays overall are chosen to ensure a systematic coverage of all important scholarly debates but they also reflect the interests and perspectives of the individual editors which gives each volume a distinctive flavour. I am very grateful to all the editors for the enthusiasm and experience they have brought to the difficult task of selecting essays which bring out the central controversies over the interpretation and understanding of the work of the enduring figures and schools in the history of philosophy. The International Library of Critical Essays in the History of Philosophy complements the highly successful International Research Library of Philosophy, edited by Professor John Skorupski, which now runs to over 20 volumes and is widely used throughout the world. The series owes much to the vision and persistence of John Irwin and the great work done by Valerie Saunders, Sonia Hubbard and the Ashgate editorial team. TOM CAMPBELL Series Editor Faculty of Law The Australian National University

Introduction Leibniz's Life and Work Gottfried Wilhelm Leibniz (1646-1716) is traditionally classified, along with Rene Descartes, Benedict Spinoza and Nicolas Malebranche, as one of the Continental Rationalist philosophers. The Rationalists are often regarded as precursors of their critics, the British Empiricists John Locke and David Hume. In some respects, the distinction between Rationalists and Empiricists is a useful one, and Leibniz clearly belongs with the former since he admired mathematical demonstrations, employed a scholastic vocabulary, and believed that a great deal could be known about the world a priori. Moreover, he asserted that nothing happened without a reason, and he appealed to the infinite wisdom and power of God to explain why things are as they are on earth. He thought that human intelligence raised us above the level of other animals, that it illuminated and dispersed shadowy moral problems, and that the mysteries of the Christian religion were not unintelligible. He thought that rational inquiry was leading to social progress. Yet Leibniz also belongs with the Empiricists. He considered his predecessor, Descartes, prone to airy speculations and deductions. He thought that the idea of a disembodied mind - or a mind that causes movements in its body - was absurd, and he professed to find Berkeley's Malebranche-inspired account of the perceptual world as existing in the mind a 'paradox'. He thought, I suspect, that humans differed in degree but not in kind from other animals - or at least from other possible animals - and that all living things existed in a delicate state of equilibrium with their environments. He pleaded with natural philosophers to open their eyes, adjust their microscopes and appreciate the importance of insensible corpuscles, invisible animalcules and unconscious perceptions - the new empirical entities of his era. Leibniz was neither especially traditional nor wholly modern, neither simple nor impossible to understand. He caught the drift of everything fresh and innovative in his era, from mathematical physics, the calculus and combinatorial mathematics to preformation and Galilean relativity, and he mingled the new with what he admired of the old - Aristotle, Plato, the Neo-Platonists, Islamic-Jewish philosophy and mystical theology. Some of his writings, including his famous Monadology can be read in a single sitting, like a novel. Others, like his early jottings on metaphysics, cause the specialist hours, days or years of mental torture. Studies on Leibniz are alive and well at the beginning of the twenty-first century and on many major interpretive questions it is still too early to close the books. Leibniz was born on 1 July 1646 in Leipzig. A gifted, precocious child, he was raised by his mother after his father's early death. Given the freedom of the household's large library, he taught himself Latin - by his own account from picture books - and went on to acquire a BA and then an MA degree in philosophy at the University of Leipzig. He proceeded to a doctorate in law which he earned from the nearby University of Altdorf at the age of 21. Foregoing the opportunity of an academic career, he moved to Mainz, where he acquired a patron in the person of a local Catholic nobleman, J.e. von Boineburg and was introduced in

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tum to the Elector of Mainz, for whom he worked on legal reform and proposals for legal education. He began, at the urgings of Boineburg, to draw on his philosophical training to try to formulate some principles of rational theology in terms acceptable to both Catholics and Protestants in the hope of putting an end to the bloody conflicts which, in the wake of the brutal and exhausting Thirty Years' War, still seemed interminable. Leibniz's curiosity and breadth of interest were aleady evident. He liked any kind of problem, practical or theoretical. Fascinated by artificial languages and combinatorial systems, he had begun to study the new proposals for a universal language of Athanasius Kircher, George Dalgarno and John Wilkins, and had dabbled in cosmology, chemistry and optics. But he was an autodidact in these areas, his mathematics was elementary, his physical theories were eccentric, and he lacked able critics. His natural philosophy was a mishmash of scholastic ideas and what he had gleaned of the 'moderns' - mainly Thomas Hobbes. Meanwhile, in Paris and London, the newly founded scientific academies, the Academie Royale des Sciences and the Royal Society of London, were organizing physical and mathematical inquiry with increasing rigour, results and significance. Leibniz was able to engineer a trip to Paris on a vaguely conceived diplomatic mission and, to his great benefit, managed to prolong his stay for four years. Here, his native genius received good direction. He read the works of Pascal and Descartes, Spinoza's radical theology, some of the English natural philosopher Robert Boyle, and even a few Platonic dialogues. He met with Malebranche, Antoine Arnauld and Simon Foucher, critics and disciples of Descartes, whose influence more than 20 years after his death was still profound. Prompted by Christiaan Huygens to learn some up-to-date mathematics and geometry, Leibniz worked his way through the existing theory of infinitesimal quantities and discovered differential and integral calculus. By 1676 he was brooding on the implications of the Cartesian theory of perception and action and on the problems of divine beneficence and free will. Recalled, to his great disappointment, to his job in Hanover, he managed a side trip to England where he met members of the Royal Society, and to Holland, where he met briefly with Spinoza, whose shocking Ethics, intended to prove by deduction from self-evident axioms the identity of mind and body and of God and the physical world, would be published posthumously in the following year. On his return, Leibniz bowed to the necessity of earning his keep as an attache and signed on as a political-Iegal--economic-theological adviser to the Duke of Brunswick, Johann Friedrich. He remained an employee of the House of Hanover for his entire life, serving as official historian, librarian and technical adviser. He was bored by the history assignment, which required him to write the history of the family from its ancient origins, but it gave him opportunities to travel through Italy and Austria and to study geology and natural history. The long solitary hours passed in carriages were conducive to metaphysical meditations. Leibniz seems to have enjoyed the library work, conceiving the idea of arranging books in alphabetical order by author, and the technical advising as well. He tried to improve the Duke's mining operations in the Hartz Mountains and proposed numerous mechanical inventions. Leibniz published only a fraction of what he wrote over his lifetime; his notes and drafts are still being edited and published and his major essays re-edited and reissued. We possess few complete philosophical works from the period up to 1686, but especially notable amongst his early unpublished compositions are a 1672 dialogue on freedom and divine providence, the Philosopher's Confession, and a difficult and long unpublished dialogue on space, time,

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divisibility and matter, the Pacidius Philalethi from 1676. In addition, there are notes and drafts on theological and logical problems and on God, matter, perception and the mind, the most provocative of which have recently been retranslated and re-edited under the title De Summa Rerum. Two significant early published works were the sketch of epistemology, the Meditations on Knowledge, Truth and Ideas, in the Leipzig Acta Eruditorum (1684) and the short Galilean-style demonstration that Cartesian mechanics falls into contradiction by failing to recognize force as a quantity distinct from motion, the Brief Demonstration on a Notable Error of Descartes (1686). In the same year Leibniz tested the philosophical waters by sending to the Paris theologian, Antoine Arnauld, a summary of a treatise he had composed consisting of 37 sections covering the topics of substance, force, causality, perception, miracles, the laws of nature and divine goodness. Posthumously published as the Discourse on Metaphysics, it was intended to be a sketch of a metaphysics acceptable to Protestants and Catholics, as well as to Aristotelians and Cartesians, and is generally considered to be a landmark in Leibniz's struggle to articulate a systematic metaphysics. The Discourse was written with several aims in mind. It was supposed to refute materialists and religious sceptics - those who murmured aloud or to themselves that, if God existed, he could have done a better job creating and supervising the world. And it was supposed to mediate between Calvinist and Jansenist believers in God's inscrutable election of the few and their opponents who believed that the possession of personal merit, as this was revealed to conscience and under the individual's control, was a means to salvation. In addition, Leibniz tried to explain how there could be forces and activity in the created world that were neither demonic nor occult. In the Discourse, Leibniz characterizes individual persons like Adam or Julius Caesar as paradigmatic 'substances'. He supposes that each passes through a defining, predetermined series of mental and physical states, corresponding to its life history, and he denies that one substance can really cause a change in another. He claims that, in all true propositions, the subject 'contains' the predicate and infers that all substances 'contain' their entire pasts and their futures as well. Adam's sin was inevitable, for, had the first man not sinned, he would not be Adam. But it was not necessary for Adam to sin, for, in another possible world, Adam would not even have existed. These propositions were poorly received by Arnauld, who, even with Leibniz's lengthy attempts at explication, found their logic flawed. Moreover, the conclusions were at once shockingly fatalistic and too charitable in their view of divine and human nature for Arnauld's Jansenist sentiments. Somewhat daunted, Leibniz turned to the role of a Descartes critic. In addition to many short papers, he worked on an important commentary, the Critical Thoughts on the General Principles of Descartes, a preliminary to his own system of dynamics, published in short form as the Specimen Dynamicum in 1695. In the same year a short anti-Cartesian essay, the New System of the Nature and Communication of Substances, appeared in the Paris Journal des Savants, arguing that the mind and body ran along separate tracks and did not influence each other, although the state of the mind at a given moment always corresponded to the state of body. In addition to introducing this divinely instituted 'pre-established harmony', Leibniz first referred in this essay to the 'metaphysical point' which he thought of in contradistinction to the physical atom as the true building block of the world. On Nature Itself (1698) constituted an attack on the occasionalist doctrine that God was the only active substance and that matter was purely passive. These works were followed in their composition by the commentary on Locke's

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1690 Essay Concerning Human Understanding, the New Essays on the Human Understanding, completed in 1704, the commentary on Pierre Bayle's Letters to a Provincial, the Theodicy (1710), and by the Principles of Nature and of Grace and the Monadology, both completed in 1714. The Theodicy was the only full-length purely philosophical work published during Leibniz's lifetime. He was, however, a prodigiously productive writer and covered hundred of thousands of sheets of paper with notes and drafts, some repetitious of what he says elsewhere, some startlingly different and some incomprehensible. Throughout his life he maintained an extensive correspondence with learned men and women. Leibniz read books by the stack. By his own account, he was a skimmer, on the lookout for what he could use. But he was also a focused and patient critic and commentator. His last writings were the set of letters composing his side of the Leibniz-Clarke correspondence, his critique of the Newtonian theory of absolute space and gravity and his defence of his favourite metaphysical principles, the Identity ofIndiscernibles and Sufficient Reason. His last years were darkened and confused by the absurd accusations of calculus plagiarism trumped up by Newton's henchmen. Leibniz died in 1716 at the age of 70 and was given an undistinguished funeral. His theory of monads, unlike the more accessible and popular theory of pre-established harmony, suffered from general incomprehension, and he was harassed by theologians about his account of transubstantiation, the problem he had longed to put an end to with good metaphysics even in his youth. Although he claimed to be proud that he had not founded a school and had no disciples, unlike the Cartesian sectarians, he was perhaps somewhat disappointed at his reception, and even ambivalent about his own theories. It was persistently rumoured that he was an atheist and that he considered his own monadology as an elaborate joke. His reputation languished through the first half of the eighteenth century, but revived markedly after 1765 with the publication of the New Essays, whose beauty and profundity were quickly acknowledged. The rise of the life sciences in the second half of the eighteenth century brought Leibnizian doctrines into prominence. Although Leibniz had always maintained that everything that happens in the body happens mechanically, he had denied that there are any bodies that are not either ensouled or composed of ensouled creatures. His conception of the world as a plenum of living beings and of the organism as a federation of living, active, sensitive beings lent themselves well to the natural history and physiology of the era. Ignored again in the practically minded nineteenth century, his reputation began to rise for quite different reasons when, in the early twentieth century, his logical manuscripts were rediscovered and edited by Louis Couturat, and the complexity and interest of his metaphysics was brought to the attention of the public by Bertrand Russell. Now, at the beginning of the new millennium, Leibniz's flashing insight, the range of his intelligence and his love of the world continue to enchant and engage receptive readers.

Leibniz's Main Doctrines Leibniz wrote against the background of the rise of the mechanical philosophy. First Bacon and Galileo, then Descartes, Gassendi and Boyle, had worked to revive the Epicurean theory of atoms and to challenge the doctrines and the institutional hegemony of the philosophers known as the Schoolmen, who, since medieval times, had drawn on Christian, Islamic and Aristotelian sources. The Schoolmen supposed that all bodies were composed of 'form' and

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'matter' and that nature consisted of numerous different types of 'substances', all of them endowed with a principle of motion or self-development. Substances embraced the various formally distinct species - humans, dogs, horses and so on - but also qualitatively distinct 'stuffs', such as blood, bone, glass or opium. To the form-matter ontology was bound a geocentric, Ptolemaic cosmology, based on the notion that the heavenly bodies were themselves alive, or moved by intelligences, or carried in crystalline shells, or all of these things, and that they were of a 'fifth essence' - an element not to be found below the moon. The heavenly bodies, though they controlled the passage of seasons and generation, were not entirely benign, and some stars were distinctly evil and poisoned people and animals or made them ill. Superimposed Christian elements included the notion of providential care and the rationale for the existence of the world: its purpose was to glorify God, to be a home for God-glorifying humans, and to serve as the stage on which they could perform their moral dramas to earn damnation or redemption. By 1600 the picture offered by Renaissance philosophy was beginning to collapse under its own load of accretions and syntheses, and the perceived futility of comprehending and reconciling them. In place of humanistic learning, the modems called for a simplified ontology that would explain and further human trans formative powers. The elements of the new worldview were corpuscles, particles of matter, purified of all 'forms' and 'qualities' except magnitude, figure and motion. This new matter was universal; it filled space invisibly and composed the sun and moon as well as terrestrial bodies. It was passive and did nothing of its own accord; it had to be moved by a mind or by God, although motion could be transferred between bodies through impact. Galileo took up the defence of Copernicus's heliocentric system, and argued that the planets moved naturally in circular orbits through space. Descartes envisioned them as carried along in celestial whirlpools of tiny particles; in any case, the heavenly bodies were not intelligent, and the stars were too far away - according to the new systems - to shoot anyone with their rays or influence events on earth. Like the telescope, the microscope revealed 'new worlds' and instilled at once a new confidence and a new modesty about human knowledge. The earth was not at the centre of the universe, and there were probably numerous other worlds in space with numerous other living creatures on them. The Democritean theory that qualities such as bitter and sweet, white and black, cold and hot, do not exist in things but arise in perceivers affected by atoms was revived in place of the Aristotelian view that perception involves the reception of forms without matter. Drugs and poisons worked not through 'occult' influences but through the action of insensible corpuscles on the 'texture' or corpuscular constitution of bodies, and these bodies, including the human body, were, like the solar system, 'machines'. These machines, Descartes influentially argued, could arise if matter were 'agitated' according to certain laws, without God's engaging in a special creation of substances or species. By implication, they could also be permanently ruined or stop working suddenly and forever, like clocks. Moral theory was reconstructed to be independent of Christian dogma. It was urged that virtue was its own reward - not a way to earn a place in heaven - and that freedom consisted in rational and autonomously directed behaviour. These new views, the means by which they had been arrived at, and the fact that they had been arrived at outside the official educational and order-keeping institutions, posed problems for politics, ethics and religion. The divine right of kings was threatened by the distance of the philosophers' God and by their insistence that situations and events, including the existence of

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humans and nations, all have their causes but serve no higher purpose. That God had a special concern for the inhabitants of this planet and had nevertheless decreed that all its inhabitants would be born into a condition of degradation through original sin that could only be ameliorated by submitting to the authority of princes and priests was no longer so evident. The great philosophers assumed responsibility for preventing moral-political chaos. Not simply out of fear, or prudence, but out of genuine moral concern, they made an essential place for God, obedience and self-discipline in their philosophies. Such accommodations are conspicuous in the work of Descartes and Spinoza, but also in Locke and in Leibniz. Indeed, Leibniz's metaphysics was a protracted and remarkable attempt to reformulate traditional ethical, political, and religious values in such a way that they did not conflict with the new science to which he himself was a major contributor. Leibniz was particularly worried that the uniformitarian tendencies of the new philosophy destroyed the existing rationale of government, that the weaker needed to be led by the wiser. The materialist Hobbes who thought that everything, including thought and sensation, was the result of corpuscles-in-motion, had argued that desire is the only motivating force in human nature. Governments, he thought, are a lesser evil than the anarchic struggle amongst basically equal individuals that would occur in their absence. But the sovereign has nothing in common with God and need have no personal merit. Leibniz was troubled by the separation of power from value, and he fabricated his metaphysical system in meritocratic terms. The world, according to his reconstruction, consists of a graded series of living entities, and those at the top of the ladder who are closer to God have more agency and clearer knowledge than those below them. Further down are somnolent and barely perceptive creatures that scarcely seem to be alive. From the perspective of physics and medicine, Leibniz acknowledged, man was a machine whose wheels were turned by the environment, but he posited a higher order of explanation and a separate level of reality. The metaphysician could demonstrate that the 'simple' substances composing the world were not material particles moving according to the laws of efficient causes. They were free, spontaneous, more-than-material and immortal. The experiences and appetitions of these substances - which he called 'monads' to emphasize their unity and lack of parts - were the underlying basis for the perceived behaviour of all composite bodies, from billiard balls to animals with their complex interiors. Substances, which Leibniz first conceived as tightly bound, indestructible Aristotelian form-matter composites, undergo a process of self-development, striving purposively for greater perfection. For Leibniz, as an immaterial atomist, the three-dimensional world of obstacles and resistances, of one thing making another happen, of bodies subject to control by a mind that they sometimes evade, is a benign illusion, just as, for the material atomist, the blue of plums and the sweetness of honey are illusions, although they have a foundation in something real. The New Essays, a paragraph-by-paragraph response to Locke, have inspired much recent scholarship. One central theme of Locke's Essays was his rejection of Cartesian 'thinking substance', his insistence that only desires, not ideas, had genuinely motivating power, that moral judgement and legal practice had to be based on psychology, not on the metaphysics of the soul. Another theme was that knowledge extending beyond the sensory realm was unavailable to human beings, and that technological aids such as optical instruments were of little avail. Leibniz confronts Locke's moral and scientific scepticism with his own optimism and Locke's crypto-materialism with his own theory of monads. At the same time, he endorses Locke's

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anti-Cartesianism and displays a striking willingness to accommodate his psychology and to engage in Locke's own terms with the issues he raises concerning the limits of scientific knowledge, meaning and reference, consciousness and matter, and freedom and motivation. Leibniz's philosophy is intricate and fascinating not simply for its positive content, but on account of the relationship between his moral-political and theological doctrines and his underlying logic and physical theory. In logic, he began to study predication set-theoretically. Rather than thinking, as the modem logician does, of A's being an element ofB as 'A implies B', he thought of it as subject A's 'containing' predicate B. Thus, for Leibniz, the class of diamonds contains hardness, and the class of humans contains animality, whereas we would tend to say that the class of humans is a subset of the class of animals, and the class of diamonds a subset of the class of hard things. Leibniz grasped that concepts could be understood combinatorially, as clusters of predicates, and he began to try to work out their algebra, although his schemes for doing so are still imperfectly understood. In the process he came to see 'containment' as a very general and fundamental explanatory concept. Subjects evidently contained all their predicates, and numerous microscopical observations suggested that 'seeds' also contained the whole plant or animal that would grow from them. It occurred to him that the mind might contain all the thoughts and ideas that could ever issue from it, and that 'substances' must contain all their future experiences. If substances were collections of experiences and actions as subjects were collections of predicates, it was possible to understand why certain individuals actually existed while others were merely possible. The set of actual beings corresponded to the largest set of substances whose life histories were compatible with one another. And, in certain more idealistic versions of the theory, substances were not even to be identified with embodied persons, but with strictly immaterial beings, and their life histories were simply their experiences. The monads were 'windowless'; nothing entered or left. Their experiences were mutually consistent, but they did not occupy a common absolute space. To Leibniz, mathematics and physics seemed progressively to confirm his intuitions. Mathematics revealed the existence of infinitesimal qualities and taught him that - in addition to the 'physical' point that can be drawn on paper but is really a divisible and hence destructible composite and the simple, indivisible, but admittedly imaginary 'mathematical' point - there was room for a third concept, the 'metaphysical' point that is real but unextended. Zeno's paradox, that we can find no smallest entities to compose the world, is insoluble only if we restrict our search to the material and the mathematical, ignoring the metaphysical. Snell's Law in optics suggested that the laws of nature seek to accomplish the most with the least, and the behaviour of falling and colliding bodies taught him that there is a quantifiable 'force' in matter, which he called the vis viva, that the Cartesians, in their haste to banish forms and qualities, had overlooked. This force, was a sign or echo of something powerful, active and resident in matter that mechanism could not explain. Further, a consideration of the laws of motion, badly mangled by Descartes, revealed that mind-body interaction as envisioned by Descartes was impossible. The mind could not alter the direction or flow of 'animal spirits' in the brain and body to make the limbs move, for force and its direction were conserved in all encounters. Further, Huygens had shown that the laws of mechanics held constant in all ordinary frames of references. This implied that observers could not tell from experiments with, or observation of, the objects around them whether they were 'really' in motion or at rest: they could only determine that they were in motion relative to some chosen frame. Leibniz inferred that absolute motion, absolute time and absolute space were all fictions. This in tum implied to

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him that two empirical entities could never be distinguished by their spatial or temporal location alone. Any two pebbles, leaves, corpuscles, intervals of time or regions of space had to be qualitatively distinct. Chemistry and natural history, finalIy, seemed to Leibniz to confirm his estimate of corpuscularian ism as a useful but superficial ontology - good for practical physics and medicine, but metaphysicalIy nugatory. The discovery of micro-organisms in pond water by Antonie van Leeuwenhoek stimulated him to think that living and sentient creatures existed in all degrees of complexity. Chemistry showed that substances that had disappeared as far as the naked eye was concerned in certain reactions could be retrieved later, and he hoped to find in such demonstrations and in the awakening of seemingly dead caterpillars as butterflies natural, nonmiraculous models for immortality. Leibniz's optimism, his doctrine that this is the best of all possible worlds, was ridiculed by Voltaire through the character Dr Pangloss in his novel Candide. But Leibniz did believe, with some evidence, that his world was growing more enlightened, more tolerant, and less superstitious and conflict-ridden. He denied that God could have made a better world. The human mind, he thought, could vaguely conceive of worlds that are more pleasant for the conceiver, but their goodness is superficial, purely local or temporary. The only answer he could find to the question why we have this world and not another was that it was the best: no other possible world could have contained such a plentitude of creatures, such simple and general laws. And he toyed with the unorthodox idea that the optimal world could bring itself into existence through a kind of 'struggle for existence' amongst the possibles in God's mind. We still do not know how far Leibniz was tempted by Spinoza's view that God should not be conceived by the philosopher as he is in the popular imagination as a father, supervisor and judge, and how far he identified God simply with the power and order of the world itself.

The Essays in this Volume This colIection of essays covers a range of topics. The monads and the pre-established harmony make numerous appearances , and so do Leibniz's discussions of causality, relations, individuation, nature, freedom, consciousness and divinity. In addition to sections on Leibniz's physics and his theory of substance, I have included a number of essays on his philosophy of mind that draw heavily on the New Essays, several essays on metaphysical and theological issues, and a section on Leibniz 's relationships with his contemporaries and predecessors. The Leibniz scholar may note that the younger generation of scholars, welI represented here, has moved into some new territory. Fewer essays are being published on modality and predication, not only because these topics have, for the most part, been thoroughly researched and expertly handled by earlier commentators, but also because historiographical methods have evolved that permit scholars to treat metaphysical and theological issues more adequately. Contextual scholarship has become interesting and exact while maintaining the sense of conceptual architecture that distinguishes the history of philosophy from intellectual history generally. Several criteria governed the choice of essays. First, each selection had to be drawn from the periodical literature and be previously unreprinted and unpublished in book form . Second, each had to be a fully self-contained essay, not a discussion-piece, capable of being read with

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profit by an upper-level undergraduate in a single sitting, yet conducive to further research and inquiry. Third, the selection had to be in English. Even with these criteria in place, there were still far more deserving essays than I had room for. The reader is urged to explore the earlier collections and the recent English monographs listed below in the Bibliography, but he or she should be aware that there is a voluminous and, from a scholarly point of view, indispensable critical literature in French and German, of which few Anglophones can claim to possess an overview. In the meantime, I hope the present selection will demonstrate the breadth of contemporary Leibniz scholarship and will bring to the attention of readers some older material that retains its freshness and usefulness. For an editor, deciding what to include of one's own usually comes down to looking for a gap and trying to fill it. In addition, I had hoped that a curious reader might clear up the mysterious matter of Leibniz's supposed letter on continuity. In the interim, Professor Herbert Breger has confirmed my suspicions in his admirable article on Leibniz and the Principle of Least Action, leaving only the first rationale actual. Bibliography 1. Editions of Leibniz s Work A comprehensive multilingual guide to editions of Leibniz's work, currently in use, can be found on pp. ix-xi of the Cambridge Companion to Leibniz, edited by Nicholas Jolley, Cambridge, Cambridge University Press, 1995. For the convenience of the English-speaking reader, I list below the main translations available in libraries and bookstores. Alexander, H.G. (1956), The Leibniz-Clarke Correspondence, Manchester: Manchester University Press. Ariew, Roger and Garber, Daniel (1989), Leibniz: Philosophical Essays, Indianapolis: Hackett. Farrer, August and Huggard, E.M. (tr.) (1985), Theodicy: Essays on the Goodness of God, the Freedom of Man, and the Origins of Evil, La Salle: Open Court. Loernker, Leroy (tr. and ed.) (1969), Gottfried Wilhelm Leibniz: Philosophical Papers and Letters, (2nd edn), Dordrecht: D. Reidel. Mason, H.T. (tr.) (1988), The Leibniz-Arnauld Correspondence, Manchester: Manchester University Press. Martin, R., Niall, D. and Brown, S. (1988), G. W Leibniz: Discourse on Metaphysics and Related Writings, Manchester: Manchester University Press. Parkinson, G.H.R. (tr. and ed.) (1966), Leibniz: Logical Papers, Oxford: Clarendon. Parkinson, G.H.R. (tr. and ed.) (1992), De Summa Rerum, New Haven, CT: Yale University Press. Remnant, Peter and Bennett, Jonathan (tr. and ed.) (1981), New Essays on Human Understanding, Cambridge: Cambridge University Press. Rescher, Nicholas (ed.) (1991), G. W Leibniz s Monadology: An Editionfor Students, Pittsburgh: University of Pittsburgh Press. Riley, Patrick (1972), The Political Writings of Leibniz, Cambridge: Cambridge University Press. Rosemont, H. and Cook, Daniel (1977), G. W Leibniz: Discourse on the Natural Philosophy ofthe Chinese, Honolulu: University of Hawaii. Wiener, Philip P. (tr. and ed.) (1951), Leibniz: Selections, New York: Scribner's. Woolhouse, Roger and Francks, Richard (ed. and tr.) (1977), Leibnizs 'New System,' and Associated Texts, Oxford: Oxford University Press. 2. Suggested Further Readings Studia Leibnitiana is the main venue for European as well as Anglophone authors and publishes an

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annual bibliography of articles and books on Leibniz. In the United States, the Leibniz Review, an annual volume, has been established under the editorship of Glenn Hartz to publish, review and discuss works by and about Leibniz. Many of the books and collections cited below have substantial bibliographies of their own. Adams, Robert (1995), Leibniz: Determinist, Theist, Idealist, New York: Oxford University Press. Aiton, Eric J. (1985), Leibniz: A Biography, Boston, MA : A.Hilger. Brown, Stuart (1985), Leibniz, Minneapolis: University of Minnesota Press. Brown, Stuart (ed.) (2000), The Young Leibniz, Dordrecht: Kluwer. Chappell, Vere (1991), Essays on Early Modem Philosophy. Vol. 12: Leibniz, New York: Garland. Coudert, Allison (1995), Leibniz and theKabbalah, Dordrecht: Kluwer. Coudert, Allison, Popkin, Richard and Weiner, Gordon M. (eds) (1998), Leibniz, Mysticism and Religion, Dordrecht: Kluwer. Cover, lA. and O'leary-Hawthorne, John (1999), Substance and Individuation in Leibniz, Cambridge: Cambridge University Press. Deleuze, Gilles (1993), The Fold: Leibniz and the Baroque, trans. Tom Conley, Minneapolis: University of Minnesota Press. Hooker, Michael (ed.) (1982), Leibniz: Critical and Interpretive Essays, Minneapolis : University of Minnesota Press. Ishiguro, Hide (1990), Leibniz's Philosophy of Logic and Language (2nd edn), Cambridge: Cambridge University Press. Jolley, Nicholas (1984), Leibniz and Locke: A Study of the New Essays on the Human Understanding, Oxford: Clarendon. Kulstad, Mark (1991), Leibniz on Apperception, Consciousness and Reflection, Munich : Philosophia Verlag. McCullough, Laurence B. (1996), Leibniz on Individuals and Individuation , Dordrecht: Kluwer. Mates, Benson (1986), The Philosophy ofLeibniz: Metaphysics and Language, Oxford: Oxford University Press. Okruhlik, Kathleen and Brown, J.R. (eds) (1985), The Natural Philosophy of Leibniz, Dordrecht: D. Reidel. Rescher, Nicholas (ed.) (1989), Leibnizian Inquiries: A Group of Essays, Lanham, MD: University Press of America. Riley, Patrick (1996), Leibniz's Universal Jurisprudence , Cambridge, MA: Harvard University Press. Ross, G. MacDonald (1984), Leibniz, Oxford: Oxford University Press. Russell, Bertrand (1993), A Critical Etposition ofthe Philosophy of Leibniz: With an Appendix of Leading Passages (2nd edn), reprint, London: Routledge. Rutherford, Donald (1995), Leibniz and the Rational Order ofNature, Cambridge: Cambridge University Press. Savage, Reginald Osburn (1998), Real Alternatives: Leibniz sMetaphysics of Choice, Dordrecht: Kluwer. Sleigh, Robert, Leibniz and Arnauld: A Commentary on Their Correspondence, New Haven. CT: Yale University Press. Vailati, Ezio (1997), Leibniz and Clarke: AStudy of Their Correspondence, New York: Oxford University Press. Wilson, Catherine (1989), Leibnizs Metaphysics: A Historical and Comparative Study, Princeton, NJ : Princeton University Press/Manchester: Manchester University Press. Woolhouse, Roger (ed.) (1994), G. W. Leibniz: Critical Assessments, 4 vols, London: Routledge.

Part I Matter, Space and Relations

[1] LEIBNIZ'S ATTACK ON THE CARTESIAN DOCTRINE OF EXTENSION·

By

JOHN

W.

NASON

For the author of the Monadologyl extension and all its modessize, figure, and motion-were unreal. "The Monad, of which we shall here speak, is nothing but a simple substance, which enters into compounds. By' simple' is meant' without parts. ' And there must be simple substances, since there are compounds; for a compound is nothing but a collection or aggregatum of simple things. Now where there are not parts, there can be neither extension nor form nor divisibility. These Monads are the real atoms of nature and, in a word, the elements of things. "2 The common sense world of space and of objects in space was for Leibniz at its worst a contradictory, illusory product of the imagination and at its best a set of phenomena bene fundata. The same argument applies to time. Spatial and temporal objects have their laws which it is the business of natural science to investigate, but as spatial and temporal they are not ultimately, i.e., metaphysically real. This was Leibniz's final position. It was not, however, his initial one. In his youth he was strongly attracted to the "reformed philosophy." For some ten or fifteen years his thinking moved largely within the Cartesian setting. It would hardly be accurate to call him a "good" Cartesian, a but his writings in this • Portions of this paper were read at the meeting in celebration of the tercentenary of Leibniz held by the Conference on Methods in Philosophy and the Sciences at the New School for Social Research, New York City, May 5, 1946. 1 Throughout this article the following abbreviations are used: G.-Gerhardt.: Die philosophischen SchMften von Gottfried Wilhelm Leibniz (7 volumes). L.-Langley's translation of the New Essays concerning Human Understanding. C.-Couturat: Opuscules et fragments in.edits de Leibniz. D.-Duncan: Philosophical Works of Leamitz. M.-Mont.gomery: Leibniz' Discourse on Metaphysics. B&C.-Buchenau und Cassirer: G. W. Leibniz, Philosophische Werke (4 volumes). N. E .-Nouveaux Essais. 2 Monadology, Sees. 1-3. a From the very beginning Leibniz showed the eclectic spirit which characterizes all of his philosophy. Note his early attempt to harmonize Aristotle and Descartes. While he wrote to Thomasius in 1669 that he was "anything but a Cartesian," that in fact he approved of more things in Aristotle's Physics than in Descartes' Medita447

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early period contain so many of Descartes' doctrines that it is not misleading to speak of a Cartesian period. His treatment of the basic Cartesian notion of extension constitutes an instructive illustration of the way in which he arrived at his independent philosophical convictions. Fortunately we have a letter, written in 1669 to Thomasius when Leibniz was twenty-three years old, in which he outlines his early philosophic position.~ The predominance of Cartesian doctrines is striking. Extension is both real in itself and important in explaining natural phenomena. Primary matter consists of extension together with antitypia or impenetrability. Matter, whatever other qualities it may possess, is extended, i.e., it is quantitative and continuous. The diversity of particular things is produced by motion. Rest is admitted. Space or extension is considered as a substance. Motion, which is not deducible from extension, is due to the action of intelligence, and that means in the final analysis to God. Similar doctrines are to be found in the essay, Confessio Naturae contra Atheistas,5 written in the same year, and in a fragment, dated 1671,5 At the same time these documents contain suggestions of nonCartesian doctrines which gradually develop into the anti-Cartesian position that Leibniz had adopted in fairly complete form by 1686. Leibniz's early training in and unwavering allegiance to Aristotle and the schoolmen were in part responsible for his insistence on the scholastic doctrine of substantial forms. While he admitted the reality of extension, he denied that it is the essence of matter or substance, giving as his reasons the impossibility of explaining the properties of matter in terms of extension and the impossibility of accounting for the Christian doctrine of the Eucharist in terms of Descartes' res extensa. Further, in the fragment dated 1671, he reversed his position of two years previous, denying that there can be such a thing as rest, or at least asserting that matter at rest is not real. The strength of the Cartesian influence is nowhere more striking than in a letter to Claude Perrault, member of the Paris Acadtions (G. I, 16; Langley, 634), the fact remains that a strong Cartesian influence dominated this period of his thought. ~ This is given in G. I, 15-27 and translated by Langley, 631-51; a slightly different version is given in G. IV, 162-74. S G. IV, 105-10. II G. VII, 259-60; Langley, 651-2.

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emy of Sciences, with whom Leibniz was in touch during his stay in Paris. In this letter, written according to Gerhardt in 1674 or 1675, Leibniz concludes with so complete an affirmation of the Cartesian doctrine that the laws of motion and of corporeal phenomena are ultimately susceptible of a purely geometrical explanation, that I give his words in full. A long chain of exact and geometrical reasoning, however, would be necessary to deal with this problem fairly. Nevertheless, I believe that it is within our power, and that we have enough phenomenal data for a rigorous analysis and deduction of the true constitution of this sublunary system. If anyone would devote himself to this, he would find that in the end the whole difficulty is one of the solution of problems in pure geometry; just as I believe that I can at present satisfy the laws of motion by purely geometrical demonstrations which involve neither assumptions nor empirical principles. We shall ultimately be able to treat this subject purely in terms of mathematics and geometry. Thus I think that we are at present in a position to hope for a true and non-hypothetical physics. If one were to combine my slight skill in geometry plus the method of general analysis, which I have now used for some time and by means of which, once the phenomenal data are given, one can proceed by strict geometrical arguments and without recourse to guessing-if one were to combine these with the meditations of people like yourself who are so well acquainted with the details of physics, I should dare to hope that we might arrive at something really useful for our age. .As it is, we are still ignorant, as I noted above, of many matters which would be within our power if we only reasoned with sufficient vigor; and if we continue in our present fashion in the investigation of nature, posterity alone will profit from our pains. 7

On the other hand, Leibniz had begun to realize by 1676 the difficulties latent in what is conventionally known as "the problem of the continuum. "8 The purely geometrical account of motion prophesied in the letter to Perrault presupposes the continua of extension, duration, and motion. In Pacidius Philalethi Leibniz discusses the apparent contradictions involved in the notion of a spatial continuum in a way that foreshadows the universe of monads in which space and time are creatures of reason without real basis in the actual world. I do not know what brought about this change. Leibniz's typical doctrine of force, with which he A,.chiv fil,. Geschichte de,. Philosophk, I, 574-5. Cf. the extremely important dialogue, Pacidius Philalethi, written on shipboard as Leibniz was crossing from England to Holland. It is given in Couturat, 594-627. 7

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opposed the Cartesian laws of motion, does not appear in either writing. Indeed, its first mention, so far as I am aware, is in 1686. Unfortunately we have relatively few letters from Leibniz during the period from 1676 to 1686. What few there are indicate clearly that he was becoming more and more critical of Cartesianism, but they throw more light on his reasons for dissent than on the positive grounds for his own constructive position. By 1686, however, many of the important features of Leibniz's philosophy had become fixed. He was then forty. In the Discourse on 1Y1 etaphysics written at this time and in the renewed correspondence with Arnauld we can see in truth that Leibniz was" anything but a Cartesian. " Extension was no longer treated as real. The Cartesians were accused of wrongly assuming that it is a simple, primitive notion when in fact it is complex, derivative, and relative. Leibniz had never held that extension was sufficient in itself to explain corporeal phenomena, but from this time on he drove his argument home with illustration after illustration of its inadequacy. In short, as Leibniz made clear in the Discourse, extension and all its modes are imaginary. I have thus far been tracing the evolution of Leibniz's views on the subject of extension. I have sought to show that, while never a disciple in the usual sense of the term, he was nevertheless strongly influenced by various Cartesian tenets as late as 1674 or 1675 when he desiderated a purely geometrical explanation of motion j that he was moving definitely away from Cartesianism by 1676 j and that, so far as the doctrine of extension is concerned, he had arrived in substance at his final view by 1686. I shall now turn to a consideration of the arguments by which Leibniz sought to combat the Cartesian doctrine of res extensa and by which he advanced his own pos~tion. These arguments are not sufficient in themselves to establish a doctrine of monads, but they are clearly instrumental in the development of such a doctrine, and they are necessary to it in the sense that any such doctrine would be impossible if there were not valid grounds for rejecting extension and space as purely phenomenal. Leibniz's detailed discussion of this problem falls into five arguments and a conclusion. I shall call these (A.) the argument from transubstantiation, (B) the inadequacy of extension in explaining phenomena, (C) the argument from individuality, (D) the argument from the principle of plenitude, (E) the argument from complexity and relativity. These

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lead to the conclusion (F) that extension and extended objects are unreal. (A) The argument from transubstantiation. Around 1669 Leibniz became acquainted with the Baron von Boineburg, a man of profound religious piety, who was instrumental in his entering the service of the Elector and Archbishop of Mainz. Both patrons were concerned with the reunion of the Catholic and Protestant faiths and with the problems of Christian theology. Having a lively interest in such questions and a natural aptitude for them, Leibniz entered whole-heartedly into their plans. One of his earliest attacks on the Cartesian doctrine of extension as the essence of corporeal substance arose from his preoccupation with the theological problem of the Eucharist. How can the visible bread and wine be the actual body and blood of Christ, as the Church asserted it to be' In particular, as Leibniz remarks in a letter to Arnauld (1671), how can one substance, namely Christ's body, be in many different places at the same time and under different species, i.e., as bread and as wine 19 This is the "mystery of the Eucharist" which Leibniz set himself to explain. He was clear from the beginning that a rational explanation would need a different basis from anything provided by the Cartesian doctrine of res extensa. This is an important question for those who take seriously the traditional Christian faith. However modified and diluted the views of modern Protestant liberalism, it is important today for all Roman Catholics and many Fundamentalists. Traditionally it has been the cardinal article in the Christian faith, being the one occasion of direct communion with God. Thus Thomas Aquinas speaks of it as "the consummation of the spiritual life. '110 In the theological atmosphere of the 17th century it was highly important that any philosophy make possible this "mystery," and Leibniz could legitimately use the Cartesian failure on this point as constituting a charge of atheism against Cartesianism. In order to understand Leibniz's treatment of the problem it is necessary to trace the development of the doctrine. In the early period of the Middle Ages the Christian view had wavered between the purely spiritual interpretation of the Eucharist defended by Augustine, and the quite literal, almost materialistic interpretation, one of the chief exponents of which was Ambrose. According 9

G. I, 75.

10

Summa Theologica, III, Q.73, A.3.

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to the Thomist synthesis in the Summa Theologica and the official position of the Roman Catholic church today, Christ's body and blood are literally in the sacrament in place of the bread and wine/ 1 and his whole body is in each species and in each part of each species. 12 The conversion of the bread and wine into Christ's body and blood is a supernatural change brought about by divine act. The change is one of literal transubstantiation/ 3 which is analogous to creation or transmutation. u Nevertheless, the host continues to look and taste like bread and wine because the sensible properties of the bread and wine-the "real accidents" of scholastic terminology-remain in spite of the conversion or transmutation of one substance into another.lS But since accidents exist in a subject or substance, we would normally expect the accidents to disappear along with the substance in which they inhere. This at least was the Aristotelian doctrine. Christian theologians escaped from this dilemma by appealing to the supernatural power of God, to miracle. In the single instance of the Eue,harist we have a case of the separation of accidents from substance and the continued existence of the accidents after the substance has disappeared. 16 Thus, Christ's body and blood while really present cannot be seen because the appearance of bread and wine remain, and they must therefore be taken on faith alone.l1 Furthermore, while the original bread and wine are in space Ibid., III, Q.75, A.I. 12 Ibid., Q.i6, A.I-3. Ibid., Q.75, AA. u Ibid., Q.75, A.B. 15 Ibid., Q.75, A.5; Q.77, A.l. The Schoolmen following Aristotle called all kinds of being save substance "accidents"; while substance exists in se, the other categories all exist in alio. To distinguish this use of the term from its use in logic where an accident is contrasted with a property, the Schoolmen frequently used the phrase "real accident." Thlis, the whiteness of the bread and the sweetness of the wine--what I have referred to in the text as the "sensible properties"-are real accidents, or to use another scholastic phrase of equivalent significance in this context, they are the "sacramental species." 18 Cf. Mercier, A Manual of Modern Scholastic Philosophy, 3rd English ed., 487-91, from which I cannot forebear quoting the following sentences: "This official decision of the Council [of Trent] asserts the separability of accidents from their natural substance. The possibility of this separation philosophy, left to itself and guided by experience, would most likely never have snspected. But enlightened by the doctrinal authority of the Church, the Christian philosopher professes not only the possibility but the fact." 11 Sum. Theol., Q.75, A.l. 11

IS

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and while the sensible properties of the bread and wine continue in space after the transubstantiation, Christ's body and blood are not spatially extended and spatially located. They are" not in the sacrament as in a place," according to the words of Thomas Aquinas, and by this subtle distinction he sought to avoid the paradox involved in holding that the whole body and blood are in as many different places as there are consecrated hosts. 1s There is at least the merit of audacity in this account. It may make sense, although it is difficult to see what this sense is. How can a single substance become plural except by division, which is expressly denied' How can a physical substance avoid being" in a place" T True, substantial forms are not material entities, but principles of being. Still, the substantial form of a physical substance exists in intimate connection with matter, and it is the resulting "body" or physical thing which is alleged to be present in the sacrament. In any event, it ought to be clear that any philosophy which finds the essence of body in extension will have even greater difficulty with this cardinal doctrine of Christianity than did Thomas Aquinas and his fellow mediaeval philosophers with their substantial forms. But that the essence of matter is extension is precisely what Descartes did hold, and it was his attempt to reconcile this important tenet of his own philosophy with the doctrine of the Eucharist that led to much of the criticism and persecution which his followers endured. 19 In one respect Descartes offers a simpler explanation than the Schoolmen, who were forced to explain the continued presence of the sensible properties of the bread and wine after the consecration by an appeal to the miraculous separation of the" real accidents" from their proper substance. According to the philosophy of Descartes the sensible properties of objects are the result of the motions of the particles on their surfaces, these minute surface motions affecting the sense organs of the observer and producing the sensed qualities. 20 Now since the sacramental conversion is Ibid., Q.75, A.I; Q.76, A.5. Cf. Bouillier, Histoire de la philosophie cartesienne, vol. I, ch. XXI. Descartes was not so prone to theological speculations as Leibniz, and his treatment of this topic, made in part in reply to criticisms of Arnauld to his Meditations, was his only excursion into the field. The chief grounds for the later criticisms lay in two letters which Descartes wrote to Father Mesland, who made them public contrary to Descartes' request. For Descartes' attitude toward theology, cf. Gouhier, La pensee religieuse de Descartes, Part II, ch. IV. 20 Cf. Reply to the Fourth Objections, Haldane and Ross edition of The Philosophical Works of Descartes, II, 116-22. 18

19

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a literal transubstantiation, the surface remains the same although the substance has changed. Therefore it is only natural that the sensible properties continue unaltered in spite of the miraculous conversion. However satisfactory the solution to this problem, it leaves the other aspects of the "mystery" of the Eucharist in worse straits. If the essence of material stuff is its extension, and if the volume or extension of the host remains the same, how can it be said that the bread and wine have been converted into the body and blood of Christ' More difficult yet is the question, how can the body and blood of Christ be in many different places at the same time T Descartes sought to satisfy these questions in his two letters to Father Mesland. 21 There is a difference, he argues, between an inorganic and an organic body. The former's essence does consist in extension, and any change in its extension implies a change in its substance. But the essence of an organic body lies in its connection with the soul. A man's body changes both in form and in material content. It grows from infancy to manhood; its material particles are continually being renewed. We call it the same body because it is connected with the same soul, or, as Descartes expresses it in scholastic language~ because it is "informed" with the same soul. Re further illustrates this point by arguing that the food we eat becomes incorporated in our bodies, the minute material particles being taken into the blood system and distributed about the body in such a way that, had we the ability actually to see the minute constituents of our systems, we should observe these particles of food composing our bodies. Thus, when Christ ate the bread and drank the wine, their constituent particles became naturally a part of his body. In the sacrament,however, the change takes place "by the force of the words of the consecration." The host is the actual body and blood of Christ 'because after the consecration it is united with the soul of Christ; and this is true of all the hosts at all the altars because each is in the same way united with his soul. I have summarized the solution as Descartes gave it. Many Catholics, and particularly the Jesuits, were quick to see the difficulties in this explanation and to condemn it accordingly. In the first place, the suggestion that the essence of organic bodies lies 21

Descartes, Oewvres, ed. Adam et Tannery, IV, 162-170, 345--348.

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in the relation to the soul will not stand examination, for no organic body except man, on Descartes' own principles, has a soul. If extension is the essence of the inorganic, relation to the soul the essence of the human body, what is the essence of all other organic bodies which like man change in form and undergo a continual renewal of their material particles' Much more important, however, is the flagrant inconsistency between Descartes' basic doctrine that the essence of matter is extension and his special doctrine that in certain types of organic matter the essence is the soul. When all is said and done, the Cartesian philosophy is famous for its division of all finite existence into res extensa and res cogitans. Now a human body, no matter how animated, is still res extensa. As extended it is part of the one whole of extension which in reality for Descartes constitutes a single material entity. Bodies in the plural are so many parts of this whole temporarily distinguished by the different motions which give them distinguishable sensible properties. Their unity lies in the fact that this particular part of extension has a pervading motion which differs from that of its neighbors. Another bit of extension may have a similar motion, or set of motions, and hence be like it, but it will still be a different body. If the essence of the body lay in its characteristic motion, or set of motions, then the same body-idem numero, as Descartes saidmight well vary in size and even shape. It need hardly be repeated, however, that for Descartes the essence of body lies not in motion but in extension. Either then this basic cQncept must be abandoned or the "explanation" of the Eucharist is unsatisfactory. Finally, it is worth noting that Descartes' view amounts to the doctrine that the various bits of bread and wine become the body and blood of Christ by becoming connected with Christ's spirit. In itself, this is not an implausible treatment of the problem, but it smacks of the figurative or spiritual interpretation of Augustine 22 rather than of the literal interpretation of Ambrose and Aquinas. While Descartes could quote the words of the Council of Trent, "ea existendi ratione quam verbis exprimere vix possumus," the fact remained that the theologians of the Church sought an explanation in terms of literal, not figurative, transubstantiation. It is ironic 22 As Bouillier points out in the chapter referred to above, Descartes' stoutest defenders were usually to be found among the Augustinian orders.

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that Descartes should himself in his treatment of these difficulties deviate, in implication if not in explicit statement, from the basic tenets of his philosophy and play into the hands of Leibniz, who clearly saw that there could be no final solution in terms of a philosophy which placed the essence of matter in extension. I have dealt with Descartes' treatment of the "mystery" of the Eucharist in some detail partly because it raises the specific difficulties which Leibniz attacks and partly because Leibniz himself, although quite positive in his condemnation, does not elaborate his reasons for rejecting it. There is some historic justification for this. Cartesianism and the Cartesians were savagely attacked in the second half of the seventeenth century on the ground of atheism; and the reason for this charge lies in the difficulties just discussed. Leibniz, indeed, seems to take it for granted that the recipients of his letters on the subject-the Duke John Frederick, Arnauld, and the editor of the Journal des Savants-are so familiar with the controversy that he need merely assert categorically that a solution is impossible so long as the essence of matter is taken to be extension. 23 How can one extension take upon itself a foreign extension? he asks in one place. How, if extension be the essence of matter, can the same substance be in several different places at once The inquires in another. His further criticism that it is difficult and inconvenient to explain the persistence of the sensible qualities of the bread and wine without an appeal to real accidents, we have already seen to miss the mark. But surely he is right on the first two points. Leibniz is careful not to accuse Descartes of being an atheist, but he is quite certain that this is one of several reasons why Cartesianism inevitably falls into atheism. For that reason, if no other, it must be rejected. Leibniz is equally positive that he has the only solution to the problem. The problem, he repeats more than once, is to give a rational explanation, one that will refute once and for all the sceptics and atheists who assert that no intelligible explanation is possible. Writing to Arnauld in 1671 he insists that the essence of body lies in motion or in a principle of motion; that the very notion of extension is irrelevant to such a principle; and hence that the substance of body is not subject to conditions of place or ex23 Cf. G. I, 62, 70, 75; G. IV, 345 j Nouveaux Essais, IV, xx, 10 (Langley, 612). These are, so far as I know, the only references Leibniz makes to the subject.

13

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tent.2t Writing a short time later to the Duke John Frederick he expresses himself as convinced that "there is in every body an internal, incorporeal, substantial principle distinct from mass, and it is this that the ancients and the schoolmen have called substance.' '25 I have already suggested that there is something to be said for the doctrine that motion constitutes the essence of body. Such a view at least has certain obvious advantages in dealing with transubstantiation. So far as I am aware, however, Leibniz never again recurs to this doctrine. We shall meet again, and that frequently, the" internal, incorporeal, substantial principle, " in other words the substantial form of Aristotelian and scholastic philosophy gradually transformed into the monad of Leibniz. Descartes in the letters to Father Mesland reverted in spite of himself to a scholastic point of view. Leibniz openly accepts such a position. The only claim that he might have made that he had advanced beyond the schoolmen lies in his treatment of space and time as phenomenal only. If space with all that it involves is an entity of reason and not ultimately real, then indeed one might say that the extensional and positional problems raised by the Eucharist are of no great importance. Contradictions and absurdities matter little among phenomena. But at the time Leibniz wrote these two letters he had not arrived at the doctrine of the unreality of space and time and could not claim the advantages of their unreality. Consequently, it is difficult to see in what sense, if any, his position around 1671-72 was any advance over that of Aquinas or avoided any of the difficulties inherent in the Catholic "solution." His case against the Cartesian position, however, stands. It amounts in the end to this: Christianity is true; the transubstantiation involved in the Eucharist is a cardinal tenet of Christianity; such transubstantiation is irrational and unintelligible if the essence of body is extension; therefore, the essence of body is not extension, and Descartes was wrong in his fundamental contention. (B) The inadequacy of extension to explain phenomena. The two basic principles of Leibniz's philosophy are the principle of contradiction and the principle of sufficient reason. 28 The importance of the latter, according to which nothing happens without a reason, or there must always be a reason why a thing is as it is

2' G.

I, 75. 25 G. I, 62. Cf. C. 519; G. VII, 309, 35fHl. These are but three of innumerable references to these principles or axioms in Leibniz's writings. 26

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rather than otherwise, can hardly be overestimated. One variant of this principle is the core of the present argument. "Since there is nothing in things without a cause, " Leibniz wrote to Thomasius in 1669, "bodies must not be assumed to possess any properties the cause of which cannot be made to appear from their primary constitutive principles.' 121 According to Descartes there is one property, and one property only, possessed by all physical objects, namely extension. This is the essence of all matter or body or corporeal substance. 28 The fourth Principle of the Second Part of Descartes' Principles of Philosophy reads: "That the nature of body consists not in weight, nor in hardness, nor color and so on, but in extension alone." And the argument begins: "In this way we shall ascertain that the nature of matter or of body in its universal aspect does not consist in its being hard or heavy or colored or one that affects the senses in some way, but solely in the fact that it is a substance extended in length, breadth, and depth." It follows from this that there can be no real distinction between body and space. They are in truth the same and differ only in our way of looking at them. 29 This famous doctrine has the merit of great simplicity, but the disadvantage of being demonstrably false. It is beset with difficulties. Can the various properties of matter be deduced from the nature of extension' The answer is clearly no. Neither extension nor its "modes "-size, form, and motion-will suffice to explain the properties which bodies are found by experience to possess. It is not necessary to enumerate all sucll properties. It will suffice to show that certain pervasive and scientifically important features of physical objects are not deducible from their extension. Leibniz selects three and demonstrates that extension cannot account for (1) antitypia, (2) inertia, and (3) force. (1) One such property is antitypia. In various places Leibniz equates this word, sometimes given in Greek, sometimes in Latin, with impenetrability, resistance, density, the power of filling space, the inability of a body to exist with another in the same space. 30 G. I, 26; G. IV, 173; Langley, 647; cf. also G. IV, 464; D. 42. I shall for the present use these terms interchangeably, as Descartes and Leibniz did. I shall examine below the question whether on Leibnizian principles it is proper to speak, as Leibniz all too frequently and confusingly does, of corporeal substance. 21

28

29

Pt. II, Prine. X, XI.

30

G. I, 17, 24, 26; G. IV, 165, 171, 173; Langley, 637, 645, 647.

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459

Literally it means "repulsiveness." The most frequently used equivalent is resistance, but since Leibniz also uses this term to cover inertia, it will avoid confusion if we translate antitypia as impenetrability. Leibniz holds that it is a universal property of all bodies or corporeal substances. s1 It is clearly different from their extendedness. Since it cannot be derived from the concept or definition of extension, primary matter is composed of both extension and impenetrability. It is important to be clear on just what points Leibniz agrees with Descartes and on what points he differs. He agrees that it is in the nature of body or matter to be extended. s2 He is just as positive about this in later life when he had arrived at the position that space and hence bodies are phenomenal as he was in his earlier Cartesian years when he considered matter as real. He agrees also that wherever there is extension there is matter or body. There is no empty space, the apparent emptiness of certain areas of space being a sensible illusion. ss He does not agree, however, that extension and matter are one and the same thing. Hence he does not agree that extension is the essence of matter. He insists upon distinguishing between space as a primarily extended entity or "mathematical body" and matter as a secondarily extended entity or "physical body.m4 And the difference is not merely one of our mode of conceiving them, although Leibniz's frequent statements about space as an abstraction from extended objects might seem to suggest this. It is a real difference, for the property which all physical bodies possess in addition to extension, and which extension abstractly considered in itself does not possess, is antitypia. In his Animadversions on Descartes' Principles, written in 1692, Leibniz attacks the doctrine that extension is the essence of matter. In his comments on the fourth Principle of Part II he distinguishes between hardness as that property of some bodies by which they preserve their form, and impenetrability or the inability of two homogeneous bodies to exist in the same space-a property of all bodies asserted apparently on the basis of empirical evidence. Leibniz, as was his custom, circulated these Animadversions among Sl In one passage he speaks of it as the essence of matter or form of corporeity (G. I, 17; G. IV, 165; Langley, 637), but this suggestion is quickly discarded. 32 For a few references taken from different periods of his life cf. G. I, 18; G. IV, 165; Langley, 637; G. IV, 466; D. 44; G. VI, 581. 3S G. I, 26; G. IV, 173; Langley, 647. 34 G. I, 24; G. IV, 171; Langley, 645.

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a number of his learned friends for comments and criticisms. Bayle's comments were transmitted to him by Basnage de Beauval, the editor of the Journal des Savants. Bayle could not understand how bodies could possess internal principles of resistance by which they make an effort to remain in the same place. If, he suggests, this phenomenon could be explained by an external principle, it would still be true that the essence of bodies is extension. 35 Leibniz's reply is instructive. "I do not conceive that a thing which has only extension for its essence could resist by means of an external principle, for even if one should grant this external principle, I hold that it is not possible for it to produce resistance in a subject which is merely extended, because it is inconceivable that resistance be a mode of extension. "38 Here Leibniz is clearly right. There is nothing in the nature of extension from which we can deduce the property of impenetrability. The property of filling space to the exclusion of other objects is distinct from the property of being extended, even though we hold that the two are in fact inseparable in physical objects. (2) According to classical physics inertia is the primary property of matter. aT "Whatever can be changed in motion only by the application of force is called matter. That property which requires force to change either the magnitude or the direction of the motion of a body is called inertia. Inertia is the distinguishing characteristic of matter.' ISS This highly familiar notion was first made explicit in the seventeenth century, although it was far from being commonly or accurately understood. Galileo is generally given the credit for having first discovered the so-called law of inertia, and both Huygens and Newton understood its significance. 39 Leibniz also grasped its nature and importance. This is well illustrated in his correspondence with de VoIder, who objects to his emphasis on inertia, contending that the quality by which a body remains in the same state is a necessary consequence of the extension of the body, and that the body will not change unless there is some reason or cause for that change. LeibG. III, 92. 38 G. III, 97. I nse the phrase "classical physics" to denote that body of knowledge which was increasingly systematized from the 17th to the 19th centuries and to distinguish it from certain modern positivistic views according to which inertia, motion, force as used in this chapter are meaningless concepts. 38 Ferry, General Physics, 3-4. 3W Cf. Mach, The Science of Mechanics, passim. 35

3T

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niz replies; "Let there be in matter a force of preserving its own state; that force can in no way be deduced from extension alone. I admit that every single thing perseveres in its own state until there is some reason for change-a principle of metaphysical necessity. But it is one thing to preserve a given state until something brings about a change, since it is in itself indifferent to rest or change; it is another and a far more important matter to be not indifferent and to have a force or inclination as it were for maintaining a given state and hence offering resistance to a cause of change. "40 This is Newton's "resident force" or I t vis insita." Leibniz differs from the classical physicists in that he does not view inertia as the distinguishing characteristic of matter. For Leibniz matter is essentially passive; it is the combination of impenetrability with inertia or resistance. Together they constitute the "passive principle" of materia prima or mass. 41 Can inertia be deduced from extension 1 Extension is indifferent to motion and rest. Inertia, however, is not mere indifference; it is actual resistance to change. If motion or change involves positive force, then inertia is a kind of negative force. It involves a dynamic quality whereas extension is purely geometrical. Hence inertia, more obviously even than in the case of impenetrability, is not derivable from extension.'2 Another way of demonstrating the same conclusion is by considering the laws of motion. This is a topic which I hope to treat in some detail at a later date, but as one aspect of the conflict between the Cartesian laws of motion and the Leibnizian laws of force is highly relevant here, I must anticipate briefly one of the arguments. If, Leibniz argues, the essence of bodies were extension, then, since extension is indifferent to motion and rest, body A in striking body B ought not to lose any of its original velocity, and the two ought to continue together after their concurrence with the velocity of body A. Experience teaches us plainly that this is not the case. The actual laws of motion necessitate a property in bodies distinct from extension, namely resistance or natural inertia. 43 (3) Besides extension, impenetrability, and inertia all bodies G. II, 170. 41 G. II, 171; G. IV, 510; D. 127. Cf. On Nature in Itself, #11. 43 This argument is stated in a number of places, but nowhere more clearly and concisely than in two letters to the editor of the Journal des Savants, one written in 1691, the other in 1693. Cf. G. IV, 464-7; D. 42-6. 40

42

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possess the property of force. We approach here one of the most complex and one of the most fertile concepts in Leibniz's philosophy. Here again I hope later to devote careful attention to unraveling the steps by which Leibniz arrives at this centrally significant notion and to showing its consequences. All true substances are for Leibniz active. In other words, the concept of substance and the concept of active force are intimately connected. This is not a position at which he arrives over-night. If in the present connection I make dogmatic assertions or seem to beg important questions, I can only plead the impossibility of treating all aspects of Leibniz's philosophy simultaneously. There is such a thing as action or activity. Bodies apparently at rest do begin to move; those in motion are brought to a stop; the velocity of motion may be accelerated or retarded. In short, changes do occur, and a change necessitates an active cause of change, i.e., force. Now force differs from motion, for it is force that causes and controls motion. Motion might conceivably be deduced from force, as the effect from the cause, but force cannot be derived from motion. And if motion is not deducible from extension, as Descartes himself admits in ascribing all motion ultimately to the will of God and thus importing it from without into his geometrical universe, it follows a fortiori that force is not deducible from the concept of extension. Leibniz seeks to drive this conclusion home in a number of ways. Motion is change of place; it is an alteration in the spatial relations of two or more bodies. It is relative in the sense that an alteration in spatial relations does not tell us which of the two or more bodies has actually moved. As relative, motion is not ultimately real. Nevertheless, behind phenomena like motion there must be some metaphysical reality. Leibniz maintains that the ultimate reality underlying motion is force. 44 Further, the general property of resistance (here interpreted to include both impenetrability and inertia) is said to involve, in some obscure way yet to be determined if possible, activity and passivity. Once action is granted, the necessity of the concept of force immediately follows.'5 Finally, inertia, or resistance in the narrower sense, while not deducible as we have seen from extension, is explicable in terms of the laws of force. 46 There is a certain ambiguity here in Leibniz's statements. H 45

Cf. Discourse on Metaphysics, #18. Cf. G. IV, 465; D. 44; G. II, 227.

4e

G. III, 94.

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On the one hand, he argues that resistance to motion, although a passive force, is nevertheless a manifestation of force in general and hence to be explained in terms of the general concept of force. 1T On the other, he contends that matter and its constitutive principle of resistance are primarily passive, and hence that we must have recourse to some distinct and positive source of activity, namely force.'s The conclusion is obvious. So far is force from being explicable in terms of extension that, on the contrary, the very principles of the extended world of mechanics are to be sought in the metaphysical realm of dynamics. This is well summed up in the letter of1691 to the editor of the Journal des Savants already referred to. All this shows that there is in matter something other than what is purely geometrical; that is, than extension and its changes pure and simple. When we consider matter attentively we perceive that there must be joined to it some higher or metaphysical notion, to wit: that of substance, action, and force j and that these notions show that everything which suffers must act reciprocally, and that everything which acts must suffer some reaction; and consequently that a body at rest cannot be carried along by another in motion without changing something of the direction and the velocity of the agent. . . . This consideration seems to me important, not only in order to know the nature of extended substances, but also in order not to slight in physics the higher and immaterial principles to the prejudice of piety. For although I am persuaded that everything takes place mechanically in corporeal nature, I do not cease to believe also that even the principles of mechanics, i.e., the first laws of motion, have a more exalted origin than that which pure mathematics can furnish. 4S

Extension is unable to account for various important properties which bodies do in fact possess. This is the essence of the present section. We have now examined the situation with respect to three such properties, and we have found that from the purely geometrical concept of extension it is impossible to deduce the properties of impenetrability, inertia, and force. If we accept the principle of sufficient reason, according to one aspect of which there can be nothing in bodies which is not deducible from their inner nature, we must agree with Leibniz that the concept of bare extension is hopelessly inadequate for the concept of matter or corporeal substance. G. III, 94; G. IV, 466; D. 44. G. VI, 587; B&C IT, 370; On Nature in Itself, #11. 49 G. IV, 465-6; D. 44. Cf. also Discourse, #18; On Nature in Itself, #11; .4f1imadversions, II, Prine. 64; G. IV, 472, 478; L. 300; G. IT, 24l. 41

48

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(0) The argument from individuality. There are compounds, says Leibniz at the beginning of the Monadology, and therefore there must be simple substances. Many people would agree with Leibniz on this point. An automobile, a book, a building are compounds. They are composed of their constituent parts which may be simple or themselves compounds. In the latter case we must seek the parts of the parts until we come to the simple ingredients. The science of physics has been much occupied with this investigation and has offered at different stages in its history a variety of simple entities as the ultimate building blocks of the physical universe. Physicists have for the most part been content with physical units-minute, but nevertheless actually extended entities which possess in addition to extension one or more non-geometrical properties. Unfortunately for the harmony of physics and metaphysics, this attempt on the part of the physicists has always seemed to ultra-rationalistic philosophers to be futile. Leibniz insists time and again that whatever is extended is at least in theory divisible and hence not simple. Indeed, Leibniz holds, as we shall see, the peculiar doctrine that every extended thing is not only theoretically divisible but actually divided ad infinitum. As one of the most thoroughgoing rationalists in the history of metaphysics, he asserts the proposition that the ultimate constituents of reality must be absolutely simple, i.e., that the ultimate elements of physics must be metaphysically ultimate and simple as well. It is clear that when the physicist calls the atom or the electron simple and when the metaphysician denies this, they are using different meanings of simplicity. And when we consider the internal complexity of Leibniz's monads, his simple substances, and contrast them with the internal simplicity of the physicist's ultimate units, the difference in meaning becomes even more apparent. Three different meanings are important in this connection. 50 (i) Wbat is simple is in contrast to the complex. In this sense electrons are simple, but monads are highly complex. (ii) The simple is that which is without parts, meaning here by "part" any structure within the whole object which stands out by virtue of its own form or intrinsic property. Thus a book, a melody, a consciousness 50 I have taken these from the admirable and illuminating analysis of the term "simplicity" in Herbert Spiegelberg's Uber das Wesen der I dee, 1. Abschnitt. This essay first appeared in the Jahrbuch fur Philosophie und PhiinomenoZogische ForschungJ Bd. XI, and was reprinted separately in 1930 by )la:x Niemeyer.

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have parts, whereas a line, pure time, the spectrum, indeed any continuum, have none. In this sense electrons are simple, but monads are not. (iii) The simple is the indivisible. The difference between this meaning of the term and the preceding can be expressed by saying that according to the second view a simple entity is "Without divisions, while according to the present distinction it is incapable of division. In this sense atoms and electrons are clearly not simple since they are capable of at least theoretical division, while in this sense, and only in this sense, monads are simple. Thus monads are not internally simple; and since each monad is a universe in itself the "parts" of which can be distinguished, they are not. simple in being without parts. They are, however, simple in the sense of being unextended and hence without physical parts either actually or theoretically. With this meaning of simplicity in mind let us turn directly to Leibniz's arguments. By invoking again the principle of sufficient reason Leibniz seeks to show that the Cartesian concept of extension cannot explain the simplicity, the individuality, the self-identity of the metaphysically necessary constituent substances of the universe. It is obvious from the foregoing that simple elements cannot be deduced from extension. Whatever is extended is necessarily composite; the very notion of extension involves plurality. This is so important an aspect of Leibniz's attack on extension that I shall leave its elaboration and proof to section (E). Leibniz of course recognizes that any given extent, sayan inch or a foot, may be treated as a unit. But this is an arbitrary unity imposed by our way of thinking. It is in Leibniz's language abstract and not in the nature of things. 51 Such a unit is simple in the second sense defined a bov~, for as any given extent it is a continuum without actual parts. But nothing extended is simple in the third sense, for nothing which is extended can escape at least theoretical division. In Leibniz's sense of the term the simple cannot be found in extension. If extension cannot account for the simplicity of ultimate substances, can it account for the individuality of physical objects' How is it that one object differs from another-this book from that ODe 1 What is it to be one individual thing, identical with itself, and different from all others' For Descartes the one, solid, extended, substantial world is carved up into particular physical objects by motion. When the motion or set of motions in one part 51

G. II, 170.

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of space differs from that in adjacent parts, we distinguish different objects with different sensible qualities. And it must be added that on Cartesian principles, since space is real, we can distinguish different objects by locating them in different parts of space. Leibniz is clearly right in holding that this explanation is quite unsatisfactory, although all of his reasons are not equally convincing. His most frequent basis of attack is another important principle or axiom-the principle of the identity of indiscernibles. This may be stated in a number of ways: where there are no discernible differences, there is no plurality; two objects or things cannot be two unless they possess at least theoretically discernible qualitative differences. So stated this sounds like a principle of epistemology; but while it has uses in epistemology, its real nature is metaphysical. Leibniz is not really telling us how we can know that two objects differ; rather he is asserting that they cannot in fact be two, or differ even in number, unless they possess some qualitative difference. This is Leibniz's answer to the problem of individuation. It is opposed to the Cartesian theory which distinguishes individuals by their peculiar motions and locations in space and time. It follows from this theory that two objects may be identical in all their material and sensible properties and still be two, provided that they have different spatial and temporal attributes. Leibniz, however, as I have pointed out, had by 1686, if not ten years earlier, ceased to believe in the reality of space and time. Hence space and time could not be used by him as principles Of individuation. Hence further, if two objects are to differ in the numerical sense of being two, they must also differ in some qualitative sense. Since, according to the variant of the principle of sufficient reason which underlies all of the present arguments, there can be nothing in things which does not follow from their nature or essence, the qualitative differences of two material objects must flow from some inner substantial difference. Leibniz considers this a striking confirmation of his insistence upon the necessity of substantial forms for any ultimate account of mechanical phenomena. 52 If space is unreal, it is natural to consider extension as likewise unreal. Leibniz, as we shall see, reverses the argument: extension is unreal, and hence space is merely an entity of reason, the order of all possible coexistertces. It is not logically necessary to hold 52

345.

Cf. Discourse, #12; M.135, 154-5, 161,162,190-2; New System, #3; G. IV,

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such a view. Space might indeed be phenomenal, while material objects possess the quality of being extended. This is an odd position, but it happens to be the one ''1thich Leibniz temporarily adopts-perhaps for the purposes of argument-in discussing the pro blem with the Dutch disciple of Descartes, de Voider. ' , You are of the opinion," Leibniz writes in 1703, "that those who distinguish bodies solely by the modes of extension (as they call them), as nearly everyone does today, do not deny that bodies differ only modally-at least if the vacuum is excluded. But two individual substances must be distinguished more than modally. Otherwise according to common doctrine it will be found that they differ not even modally. For if you take two bodies, A and B, equal and with the same figure and motion, it will follow from such a notion of body-that is, from one drawn from the putative modes of extension only-that there is no intrinsic property by which they are distinguished. Are they therefore diverse individuals? Or is it possible for things to be diverse which can in themselves in no way be distinguished T Such consequences and innumerable others of the same kind show clearly enough that the true notions of things are plainly subverted by that new philosophy which forms substances from matter alone or from what is passive. Whatever things differ must differ in some way or other or must have an assignable diversity in themselves, and it is astonishing that men have not made use of this most obvious axiom together with so many others." 53 In itself this is an inadequate reply to Descartes. If I hold that space and time are principles of individuation and therefore that two contemporary objects in different parts of space are nevertheless different although identical in all other respects, it is not sufficient to reply that my conclusion is absurd because space and time are not real and hence not valid principles of individuation. My conclusion may be false if my premise is false, and it is my critic's duty to demonstrate its falsity. Now Leibniz's grounds for impugning the reality of space and time are to be found primarily in his criticisms of the Cartesian doctrine of extension, and one of these criticisms is that it cannot account for the individuality of different objects. Considered in itself, therefore, the argument is circular. Leibniz, however, has other and quite independent arguments by which he seeks to show the unreality of space and time. When we combine these with the present line of reasoning, we get 53

G. II, 249.

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a better understanding of the real grounds for Leibniz's rejection of the Cartesian doctrine of extension. There is another difficulty in explaining individuality or selfidentity in Cartesian terms-a difficulty which Leibniz never clearly states, but which may be implied by certain statements in the not entirely clear thirteenth section of the essay, On Nature in Itself. For Descartes, it will be remembered, particular extended objects are precipitated out of the one substantial whole of res extensa by motion. Any given physical object, such as a book, is the subject of two different motions. There is that internal motion, or set of motions, by which the object is primarily characterized and by which it gets those sensible properties we ordinarily discover in it. There is also, or there may be, an external motion or translation by which the object gets from one part of space to another, as when I take a book out of the bookcase and put it on the table by my typewriter. Thus, in so far as a body moves, it would seem that a characteristic motion, or set of motions, is literally transferred by another motion from one part of space to another. But the first kind of motion can be nothing but the second kind of motion applied to what for convenience I call the constituent particles of the object in question. What constitutes a particle, however' If the essence of matter is extension, if all variation is due to motion, then the particles which are subject to the motion of translation must in turn be constituted by another motion or set of motions-namely, those which give them whatever characteristics they possess as particles. But this is an infinite regress. If it were a true account, we should never have any particular objects with specific properties. Hence any attempt to place the essence of matter in pure extension and the determining factor of individuation in motion is bound to break down. Thus the answer is clearly "no" to our original question, can we deduce from extension the simplicity and individuality which it is metaphysically necessary that some substances possess 1 After distinguishing between various meanings of the term" simplicity," I have sought to show that Leibniz is correct in maintaining that whatever is extended is not (in his sense) simple since it is theoretically, if not actually, divisible-although I have not given in this section his proofs for this doctrine, nor have I taken sides in the issue whether theoretical divisibility is important where actual division is either impossible or does not in fact occur. I have

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further tried to show that Leibniz is in principle correct in his contention that extension cannot account for the individuality of things. Granted the principle of the identity of indiscernibles and granted the unreality of space and time, this conclusion is unavoidable. But quite apart from these two presuppositions, it is possible to show not only that extension alone is inadequate, but also that extension together with motion (Descartes' real position) is inadequate to account for the individuality of self-identical things and the differences of different objects. (D) The argument from the principle of plenitude. The world we live in is a motley world, full" of shoes and ships and sealing wax, of cabbages and kings." So much will be granted by everyone. For Leibniz, however, the world is not only multifarious; its diversification is infinite. God has not been niggardly in his creation. He did not create in a haphazard or capricious fashion. He created everything which it was possible for him to create in the best of all possible worlds. That does not mean that he created everything, for God's intellect envisages an infinite number of possible universes, no one of which is compossible with any of the others. Why did he create this particular one' Because it is the best. Why is it the best? Because-at least this is part of the reason-it is the richest, the most varied and complex, the most diversified, the fullest. We have here an instance of that metaphysical dogma which Lovejoy calls in The Great Chain of Being the principle of plenitude. He describes the principle as "not only the thesis that the universe is a plenum fonnarum in which the range of conceivable diversity of kinds of living things is exhaustively exemplified, but also any other deductions from the assumption that no genuine potentiality of being can remain unfulfilled, that the extent and abundance of the creation must be as great as the possibility of existence and commensurate with the productive capacity of a 'perfect' and inexhaustible Source, and that the world is the better, the more things it contains.' '6' If we follow Lovejoy, the principle of plenitude fuses with the principle of sufficient reason in the philosophies of Spinoza and Leibniz. Everything which exists must have a sufficient reason, and this is God. But God, who is complete and self-sufficient, must have some reason for creating one kind of a world rather than an64 P. 52. I am particularly indebted to chapter V which contains a valuable and instructive discussion of several aspects of Leibniz's philosophy.

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other. Now this reason can only be one of value or good. If it is good to exist, or if it is better to exist than not to exist, then a rational God will create that world which contains a maximum of existence. What is to be the criterion of the maximum of existence f At least one is suggested by Leibniz in his assertion that God creates everything which is compossible in the fullest and richest of possible worlds. It is important to note, however, that while the principles of plenitude and of sufficient reason work in close cooperation in the philosophy of Leibniz they are nevertheless distinct principles. The one asserts that everything which exists must have a sufficient reason; the other tells us what that reason is. The proposition that existence is better than non-existence cannot be deduced from the principle of sufficient reason; it is merely a restatement of the principle of plenitude. It is conceivable that God might have had some other reason in creating the world, some other criterion of what would constitute the best. He might, for example, have been moved by an aesthetic consideration and preferred a neat and tidy universe to an overstuffed one. Nor do I see that such a standard would be any less rational than the principle of plenitude. Indeed, even Leibniz exhibits a certain uncertainty as to the ways of God. As Lovejoy points out, he wavers in interpreting the criterion of compossibility between a purely quantitative view according to which the greatest numerical variety of existents was created and a qualitative view according to which, humans being worth more than earthworms, the greatest "intensive" amount of existence would be created. Be that as it may, we live in a wonderfully rich and diversified world. So far as the argument of the present essay is concerned, the real question is: can this diversity and richness be explained in terms of extension or of ~xtension and motion T There is nothing in the concept of mass itself or of mass in motion from which one could deduce the infinite variety of the actual world. The Cartesian metaphysics stands condemned by the principle of sufficient reason, and even the addition of the principle of plenitude would not suffice to overcome the difficulty. Whether this is sufficient justification for the re-introduction of Leibniz's beloved substantial forms or whether they in themselves can account for the richness and variety of the world need

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not concern us now. VVb.ile the positive aspect of Leibniz's position may be doubtful, the attack on Descartes is valid. ss (E) The argument from complexity and relativity. In section (C) of this essay I made use of the argument that what is extended is for that very reason not simple, that whatever is extended is at least theoretically divisible. It was not necessary in that connection to examine in detail Leibniz's reasons for this statement. The argument of section (0) was hypothetical. It ran: if extension is by its very nature composite, then it obviously cannot account-as the principle of sufficient reason demands that it should-for the absolutely simple substances which are the building stones of our metaphysical universe. It is the business of this section to examine Leibniz's reasons for insisting that extension is a complex notion. There is no appeal here to the principle of sufficient reason j it is a question of what is involved in the ordinary meaning of the term extension. For Descartes extension is a simple notion, a clear and distinct idea, a primitive concept not subject to further analysis. This, according to Leibniz, is the root of all the difficulties in Cartesianism. Extension is not a simple or primitive concept, since it is susceptible of analysis. It is not a clear and distinct idea, since it gives rise to all the problems of the continuum. 56 It is not plain precisely when Leibniz gave up his early adherence to the Cartesian position, but the problem of the continuum was clearly bothering him by 1676, and in the essay entitled Genemles I nquisitiones de .A nalysi N otionu'}11, et Veritatum, written in 1686, his more mature view is fully apparent. Among primitive simple ideas seem to be classified all the notions which contain matter of some quantity, or in which homogeneous things harmonize with one another, in the sense of having magnitude whether extensive, intensive, or enduring; but unless I am mistaken these notions can still be resolved. It is especially open to doubt whether the notions of what is extended or thinking are simple. Many think that these are notions which are conceived through themselves and need no further resolution, but it would seem that an extended object is a continuum having coexistent parts. 51 5S Cf. M. 193; On Nature in Itself, #13; G. II, 226-7, 249-50; G. IV, 399-400; Langley, 705-6. 5& Cf. C, 361; M.163, 194; B&C II, 376; G. II, 183, 269; G. IV, 393-4; Langley, 699-700; Animad, I, 52. 51 C. 361.

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Extension involves continuity, coexistence of parts, and plurality. Leibniz returns time and again to an emphasis on these three aspects of whatever is extended. 88 If the concept of extension contains these notions, then it is clearly not simple, primitive, and unanalyzable. It is obvious that whatever is extended involves a continuum with coexistent parts. These parts need not be actual, like the parts of a picture puzzle. It suffices that they can be discerned by the mind. Further, if extension is spreadoutness or diffusion or repetition, there must be something which is spread out, diffused, repeated. Those who hold that extension itself is a substance reverse the order of words as well as of thoughts. Besides extension there must be a subject which is extended, that is, a substance to which it belongs to be repeated or continued. For extension signifies only a repetition or continued multipli. cation of that which is extended-a plurality, c01Itinuity, and coexistence of parts; and hence extension is not sufficient to explain the nature of the extended or repeated substance, the notion of which is anterior to that of its repetition. s9

Extension is like number, which presupposes something that is numbered. "But hence it appears that something is presupposed which is continued or diffused, as whiteness in milk, color, dudibility, and weight in gold, resistance in matter. For in itself continuity (extension being nothing else than simultaneous continuity) no more constitutes a substance than does multitude or number, since it is necessary that something be numbered, repeated, continued." 60 Since whatever is extended is continued, diffused, repeated, and since whatever is extended involves something other than the continuity, diffusion, or repetition, it follows that what is extended is always an aggregate, a plurality. It is like an army or a flock or a herd, or again like a cheese full of worms-the illustrations are Leibniz's. Extension is "only an attribute of an aggregate resulting from several substances." 61 Whatever it is that is diffused or repeated in extended objects must therefore be the ultimate constituents of things. These are Leibniz's simple subS8 Cf. C. 361, 408; G. II, 169-70, 183, 227, 269; G. IV, 393-4; Langley, 699-700; G. VI, 584; Animad. I, 52; N.E. II, xiii, 15. 59 G. IV, 467; D. 46. 60 G. II, 170; cf. also G. II, 241, 269; G. IV, 393-4; Langley, 699-700; G. VI, 584. 61 G. II, 187; cf. also G. II, 193, 205.

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stances, his substantial forms or entelechies, his units of forcein short, his monads. 62 Leibniz has made out his case: according to one very important sense of simplicity, what is extended is not simple. I should like to leave the matter so, but unfortunately IJeibniz's arguments raise two questions which we must face. (1) What is the relation between extension and the extended T (2) Is it possible to hold that the extended can be constituted by non-extended entities T (1) Leibniz's answer to the first question is that extension is an abstraction from the extended. 53 It is an incomplete or abstract or mathematical notion. There is such a thing as mathematical or arithmetical unity, but this is quite different from the true unity of substance. Leibniz makes some illuminating comments on this point in his remarks on Foucher's objections to his New System/'4, Any given extent is divisible, as we have seen. Likewise any number can be broken up into smaller number or fractions. Thus 1/2 is 2/4 or 4/8 or 8/16 and so on. This is an endless process, and it indicates to Leibniz something indefinite and incomplete in such abstract notions. On the other hand, the fraction 1/2 is in one sense a simple unity of its own. We do not arrive at it by first compounding it out of fourths and these out of eighths and so on. On the contrary we arrive at the notion of fourths by dividing 1/2.65 'When we deal with concrete reality, however, the story is quite different. An automobile is not anterior to its constituent parts. An ideal automobile may be, i.e., one existing solely in the engineer's mind or on his blue-prints, but an actual automobile is clearly dependent upon the existence of all its essential parts. The actual whole-i.e., a real existent object, a "complete being" in Leibniz's phrase-presupposes the actual existence of all its parts. An actually extended object, therefore, presupposes the existence of its constituent elements. What does Leibniz mean when he calls an extended object Cf. G. IV, 491-2, L. 329-30; and various of the references above. Cf. G. VI, 582, 584; N.E. II, xiii, 15. 6' Cf. G. IV, 490-2; L. 329-30; cf. also G. II, 170, 268-9. 65 "Hence it may be said that, considered in the abstract, 1/2 and 1/4 are independent of one another, or rather the total ratio 112 is anterior-in the order of reason, as the Scholastics say-to the partial ratio 1/4, since it is by the subdivision of the half that we come to the fourth, following the order of what is ideal; and the same is the case with the line, in which the whole is anterior to the part because the part is only possible and ideal." (G. IV, 492; L. 330.) 62

63

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complete and mere extension incomplete 1 In Section 8 of the Discourse he identifies the concept of a complete being with the concept of an individual substance. In writing to Arnauld he denies that extension can constitute a complete being on the grounds that in extension there is only the present, and that past and future, action and change, are lacking from the concept of extension. 6a To Bernoulli he characterizes incompleteness as suffering without acting and vice versa. 67 Bayle's article Rorarius draws the comment that a complete being is to be defined as one which contains in itself the source of all its actions. 6s I take it that these later statements are all variations on the thesis of the Discourse, and that they are so many ways of describing the various characteristics of an individual substance. A complete being, then, is one that can, in the world of real objects, stand on its own legs. It is that which needs nothing else save God in order to exist. It is that which can be conceived in and through itself. To be complete is, among other things, to be concrete. To be incomplete is not necessarily to be abstract, but what is abstract is for that very reason incomplete. An extended material object is an instance of the one; extension, of the other. One other question concerning the relation of extension to the extended must still be raised. If extension is always abstracted from the extended, it would follow that there can be no extension which is not the extension of something. This is precisely what we have seen Leibniz to hold. But is it true 1 Many today believe that we live in an extended universe which is mostly empty space, that there are inter-stellar distances which are not the extensions of any thing. In similar fashion no contemporary physicist denies that there is extent or volume in a vessel from which all the air, or nearly all, has been exhausted. It is true that some speculators have postulated the existence of an ether which prevades these allegedly empty spaces, but the reason for this assumption lies in the supposed necessity for some material medium for the propagation of light. The ether, however, is in disrepute. Its supporters are metaphysicians, not physicists, and it is pertinent to ask whether it is not an unnecessary concept. To a twentieth-century Leibnizian it would still be necessary for the very existence of inter-stellar distances, and with this we are back to the original argument which we must now examine more carefully. 66

M. 155.

67

B&C II, 373.

68

G. IV, 543-4.

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I cannot but think that Leibniz is guilty of serious confusion between extension and extended objects. I grant that extension is not a simple notion, and hence that he is right in criticizing Descartes for a failure to carry the analysis to its conclusions. I grant that there is something more to an extended object than its extent, and therefore that extension is not sufficiEmt in itself to account for the nature of material things. There is an obvious difference between the three-foot width of an open door and the three-foot door which sometimes fills it. The distance or extent is the same, but I can walk through the three-foot extent of the open door while I cannot walk through the door itself. I grant further that extension in a certain sense is abstract. But here is the confusion. We often mean two quite different things by extension. We mean sometimes extent and sometimes extendedness. Now extendedness as the common quality of all extents is abstract, just as redness is abstract. And this is equally true of the determinate forms of the determinable extendedness. Three-footness is abstract j it is a property shared in common by certain doors and doorways, by yardsticks, and by the sides of many bridge tables. I frequently meet with three-foot lengths in my experience, but I have never yet met three-footness. It does not follow, however, that because a universal is abstract a specific manifestation or instance of it must be so. This Leibniz would admit, holding that all embodiments of such a universal are material extended things. But the specific distance between point A and point B, a distance let us say of three feet, is not itself the universal although it manifests it j nor need it be the extent or distance of some material thing. The argument that it must is based upon the assumption that what is not the extent of some material object must be an abstraction, and this in turn is based on the confusion between extension as extendedness, which is an abstraction, and extension as extent, which may be specific. It might be retorted that the view which I am here defending presupposes the reality of space and time and that Leibniz denies this. I should grant the retort, but not its implication. For in the end Leibniz's denial of the reality of space and time depends in part at least upon his doctrine of the abstract, incomplete, and hence unreal character of extension. If he can establish the unreality of spatial and temporal phenomena by other arguments, then extension will pass into the limbo of phenomena bene fundata

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with them. But it still remains true that the present argument does not suffice in itself, as Leibniz thinks it does. (2) Can extended aggregates be constituted by non-extended entities' This is a very important metaphysical question. We have seen that what is extended is for Leibniz an aggregate. To be extended is to be theoretically divisible. Indeed, Leibniz holds that the world of extension is not only infinitely divisible, but infinitely divided, although his reasons for this opinion do not concern us here. Here, however, is the problem. In the division of the extended world we never come to any parts which are not themselves extended and hence further divisible. How, then, can Leibniz hold that extended objects are ultimately composed of indivisible entities T To be indivisible is on his grounds to be unextended. While this may be an accurate description of simple substances or monads, how are we ever to arrive at these "units" by an analysis of the extended-an analysis which in the nature of the case never leads to the unextended? Or, to reverse the order of the problem, how can a world which is infinitely divisible and infinitely divided be composed of indivisible and unextended units or entities T Is not such a contention palpably impossible T It is not surprising that de VoIder was confused by the apparent paradox. To his objections Leibniz replies: Whatever thing can be divided into several things (now actually existing) is composed of several things; and whatever is an aggregate of several things is not one save in the mind, nor has it any reality save that borrowed from its contents. From this I inferred that there are consequently indivisible unities in things, since otherwise they would have no true unity nor any independent reality-which is absurd. For where there is no true unity, there is no true multiplicity. And where there is only a derivative reality, there will never be any reality, since reality must belong to some subject. . .. But you substitute a somewhat different conclusion from mine, and I do not follow how you think it can be inferred from my words. For you would have as the right conclusion that indivisible unities do not belong to corporeal mass. But I think that the contrary follows, namely that in bodily mass or in the things constituting bodies we must have recourse to indivisible Unities, or prime constituents as it were. Perhaps you mean that the conclusion is correct that corporeal masses themselves are not indivisible unities. I admit this, but that is not the question. For bodies are everywhere and always divisible, nay actually divided as well, but this is not true of their constituents. s9 69

G. II, 267-8.

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I think that Leibniz's position on this point is neither absurd nor self-contradictory, although I doubt whether all his arguments can be defended or whether he can be said to have proved his point. Is there, after all, any valid reason for holding that extension or extended objects cannot be composed of non-extended entities' Extension would of course be phenomenal on such a view. It would be an appearance different in kind from the constituents which give rise to it. But this is precisely Leibniz's position with regard to extension and all its manifestations. The world of extension consists of phenomena bene fundata. It is not difficult to find certain parallels which may do something to allay the suspicion of the sceptic. Kant held that behind the phenomenal world of space and time and necessity lay a noumenal world out of space and time and undetermined. Modern absolute idealists, like Bradley, have insisted that reality is vastly different in kind from the world of appearance. In this case the parallel to Leibniz is striking, for Bradley's realm of appearance is somehow included within and the necessary manifestation of the underlying realm of reality, even though the two are totally different in nature. Or again modern scientists are telling us that the fundamental constituents of physical matter are far different from the solid, substantial character of macroscopic objects, like tables and chairs. There is not complete agreement here, but certainly it is true that many find electrons and protons to be of a fundamentally different kind of " stuff" from the gross material of ordinary experience. So far as I can see, it is impossible to show how these transformations come to pass-how moving charges of energy become solid mountains, how reality becomes appearance, how non-extended substances give rise to phenomenally extended bodies. This is a "mystery." It may conceal difficulties, even contradictions, but it is not obvious that it does. I am not here concerned with defending the truth of Leibniz's position or the analogous positions of Kant, Bradley, and modern physics, but with defending Leibniz against the hasty charge of propounding an absurd or impossible position. On the other hand, this conclusion is neither so simple nor so obvious as Leibniz apparently considers it. One aspect of his reply to de VoIder is particularly open to criticism. It is an argument which has recurred more than once in the complex discussion of extension in this essay. No one will question the obvious truth

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of Leibniz's contention that where there is mUltiplicity there must be units out of which the multiplicity is composed. But must these units be metaphysically simple, in Leibniz's sense of the term T We have already seen that there are different meanings of the term simplicity. Is there any good reason for accepting Leibniz's meaning to the exclusion of all the others 1 Is there, for example, anything inherently absurd or contradictory in the old atomist position' Democritus said that the world is composed of extended but indivisible atoms. We may divide them in theory, but we cannot split them up in fact. But whatever is extended is continued, diffused, repeated, cries Leibniz. Quite true. The material stuff of atoms, whatever that is, is continued, diffused, repeated throughout the volume, however minute, occupied by each atom. Their unity, however, is not merely mental; it is factual. This is a tenable position. It suggests that Leibniz was quite arbitrary in insisting that we must continue our analysis or division of the extended until we arrive at the unextended and theoretically indivisible. It can be said in Leibniz's defence that he was no more arbitrary than many other rationalists, particularly rationalists of the seventeenth century. But that does not prove that his position was sound. Grant Leibniz the assumption that simplicity entails theoretical indivisibility, and his position, or something like it, follows. I am not arguing that this assumption ought not or must not be made; it may be that a more comprehensive and consistent system of metaphysics can be founded upon its acceptance than upon its rejection. All I am now insisting upon is that there is an important assumption involved, that it is not the self-evident principle Leibniz took it to be, and that its contradictory is not absurd. Before passing to the final section I shall summarize briefly the main points of the present section. Is the concept of extension simple or complex T Descartes claimed that it was a simple, primitive, clear and distinct idea. Leibniz has little difficulty in showing that it is not simple but analyzable into continuity, coexistence of parts, and plurality. This raises the question of the relation of extension to what is extended. Leibniz holds that extension is an abstraction from the extended, and hence that it is ideal, incomplete, phenomenal. It follows from this that there can be no empty distance or extent. I have argued that extension is abstract in the sense of extendedness, but that any attempt to go farther than this rests on circular reasoning; for a specific

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extent is abstract only if space is unreal, and the unreality of space cannot be demonstrated, as Leibniz in part tries to do, by appealing to the abstractness of specific extents. The last part of the section is concerned with the intelligibility of Leibniz's doctrine that the extended world can be constituted out of non-extended entities. I have sought to show that this doctrine is prima facie intelligible in the sense that there is nothing obviously contradictory in the assertion. I have questioned Leibniz's conviction that he has proved the truth of this assertion by pointing out the assumption on which it rests. His view may still be correct, but it has not been demonstrated. And this, as we shall see, is damaging to Leibniz's position, since he obviously places great reliance on the arguments of this section. (F) The status of extension and extended objects: conclusion. Extension is abstract and ideal. I was forced to anticipate this conclusion in discussing the complexity of extension, and it is not necessary to repeat Leibniz's arguments for this position. It will be well, however, to supplement this view with certain related statements which Leibniz makes from time to time. The abstract and idea] character of extension put it in the realm of appearance, but they do not condemn it as chimericaVo It is unreal, but not a complete illusion. It is imaginary in the sense that color and heat are imaginary. a Thanks to the infinite divisions which actually occur in all extended objects, no body has a precise and determinate figure. The apparently definite shapes of bodies are in fact only rough and ready approximations. They appear or are perceived as definite, whereas in fact they cannot be so. Thus they are imaginary in the sense that they do not really exist as they appear/2 In one place, indeed, Leibniz goes so far as to brand pure extension as self-contradictory. He replies to an objection of de VoIder's ~ "Your objection-made as if I must not admit itI do indeed admit, namely that if an extended thing were conceived through itself alone, it would not be extended, for the notion of such an extended thing implies a contradiction. I also hold for certain that what is conceived through itself alone cannot be in a place. For to be in a place is not a purely extrinsic denomination; nay, there is no purely extrinsic denomination that does not have an intrinsic one for it~ basis-a fact which is to my way of thinking among the kurias doxas." 73 70 72

G. IV, 491-2; Langley, 329-30. 71 Discourse, #12. M. 163; G. VII, 314. 73 G. II, 239-40.

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For Leibniz extension, space, and extended objects-the same is true of everything else involving continuous quantity such as time and motion-are in the end phenomena bene fundata. They are not chimeras, hallucinations. They have their own laws and order. They fall between the absolutely metaphysically real and the completely subjective and unreal. Space and all its cognate relations are the ground of the order and sequence of phenomena, the general order of all possible coexistences.14 It is obvious here that such a conclusion is the product of Leibniz's rationalism. Leibniz, like Bradley after him, is prepared to insist that whatever else reality is it is self-consistent. Whatever shows the slightest trace of internal inconsistency or contradiction is banished from the true heaven of reality to a purgatory which is between reality and nothingness. It is the same region, and fulfills the same function, whether called appearance or the realm of phenomena bene fundata. "Matter and motion are mere phenomena or contain in themselves something imaginary; and from this we can understand how diverse and contradictory hypotheses can be made concerning them-hypotheses, however, all of which completely satisfy phenomena such that no reason can be invented for determining which is to be preferred. In the world of reality, however, every truth can be accurately discovered and demonstrated." 75 Hence, like the rationalistic Bradley, Leibniz banishes extension, motion, figure, size, space, et. al., to the realm of phenomena-a realm where their contradictions can live in peace and harmony with one another. Descartes was also a rationalist. The difference between him and Leibniz is not one of temper but of analysis. Descartes thought he had offered a consistent and satisfactory account of reality in terms of extension and thought. To Leibniz his attempt marked a failure of thorough-going analysis. 76 On this point Leibniz is right, whatver we may think of the very different conclusions which he seeks to base on his own analysis. I shall conclude with some brief remarks on what Leibniz calls the labyrinth of the continuum. It will be evident to anyone who has referred to the many references given in this essay that Leibniz was much disturbed by this famous mathematical puzzle. His M. 193, 222; G. IV, 523, 568. C.185. 76 Cf. Langley, 13. 14 75

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conviction that any continuum contains contradictions underlies much of his attack on the notion of extension. How can that phenomenal aspect of reality be ultimately real, if to be ultimately and metaphysically real is to be free from all contradictions' This is a consideration of the gravest importance for any metaphysician. It has been the root of most idealistic rejections of the world of space and time. If reality is rational, and if the continua of space and time are a maze of contradictions, then reality clearly cannot be spatial and temporal. First, let us be clear as to the exact way in which Leibniz envisages the difficulty. Whatever is continuous involves the continuation, diffusion, repetition of the subject which is said to be continuous. 17 Now with respect to space or extension this subject cannot itself be extended, since what is extended is always further divisible. Two alternatives only seem left. Either this subject is a point and continuous extents are composed of points, or it is not a quantitative conception at all. Leibniz takes the latter alternative, using the difficulties with the doctrine of points as demonstrating the truth of his own philosophy of monads. Thus he can say·that his own simple substances are more clear than the concept of extension, since the latter leads directly into the labyrinth of the continuum/ 8 and again that there can be no solution to the problem so long as extension is taken to be real rather than ideal. 19 Phenomena willingly embrace contradictions; it is only reality that scorns them. One of Leibniz's clearest treatments of the problem of the continuum is to be found in the dialogue Pacidius Philalethi, written in 1676. The chief subject of the dialogue is the nature of motion, but since motion can itself be viewed as continuous, it involves the concept of the spatial continuum. Can motion be the transition of an object from one point to the next Y "If you admit this," says Pacidius, "all the difficulties signified by the famous name of the labyrinth burst in upon you in a throng." 80 The problem of the continuum is made to turn about the number of points in a line. Is a finite line composed of a finite or of an infinite number of points? It cannot be composed of a finite number, for the line Cf. the discussion under section (E). M. 163; G. IV, 393-4; Langley, 699-700; G. II, 262; G. VII, 314. 79 M.192; B&C II, 377; G. IV, 491, 502; Langley, 329-30, 334-5. 80 C. 609. 17

18

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could still be conceivably divided in such a way as to necessitate the division of a point-and this is absurd, since points are by definition indivisible. Nor can it be composed of an infinite number, for that leads to equal absurdities. If we take a rectangle and draw the diagonal, there will be one point on the diagonal for every point on each of the sides-as can be demonstrated by drawing parallels to the base from the sides. But if lines are composed of points, equal lines will have an equal number of points. Since there is an equal number of points in the side and in the diagonal, we have the absurdity of the side of a rectangle being equal to its diagonal. Or to put the same principle in another way, a section of the diagonal equal to one of the sides will have as many points as the side. But this is true of the diagonal as a whole. Therefore a part of the diagonal will be equal to the whole diagonal,81 It seems self-evident to Leibniz that a part cannot be equal to the whole and therefore that infinite aggregates-whether of points in a line, instants of time, members of a thing-are a contradiction in terms. He rejects the much sounder insight of Galileo who solved the paradoxes by asserting that "the words greater, equal, and less have no place in infinity." 82 Infinite numbers, as modern mathematicians have pointed out, differ in certain highly significant respects from finite numbers. "The difficulties that so long delayed the theory of infinite numbers were largely due to the fact that some, at least, of the inductive properties were wrongly judged to be such as must belong to all numbers j indeed it was thought that they could not be denied without contradiction. The first step in understanding infinite numbers consists in realizing the mistakenness of this view." 8S One of the inductive properties of finite numbers is that a part cannot be equal to the whole. This is not a property of infinite numbers where" equality" has the meaning of one-to-one correlation-a relation that a part of an infinite series may have to the whole of the series. Put in another way, we can say that it is one of the characteristics of infinite numbers to possess features which, put in ordinary language, sound like the paradox of the part equalling the whole. This would be a contradiction for finite numbers, but it is not for the infinite. An archrationalist like Leibniz may still be right in holding that whatever else nature is it is self-consistent, and yet wrong in attacking the 81

83

c. 610-11. 82 C. 612. B. Russell, Introduction to Mathematical Philosophy, 79.

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doctrine of infinity as self-contradictory. What Leibniz needs is a broader concept of consistency. To say this is not to give the whole answer to the labyrinth of the continuum. There is still the problem of how a continuous extent is constituted, since it is not clear how a finite length can be composed of un extended points. Many answers have been given to this question, of which Whitehead's principle of extensive abstraction is an interesting contemporary illustration. I shall not go into this aspect of the question here. The concept of a continuum has been branded as contradictory, primarily on the ground that it involves the notion of infinite series with contradictory properties. This is Leibniz's typical attack, as we have just seen. If it can be shown that this attack is unjustified, then the usual ground for rejecting continua, one form of which is space or extension, is removed. There are some today who are still unsatisfied with the answer that Russell and other mathematicians give, some who would hold that Leibniz was right after all. I am not a mathematician, but I shall venture to suggest one or two considerations in conclusion. First, if the argument of Russell's Principles of Mathematics and Introduction to Mathematical Philosophy (to cite only two of many recent treatments of the topic) is inconsistent or inadequate, it behooves the critics to point out the error. All too often they are content with the simple assertion of being unconvinced! Second, where so many able and honest men are in agreement, there is a certain presumption that there is some truth in their doctrine. This is not itself proof by any means, but it ought to be a caution to the critics. Finally, if it is possible to work out a theory which will permit the obvious and pervasive phenomena of ordinary life, the phenomena of space, time, and motion, to be real, such a theory has an enormous advantage over any system which, by calling them mere appearance, illusory, phenomena bene fundata, runs counter to ordinary experience. I am fully aware of the weakness of this plea. Familiarity is no proof in metaphysics. Still the strange and exotic have nothing in themselves to recommend them save to the jaded spirit of a perverse, if not perverted, metaphysician. Swarthmore Oollege.

[2] Perceptions and Relations in the Monadology By JOHN EARMAN (MINNEAPOLIS)

Zusammenfassung Leibniz vcrtrat auf der einen Scite die Oberzeugung, es gcbe Rclationen weder als abstrakte Universalien noch als konkrete Akzidenzen. Auf der anderen Seite war er iiberzeugt, daB es relationale Eigenschaften von physischen Gegenstanden, die nicht auf nicht-relationale Eigenschaften dieser Objekte reduziert werden konnen, gebco Die wirklichen Einzeldinge haben jedoch keine nicht-formalen relationalen Eigenschaften. Sie stehen zwar in Beziehung oder sind miteinander verkniipft, aber nur durch Perzeptionen, so daB der Begriff Beziehung hier cin Begriff der zwciten Ordnung ist. Die physische Welt mit ihren re1ationalen Eigenschaften ist fundiert in den Monaden. Die Fundierung ist cinc Reduktion, aber es ist ein Mi6verstandnis, wenn man diese Reduktion so beschreibt, als impliziere sie eine Reduktion von relationalen Eigenschaften physischer Gegenstande; denn ihre nicht relationalen Eigenschaften werden in gleicher Weise reduziert.

1. Introduction: the status of relations The difficulties in understanding some aspects of Leibniz's philosophy stem from the fact that Leibniz said too much. This is certainly the case with the doctrines about necessary and contingent truth where even the initial task of sorting out the various ways in which the problem of contingency arises and the many different approaches Leibniz took to the problem is a major undertaking. In part, however, the difficulties in reconsttucting Leibniz's views on relations arise in just the opposite way - Leibniz says too little that is of direct help. There are, to be sure, a number of passages dealing with the nature of relations, but many are of a fragmentary character and, in contrast to the case of necessary and contingent truth, no sustained and systematic treatment is given. But there is also a second and more vexing source of difficulty; Leibniz's views on relations cannot be reconstructed independently of the rest of his philosophy, especially the monadology. It is little wonder then that more controversy has swirled about the status of relations than perhaps any other facet of Leibniz's philosophy. Much of the controversy has centered on what has (somewhat inaccurately) been called the issue of the reducibility of relations. Studia Leibnitiana, Band IXI2 (1977) @ Franz Steiner Verlag GmbH, D-62OO Wiesbaden

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To introduce this issue, I will look briefly at the two most often quoted passages on relations, the first from a letter to des Bosses and the second from the fifth letter to Clarke. "My judgement 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 individual ... " (L. 609)1. "The ratio or proportion between two lines Land M may be conceived in 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 ... 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 would 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" (L. 704).

These passages lie at the confluence of two main streams in Leibniz's philosophy: his nominalism and his subject-predicate logic. Because of the first, he denies relations as abstract universals, and because of the second, he denies relations as concrete accidents that straddle two or more subjects. So strictly speaking, these passages have nothing to do with the reducibility of relations. There are, Leibniz is saying, no relations, and thus talk about reducing relations is out of place. On the other hand, Leibniz seems to be acknowledging that the accidents of an individual will typically be relational - among David's accidents is that of being the father of Solomon, among the line L's accidents is that of being twice as long as M, etc. Of course, one can go on to ask whether Leibniz thought that such relational accidents are in some sense reducible to non-relational accidents. This is a real issue, and it is the source of a very strong polarization in Leibniz scholarship. The polarization is quite complex, 1 The following abbreviations will be used in giving references to Leibniz's works: C= L. COUTURAT, Opl/sCl/les el Fragmenls litMils de Leibniz (Hildesheim: Olms, 1961); G = C. 1. GERHARDT, Die philoJophischen Schriflen von C. W. uibniz, 7 vols. (Berlin: Weidmann, 1875-1890); Gr=G. GRUA (ed.), G. W. LEIBNIZ, Textes Illidils, 2 voIs. (Paris: Pro Univ. de France, 1948); L = L. E. LOEMKER (ed.), LEIBNIZ, Philosophical Papers and Letters (Dordrecht: Reidel, 1970); La = R. LATTA (ed.), LEIBNIZ, The Monadology and Olher Philosophical Essays (Oxford: Oxford Univ. Pr., 1971); NE = New Essays Concerning Hllman UnderJlanding (London: Macmillan, 1896); PL=G. H. R. PARKINSON (ed.), LEIBNIZ, Logical Papers (Oxford: Clarendon Pr., 1966); PP=G. H. R. PARKINSON (ed.), LEIBNIZ, Philosophical Writings (London: J. M . Dent, 1973); T = Theodicy (New Haven : Yale Univ. Pr., 1952).

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but there is a principal axis. On one end lies Parkinson 2 who holds that Leibniz is committed to the position that relational accidents of an individual are reducible to non-relational accidents of that individual alone. On the other extreme is Ishiguro 3 who rejects Parkinson's reduction thesis and most of the milder ones as well. I believe that the truth of the matter lies not so much in the middle of this spectrum as outside it. And I believe that a failure to keep distinct two levels of analysis has generated some pseudoproblems and at the same time has obscured some real ones. On one level of analysis, one can ask: Are relational properties of the vulgar individuals - David, Solomon, tables, chairs, etc. - reducible to non-relational properties of these individuals? Here I side with Ishiguro. Leibniz would respond that with some exceptions, most notably concerning certain "relations of comparisons", the answer is no. On the next level, we can ask: Are relational properties of the true individuals, the simple substances or monads, reducible to non-relational properties of such individuals? Here I think that Leibniz's mature doctrine is even more radical than that Parkinson's reduction thesis would indicate. Leibniz would say that the presumption of the question is false since there are no (nonformal) relational properties of monads. I will not argue here for my answer to the first question. But I will defend and explore the implications of the answer to the second question 4 • One immediate implication is a seeming incommensurability. Leibniz holds that the realm of physical objects is founded on the realm of monads. But how can this founding take place if, as I 2 G. H. R. PARKINSON, Logic and Reality in Leibniz's Methaphysics (Oxford: Clarendon Pr., 1965); see especially pp. 45, 141-150. 3 H. ISHIGURO, (a) Leiblliz's Dmial of the Reality of Space alld Time, in: Annals of the Japan Association for Philosophy of Science, 3 (1967), 33-36; (b) Leibniz's Theory of the Ideality of Relations, in: FRANKFURT (ed.), Leibniz (Garden City: Anchor Books, 1972); (c) Leibniz's Philosophy of Logic and Language (Ithaca: Cornell Univ. Pr., 1972). For other interpretations of Leibniz's views on relations, see B. RUSSELL, A Critkal Exposition of the Philosophy of Leiblliz (London: George Allen and Unwin, 1971) ; pp. 12-15; N. RESCHER, The Philo!ophy of Leibniz (Englewood Giffs: Prentice Hall, 1967), Ch. 6; K. C. CLATTERBAUGH, Leiblliz's Doctrine of Individual Accident! = Studia Leibniliana, Sonderheft 4 (Wiesbaden: Franz Steiner, 1973), Ch. 3;C. D. BROAD, Leibniz, An Introduction (Cambridge: Cambridge Univ. Pr., 1975), pp. 36-39; B. MATES, Leiblliz 011 Possible Worlds, in: FRANKFURT, op. cit.; J. HINTIKKA, Leibniz on Plenitude, Relations, and the' Reign of Law', in: FRANKFURT, op. cit. The interpretation of Leibniz I will develop below owes something to many of these works, but it also differs from all of them. 4 This answer has to be refined in the light of the discussion below, see Sec. 2.

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claim, the first realm is characteristically relational while the second is intrinsically non-relational? Some commentators have counseled dispair. For example, Jonathan Bennett says: "Leibniz makes no suggestions, and simply evades the whole problem. If that seems incredible, remember that for him fundamental reality consists of nonextended monads; so that he envisions replacing statements about how extended items are spatially interrelated by statements which are 'monadic' in both senses i.e., non-relational statements about monads. That implies that all such replacements operate across a boundary which is in any case mysterious, with ultimate reality on one side and the whole extended world on the other; and that might seem to explain why illustrative examples cannot be given".5

While I am not as pessimistic as Bennett, I agree that there are major problems lurking here. But seeing more precisely where they lie and how Leibniz might resolve them casts a good deal of light on Leibniz's notion of perception in particular and the monadology in general. It is to these matters I now turn. For ease of expression, I will sometimes speak with the vulgar in tallcing about relations instead of using the more proper but cumbersome terminology of relational properties. 2. Perception in the mature monadology As working hypotheses for understanding Leibniz's mature monadology I propose: (H 1) There are no non-formal relations among (or more precisely, no non-formal relational properties of) monads. (HZ) The formal relations of identity and otherness are automatically reduced via the combination of the principles of Identity of Indiscernibles and the Indiscernibility if Identicals: for any monads ml and m2, ml = mz ~ ('II P)(P(ml) -- P(mz» where the quantification ranges over the non-formal (and therefore, non-relational) properties.

The key hypothesis is obviously (H1); if it is established, (H2) will readily be granted. (H 1) is based on two doctrines: (D 1) Ultimate reality is characterized completely by the monads and their perceptions and appetitions. (D 2) The perceptions of a monad are purely internal states of that monad.

5

J.

BENNETT,

Kant's Dialectic (Cambridge Univ. Pr., 1974), p. 48.

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It seems beyond dispute that Leibniz, in at least some moods, held (D1)6. For instance, in a letter to de VoIder dated June 30, 1704, he says: "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" (L. 537).

Similar sentiments are also found in the New Essays (see NE. 2. 12.5). Because nothing important in what follows turns on appetition, I will set it to the side. (D2) is more contentious. Ishiguro rejects (D2) under any reading that supports (H1). She contends that "For Leibniz to say of a substance that it perceives, or mirrors, or represents, another object, presupposes that the monad stands in a certain connection to that other object" (Ishiguro, (b), p. 211).

To turn this contention into an argument against (H1), two premises are needed: first, that basic to an understanding of the monadology is the notion that one monad perceives another; and second, that ml perceives m2 entails that R(m!, m2) in contradiction to (Hi). For sake of discussion, I will temporarily grant the first premise. But the crucial second premise does not follow even if it is further granted that ml perceives m2 entails that ml and m2 stand in "certain connection", for there is an ambiguity in the notion of connection. Recognizing this ambiguity leads to a refinement of (H 1). The point is that "mJ perceives mz" might be analyzed along the following lines: ml is in a certain internal state s 1 characterized purely in terms of non-relational properties of ml; m2 is in a certain internal state S2 characterized purely in terms of non-relational properties of m2; and s 1 exhibits a (partial) structural isomorphism to s 2 7. 1£ you like, that ml perceives m2 does entail &l(ml' m2), but &l is not a first order relation because £3t'(ml, m2) means that there exist certain first order, non-relational properties of ml, certain first order, non-relational properties of m2, and that there is a second order structural relation between th~se two sets of first order properties. Thus, the refinement 6 Most statements about Leibniz's philosophy have to be relativized to a time and/or a correspondent and/or a mood; and even then, one finds incompossible assertions. Rather than clutter up the discussion in this and the following two sections with numerous ca v eats and cautionary remarks, I will emphasize what seems to me to be a central line of thought in Leibniz's mature philosophy. This view will then be balanced by some contrasting views in Sec. 5. 7 Various features of perception will turn on just how partial or total the isomorphism is; e. g., if it is total, then Ishiguro's relation of perception is symmetric.

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of (Hl): "relations" in (Hl) means first order relations 8. Leibniz certainly did not have the apparatus to make these distinctions explicit, but as will be seen shortly, there is evidence that the distinctions are implicit in his conception of perception. Turning now to the textual evidence, it must be admitted that Leibniz's general theoretical explanation of perception as "representation" or "expression" and his explanation of expression as a "constant and regulated relation between what can be said [i. e., the predicates] of the one and of the other" (G. II. 112 = L. 339) fits both Ishiguro's interpretation and mine; indeed, Leibniz's explanation seems to be intentionally framed in such general and abstract terms as to accommodate practically any interpretation. Nor does it help to be told that perception is a special species of representation in which there is "expression of plurality in a unity" (G. III. 69). All plausible accounts of perception will agree that what is doing the perceiving - a monad - is a unity, but the accounts may differ on what constitutes the plurality that is represented in perception and just how the representation is done 9 • Of even less help are the analogies Leibniz uses to illustrate his theoretical terms. If taken literally, the mirror analogy seems to side with Ishiguro's reading 10 • But Leibniz himself warns us not to take too literally the mirror analogy for perception in general, the spatial perspective analogy for "point of view", or any of the other analogies he uses to give the reader a feeling for his theory (see G. II. 438, G. III. 357). We can do no better than to heed his warning. One of the most delicate and exasperating problems in Leibniz commentary is that of separating the artifacts of his analogies from their theoretical content, and often this separation can be performed only after one is already in possession of a full understanding of the theory which the analogies ate supposed to help us grasp. There are, however, a few passages in which Leibniz is more specific. One of the most striking occurs in a letter to des Bosses of May 26, 1712, in which Leibniz says that the monads "correspond to each other through their own phenomena and not by any other intercourse or connection" (G. II. 444 = L. 602). It is my contention 8 With this understanding, (H 1) and (H2) together with the phenomenalistic founding of relations to be explained below constitute part of the explication of Leibniz's doctrine that there are no purely "extrinsic denominations"; see Sec. 4 below. 9 See Secs. 4 and 5 below for some alternative accounts. 10 Not surptisingly, Ishiguro does take the mirror analogy quite literally; see ISHIGURO (b), p. 212.

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that if he could avail himself of the resources at our command, Leibniz would explain this passage in just the terms I used to interpret the "connection" between monads. Unfortunately, the citation is less than perfect for present purposes, for Leibniz's assertion is made conditionally on the rejection of the hypothesis of a substantial chain (vinculum subtantiale) superadded to the monads. But Leibniz never rejects this hypothesis in the lengthy correspondence with des Bosses; indeed, he dangles it before des Bosses throughout. Like many commentators, I believe that the vinculum substantiale is largely an artifact of one of the issues of the correspondence - the theological doctrine of transsubstantiation - but I will not argue for this view here l l . In any case, it is clear that the vinculum subs tan tiale will not provide the kind of "connection" needed for Ishiguro's interpretation of perception. Another closely connected matter first surfaces in the correspondence with Arnauld, to whom Leibniz writes that the state of an individual substance follows from its own preceding states "as if there were only God and itself in the world" with the result that "each individual substance or complete being is a world apart, independent of every other thing but God" (G. n. 57 = L. 337). On Ishiguro's reading, this is a "strange mistake" on Leibniz's part (Ishiguro, (b), p. 210). But it is surely not a mistake. Similar statements are found in the New System: "The perception or expressions of external things come into the soul at their own appropriate time, in virtue of its own laws, as in a world by itself and as if there existed nothing but God and the soul" (La. 313).

and in a letter to des Bosses of February 5, 1712: "a monad, like the soul, is a world by itself, having no intercourse of a dependent nature except with God" (L. 600).

and in the letter of May 26 quoted above in which the cited passage is used to justify the assertion that each monad "is as it were a separate world" (G. II. 444 = L. 602). And these passages are certainly not strange on the reading I have suggested. Nor is the force of these passages undermined by the qualifying phrases "as if" and "as it were". These caveats are easily explained by the fact that Leibniz's phenomenalistic construction of the physical world (see Sees. 3 and 4 below) presupposes a plurality of monads and by the fact that the monads are 11

For a more detailed account of this issue see

BROAD,

pp. 124-129.

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not entirely separate worlds since they are linked by second (and maybe even higher order) relations. Finally, and perhaps most significantly, Leibniz joins the "separate worlds" doctrine with a proof of God's existence via the need for a pre-established harmony. To de VoIder he writes on January 21, 1704: "And if anyone conceded to me an infinity of percipients, in each of whom there is a fixed law of 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 I claim in the matter ... " (L. 535).

On the interpretation of perception suggested by this and the other passages cited above, the basic notion of perception is not that of a monad perceiving other monads but rather that of a monad perceiving a "physkal" state of affairs 12• A direct consequence of this reading is the necessity for some hypothesis of harmony in order that the monads will correspond with each other through their phenomena. If harmony reigns in that all the monads are perceiving - i. e., representing - the same state of affairs, then although their various representations will be different due to their different points of view, they will none the less mirror or represent each other as a consequence 13. But this latter sense of perception is secondary and it is parasitic on the harmony. As Leibniz puts it in the Theodicy: "It is true that the same thing may be represented in different ways; but there must be an exact relation between the representation and the thing, and consequently between the different representations of one and the same thing ... each soul represents the universe according to its point of view, and through a relation which is peculiar to it; but a perfect harmony always subsists therein" (T. par. 357).

It is easy to see then why Leibniz took the pre-established harmony to be "one of the strongest proofs of the existence of God" (G. II. 115 = L. 341). But it is not so easy to see how this could be true on Ishiguro's interpretation. Because of the crucial importance of this issue, I will examine the possibility of disharmonious worlds in some detail in the next section. This reading of Leibniz is developed by M. FURTH, Monadology, in: FRANKop. cit. 13 On this construal of perception, the state of a monad reflects the perceptions of any other monad but it need not reflect the apperceptions (or conscious awareness) of other monads. 12

FURT,

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3. Disharmonious worlds Dispite the impression Leibniz sometimes leaves, serious obstacles are encountered in trying to regard disharmonious worlds as live possibilities. If these obstacles cannot be overcome using the account of perception and relations I am trying to develop, then many of the distinctions I claimed to have such importance make little difference. The first obstacle concerns Leibniz's conception of possible worlds as maximal compossible sets of individual concepts. On the interpretation I put forward in the preceding section, the concept of a true individual is composed of simpler concepts which, when instantiated by a monad, become the internal perceptual states of that monad. Now either harmony of perceptual states is required for compossibility, or else it is not. In the former case, no possible world is disharmonious. In the latter case, the compossibility relation threatens to become trivial, i. e., the individual concepts C 1 and C 2 are compossible if and only if C 1 is possible and C 2 is possible, in which case there is only one possible world, a world of maximum disharmony. One way between the horns of this dilemma is to argue that there is an ambiguity in the notion of "a (possible) world". Harking back to the earlier distinction between two levels of analysis, a "world" can be taken to mean either a world of physical objects or a world of monads. Perhaps the construal of a possible world as a maximal compossible set of individual concepts is meant only for the former reading where the individual concepts contain relational properties that do give rise to non-trivial conditions for the successful interlocking of two or more such concepts and, thus, to a non-trivial compossibility relation . The viability of this tack depends in part on the handling of a second and much more formidable obstacle. The view of perception for which I argued in Sec. 2 is part and parcel of a phenomenalistic reduction of the physical world. Leibniz's commitment to this reduction is graphically expressed in a letter to de VoIder of June 30, 1704: "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" (L. 537).

and again in the letter to des Bosses of February 5, 1712, where Leibniz says that (on the hypothesis of the rejection of the vinculum subs tan tiale):

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"all bodies along with 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" (L. 600).

As already noted, the basic notion of perception here is that of a monad percelving a physical state of affairs, and the reality of this state of affairs consists in the agreement among the representations of all the percipients. One way to codify this view is given in p is true iff each monad perceives 0(P)

(P)

where p is an atomic physical object proposition, e. g., the proposition expressed by "Socrates is F" for some atomic predicate F (Leibniz's own illustration is "Socrates is sitting down" (G. II. 451 £. = L. 605» and 0 (p) is the state of affairs asserted by p. If we read p v -p as "either p is true or -p is true", then in a disharmonious world, the law of excluded middle fails 14 • Leibniz may be able to swallow this consequence while maintaining that some possible worlds are disharmonious, but what he cannot tolerate is the failure of bivalance. As he puts it in the Ne1v Essays: "it is impossible that a proposition is neither true nor false" (NE. 4.2.1). Of course, Lelbniz has an easy explanation of this impossibility since he understands "false" to mean "not true": "1 define 'false in general' as not true" (PL: 61). But then he has to give up p is false (= not true) iff -p is true

(F)

for disharmonious worlds. However, Leibniz is explicit in affirming (F) :

"If B is a proposition, not-B is the same as that B is false" (PL. 58).

To defend the possibility of disharmonious worlds, it can be replied that (F) was asserted in the context of Leibniz's original version of the conceptual containment theory of truth which was supposed to apply to propositions with the vulgar individuals as their subjects, but with the advent of the phenomenology, this version of the theory must make way for a more sophisticated version in which the conceptual containment principle (T)

"A is F" is true iff the concept of A contains the concept of F

is to be applied directly only to propositions having the true individual substances as their subjects and then indirectly to propositions having pseudo-individuals like Socrates as their subjects by means of (P). 14

See

FURTH,

Monadology, op. cit.

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Another way to support this move is to try to apply (P) and (T) simultaneously to "Socrates is F". The result is that the concept of Socrates contains the concept of F just in case each monad perceives that Socrates is F. In a sufficiently disharmonious world, however, the monads wHl not agree on whether Socrates is F (or not-F) for any atomic F. And so the concept of Socrates is empty, which is just to say that Socrates is not an individual in the sense which makes (T) applicable. But Leibniz CalIDot say this, at least not publically. He has advertised the conceptual containment theory and all of its attendant logical apparatus as a means of analyzing ordinary discourse where Adam, David, Solomon, and Socrates are individuals in the relevant sense. Furthermore, the move under consideration undermines the strategy suggested for dealing with the first obstacle discussed above. I propose that the best way out for Leibniz is to reconstrue (P) so that it applies not to atomic physical object propositions but rather to propositions asserting a complete description of an entire physical world. Combining this with the need to distinguish between the two senses of "worlds", it would thus be better to replace (P) by (P')

The physical world W obtains (or is real) relative to the world ;r of monads iff each monad in 'i'f perceives W.

The phenomenology and the conceptual containment theory are kept out of conflict since (PI) operates holistically on possible physical worlds to determine which (if any) holds as a result of the perceptions of the monads while (T) operates as originally construed within each possible physical world. With this understanding, the threat to the law of the excluded middle vanishes. Another result is that perception becomes a global notion, both in its operation and its consequences. The basic notion of perception is now that of the apprehension of an entire physical universe, and any disharmony in any aspect of the perceptions of the monads (of 1f") means that (relative to 1Y') no physical world obtains or is real. Leibniz would surely have liked this result. It makes explicit that each monad mirrors the entire universe, and it shows just how complex and just how total the harmony needed to found the physical world is - so complex and so total that (according to the reasoning of the argument from pre-established harmony) only God could be responsible for it. Alas, all is not harmonious. If the holistic principle (PI) as opposed to the piecemeal (P) smooths over several difficulties, it also creates

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others. In particular, it seems to be less plausible that a phenomenalistic reduction of the physical world is achieved through (PI). But, like other appearances in a disharmonious world, this one is not wellfounded, or so I will argue below. 4. The founding of physical relations: the phenomenalistic view If Leibniz's mature monadology does succeed in providing a phenomenalistic reduction of the physical world, it also succeeds in founding physical relations, though in a somewhat disappointing fashion. Ultimately, there are only the monads and their perceptions. Perceptions are monadic in both senses - they are states of monads and they are non-relational in that they do not involve any (non-formal, first order) relations among the monads. But perceptions are relational in another sense; namely, the content of a perception involves physical objects standing in various relationships, especially spatia-temporal ones. And since the physical world is reduced to such perceptions, these physical relationships can be said to be reduced to non-relational properties. Note, however, that this reduction does not vindicate the usual reduction theses attributed to Leibniz since relational and non-relational properties of physical objects are treated on a par neither comes out as more basic and both are reduced in exactly the same sense. This is the appropriate place for a few words on Leibniz's statements that relations are "resultant" and need a "basis" or "foundation" in the nature of things (see C. 8-9; Gr. 547; NE. 2.25.2) and the closely related dictum that there are no "purely extrinsic denominations". In part, these assertions involve nothing more exciting than Leibniz's subject-predicate logic and his conceptual containment theory of truth; indeed, he sometimes claims that the no purely extrinsic denomination thesis follows from the facts that all propositions must be construed as having subject-predicate form and that in a true proposition the predicate inheres in the subject. Thus, in the essay First Trttths we find: "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" (L. 268).

On the other hand, the phenomenalistic founding of the world of physical objects with their relational properties on the world of

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monads with only their non-relational properties lends a deeper sense to the "resultant" nature of relations. The non-constructivist treatment of relations outlined above is not entirely satisfying, and some alternatives to it will be considered in the next section. But here I want to emphasize that while the above phenomenalistic treatment of relations is simple, the underlying phenomenalism is not. To make it work, we need a more detailed account of perception satisfying three conditions: (1) the account must explain the sense of "monad m perceives W" in a manncr that docs not make (PI) viciously circular as an analysis or reduction; (2) the account must explain Leibniz's notion of point of view and, in particular, it must explain how, in a harmonious universe, each monad perceives the same thing from its own peculiar point of view; (3) the explanation in (1) and (2) must make it clear that what Furth calls the no-residue condition 15 is fulfilled - that is, that the full content of what it is for a physical world W to obtain is captured by the right hand side of (PI). The passages from which we can try to reconstruct Leibniz's attitude to (1)-(3) are quite sparse. In what is perhaps the most specific reference, he says: "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 concerned" (L. 605).

As a response to (1)-(3), this passage is inadequate in several respects. First, it violates the holistic nature of perception to which Leibniz seems to be driven by the consideration of disharmonious universes. Second, it simply asserts, in effect, that the no-residue condition is satisfied ("we mean nothing else ... "). The assertion may be correct, but we want to be able to see from the account of perception that it is correct. When the account is adjusted so that perception proceeds holistically rather than piecemeal, it becomes even harder to see why the no-residue condition should hold. Finally, point of view is left unexplained. Here Leibniz falls back on his analogies, and, as noted above, this leaves us trapped in a catch-22 situation since we cannot evaluate the import of these analogies until we have a full grasp of the theory of perception. Perhaps Bennett is right after all, and Leibniz's claim to have provided a monadic founding of the physical world is just an elaborate

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sham. Perhaps. But I believe that Leibniz can be made to look somewhat better by following out the consequences of his doctrines about space and time, one of the consequences being a quasi-Kantian view of space and time as modes of perception. Briefly, I believe that a consistent application of the arguments from the Identity of Indiscernibles and Sufficient Reason which Leibniz uses against Newton force the conclusion that, at base, the physical world is not spatiotemporal in anything like the ordinary sense. The intrinsic nature of the physical world is characterized by what I have called elsewhere a Lei bniz alge bra lG • The details of the algebras are not important here, and for present purposes the only relevant points are these: (a) the algebras do not contain space or time in the sense of a set of points equipped with a continuity structure; (b) but each algebra is realized or represented (in a precise mathematical sense) by a spatia-temporal model; and (c) the representation can be done in many different but isomorphic ways. It becomes almost irresistible to postulate that it is the function of the monads to provide such representations. The clifferences in the representations then correspond to the different points of view. Further, in a harmonious world, each monad is perceiving the same algebra, and since there is a monad for each point of view, every possible representation of the algebra is realized in the perceptions of the monads. In this way, the full content of the algebra is captured leaving no residue. I believe that this reconstruction will rescue Leibniz from Russell's condemnation: Leibniz refuses to face the fact that all monads represent the same world, and that this world is always imagined by him to have something analogous to the space of our petceptions ... None of his devices, in short, give Leibniz any escape from an objective space, prior to the phenomenal and subjective space in each monad's perceptions .. . " (Russell, pp. 125-126).

This all too brief sketch constitutes a large promissory note. The cashing in will have to await another occasion since it would take us too far afield from the main issues of this paper l ? I now return to these issues by considering alternative ways to found relations.

1 G See my paper, Leibnizian Space- Times and Leibllizian Algebras, in: J. HINTIKKA (ed.), Proceedings of the Fifth International Congrw of Logir, Methodology, and Philosophy of Science, in press. 17 I attempt to do some of the cashing in in Leibniz on Space, Time, and Monadology, in preparation.

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5. The founding of relations: other views The older Leibniz grew, the further he moved away from his early, crude aggregate theory of monads according to which monads are in absolute space and physical bodies are spatial aggregates of monads 18. To de VoIder, he writes in 1704: "Substantial unities are not parts but foundations of phenomena" (G. II. 268 = L. 536). No doubt, part of the motivation for this change was his movement away from an absolutist to what is commonly called a relational conception of space, for on the latter, monads cannot literally be in space. But on the usual understanding of the relational view, it is still open that monads have relative spatial relations 19. However, Leibniz explicitly rejects this option: To des Bosses he writes: "For in themselves, monads have no situation with respect to each other which reaches beyond the order of phenomena" (L. 602).

and " ... there is no spatial or absolute nearness or distance between monads" (L. 604).

The more sophisticated version of the relational theory to which I alluded in Sec. 4 helps to explain why Leibniz also gives up a realist interpretation of space and why he did not pursue the middle path of constructing the physical world by assuming monads to have relative spatial relations. But my purpose here is not to push this interpretation but rather to emphasize the opposite side of the coin. For it must be admitted that Leibniz never entirely abandoned his aggregate theory. The theory survives, for example, in his doctrine that a monad has associated with it an organic body it dominates, that the organic body is, in some sense, an aggregate of monads, each of which is in turn the dominant monad of another organic body20. 18 As an example of Leibniz's early absolutist conception of space, see An Exa111ple of De1110nstration About the Nature of Things, Drawn Fr0111 Phen011Jena, L. 142-144. 19 One can be both a realist and a relationalist about space. But the point is that when Leibniz switches to relationalist view, he also switches to idealism; see below. 20 In general, any version of the aggregate theory requires that there is a way to associate monads with physical bodies, and since the bodies have (relative) spatial locations, the associated monads can be assigned the spatial locations of their bodies. But Leibniz seems to have felt that it is meaningless to ask where in the associated body the monad is located (see G. II. 253 and G. III. 357).

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The main problem with finding a coherent reconstruction of Leibniz's late aggregate view lies in combining the conception of physical bodies as sets of monads with the notions that perception is representation and that representation holds when there is a structural isomorphism. A monad has perceptions of physical bodies standing in certain relationships. Such a perception is to be a representation of (i.e., is structurally isomorphic to) the states of the sets of monads which are these bodies. But how can there be such a structural isomorphism if the states of the monads do not involve any relations among the monads? A possible answer purchases on one of the distinctions drawn in Sec. 2: although the monads do not bear any first order relations to one another, they do bear second order relations, and these are what are represented in perception as relations among bodies. As I read him, this is the sort of account C. D. Broad is advocating in his posthumously published lecture notes on Leibniz. According to Broad, what appears as a physical body is a set of monads all of which have points of view falling within certain circumscribed limits. "Suppose that what is perceived as a body A is perceived as standing in a certain spatial relation to what is perceived as a separate body B. What is perceived as body A is really a certain set Ct of monads such as I have been describing; and what is perceived as body B is really a certain other set l' of monads such as I have been describing. The basis of the fact that A is perceived as at a distance from B is that the point of view of every monad in the set Ct differs by a finite degree from that of every monad in the set !'" (Broad, p. 104).

So for Broad, perception is a downshifting operation. The first order monadic properties of having a point of view lying within certain ranges are represented as physical bodies, and the two place second order relation on these properties of having different ranges is represented as the first order relation on physical bodies of being spatially separated. Though it has some attractive features, Broad's approach is risky in resting so much on the delicate notion of point of view. And in so far as I have a grasp on it, point of view for Leibniz is not a basic quality of monads that serves as the foundation of the perceptions of other monads; rather, point of view emerges as an end product of perception, and is to be explained as a structural feature of the entire perceptual field of the monad. Any other way of understanding point of view threatens to run afoul of Leibniz's doctrine that all there is in the monads is their perceptions and appetitions. Moreover, it remains mysterious why the perceptual representations should work as Broad postulates and, in particular, why difference in

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point of view should be represented as difference in spatial location rather than, say, difference in color. No doubt, Broad was guided here by Leibniz's spatial analogies for point of view. But, as has been emphasized several times already, one of the biggest mysteries in Leibniz's philosophy concerns the theoretical import of these analogies. And it is hard to see how Broad's account, which takes point of view as a basic quality of monads, can cast light on this mystery. Finally, there is the problem of explicating the alternative account of perception that constitutes one of the main vestiges of the aggregate theory. On this account, which is repeated too often in Leibniz's later works to be ignored, a monad mirrors the universe only indirectly. "Each soul will represent proximately the phenomena of its own organic body. but remotely those of others which act on its own body" (PP. 776).

The idea is that a monad represents directly the state of the organic body it dominates. The state of this body wHl in turn reflect the state of every other body in the universe because the universe is a plenum and because each body in the plenum is affected by whatever happens in any other body. So by transitivity, the state of each monad reflects the state of the entire universe 21 . I do not see how Broad's account squares with this doctrine. A quite different approach to relations goes the opposite direction to Broad's; instead of shifting down levels, it shifts upward. Leslie Tharp22 has pointed out that the first order logic of relations can be mirrored in third order monadic logic. If we want to preserve the idea that physical bodies are sets of monads, then we will have to go up to fourth order. As an illustration, a two-place first order relation on bodies considered as a set of ordered pairs { , , ... } becomes a set of ordered pairs { < lX, f3 >, < X, 8>, ... } of the sets lX, f3, X' 0, ... of monads that are the bodies A, B, C, D, ... Such a set can be represented, for example, as the following set of sets of sets of sets: {{ {IX, ~}, {[3

n, {{x. 8}. {o}} •. . .}

Thls set is just the form of the extensional interpretation of a fourthorder monadic predicate constant. Of course, this coding is not unique, and relations are being represented in extension and not 21 See Melaphysical Consequences of the Principle of Reason (PP. 172-178); Monadology (PP. 179-194); and letter to Electress Sophia, Feb. 9, 1706 (G. VII. 567). 22

Private communication.

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intension. But these features are no drawback if one wants to emphasize the passages in which Leibniz says that relations are unreal and of a mental nature. Though Leibniz would no doubt have been delighted with this apparatus, r see no plausible way to graft it into the monadology. Perhaps the higher levels of logic can be reflected in higher and higher levels of apperception (conscious awareness of conscious awareness, etc.). But there remains the problem that the simple perceptions of monads, even the bare monads or entelechies who lack any kind of apperception, are of relational states of affairs. There are other ways of treating relations so as to preserve some of the flavor of the aggregate theory. But all of the ones of which I am aware involve difficulties as bad or worse than those which beset the two outlined above. 6. Concluding remarks The only coherent account of relations to emerge from Leibniz's mature philosophy is closely connected with the phenomenalistic interpretation of the monadology. This account is not happily glossed by saying that Leibniz believed in the reducibility of relations. He believed that there are no relations, conceived either as abstract universals or as concrete accidents. On the other hand, he also believed that there are relational properties of physical objects which are not reducible to non-relational properties of such objects. The true individuals, however, do not have any non-formal relational properties. They are related or connected, but only through their perceptions so that the sense of connection here is a second order one. The physical world with its relational properties is founded on the monads. The founding is a reduction, but again, it is misleading to describe it as involving a reduction of relational properties of physical objects since their non-relational properties are equally reduced. Whether or not it is ultimately judged as correct, this reconstruction of Leibniz is fruitful in suggesting ways to interpret the crucial notion of perception, ways to treat disharmonious worlds, and ways to construct a successful phenomenalism. These suggestions seem to me sufficiently interesting in their own right to merit further investigation. Despite the overall attractiveness of the phenomenalistic reconstruction, it must be acknowledged that Leibniz clung to various aspects of his aggregate theory of monads. I sketched two ways in

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which this theory might be used to found relational properties of physical objects. Neither is satisfactory, and one suspects that alternative modes of founding will not prove to be any more acceptable; but this is a matter that can only be settled by further study23. 23 Also needed is a detailed study of the opposing forces which on one hand drove Leibniz towards pure phenomenalism but which on the other hand held him to the aggregate theory.

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Printed ill Great Britain

Space and Relativity in Newton and Leibniz RICHARD ARTHUR*

ABSTRACT

In this paper I challenge the usual interpretations of Newton's and Leibniz's views on the nature of space and the relativity of motion. Newton's 'relative space' is not a reference frame: and Leibniz did not regard space as defined with respect to actual enduring bodies. Newton did not subscribe to the relativity of inertial motions; whereas Leibniz believed no body to be at rest, and Newton's absolute motion to be a useful fiction. A more accurate rendering of the opposition between them, I argue, leads to a wholly different understanding of Leibniz's theory of space, one which is not susceptible to the objections Newton had raised against Descartes regarding the representation of motion. This in turn suggests a new approach for contemporary theory of space, one which neither hypostatizes space nor tries to reduce it to relations among actual things,

1 The Opposition between Newtoll and Leibniz 2 Newton Oil Space and Relativity 3 Newton alld the Structure of Space 4 Relative Space alltl Absolute Motion in Leibniz 5 I.eibniz and tile Construction of Space 6 Concll/sion

I

THE OPPOSITION BETWEEN NEWTON AND LEIBNIZ

There is a very beguiling way of reading the opposition between Newton and Leibniz on the nature of space, a way which now has all the authority of tradition. This is to read Newton's relative spaces as reference frames, so that his doctrine of the onlic primacy of ahsolute space is interpreted as the • This work was generously supporled by the National Endowment for the /lumanities. with a Fellowship for 'College Teachers and Independent Scholars (FB-26897-89l, and also by a sabbatical leave from my institution. Middlebury College. I am very grateful to various members of faculty of York University for their appreciative reception of an earlier one-week-old version of this paper. 'Relative Space in Newton and Leibniz·. read to the Department of Philosophy there in January 1990. and to Hobert Rynasiewicz for criticisms of an extract read at the) 991 History of Science meeting.

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assertion that some one of these relative spaces is privileged as the space at absolute rest. Leibniz. on this account. is read as more or less inverting this view. taking Newton 's relative space-space detined relative to a given perduring body or bodies-as real. and completely rejecting Newton's absolute space. One of the reasons for the attraction of this reading is that it conforms so well with issues concerning the relativity of matiol/. Newton. as he is usually represented. thought that one could successfully identify a class of absolute motions. namely rotational motions. and argued for this in the Prillcipia with his thought experiment with the rotating bucket; Leibniz. on the other hand. subscribed to the 'equipollence of hypothese!)·. as it was called in the seventeenth century. according to which allmotioll is relative to \'v],icll body or system of bodies is hypothesiud to be at rest. and the phenomena and laws of physics are invariant under change of hypothesis. I Thus according to this almost irresistible contrast. we have Newton the absolutist. who holds that the absolute rotational motions serve to define a preferred frame of reference for all motion. absolute space; and Leibniz the relativist. who holds all motion to be relative to which body is taken to be at rest. places to be relative in the same way. and space to be any of the relative splices so determined. Up until fairly recently. the received wisdom was that Einstein had shown that Leibniz was right. His theory of Special Relativity had proven that any attempt to enshrine one of the inertial frames as being absolutely at rest would be in conflict with Maxwell's empirically well-contirmed theory of electromagnetism; and his theory of General Relativity had done away with the ·special' status of inertial frames; and by making the very structure of spacetime depend on the distribution of mass-energy in the universe. Einstein had contirmed Leibniz's insight as to the ontic dependence of space on bodies. Since the mid-1960s. however. this pOSitivistic assessment has been under attack. mainly as a result of the work of Stein. Earman. Friedman. and others. As has been pointed out many times. Leibniz did not anticipate the special relativistic dependence of time interval. mass. etc. on frame of reference; and 'il is no more true in the general theory than in Newtonian dynamics that the geometry of space-time is determined by relations amoll{l bodies' (Stein [1967]. p. 187). It is also now generally recognized that Newton. in reali7.ing the necessity for a well-defined spacetime trajectory. did anticipate (at least implicitly) the need for some spacetime structure over and above what could be 1

In his Spedmrn oJ Dyl/amics of 1695. Leibniz said: tiS Jar as phfllomrnn lIre (Ol1ffmcti. I1l1lliOIl is II pure rda/ioll .. . Therdore we must hold that however many bodies might be in motion. one cannot infer from the phenomena which of them really has absolute and determinate motion or rest. Rather. onc can attribute rest to anyone of them one may choose. and yet the same phenomena will result' (Ariew and Garber [I 'Ill'll. pp. 130-\). CI also the dear statement of his views on the relativity of motion Leibniz gives in an essay he wrote in Italy in 16X9 (Couturat [1903]. pp. 590-3). given the title ·On Copcrnicanism and the Relativity of Motion· by Ariew and Garber ([I 'lX'll· pp. 90-4).

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supplied by instantaneous spaces and a relational time (Stein [1967]). Thus the pendulum has begun to swing the other way, and Earman in particular has argued that spacetime must be granted full reality (see especially his latest treatment in Earman [1989]). But here I want to give the pendulum a push in a dillerent direction. for I am not fully in sympathy with either of the two extremes of its swing just described: neither the positivist view which sees space as being defined relative to a given observable body (Mach, Reichenbach, and, in some moods, Einstein), nor the realist view that the spacetime structure is ontologically prior to material bodies. Rather. I want to point out that the usual way of opposing the views of Newton and Leibniz seriously distorts their views on both space and relativity. The reading of Newton's 'relative space' as a global reference frame obscures his complete opposition to the relativity of motions, even inertial ones: whereas the usual reading of Leibniz as defining space in terms of relations among perduring bodies obscures the fact that his relative space is strictly instantaneous, and misrepresents his conception of true motion. A more accurate rendering of the opposition between them, r argue, leads to a wholly different understanding of Leibniz's theory of space, one which is not susceptible to the objections Newton had raised against Descartes. This in turn suggests a new approach for contemporary theory of space. one which neither hypostatizes space nor tries to reduce it to relations among actual things. 2

NEWTON ON SPACE AND RELATIVITY

According to the usual view, Newton was almost right about the relativity of motion and the nature of space. His mechanics embodies an eqUivalence of inertial frames: that is, the laws of Newtonian physics are the same in all inertial reference frames, or invariant under a transformation from one frame to another. This fact. it is said, is duly recognized by Newton in Corollary V to the Laws of Motion in the Principia: The motions of bodies included in a given space are the same among themselves, whether that space is at rest. or moves uniformly forward in a straight line without any circular motion. (Newton [J 726), p. 63 ; my translation)

Notoriously. however. Newton went on to claim that one of these spaces is absolutely at rest. namely absolute spare. His famolls argument at the end of the Scholium concerning the rotating bucket is usually interpreted as an attempt to provide a criterion (at least for the case of circular motion) for absolute motion or rest. Again. from a modern perspective, Newton's intuitions are on track. For the absoluteness of circular motion-as opposed to linearly accelerated motion-is preserved not only in the Special Theory of RelatiVity, but also in the General Theory, in spite of Einstein's expectations-a point that is not always appreciated.

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Where Newton erred, however, according to this modern perspective, was in generalizing from the case of circular motion to all motion: in assuming that linding a criterion for absolute circular motion is sufficient to establish absolute motion generally. But all that is necessary for the absoluteness of a circular motion is an absolute velocity difference, not an absolute velocity.1 A simple example should help to clarify this point. Imagine a bicycle travelling at a speed v along a straight, level road, taken to be at rest. At a given moment the top of the wheel will be moving with a speed 2v with respect to the pOint of contact between wheel and road directly beneath it. Now consider the Siillle situation from a JiITercnt frame of reference. namely one in which the bicycle is considered to be at rest. Now the road will be slipping away under the bicycle in a straight line with a velocity - v, and the point at the top of the wheel will have a velOCity of + v. Thus the velocity difference between the top and bottom of the wheel will still be 2v, and the wheel will still be rotating in the new inertial frame at the same angular velocity (namely. vir, if r is the radius of the wheel). Clearly this argument will work (in classical mechanics) for any linear change of velocity: that is, the circular motion is the same in any inertial frame. Thus Newton's dynamical argument does not succeed in establishing a unique rest frame, but an infinite family of inertial frames. This modern perspective on Newton's views about space and relativity is clearly beyond reproach as an interpretation of Newtonian mechanics as it is understood today. But the further questions arise concerning its adequacy as a historical account of Newton's own position, and the extent to which he did anticipate modern views on spactime. And from this perspective, I shall argue, it is a reading of Newton through very modern spectacles-a distortion through the lens of anachronism, one might say. The real. historical Newton is closer (especially in his early writings) to an Aristotelian (!) perspective than we are comfortable admitting. In the 11rst place, there is already a distortion of Newton's position in interpreting his 'relative spaces' as reference frames, and in interpreting his · absolute space as a specially distinguished relative space. l What Newton had in mind when he spoke of relative space was what he called a 'movable dimension' of space, defined by reference to certain bodies: that is, a region of space, like the sublunar space, or to give a more modern example, the stratosphere. This is clear from his discussion in the Principia: Absolute space, by its own nature without relation to anything external. always remains similar and immobile. Relative space is any mobile measure or dimension oDt, which is deli ned by our senses through its situation with respect I

I

This is clearly explained by Howard Stein in his /19771. Stein claims that this point was explicitly recogni7.cd by Huygens, even if not by his two illustrious successors. Newton and Lcibniz. I intend to argue this point in more detail elsewhere. in a paper tentatively titled 'Newtonian Spaces and Cartesian Places'.

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to bodies. and is commonly taken for immobile space: such as the dimension of a subterraneous. an aerial or a celestial space. defined by its situation with respect to the earth. Absolute and relative space are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth. for example. moved. the space of our air. which relatively and in respect of the earth always remains the same. would at one time be one part of the absolute space into which the ail passes. and at another time a different part of it; and thus absolutely would be perpetually changed. (Newton [1726]. pp. 46-7; my translation)

Here there is no question of an infinite class of equivalent frames. each adequate to the coordinatization of the whole infinite space, and one of which is privileged as absolute. Rather, Newton is asking us to envisage one fixed, immobile reference space, through which various bodies are moving, and along with them, certain delimited spaces defined with respect to them. A relative space is thus a delimited region of space, rather than an infinite frame, and is determined by the situation or position of surrounding bodies, which are themselves situated in immobile, absolute space. This rendering leads to a reconsideration of what Newton says about the relativity of motion. For if relative spaces are not reference frames, how could Newton have anticipated the Galilean relativity we recognize in his mechanics today? I shall argue that careful attention to his words shows that he did not, and that this is a consequence of the fact that he did not have a modern 'Newtonian' conception of the relationship between force and motion. For, despite his commitment to the principle of rectilinear inertia, Newton conSistently held in his early writings on dynamics that force is necessary to produce motio". and only gradually and incompletely emancipated himself from this conception. To a modern ear, this sounds like a contradiction. since inertial motion is motion that takes place in the absence of any forces. But Newton did not initially abide by this Cartesian collCeplion. In the (untitled and unpublished) anti-Cartesian polemic he wrote prior to the Prillcipia (in about 1669, or possibly later), now usually known by its opening words 'De Gravitatione' ,4 inertia is a force: Def 8. Inertia is the internal force of a body preventing its state from being easily changed when an external force is introduced . (Hall and Hall [1962). pp. I 14. 14H)

This is further c1arilled by Definition ') on the same page: Der 5. Force is the causal prinCiple of motion and rest. And it is either an external one which generates or destroys. or at least in some way changes. the motion • Hall and Hall 11962]. Latin text pp. R9-12I: English translation pp. 121-56. The Halls' translations are not always accurate. so I have given my own while referenCing theirs. The d6Ibid., sect. II, para. 14, p. 50 (Gracia). 6elbid., sect. II, para. 16, p. 50 (Gracia). "Nor indeed does it follow [that since the individual is only conceptually distinct from the nature] that what [the individual adds to the nature) is something conceptual. For, just as it is one thing to be distinguished conceptually and another to be only [a being] of reason-for it can happen that real things be distinguished only conceptually,-so also that which is added can be real, as it truly is, although distinguished only conceptually" (Gracia's translation).

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their substances). His second, and more subtle argument, is based on the predicate-in-notion principle, the truth of which is far from certain. If I am right in all this, Leibniz had no good reason to damn transitive action, and, therefore, has given us no good reason for rejecting Suarez's view of the nature of composite substances. But if this is the case, it seems we should prefer Suarez's view of composite substances to that of Leibniz's, as it is more in accord with our common sense notion that living things like people and trees are single substances that have real, extended bodies.

University of St. Thomas St. Paul, Minnesota

Part III Life, Mind and Action

[7] Leibniz on Personal Identity and Moral Personality* By SAMUEL SCHEFFLER (PRINCETON, N.

J.)

Zusammenfassung Leibniz unterscheidet zwischen einem Begriff der metaphysischen Identitat, welchen er gebraucht, um das Problem der personlichen Identitat zu los en, und einem Begriff der moralischen Identitat, welchen er verwendet, um das Problem, das ich "das Problem der moralischen Verantwortung" nenne, zu los en. In diesem Aufsatz versuche ich, eine systematische Darstellung des Verhiiltnisses zwischen metaphysischer und moralischer Identitat in Leibniz' System zu geben. Ich untersuche die Natur und den Umfang des Unterschieds zwischen moralischer und metaphysischer Identitat, die verschiedenen Probleme, die jeder der heiden Begriffe losen solI, und ich bestimme ihre relative Bedeutung.

Leibniz thinks that his theory of substance provides him with a metaphysical solution to what I shall call "the problem of personal identity". At the same time, Leibniz distinguishes sharply between the concept of metaphysical identity, which he uses to solve the problem of personal identity, and the concept of moral identity, which he uses to solve what I shall call "the problem of moral responsibility". Some modern commentators have agreed that Leibniz's theory of substance gives him a "built-in solution"l to the problem of personal identity. Yet the question of the relation between metaphysical identity and moral identity in the Leibnizian system appears to have escaped serious consideration in the literature. In this paper I will try to provide a systematic account of that relationship. In the first part of the paper I will examine Leibniz's explanation of the way in which his theory of substance provides a metaphysical solution to the problem of personal identity. I will try to explain why Leibniz thinks there is a problem about personal identity, and why he thinks his theory of substance succeeds in solving it while other proposals fail. I will also criticize Leibniz's remarks on these topics. With this much as background, I will turn in the second section to an examination of Leibniz's distinction between metaphysical

* I am deeply grateful to MARGARET WILSON for her detailed and searching criticism of earlier drafts of this paper. I would also like to thank ELLEN PEARLMAN for helpful criticism and advice, and BERNARD RUSSELL, who first suggested to me that Leibniz's views on personal identity deserved attention. 1 IAN HACKING, Individual Substance, in: H. FRANKFURT (ed.), Ltibniz: A Collec/ion of Critical Euays, Anchor Books, New York, 1972, p. 149. 15-

Studia Lelbnitiana, Band VIIII2 (1976)

@ Franz Steiner Verlag GmbH, D-6200 Wicsbaden

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identity and moral identity, concentrating on the different problems which each is supposed to solve. I will show why Leibniz believes that the criteria of moral identity are more stringent than the criteria of metaphysical identity, and I will try to identify the two sets of criteria with some precision. I will pay special attention to Leibniz's account of the role which memory and other psychological phenomena play in setting the criteria of moral identity. In the third part of the paper, I will assess the nature and extent of the differences between moral and metaphysical identity in the Leibnizian system. I will also assess their relative importance, arguing that Leibniz's metaphysical solution to the problem of personal identity turns out to be something 1e s s than it may have seemed at first, and that his solution to the problem of moral responsibility turns out to be something more than it may at first have seemed. For the purposes of this discussion, I shall take "the problem of personal identity" to be defined by the following question: when is it the case that a person PI existing at time T 1 is the same person as a person P 2 existing at time T2? In discussing Leibniz's response to this question, I shall avoid any detailed consideration of his views on the relation between the mind and the body. Although the two problems are obviously closely related, I believe that it is possible to discuss Leibniz's views on personal identity without a thorough analysis of his treatment of the mind-body relation. For the purposes of this discussion, it will suffice to understand that Leibniz views a person as a self-conscious monad bearing a special relation to the ever-changing aggregate of matter which is its body. I will therefore not discuss his account of the precise nature of the relation between the self-conscious monad and its body, or the precise character of the unity which they may be said to constitute. I hope this paper will vindicate the claim that one can understand Leibniz on personal identity without settling these two questions of interpretation. I.

Leibniz maintains that certain outstanding psychological phenomena, which many writers have thought to playa key role in solving problems about personal identity, are in fact neither necessary nor sufficient to establish the identity of persons over time. In other words, the fact that a person PI existing at time T 1 and a person P 2 existing at time T 2 are linked by bonds of, for example, memory, is neither necessary nor sufficient to make them the same person. I want now to

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discuss Leibniz's argument in support of his view that memory is not a necessary condition of personal identity. I shall proceed to discuss his argument to the effect that no set of psychological characteristics is s uffi den t for personal identity. Then I shall turn to a consideration of Leibniz's own solution to the problem of personal identity. Not until section II will I return to the question of the non-necessity of certain psychological phenomena other than memory. That memory is not a necessary condition of personal identity is an opinion which Leibniz expresses in his commentary on Locke in the New Essays Concerning Human Understanding: "Is it not true that we must always admit that after some interval or some great change, one may fall into a state of general forgetfulness? Sleidan (they say), before his death, forgot all he knew; and there are many other examples of this sad event. Suppose that such a man became young again and learned all anew, will he be another man on that account? It is not then memory which, propedy speaking, makes the same man . . . Memory ... is not necessary . . . "z.

Leibniz here argues that if memory were necessary for personal identity, then a person who lived after an accident that resulted in a complete loss of memory would be a different person from the person who existed before the accident. This consequence of the view that memory is a necessary condition of personal identity is so counterintuitive, Leibniz feels, that it constitutes a reductio of that position. There are two things to say about this argument. The first is that insofar as the consequence is counterintuitive, that may be at least in part because we feel that the continuity of other psychological characteristics across a gap in memory can suffice to establish the identity of a person. Thus, if an accident victim suffered a complete loss of memory but retained other important traits of personality (e. g., temperament, sense of humor, attitudes toward other people, dispositions to respond to particular situations in characteristic ways), we might feel inclined to say that there was only one person, before and after the accident. As I shall soon show, however, Leibniz 2 LA, pp. 114-115; GP V, p. 104. The abbreviations I use are: LA=NelJ1 Euays Concerning Human Understanding, ed. by A. G . LANGLEY (New York, 1896). GP = Die Philosophischen Schriften von Gottfried Wilhelm Leibniz, ed. by C. 1. GERHARDT (Berlin, 1875-1890). OC = Discourse on Metaphysics, Correspondence with Arnauld, Monadology, Open Court Publishing Company (LaSalle, Illinois, 1902). W = LEIBNIZ, Selertions, ed. by P. WIENER (New York, 1951). S = Monadology and Other Philosophical Essays, ed. by P. SCHRECKER and A. M. SCHRECKER (Indianapolis, 1965). Wherever I quote from a published English translation of Leibniz I give the reference in the Gerhardt edition as well.

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believes that no set of psychological criteria is sufficient to establish personal identity. It is therefore not entirely clear to what extent he can rightly rely on an argument against memory being a necessary condition of identity which itself depends on an intuition that some set of psychological criteria is sufficient. At the very least, his reliance on this argument - and through it, on that intuition - means that he must go on to produce independently convincing arguments against the sufficiency of psychological criteria. A perhaps more fundamental objection to Leibniz's argument against the necessity of memory is, however, that it is really not much of an argument; it is not likely to convince anyone who disagrees. Leibniz says that the idea of a memory loss "creating" two people is so counterintuitive that it constitutes a reductio of the view that memory is a necessary condition of personal identity. A defender of the memory criterion could just as well say that since memory is a necessary condition of personal identity, consideration of the memorygap case just shows that our ordinary intuitions are not very reliable on questions of personal identity. Leibniz has produced no argumen ts against this line of thought. He has simply said that since the memory criterion violates ordinary intuition, we must reject the criterion. His opponent could say that since the memory criterion violates ordinary intuition, we must reject our ordinary intuitions in this matter. The dispute between them seems to be a stand-off, on this point at any rate. Leibniz's major argument against the sufficiency of psychological conditions for personal identity is difficult and revealing but it is not clear in the end that it amounts to a much stronger argument than his argument against the necessity of memory. The argument appears twice in similar forms. The first time is in some notes which Leibniz made in May of 1686 in response to a criticism by Arnauld of his theory of substance. These remarks apparently served as the basis for a letter which Leibniz wrote to Arnauld on July 14, 1686; that letter contains the second formulation of the argument. In the May draft, Leibniz writes as follows in a discussion of Adam: .. if he had had other circumstances, this would not have been our Adam, but another, because nothing prevents us from saying that this would be another. He is, therefore, another ... Let a certain straight line, ABC, represent a certain time, and let there be a certain individual substance, for example, myself, which lasts or exists during this period. Let us take then, first, the me which exists during the time AB, and again the me which exists during the time Be. Now, since people suppose that it is the same individual substance which perdures, or that it is the me which

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exists in the time AB while in Paris and which continues to exist in the time BC while in Germany, it must needs be that there should be some reason why we can veritably say that I perdure, or, to say, that the me which was at Paris is now in Germany, for, if there were no reason, it would be quite right to say it was another. To be sure, my inner experience convinces me a posteriori of this identity but there must be also some reason a priori. It is not possible to find any other reason, excepting that my attributes of the preceeding time and state are predicates of the same subject .. . "3.

In the July letter to Arnauld, a more concise version of the argument is presented: "Besides, if, in the life of any person, and even in the whole universe anything went differently from what it has, nothing could prevent us from saying that it was another person or another possible universe which God had chosen. It would then be indeed another individual. There must then be some reason a priori independent of my existence why we may truly say that it was I who was at Paris and that it is still I and not another who am now in Germany and consequently it must be that the concept of myself unites or includes different conditions. Otherwise it could be said that it is not the same individual although it appears to be the same"f.

Needless to say, both presentations of this argument are a bit looser than one might have hoped. As I understand it, Leibniz seems to be saying something like the following. Consider any currently existing man A. Had anything in his life happened differently, there would be no reason to say that the resulting person B was the same person as A. If B were the same person as A, there would have to be a reason why that was so. Since there is no reason, we can quite properly say that B would not be the same person as A - for, indeed, he would not be. Now consider the more radical question: in virtue of what is it the case that I am the same person this week as last? Following the argument of the last example, we may say that if I am the same person this week as last, there must be a reason why tha t is so. lf there were no such reason, then one could quite properly say that I was not the same person this week as last - for, indeed, I would not be. The only candidate for such a reason must be some fact about the nature of substances which can be known apr i 0 r i 5. 3 5

OC, pp. 111-113; GP II, pp. 42-43.

4

OC, pp. 127-128; GP II, p. 53.

It is of course Leibniz's view that every true proposition must be suscep-

tible of a priori proof, drawn from the nature of the subject. Thus when he claims that the reason why I am the same person this week as last must be knowable apr i 0 r i, he may seem to be making the rather trivial claim that the reason why I am the same person this week as last must be true. In fact, I assume that Leibniz is not making this trivial claim. Rather I assume that he is implicitly claiming that the reason why I am the same person this week as last must be a reason which is

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If we object to no other step in this argument, we must surely balk at the last one. Why could it only be in virtue of some fact about the nature of substances that I am the same person this week as last? What Leibniz seems to have in mind is this. Suppose that last Thursday night I dined in Budapest, and that I spent all of this Thursday in Firestone Library. While I was dining in Budapest, a friend was seeing "Jaws" in New York. Let us call each of these episodes a "time-life slice": we can refer to my dinner in Budapest as time-life slice B, my day in Firestone as time-life slice F, and my friend's "Jaws" in New York as time-life slice J. Leibniz now poses the following question: why is there any more reason to consider the subject of time-life slices Band F to be the same person than there is to consider the subject of time-life slices] and F to be the same person? Why is it the case that the person who dined in Budapest last Thursday is the same as the person who spent this Thursday in Firestone, but not the case that the person who saw "Jaws" in New York last Thursday is the same as the person who spent this Thursday in Firestone? One natural answer to these questions is that the subjects of time-life slices Band F are the same person because they are joined by memory and other kinds of psychological continuities (as well as physical continuities). The subjects of time-life slices J and F are not so united, and that is why they are not the same person. Of course, Leibniz is aware of the importance of the psychological phenomena, and he even says that they are what convince us a posteriori that certain time-life slices are part of 0 u r lives, and that others are not. Yet in seeking a suitable reason in virtue of which it is the case that a person retains identity over time, Leibniz does not even consider memory and related phenomena as candidates. He simply asserts that "there must ... be some reason a priori", and proceeds to locate the reason in his theory of substance. In arguing from the knowable a priori by humans. For on Leibniz's view, while it is the case that every true proposition is susceptible of a priori proof, for some propositions the required proof is infinite (these are, roughly, the contingent truths), while for others the required proof is finite (the necessary truths). Only God can perform infinite proofs, so propositions which require such proofs are knowable a priori only by God. On the other hand, propositions which require finite proofs only are knowable a priori by human beings. When Leibniz claims that the reason why I am the same person this week as last must be some fact about the nature of substances which can be known a priori, I assume that he means that the relevant proposition must be susceptible of a finite proof, and hence knowable a priori by human beings.

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premise that there must exist a reason why I am the same person this week as last to the conclusion that the reason must derive from the concept of substance and be knowable a priori, Leibniz reveals that he simply refuses to count phenomena like memory and continuity of consciousness as reasons of the relevant kind. Yet in the abruptness of his transition from premise to conclusion, Leibniz further reveals that he has brought no arguments to bear in support of his view that memory and related phenomena are insufficient reasons 6. Relying on an intuition that mere psychological continuities couldn't be enough to bind sequences of time-life slices into Ii v e s, Leibniz simply begs the question by assuming the correctness of his intuition and failing even to produce arguments against the sufficiency of psychological criteria 7. 6 MARGARET WILSON has suggested (in personal communication) that there may be a more charitable interpretation of Leibniz's demand for a priori reasons. "Perhaps he feels that just because there's room for a distinction between identity of substance and identity of consciousness the appeal to a posteriori considerations would beg the question on the former issue." This is a very interesting suggestion; such reservations as I have about it derive from the fact that it seems to credit Leibniz with having a somewhat clearer picture of his own views on these topics than I believe to be obviously warranted on the basis of the various passages which I discuss in this paper. Wilson adds that even if her interpretation is correct, it stilI appears "that Leibniz's statements to Arnauld do show confusion, since he does seem to claim to know on a pos teriori grounds that he's the same substance as that particular person previously existing in France, and to be giving a theory of substantial identity intended somehow to support this a posteriori knowledge". 7 Actually, Leibniz does present one other argument against the sufficiency of psychological criteria in the New Essays: "It may be that in another place in the universe ... a globe may be found which does not differ sensibly from this earthly globe, in which we live, and that each of the men who inhabit it does not differ sensibly from each of us who corresponds to him. Thus there are at once more than a hundred million pairs of similar persons, i. e. of two persons with the same appearances and consciousnesses; and God might transfer spirits alone or with their bodies from one globe to another without their perceiving it; but be they transferred or let alone, what will you say of their person or self ... ? Are they two persons or the same? since the consciousness and the internal and external appearance of the men of these globes cannot make the distinction. It is true that God and the spirits capable of seeing the intervals and external relations of times and places, and even internal constitutions insensible to the men of the two globes could distinguish them; but according to your hypotheses consciousness alone discerning the persons without being obliged to trouble itself with the real identity or diversity of the substance, or even of that which would appear to others, how is it prevented from saying that these two persons who are at the same time in these two similar globes, but separated from each other by an inexpressible

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Leibniz believes that his notion of substance does have what it takes to bind sequences of time-life slices into lives. On Leibniz's view, substances or monads are the fundamental metaphysical entities; they are indivisible and immaterial. It is famously Leibniz's doctrine that the concept of an individual substance includes everything that will ever happen to it, and that at any given time, any individual substance contains traces of all that ever has happened to it and all that ever will happen to it. Successive states of a substance are the result exclusively of its preceding states, and substances are not liable to external causation. There is a hierarchy of kinds of substances, characterized by differences in the degree of their perceptions (in the rather special sense in which Leibniz uses the term 'perception'). Human beings are rational, self-conscious substances, each bearing a special relation to its human body. Leibniz finds in this conception of substance a satisfactory solution to the problem of personal identity. Given this conception of substance, Leibniz can say that a person PI existing at a time TI and a person P2 existing at a time T2 are the same person if and only if what happens to PI at TI and what happens to P 2 at T 2 are both included in the same substance-concept. The concept of substance, according to Leibniz, explains why there are lives instead of just episodes, and it provides the ironclad metaphysical guarantee of personal identity which Leibniz insists we need.

II. Let the "problem of moral responsibility" be defined by the following question: when is it the case that a person PI existing at time T2 is morally responsible for an act committed by PI at an earlier time T I? For the purposes of this discussion, I shall assume this question to be equivalent to the question: when is it the case that a person possesses "moral identity" or "moral personality" from T I to T 2? I shall also assume that these questions are equivalent to the question: when is it the case that a person PI existing at time T 2 is a morally responsible agent with respect to an act committed by PI distance, are only one and the same person; which is, however, a manifest absurdity." (LA, pp. 255-256; GP V, pp. 227-228). This argument is quite clever, although not obviously successful. I will not discuss it here, except to suggest that it is not clear that it succeeds against the position that certain kinds of psychological continuities are sufficient for personal identity, or against the position that a combination of psychological and ph ys i c a I continuities is sufficient.

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at Tl? I shall now proceed to dicuss Leibniz's views on the question what conditions a monad must meet in order to possess moral identity, or in order to be a morally responsible agent, over an interval of time. We shall see that Leibniz's solution to this problem is different than his solution to the problem of personal identity. Leibniz does not believe that being a human monad is a sufficient condition for being a morally responsible agent. That is, I maintain, he believes that there is a further substantive condition which such monads must meet in order to qualify as morally responsible agents. By a substantive condition, I mean a condition which a human substance could fail to meet while still remaining a human substance. In the Discourse on Metaphysics, he writes as follows: " not being able to reason, they [animals] are unable to discover necessary and universal truths. It is also because they do not reflect regarding themselves that they have no moral qualities, whence it follows that undergoing a thousand transformations, as we see a caterpillar change into a butterfly, the result from a moral or practical standpoint is the same as if we said that they perished in each case, and indeed we can say it from the physical standpoint in the same way we say bodies perish in their dissolution. But the intelligent soul, knowing that it is and having the ability to say that word'!, so full of meaning, not only continues and exists, metaphysically far more certainly than the others, but it remains the same from the moral standpoint, and constitutes the same personality, for it is its memory or knowledge of this ego which renders it open to punishment and reward" 8.

Here Leibniz expresses the view that human souls are distinguished from animals and rendered liable to moral responsibility by their possession of memory in combination with self-consciousness. He thus distinguishes the mere metaphysical identity which all substances possess (and which, as we saw in part I, he uses to solve "the problem of personal identity"), from moral identity or moral personality (which Leibniz, confusingly, usually refers to as "moral or personal identity", and which he uses to solve "the problem of moral responsibility"). Of course, while distinguishing conceptually between metaphysical and moral identity in the passage just cited, Leibniz also seems to assume in that passage that metaphysical and moral identity always coincide in htlmans. I shall be arguing shortly that this is not Leibniz's considered view. Before doing so, however, I wish to call attention to some additional passages in which Leibniz distinguishes between metaphysical and moral identity. In the New Essays, for example, he writes: 8

OC, p. 58; GP IV, pp. 459-460.

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" consciousness or the perception of the ego proves a moral or personal identity. And it is by this that I distinguish the incessability of the soul of an animal from the immortality of the soul of man: both preserve physical and real identity, but as for man, he is conformed to the rules of divine providence so that the soul preserves also identity moral and apparent to ourselves, in order to constitute the same person, capable of feeling chastisements and rewards" 8.

Here again, Leibniz distinguishes the identity which all substances possess qua substances from the moral personality which human substances possess when they possess the combination of memory and self-consciousness. Leibniz believes that while the first notion is sufficient to solve the problem of personal identity as defined in the first section of this paper, the second notion is additionally necessary to solve the problem of moral responsibility. Still another passage from the New Essays expresses the same view succinctly. Commenting on a kind of transmigration of the soul which he believes to be possible although "not ... conformed to the order of things", Leibniz remarks: "But ... in case such a transmigration were true ... The identity of substance would occur therein, but in case there were no connection of memory between the different persons ... there would not be sufficient moral identity to say that it would be one and the same person"10.

There is, as I have hinted, an objection which can be raised to my claim that memory is a further substantive condition which human souls must meet in order to qualify as morally responsible agents. Before considering that objection, however, I want to take note of an important obscurity in Leibniz's argument which I have until now been content to incorporate into my account of his argument. The obscurity pertains to Leibniz's identification of those psychological phenomena which a human substance must manifest in order to satisfy the requirements of moral identity. The obscurity arises out of the somewhat casual way in which Leibniz tends to interchange different psychological phenomena in different statements of his position. In some contexts he identifies memory 11 as the relevant phenomenon, in others self-consciousness 12, and in still others he mentions both intelligence 13 and rationality 14. Sometimes he mentions a combination of two or more of these phenomena IS. Obviously, LA, pp. 245-246; GP V, p. 218. 10 LA, p. 243; GP V, p. 216. LA, p. 243;GP V, p. 216. 12 LA, pp. 245-246; GP V, p. 218. 13 OC, p. 58; GP IV, p. 459. u S, p. 152; GP VI, p. 611. 15 OC, p. 58; GP IV, pp. 459-460. OC, pp. 231-232; G II, p. 125. S, pp. 151152; GP VI, p. 611. 8

11

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memory, self-consciousness, intelligence and rationality are all very different phenomena. Just as obviously, all four affect our practical and moral judgments about personhood and responsibility. And indeed, taking all of Leibniz's comments on the subject into account, it seems most likely that he believes some combination of all four phenomena to be necessary for moral identity 16. This is, for example, certainly the impression one gets from reading Leibniz's discussion of the difference between people and animals in Monadology §26-30 17 • It will be helpful to bear the fact of this obscurity and its probable resolution in mind as we proceed. I want now to consider the objection, alluded to earlier, which can be raised to my claim that memory, self-consciousness, intelligence and rationality are, for Leibniz, further substantive conditions which human souls must meet in order to qualify as morally responsible agents. In the three passages just cited, it is possible to read Ldbniz as saying that human souls, unlike other substances, are always liable to moral responsibility because part of what it means to be a human substance is to always possess the required combination of psychological attributes. In other words, one might read Leibniz not as suggesting that memory, self-consciousness, and the like are further conditions for morally responsible agency beyond the mere identity of a human substance - conditions which a human substance could fail to meet without surrendering its metaphysical rank -, but rather as identifying those built-in features of human substances which make them (as opposed to other kinds of substances) morally responsible agents. If part of what it is to be a human substance is to possess these qualities, and if possessing these qualities is a necessary 16 Compare RUSSELL: "s p i ri t s ... are defined by self-consciousness or apperception, by the knowledge of God and eternal truths, and by the possession of what is called reason ... Spirits also ... preserve moral identity, which depends on memory of self, while other monads are merely incessant, i. e. they remain numerically identical without knowing it." (A Crifiral Exposition of the Philosophy of Leibniz, [London, 1971], p. 141). There is a further obscurity in Leibniz's writing on this matter, which I shall mention but not pursue further. In order for PI to be morally responsible at T z for an earlier action committed by PI at Th is the requirement that PI must be rational, intelligent, and self-conscious supposed to hold at TI or T 2 , or both? 17 It is noteworthy that in none of the passages I have referred to in which Leibniz discusses the difference between persons and animals does he mention language as an important distinguishing characteristic. This is interesting in considering the relation between historical rationalism and the Chomskyan version.

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condition for being a human soul, then only in the most trivial sense is it a requirement of being a morally responsible agent that one be not only a human soul, but also possessed of the required combination of memory, self-consciousness, intelligence, and rationality. This objection does not deny that Leibniz makes an important conceptual distinction between metaphysical and moral identity. It simply maintains that, for Leibniz, a human substance possesses metaphysical identity only if it possesses moral identity. The argument for reading Leibniz in this way certainly gains support from his frequent habit of referring to human souls as "rational souls" or "self-conscious souls" or "intelligent souls". How can it be a further requirement on rational souls that they be rational, or on self-conscious souls that they be self-conscious, or on intelligent souls that they be intelligent? Although it is possible to read the three passages in question in this way, it is clear enough that it is not correct. For, as Leibniz concedes, there are a variety of ways in which a human substance could fail to possess the required combination of psychological attributes without surrendering its status as a human substance. In particular, such a substance might lack one or more of the psychological attributes in question, and still remain a human substance. He expressly concedes this with regard to memory, it seems likely that he would concede it with regard to rationality and self-consciousness, and it is possible that an analogous case could be made for intelligence. The case of memory is the clearest. For the point of Leibniz's argument against the necessity of memory for personal identity (which we considered in part I), was that a human substance could maintain its identity qua substance even if it suffered a trauma which rendered it unable to remember anything which had happened prior to a certain time. Thus Leibniz is committed to the view that a human substance could lack memory. It seems likely that he would also accept the view that certain kinds of mental disorders might render a human substance irrational or devoid of veridical self-consciousness, without causing it to forfeit its status as a human substance. This, I take it, is the point of Leibniz's rather careful phrasing of his injunction in the New Essays to distinguish "the self", as identified metaphysically, from "the phenomenon of self", or self-consciousness. "The self constitutes identity real and physical, and the phenomenon of self, accompanied by truth, joins thereto personal identity" 18. The force 18

LA, p. 247 ; GP V, p. 219.

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of the phrase "accompanied by truth" is, I believe, to express the opinion that a human substance with a "false consciousness" (comprised of false beliefs about itself, non-veridical memories, and/or diminished rationality) would not be a morally responsible agent. In such a case, the human substance would retain its metaphysical identity but not its moral personality. Thus my claim that some combination of psychological phenomena constitutes a substantive additional condition which human substances must meet in order to qualify as morally responsible, on Leibniz's view, is vindicated. It is vindicated by showing that Leibniz held that a human substance could lack at least some of the required phenomena without surrendering its metaphysical rank. So even if it sould turn out that some psychological phenomena are such that a substance could never lack them and be a human substance, my claim that there are substantive requirements beyond mere metaphysical identity which a morally responsible agent must satisfy would remain correct 19 • And even if I were wrong to deny that, for Leibniz, 10 It is important, however, to qualify to some extent my claim that while human substances must possess certain psychological characteristics in order to achieve moral identity, they sometimes lack these characteristics. I have argued that a human soul could lack memories from before a certain time, and could also lack a veridical self-consciousness. When this happens, that soul is not a morally responsible agent; it is not morally responsible for its actions. I do not claim, however, that Leibniz would hold that a human substance could be completely incapable of eve r h a v i n g any memories, or of regaining veridical self-consciousness once lost. The retention of these capacities may indeed be part of what it means to be a human soul. In fact, Leibniz may sometimes seem to require that human souls all regain lost memory and veridical self-consciousness in time for the Last Judgment. As C. D. BROAD writes, "a rational soul has to be restored to a state of comparative clearness at latest by the Last Judgment in order to recognize the justice of the verdict upon its past life and thereafter to enjoy its reward in Heaven or suffer its punishment in Hell". (Leibniz: An Introduction, [Cambridge, CUP, 1975], p. 102). What this might suggest is that memory and self-consciousness are substantive conditions on moral identity which a human substance can lack in time. When this happens, the substance is not a moraHy responsible agent, and in our relations with individuals who lack these attributes we should not treat them as morally responsible agents. At the Last Judgment, however, these individuals regain their memories and veridical self-consciousnesses, and then are liable to divine judgment even for actions committed during the time when they lacked memory and veridical self-consciousness. In other words, memory lapses can "create" several different moral identities serially "within" the same human substance. For our moral and practical purposes, these constitute distinct moral personalities, and responsibility for action before humans does not hold across intrasubstantial moral identities. However, when the Last Judgment comes, memory

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part of what it means to be a human substance is to possess all the necessary psychological characteristics, it would remain undeniably true that Leibniz makes a clear conceptual distinction between metaphysical and moral identity. His willingness to make this distinction is itself of considerable historical interest. Since my claim that there are (for Leibniz) substantive psychological requirements which human souls must meet in order to qualify as morally responsible agent appears to be correct 20, we are left with is restored (where it has lapsed) to human substances, along with clear selfconsciousness, and, as it were, a new moral identity comes into existence, superceding all the serial identities which may have existed before. This restoration operates retroactively with respect to responsibility: the unified moral personality representing the whole history of the substance up until the Last Judgment is responsible before God for all the actions of the more limited moral personalities which it supercedes. While this interpretation is intriguing, it is simply not clear, despite what Broad says, that Leibniz does require that all human souls regain lost memory and veridical self-consciousness in time for the Last Judgment. In the New Essays, for example, Leibniz writes: "I do not know whether it will be necessary for the memory of man to be exalted at the day of judgment in order for him to remember all he had forgotten, or whether the knowledge of others and above all of the just judge who cannot be deceived will not suffice." (LA, p. 254; GP V, p. 226). In fact, Leibniz is so concerned in this part of the New Essays to establish God's right to punish someone who has lost his/her memory, that he goes so far as to contradict himself by denying that memory is ever necessary for moral identity. I discuss this point further in footnote 21. zo If, despite the reservations which I expressed in footnote 19, one were to read Leibniz as insisting that all human substances do indeed regain memory and veridical self-consciousness in time for the Last Judgment, one might also proceed to offer an alternative account of the psychological requirements for morally responsible agency. One might argue that it is, according to Leibniz, part of what it means to be a human substance to regain memory and veridical self-consciousness (if lost) in time for the Last Judgment. And this capability, one might read Leibniz as claiming, is all that is necessary to confer a unified moral identity on every human substance throughout its temporal existence. Thus, one might conclude, it is not the case after all that for Leibniz, human substances can lack moral identity in time. This interpretation would indeed make sense of those passages in which Leibniz seems to assume that moral and metaphysical identity are always coincident in humans, and it would reconcile those passages with the remarks in which Leibniz concedes that people actually do suffer memory lapses in time. Despite the attractions of this interpretation, there are serious problems with it, even apart from the fact that there is reason to doubt whether Leibniz did think that human substances regain memory in time for the Last Judgment. For one thing, Leibniz himself never actually offers this interpretation. For another thing, it seems to be incompatible with several of the passages which I discuss in this paper. Again however, even if this interpretation were correct, it would still be

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the question why Leibniz refers to human substances as "rational souls", "self-conscious souls", and the like. If such substances could lack rationality and could possess "false consciousnesses", then the class of human souls and the class of rational souls are not coextensive, and Leibniz's terminology is misleading. I offer three possible explanations for Leibniz's referring to human souls by expressions which suggest incorrectly that he believes all such souls to satisfy certain psychological requirements. The three explanations are closely related and are not incompatible: 1) M 0 S t human souls meet the psychological requirements, and Leibniz was just indulging in some sloppiness. 2) Since m 0 s t human souls meet the psychological requirements, and since the manifestations of the necessary psychological phenomena by those souls which do meet the requirements are among the most striking features of such souls, convenience and ease of identification argued for identifying the whole metaphysical class of souls by reference to the propensity of many of its members to manifest these salient psychological characteristics. 3) Having distinguished the class of "metaphysical humans" from the class of "moral or personal humans", and having incorporated so much that is of moral and practical importance into the definition of the latter class, Leibniz found it difficult even to identify the former class in a recognizable way without importing some terms from the moral and practical realm. This suggestion foreshadows a conclusion I shall draw later about the relative importance of "metaphysical identity" and "moral or personal identity". To sum up, we have seen that Leibniz uses his theory of substance and the notion of metaphysical identity to solve "the problem of personal identity", as defined in part I. However, he denies that mere metaphysical identity is sufficient to make the human soul a morally responsible agent with respect to any act. I have so far been assuming that metaphysical identity is a necessary condition for moral identity, but I will question that assumption shortly. We have seen that a combination of psychological characteristics is necessary for morally responsible agency, although Leibniz is a bit vague about exactly which characteristics go into the combination, and to what degree the case that Leibniz acknowledged a conceptual distinction between metaphysical identity, which all substances possess qua substances, and moral identity, which human substances possess in addition to metaphysical identity, in virtue of certain special features which human substances exhibit.

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they must be present 21. We will be able to settle the question whether this combination of psychological characteristics is itself sufficient for moral identity, or whether instead these characteristics and metaphysical identity are jointly sufficient for moral identity, only when we have seen whether metaphysical identity is necessary.

21 Actually, Lcibniz makes some remarks in the New Buoys which suggest that memory is not, after all, a necessary condition of moral identity (although these remarks do not impugn the necessity of rationality, intelligence, or self-consciousness). He writes: "if a disease had caused an interruption of the continuity of the bond of consciousness so that I did not know how I came into the present state, although I could remember things more remote, the testimony of others could fill the void in my memory. I could even be punished upon this testimony, if I had just done something bad of deliberate purpose in an interval I had forgotten a little after on account of this disease. And if I had just forgotten all past things and would be obliged to let myself be taught anew even to my name and even to reading and writing, I could always learn from others my past life in my previous state ... All this suffices to maintain moral identity, which makes the same person." (LA, p. 246; GP V, p. 219). In this passage, Leibniz defends the puzzling position that memory is not necessary for moral identity, if the memory gaps can be filled by external testimony. But memory gaps can almost always be filled by external testimony, so the memory requirement would become almost vacuous with this qualification. It is puzzling that Leibniz should defend this view, since it appears in flat contradiction with the passages cited throughout this paper in which Leibniz asserts unequivocally that memory is a necessary condition of moral identity. There seems to me no plausible way of interpreting this passage so as to make it consistent with those others. My feeling is that the other passages represent Leibniz's dominant view. The key to understanding the puzzling passage just cited is found, I suggest, a few pages further along in the New EuoYJ, when Leibniz argues that God has the right to judge people at the Last Judgment even if they lack memory (LA, p. 254; GP V, p. 226). My conjecture is that Leibniz was afraid that having made memory a necessary condition of moral identity, he was in danger of denying God the right to judge all human substances (including those lacking memory) at the Last Judgment. There are two ways out of this predicament. The first is to argue that all human substances do regain memory in time for the Last Judgment, and Leibniz makes a gesture in this direction when he says that "it is not reasonable that the restitution of memory becomes forever impossible, the sensible perceptions ... serving here ... to preserve the seeds". (LA,p.250; GPV, p.222). The second is to argue that memory is not a necessary condition of moral identity, and this is what Leibniz does in the passage I have quoted above. This puts him in a position to suggest that a person lacking memory can be judged on the basis of "the knowledge of others and above all of the just judge who cannot be deceived". (LA, p. 254; GP V, p. 226). Unfortunately, this approach is inconsistent with the other passages in which Leibniz flatly asserts the necessity of memory for moral identity.

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III. In a letter to Arnauld dated October 6, 1687, Leibniz explains why it is that human souls, unlike lesser substances, must possess the psychological characteristics which make them eligible for moral responsibility: "It is this universal society or republic of spirits under this sovereign monarch which is the noblest part of the universe, composed of so many little gods under this one great God; for, it can be said that created spirits differ from God only in degree, only as the finite differs from the infinite, and it can truly be said that the whole universe has been made only to contribute to the beautifying and to the happiness of God. This is why ... it must be that spirits keep their personalities and their moral qualities so that the city of God shall lose no member and they must in particular preserve some sort of memory or consciousness or the power to know what they are, upon which depends all their morality, penalties, chastisements. Consequently they must be exempt from those transformations of the universe which would render them unrecognizable to themselves and, morally speaking, would make another person of them. For animal substances, however, it is enough if they remain as the same individuals in the metaphysical sense, while they are subjected to all imaginable changes because they are without conscience or reflection"22.

With regard to this passage, there are two points which I want to note, and two questions which I want to raise. The first point is that Leibniz once again seem to assume (although he does not explicitly claim) that all and only individual human substances possess moral identity, and that they possess it at all times. Yet, as we have already seen, Leibniz concedes elsewhere that it is not the case that all such substances possess moral identity, for it is not the case that all such substances are "exempt from those transformations of the universe which ... render them unrecognizable to themselves and, morally speaking, ... make another person of them". Thus it is not the case that all human substances always possess moral identity. The first question I want to raise is whether only such substances possess moral identity; is metaphysical identity a necessary condition of moral identity? The second point is that although substantial identity is what is important from a metaphysical point of view, in Leibniz's system, the passage just cited makes it clear that from a theological point of view, moral identity is crucial. Thus the second question I want to raise is what the relative importance of the two kinds of identity is in solving different kinds of problems? 22

DC, pp. 231-232; GP II, p. 125.

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I have, then, queried the relationship between metaphysical and moral identity and their relative importance. We already have some information pertinent to the two questions I have raised, and what more we need can, I believe, be found in Leibniz's commentary on Locke in the New Essays. In responding to Locke's analysis of personal identity, Leibniz makes some crucial concessions. The first concession is made in a passage cited already, in which Leibniz is considering a kind of transmigration of the soul which he believes to be possible but "not for that reason conformed to the order of things" 23. He comments that "The identity of substance would occur therein, but in case there were no connection of memory between the different persons ... there would not be sufficient moral identity to say that it would be one and the same person"24. Here Leibniz admits what we have already seen him to be committed to: that metaphysical identity is not sufficient for moral identity, and that two or more "moral identities" could exist serially in the same substance 25. A second set of crucial concessions is made in response to questions by Locke as to whether moral identity might be found without metaphysical identity. Leibniz makes two important comments in response to this question. The first follows: LA, p. 243; GP V, p. 216. 24 LA, p. 243; GP V, p. 216. Now one might think that in making the comment quoted in this paragraph, Leibniz means only to concede that it is metaphysically possible (non-selfcontradictory) that a human substance possessing metaphysical identity might lack moral identity. Nonetheless, one might suppose him to be saying, this logical possibility is ruled out as a physical possibility by the principle of the best. This suggestion is obviously related to the suggestion considered earlier, that part of what it means to be a human substance (on Leibniz's view) is to possess moral identity. This suggestion fails for the same reason. Although it would make good sense of the passages in which Leibniz seems to be assuming that metaphysical identity and moral identity are coincident in humans, it does not appear to be possible that this is what Leibniz means. For from the discussion in sections I and II, it should be clear that Leibniz admits that some human substances actually do lack characteristics like memory and self-consciousness which are necessary for moral identity. Such cases actually occur, Leibniz concedes. Indeed, as we have seen, he himself says that there are "many examples" (LA, pp. 114-115; GP V, p. 104) of people who suffer losses of memory. Thus he concedes not only that if a human substance lacked certain psychological characteristics, it would lack moral identity, but also that some human substances really do lack these characteristics. Thus he is committed to the view that some human substances actually do lack moral identity, and so he can hardly be claiming (unless one takes him to be unaware of his commitments) that such a possibility is precluded by the principle of the best. Z3

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"It seems that you, sir, hold that this apparent identity [moral identity] could be preserved if there were no real identity [metaphysical identity]. I should think that might perhaps be by the absolute power of God ... If man could be merely a machine and with that have consciousness, it would be necessary to be of your opinion, sir; but I hold that this case is not possible at least not naturally"26.

The second comment occurs later in the same chapter of the New Essays: "I confess that if God caused consciousness to be transferred to other souls, it would be necessary to treat them, according to ethical ideas, as if they were the same; but this would be to disturb the order of things groundlessly ... "27.

In these two passages, Leibniz concedes that it is within God's power to allow moral identity to attach to a mere aggregate of matter, without depending on any human substance, or to allow a mora] identity to cut accross metaphysical lines, with the same continuous moral identity being "transferred" from metaphysical substance to metaphysical substance. God does not in fact do these things because it would offend against the natural and rational order of things. In other words, although it would be logically possible to have moral identity where there was no metaphysical identity, this possibility is ruled out by the principle of the best. Thus we seem to have an answer to the question whether metaphysical identity is a necessary condition of moral identity. It is not a logically necessary condition, but it is a morally necessary condition. For in Leibniz's terms, to say that a logically possible state of affairs is not chosen by God because it would be disorderly just is to say that the non-actuality of that state of affairs is morally necessary. In this case, since the occurence of moral identity without metaphysical identity would be disorderly, metaphysical identity must be a morally necessary condition of moral identity. I want to argue, however, that Leibniz's claim that it would be disorderly (i. e., not for the best) to allow moral identity where there was no metaphysical identity represents an ad hoc application of the principle of the best 28 • It is ad hoc in the following sense. Leibniz 26 LA, p. 246; GP V, pp. 218-219. 27 W, p. 446; GP V, p. 224. This is a slight oversimplification. We have seen that Leibniz concedes two ways in which moral identity might be allowed by God without metaphysical identity. The first is if moral identity were to attach to a machine. This is roughly the thesis of mind-body materialism, and Leibniz does have arguments against materialism (see, on this point, MARGARET D. WILSON, Leibniz and Materialism, in: Canadian Journal of Philosophy, Volume III, Number 4, June, 1974, pp. 495-513). 28

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usually uses the principle of the best to show that actually existing states of affairs are for the best. Since God always chooses the best, any actual state of affairs must be for the best. Here, however, Leibniz's use of the principle is very different. He is confronted with two possibilities: either, (A) moral identity actually can occur without metaphysical identity, or (B) moral identity can never occur without metaphysical identity. Faced with this choice between two logically possible states of affairs, Leibniz simply asserts that (A) would be disorderly and not for the best, and that therefore (B) must be the actual state of affairs. In other words, he argues not from an actual state of affairs to the claim that state of affairs must be best, but rather from the principle of the best to the claim that a particular logically possible state of affairs must be actual. Now making the first kind of argument, from the actuality of a particular state of affairs to its being for the best, does not involve an ad hoc application of the principle of the best. This is so because Leibniz gives independent arguments designed to show that God always chooses for the best, and hence he is entitled to claim that any particular state of affairs must be for the best. The case is quite different for the second kind of argument. When there are two logically possible states of affairs (A) and (B), one and only one of which must be actual, and when we don't know which state of affairs is the actual one, it is an ad hoc application of the principle of the best to claim, in the absence of supporting reasons, that (B) is more orderly (i. e. for the best) and must therefore be the actual state of affairs. It is ad hoc because the principle of the best does not in itself give us a way to decide which of two logically possible states of affairs is the actual one. All it tells us is that whichever of the two states of affairs is the actual one, that state of affairs is for the best. But additional argument is required to show that, for example, (B) is for the best, and hence is the actual state of affairs. Yet it is precisely this kind of ad hoc judgment that Leibniz makes when he claims that moral identity cannot actually occur without metaphysical identity. He claims that the contrary supposition It is the second way, which involves allowing a continuous moral identity to cross substantial borders, that Leibniz rules out only by the ad hoc restriction I discuss. It is obvious that this possibility is the more problematic one for Leibniz, since it seems (unlike the thesis of materialism) to be compatible with the basic principles of Leibnizian metaphysics. To my knowledge he produces no good arguments against it.

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would "disturb the order of things groundlessly", which is to say that it would not be for the best. But this is hardly satisfactory as an argument in defense of the claim that metaphysical identity is necessary for moral identity. For how does Leibniz know that the contrary supposition would "disturb the order of things groundlessly", and would not be for the best? After all, it is frequently not obvious to humans which states of affairs are for the best; witness the surprising fact that on Leibniz's view all actual murders, massacres, and wars are for the best. They do not "disturb the order of things groundlessly". Thus it is hardly safe to assume that what one would expect to be for the best is for the best. The Lord works in strange ways, and so on. Indeed, in the case at hand, what relevant considerations there are would seem to suggest that it is at least as likely that God would find a choice of (A) (allowing moral identity without metaphysical identity) to be for the best as that he would find the contrary, (B), to be more conformed to the order of things. For we have already seen that Leibniz is committed to the truth of the converse of (A): that is, metaphysical identity can occur in a human substance without moral identity. So why is it any more disorderly to allow moral identity without metaphysical identity? If I am right about this, it suggests an answer to our second question as well. For we see that a significant wedge has been driven between metaphysical identity and moral identity in the Leibnizian system. Two or more (moral) persons could exist "in" one (metaphysical) substance. And only an ad hoc application of the principle of the best prevents it from being the case that two or more (metaphysical) substances could "support" one (moral) person. Moreover, for moral, practical, and even theological purposes it is by Leibniz's own account moral identity which is the crucial notion. Thus Leibniz's metaphysical solution to "the problem of personal identity" as defined in part I turns out to be something less than it might once have seemed. It turns out to be the solution to a question about the identity of human substances, but it is of no help at all in solving problems about the endurance of moral personalities over time. On questions of the latter sort, Leibniz resorts to the familiar psychological criteria. Indeed, his solution to "the problem of moral responsibility" as defined in part II turns out to be something more than it might once have seemed. It turns out to be a solution to questions not only of moral responsibility, but also to questions about the identity over time of what, for all moral and practical purposes, we may call persons.

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I should like, in closing, to take very brief issue with a claim which Leibniz makes about the connection between memory and the desirability of living forever. He writes in the Discourse on Metaphysics: "Suppose that some individual could suddenly become King of China on condition, however, of forgetting what he had been, as though being born again, would it not amount to the same practically, or as far as the effects could be perceived, as if the individual were annihilated, and a king of China were the same instant created in his place? The individual would have no reason to desire this" 29.

It is interesting, by the way, to note Leibniz's reaffirmation in this passage of the view that psychological discontinuities could "create" two moral identities "in" one rational substance, and to compare this passage to the one cited earlier in which he attacks Locke for holding that a radical memory lapse could "create" two persons. Here he concedes Locke's point for moral and practical purposes, revealing that his theory of substance - so far from refuting Locke just posits the morally and practically irrelevant endurance of metaphysical identity across moral personalities. This of course supports the evaluation of Leibniz's theory which I have been arguing for, but I wish here to take issue with a different feature of this passage. Leibniz says that a man would have no reason to desire his continued existence as king of China if he would remember none of his previous life. This seems arguable at best, and surely what one would desire in such a case would depend on what one's options were. If it were a choice between continued existence as usual (with memory) or existence as king of China (without memory), then most (but not obviously all) people probably would choose continued existence as usual. But if the choice were between complete annihilation of oneself or existence as king of China (without memory), it would strike me as not at all irrational to prefer the latter. Leibniz seems here to have carelessly overlooked the significance which other psychological continuities can have. If I were given a choice between annihilation or having there exist a king of China with my temperament, outlook, attitudes and even body (if all this could be imagined), I might well prefer the latter, and take comfort from its possibility. Would I have no reason for this preference? I hardly think so; Leibniz seems here to have overestimated the significance of memory relative to the other psychological (and physical) phenomena whose importance he notes elsewhere.

28

OC, p. 58; GP IV, p. 460.

[8] Leibniz, Animals, and Apperception By MARK KULSTAD (HOUSTON, TEXAS) Zusammenfassung Die folgenden Ausfiihrungen gehen der Frage nach, ob Leibniz die Auffassung vertreten hat, dill nur Geister apperzipieren. Die Untersuchung dieser Frage fuhrt zu neuen Einsichten in die Bedeutung des Begriffs der apperceptio, welcher zu den zentralen Begriffen der Leibnischen Philosophie gehort. Der Aufsatz ist in drei Teile gegliedert: 1. die herrschende Meinung, 2. Gegenargumente gegen diese Meinung, 3. die Bedeutung dieser Argumente fur die herrschende Auffassung.

A widely-held belief among contemporary Leibniz scholars is that the author of the system of pre-established harmony ascribes apperception to spirits only, so that while humans may be said to apperceive, animals are denied this ability. There is much to be said for the view, as will be seen later. But to hold it as self-evident or incontestable is questionable, if only because Leibniz seems never to state the view explicitly·. Typically, one supports the view by drawing inferences from various passages, usually taken from more than one work. It is more than just the apparent lack of explicit statements, however, which gives one pause concerning the standard view (as we shall call the thesis set out in the first paragraph). There is also direct and indirect textual evidence which opposes it. Though one does not find such evidence at every turn in Leibniz's writings, enough of it exists so that a number of commentators of an earlier era felt comfortable with interpretations which are, in varying degrees, opposed to the (presentday) standard view2 • 1 The assertion that Leibniz never stated a particular view is, of course, always perilous. The insertion of 'seems' is an acknowledgement of this fact. For some support of the claim from an independent source, see ]. CAPESIUS, Der Apperceptionsbegriff bei Leibniz und dessen Nachfolgem. Eine terminologische Untersuchung (Hermann stadt, 1894), esp. pp. 16-17. I wish to acknowledge the support of the Alexander von Humboldt-Stiftung, whose assistance made it possible for me to do the research and writing for this paper during a year in the Niedersachsische Landesbibliothek in Hannover. Very special thanks are due to my advisor during the year, Dr. Albert Heinekamp. 2 See KARL LANGE, Ober Apperzeption. Eine psychologisch-padagogische Monographie, 7th ed. (Leipzig, 1902), p. 92; ]. CAPESIUS, op. cit., pp.14, 16-17. ANTON STICKER, Die Leibnizschen Begnffe der Perception und Apperception (Bonn, 1900), p. 58; and KURT GRAU, Die Entwicklung des Bewufltseinsbegnffes im XVI!. und XVI!I.

Studi. L (3G c B)(Gx & 0 (x)(Gx c Fx)). It is also worth noting a third form of superveniencc which is usually designated "global supervenience" defined in temlS of possible worlds thus: "The mental globally supervenes on the physic:l1 if and only if :lny two possible world s (of the appropriate grade of possibility) that are physically indistinguish:lble :lrc also mcnt.'lily indistinguishable." 17

It is fairly evident that all of these definitions are compatible with the Leibnizian doctrine of pre-established hannony and thus are compatible with the denial of materialism. It follows that supervenience cannot by itself provide the content of materialism, even of a minimal sort. To put the difficulty bluntly, and in line with me Leibnizian objection we are pursuing, there is no way in me available definitions of supervenience to distinguish between a mental-physical supervenience based on constitution and one based on mere correlation. Although me distinction between constitutive and correlational supervenience is intuitively quite clear, it is difficult to strictly define me difference. However, our problem of me liquidity of water provides a straight-forward example of constitutive supervenience - it is evident that me precise molecular structure of water (between a and 100 degrees at nonnal pressure) bom underlies and makes up me macroscopic porperty of "being wet". Consider now a simple physical situation in which mere is a moving electric charge. A magnetic field is generated, and mere is a supervenience of this magnetic field on me specific characteristics of me moving charge. Yet obviously the moving charge does not constitute me magnetic field but rather, as we would naturally say, causes it. With regard to me mind-body problem, almough mere is no shortage of evidence mat physical states of the brain are correlated wim psychological states, and states of consciousness in particular, there is great difficulty in assimilating this IS Jaegwon Kim: Concepts 0/ Supervenience, in: Philosophy and Phenomenological Research, 45, 1984, p. 163. 16 Ibid., p. 165. 17 For detailed presentation of two fonns of global supervenience see Geoffrey Hellman and Frank Thompson's Physicalism: Ontology, Determination and Reduktion, in: The Journal 0/Philosophy, 72, 1977, pp. 551-64; and John Haugeland's Weak Supervenience, in: American Philosophical Quarterly, 19, 1982, pp. 93-103.

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correlation to the paradigm of constitutive supervenience seemingly demanded by physical resolution. Several modems have belatedly come to agree with Leibniz, perhaps most notably Thomas Nagel 18 but also Colin McGinn l9 , Frank Jackson 20 and William Robinson21 • However, such philosophers diverge on an important point which reveals the lapse for which I accused Leibniz at the outset. It is then time, after pausing briefly to honour Leibniz for his prescience, to consider finally whether his argument fully succeeds or whether a viable position on the phenomena of consciousness remains to the materialist. Leibniz's argument proceeds from the premise of the inexplicability of the relation between matter and consciousness to the conclusion that consciousness is not constituted out of matter or the modes of organization of matter. This general "mode" of argument is endorsed by Leibniz in his fifth letter to Clarke. With respect to the mysterious property of gravity accepted by the Newtonians, he says: "120. That means of communication [i. e. of one massive body with another), says he [Clarke), is invisible, intangible, not mechanical. He might as well have added inexplicable, unintelligible, precarious, groundless and unprecedented. 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." 22

This sort of argument moves from an epistemological premise to an ontological conclusion, a direction of argument which is, I think, deeply disturbing. For what is an explanation? It is, at least, a tale told by humans to other humans whose function is to make some phenomenon intelligible, familiar or expeCted. Thus any explanation must meet several conditions, such as that of intelligibility, which have no bearing whatsoever on ontological matters. If the conditions governing the creation of some phenomenon exceed the grasp of the human mind, then that phenomenon's inexplicability will tell us precisely nothing about its nature. To borrow the example of Thomas NageF3, we could be in a position analogous to the position nine-year olds are with respect to understanding the world. Nine-year olds have certain cognitive limitations which preclude them from understanding (let alone formulating) many of the explanations of natural phenomena propounded by their elders. There may well be aspects of the world to which we will permanently bear an analogous relation - we will never be able to explain them. In fact, it is not hard to find candidate phenomena which appear to meet this condition. Suppose someone reports a mathematical theorem to you, say that one needs no more than four colours to colour a map such that no two adjacent countries share a colour. Of course, this theorem is famous for the central employment of computers in its proof; a computer checked through the 1482 graphs that represent all possible types of map configurations (see Appel and Haken (1978». Such a proof raises certain fundamental questions about mathematical epistemology but perhaps no really new ones (surely the possibility of undetected error was already inherent in mathematical practice). But I am 18 See his famous What is it Like to be a Bat? in: Philosophical Review, 83, 1974, pp. 435-50 or his more recent The View}Tom Nowhere, Oxford (1986). 19 Can We Solve the Mind-Body Problem, in: Mind, 98, 1989, pp. 349-66. 20 Epiphenomenal Qualia, in: Philosophical Quarterly, 32, 1982, pp. 127-36. 21 Brains and People: An Essay on Mentality and Its Causal Conditions, Philadelphia (1988). 22 Ariew and Garber, op. cit., p. 345. [GP VII, 418.) 23 The View From Nowhere, ch. 6.

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more interested in the consequence that although we now know that the four-colour theorem is trUe, in an important sense no one knows why it is trUe, simply because no one can go through all the possible configurations and "see" (in the sense of this term that mathematicians adore) why four colours always suffice. Of course, I am assuming that the computer itself does not understand the proof which is certainly trUe of the computer used for this proof, but - to maintain the requisite open mind on this issue - may not be true of all computers that will be used in mathematics in the future. It may be that this case represents only a difficulty in the explanation rather than a lack of explanation in that it is possible for someone to go through all possible configurations, but it is easy to imagine harder proofs of the same nature. (E. g.the recently reported proof that there are no finite projective planes of order 10 - whatever these are - required 3000 hours on a supercomputer checking some 100 trillion (!) possibilities. Even if you could check one possibility a second and never rested or did anything else, to get through the full list of possibilities would take you considerably more than 4 million years.) Leibniz does seem to recognise that the natural limitations of the finite human intellect will tend to confine our explicative efforts within certain boundaries. For instance, in many places Leibniz stresses the bounds of our imagination as a tool for understanding the world, as in this letter to Johann Bernoulli, in which he attacks the Cartesians: "We shouldn't pause over the Cartesians, who deny that there is anything in bodies analogous to the soul, since they have reason for denying it, nor does it follow that what we can't imagine doesn't exist.a 24

Perhaps, though, the human intellect has no such weakness? Leibniz would never have acceded to such an arrogant proposition. Consider these remarks from his well known reply to Johann Sturm, De Ipsa Natura, which begin with another denigration of imagination, this time as a source of knowledge of the "inherent force" in things, but end by extending the assault to the intellect itself:

"[ .. .Jforce is among those things which are reached, not by the imagination, but by the intellect. And so, when that distinguished gentleman [ ... ] seeks an explanation in terms of the imagination for the way in which an inherent law works [ ... ] I interpret him [0 mean that he wants it to be explained through the intellect [ ... J. Furthermore, if difficulty in explaining things were a reason for rejecting them then something he claims is wrongly imputed to him [ ... ) would follow, namely, that he would rather hold that everything is moved by divine power alone, than admit anything called a nature, of whose nature he is ignorant [ ... J" 2$ Further evidence for Leibniz's acceptance that limitations of the human intellect might preclude discovery of an explanation of some phenomena can be found in Leibniz's theory of scientific methodology as gleaned, mostly, from Elementa Physicae 26 • This can be roughly presented as in the appended chart (see fig. 1)27. Of present interest to us is the method of theoty generation labelled "Pure Discovery" which depends upon the direct deduction of the strUcture of the natural world from the nature of God. Leibniz provides 14 Ariew and Garber, op. cit., p. 168. [Gerhardt, C. I. (ed.) G. W. Leibniz: Mathematische Schrifien (Seven Volumes), Berlin (1849-55) (reprinted by Olms, Hildesheim (1971»; volume 3, p. 546.] 25 Ibid., p. 159. [GP IV, 507 -8.] 26 Loemker, op. cit., p. 277-90. Incidentally, this is Loemker's title; the referee for Studia Leibniliana informs me that the editors of the Academy edition have entitled it Cogitationes de Pbysica Nova instauranda (Vorausedilion, N. 141). 27 The chart is adapted from my The Principle 0/ Continuity and the Evaluation 0/ Theories, in: Dialogue, 20,1981, pp. 485-95.

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Proposed Theories

Discovery

A,B,C,D .. .

Conjectural a priori Hypothetical a posteriori Reasoning from experiments

[A BCD]

Metaphysical Principles

Pure Discovery

Continuity Simplicity Sufficient Reason

pure a priori reasoning from God's nature

etc.

[AC)

- [B D]

-+

rejected as false

Experimental Tests prediction further experimentation etc.

[C D]

rejected as false

[A]

rejected relative to B

[A B] Pragmatic Tests ease of use familiarity

this method is so difficult that it is effectively ulluseable

etc.

[K]

[81

Note : As theories A. to 0 p:tss through the sucn's.sive filters they :l re judged for both truth :tnd empiric:tl :tdequ:tcy. In this ex:tmple, only A and C :tre judged to be even potentially true; B :tnd C :tre 'met:tphysically impossible'. But met:tphysic:tlly impossible theories m:ty be useful nonetheless :tnd they are sent to the next filter, where both C and 0 :tre found wanting for empiric:tl reasons. fmally, only B is really employ:tble or practic:tl, and so it will be used even though it is known to be false. A question remains :tbout A. Could it still be true? fig. 1

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certain examples of this in very limited domains, such as the derivation of Snell's Law of refraction from considerations of how a perfectly ordered universe ought to be constructed. But in general the method of pure discovery is not very useful, and the reasons are significant. Leibniz says that it "does not seem entirely impossible. For our mind is endowed with the concept of perfection, and we know that God works in the most perfect way'. But he goes on to say that this method is "perhaps too long to be covered by men" and "the absolute use of this method is conserved for a better life"28. The implication is quite clear that use of this method strains if not exceeds the powers of the human intellect and Leibniz is well aware that nothing guarantees the success of the other methods (he explicitly compares their use to the solving of cryptograms and allows that hypotheses can attain to a "moral certainty"). This is reinforced when Leibniz continues "yet superior geniuses should enter upon this way, even without hope of arriving at particulars by means of it [ ... )" 29. Finally, consider his treatment of contingency, which absolutely depends upon the distinction between the Divine intellect and the finite intellects who are doomed to the eternal task of approaching the explanation of any contingent truth, while all the while they are guaranteed neverto attain it. Of course, it may be that the particular problem of the relation of the mind to the body does not have a contingent answer. In that case, Leibniz ought to provide us with the demonstration that mind and matter are incompatible rather than beginning with the bare appeal to inexplicability we find in the Monadology. Perhaps Leibniz thinks that he can give such a demonstration through an appeal to the distinction between a substance and mere aggregate. Or maybe he would invoke the principle of activity which enlivens all matter and, as he says, leads us on toward the concept of mind. This path also leads into the labyrinthine heart of Leibniz's metaphysics and I suspect that the ultimate basis for much of that system is something closely akin to the a posteriori mode of justification which is nowadays called "inference to the best explanation". That is, Leibniz would argue that his system ought to be accepted since it can provide an overarching explanation, or at least an outline of such an explanation, for the general structUre of the world, something which other systems cannot provide, or provide so well. This is of course a very serious contention which I cannot argue here, but I will note these remarks of Robert McRae's: "Leibniz's architeCtonic principles [ ... ] have no systematic deduction; they are presented with the a posteriori justification that they have been found to be most useful" 30. Since the role in which such principles reveal their usefulness is that of outlining the limits of possible explanations of phenomena, their acceptance is on the basis of their success at explaining phenomena. However, an obvious difficulty arises if this form of argument i s the fundamental ground of Leibniz's system for it begs the question against the limited intellect view which just accepts inexplicability as occasionally to be expected. If our minds simply cannot grasp how matter can constitute consciousness then there is no ground for accepting inference to the "best" explanation, for there has been no challenge to this explanation from the truth, which is by hypothesis beyond the grasp of human minds. As I suspect that inference to the best explanation is the main ground of Leibniz's system, I think it does fall victim to this reply.

29

Loemker, op. cit., p. 283. Ibid., p. 283.

30

Leibniz: Perception, Apperception and Thought, Toronto (1976), p. 114.

28

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This would not be so if there were no evidence that consciousness must in some way be a physical phenomenon. Then there would be no reason to think that we were hitting up against a limitation of the human intellect rather than an ontological fact when we face the apparent inexplicability of consciousness in physical terms. But the methodology of physical resolution provides a great deal of evidence that human beings are through and through physical creatures and hence that, however mysterious it undoubtedly is, consciousness too must be physicaPI. 31 This paper was originally presented to a conference held at Bishop'S University in Lennoxville, Quebec and 1 would like to thank the participants for helpful comments, and especially the organizers, George Englebretsen and Graeme Hunter, for the opportunity to once again see in Leibniz a prescient outline of current philosophical problems. (I would also like to thank Brigitte Sassen for rendering my abstract in Gennan.)

[11] LEIBNIZ AND THE LOGIC OF LIFE Catherine WILSON

An influential teaching in the history of science is that biology did not exist before 1750, and that there was no concept of "life" before that date which might have justified the establishment of such a branch of study (I). On this view, medicine and natural history, although they concerned themselves with living beings and the phenomena of life, were unaware of any area of intersection or interface, while within each field, for distinctive reasons in each case, the subject-matter was defined without reference to the distinction between organic and inorganic nature. The present paper will argue, through an examination of some of Leibniz's statements vis-a-vis those of his contemporaries, that the available accounts of the absence of biology in the late seventeenth and early eighteenth century are neither entirely accurate nor entirely adequate. The argument will have a preliminary character, for, as Jacques Roger points out in his monumental Les sciences de fa vie dans fa pensee fran~aise du XVIII siecle, no adequate study has ever been made of Leibniz's contribution to the development of the life sciences in France (2). It should nevertheless be possible to throw some further light on the problem of concept-formation in the history

(I) The claim is associated with the name of Foucault; see Michel FOUCAULT, The Order of Things. trans. of Les mots et Ie.\' chases (1971), New York, Vintage, 1973, p. 160ff. See also Fran\ois JACOB, The Logic of Life. trans. of La logiqlle dll vil'llnt (1970), Harmondsworth, Penguin. 1989, p. 71 ff. and J. ROGER, "The living world", in G. ROUSSEAU and R. PORTER, eds., The Ferment of Knowledge. Cambridge, Cambridge University Press, 1980. (2) 2nd ed. Paris, Colin, 1963, p. 461. See, however, the more recent F. DUCHESNEAU, Physiologie des Lllmihes. Empirisme. modell's et tMories, The Hague, Nijhoff, 1982, pp. 65-102, for an extended discussion of the subject.

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of science, and on Leibniz's own positive or negative role with respect to the emergence of biology.

1.

MECHANISM AND THE ALLEGED ABSENCE OF BIOLOGY

The absence of biology has been explained from the medical side as an effect of Cartesianism and the mechanical philosophy, which drew no distinction between plant and animal machines and othcr machines (3). The moderns, it might be argued, in rejecting the tripartite Aristotelian division of souls -the vegetative, the sensitive, and the rational - threw away a sturdy basis for classifying certain things as living, and negated as well the classical distinction between products of art and products of nature. For Descartes, there is a distinction in appearance and mode of origination between "natural bodics" and "artefacts" which enablcs us to tcll automata from animals. Some bodies are seen to move without being moved, to be nourished and reproduce, to come into being without human fabrication. But the ground for these faculties turns out to lie in their possession of mechanical parts too small to be detected by unaided vision or by instruments cunently in use. Descartes claims accordingly that he does not recognize "any difference" between artefacts and natural bodies, except in what pertains to the size of their micromechanisms (4). Phenomena recalcitrant to such explanations, including reproduction, regeneration, resistance to decay and irritability, were certainly noticed and sometimes commented upon as such by natural philosophers. But they were not seen as arguments for vitalism, which, on the received view, was actually a precondition for the emergence of a discipline-sustaining concept of life. Conversely, where a broad challenge to mechanism does manifest itself, as in the work of Cambridge Platonists, it is not based on any precise concept of life. Here we must beware of supposing that references to vital powers and organic structures imply the existence of such a concept. "Organic," in 17th-

(3) S.:e for ex;unple, T. HANKINS, Sciellce dnd Ihe Ellliglllelln/elll , Cambridge, Cambridge Univer~ity Prc~~, IYH5, p. 117. (4) DESCARTES, Principles of Philosophy. IV: 203. tf. in J. COTTINGHAM, R. STOOTHOFF. D. MURDOCH, ed~., The Philosophical Wrilings of Descarles, 2 vals .• Cambridge, Cambridge University Press, 1985. I : 287.

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century writing, seems to function as a kind of synonym for "mechanical", even when the term is used to generate a counter-picture to that of Cartesian mechanism. Nature is not, says Anne Conway, "a mere Organical body like a Clock, wherein there is not a vital Principle of Motion; but a living Body having Life and Sense, which Body is far more sublime than a mere Mechanism, or mechanical Motion." (5) Cudworth glosses Life as "internal energy and selfactivity" - construing it along the lines of Aristotle's physis - but he docs not tic it specifically to plants and animals: rather "there may possibly be ... one Plastick Nature or Life, belonging to the whole Terrestrial (or Terraqueous) Globe, by which all Plants and Vegetables, continuous with it, may be differently formed, according to their different Seeds, as also Minerals and other Bodies framed, ... " (6) In fact, contrary to what might be expected, Neoplatonists and other pan-animists have an overgeneralized, thus less sharp sense of "life" than their opponent Descartes. And it is to the extent that Leibniz follows the Cartesian teaching that he lays the basis for his own concept of the living. His own position is just a modified Cartesianism which rejects vital principles and the Aristotelian physiological soul alike. The vis viva which is an image of a fundamental metaphysical category of action as well as a measurable quantity in physical interactions seems at first to give a vitalistic tinge to his physics as the statements about the omnipresence of life and souls do to his metaphysics. But he upholds the traditional distinction between creatures and products of art by stating it in Cartesian terms. Artefacts, simulacra, or automata can never hc exact, indistinguishahle copies of plants and animals, because no finite craftsman can create an infinitely complex, hierarchically ordered, machine. There is then a sense in which, although we can appreciate that there is only one set of laws of nature which are mechanical and which generate the phenomena of life, we cannot imitate nature and so cannot really understand it. Hence the famous passage in the New System:

(5) Anne CONWAY, Principles of Tile MOST AncienT and Modern Philosophy. tr. and ed. P. Loplson. Nijhoff, The Hague, 19R2, p. 222. (6) "The Digression concerning the Plastick Life of Nature", True inTellectual SySTem. repro in C.A. PATRIDES, The Camhridge PlaTollisTS, Cambridge, Cambridge University Press, 1969, p. 322.

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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 things through not having grand enough ideas of the majesty of nature. They think that the difference between her machines and ours is only that between large and small ... It is necessary to understand that the Machines of nature have a truly infinite number of organs and are so well fortified against all accidents that it is impossible to destroy them. A natural machine remains a machine into all its least parts, and what is more, it always remains the same machine that it was, only being transformed through the different foldings which it undergoes, now extended, now compressed, and like something concentrated when it is thought to be lost (1). Thus indestructibility, real unity, immortality, continuity, and infinite complexity distinguish the natural machine from the machines of art. We now need to ask a philosophical question: does this statement imply that Leibniz has a set of criteria which would enable him to differentiate between all automata and living beings, or to distinguish plants from non-living things? Presumably, we and Leibniz would pick out the same objects as living on any imaginary field-trip. At the same time, it is apparent that he has additional, non reference-fixing beliefs about the metaphysical properties of those objects, which he regards as necessarily theirs. A more difficult question is whether he has a concept of life which would have supported any organized pattern of scientific activity, which could have been, in an institutional sense, discipline-sustaining. It is tempting to argue that his concept of life is not disciplinesustaining on the grounds thaI the characteristics which are necessary accompaniments of life in his view, unity, indestructibility, and so on, are not appropriate for empirical study. But this answer is incomplete. Leibniz's interest in and approval for the researches of Swammerdam, Malpighi and Leeuwenhoek, investigators who - despite their general approval for mechanism - in fact concentrated their observations or researches on characteristics of plants and animals and the analogies between them, suggests that both he and they were biologists de Jacto. This claim needs, however, more defense. As a (7) New SysTem of The Nalllre and CommunicaTioll of Substances, in Pili/osophische Sclmjlen ulld Brie!e, G.P., IV. p. 4112; L.. p. 456.

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first step, it is necessary to reconcile it with another prominent feature of Leibniz's metaphysics: his alleged belief in continuity.

2.

NATURAL HISTORY AND THE ALLEGED ABSENCE OF BIOLOGY

A blocking effect of natural history on biology was also argued for by Foucault, who observed that the idea of a scale of nature, which gave structure to the thought of natural historians, gave only a continuum of forms, not a division into the two realms of the organic and the inorganic (8). Buffon and Robinet furnish the most prominent examples of philosophers who see no gaps in the universe of beings and who, following Locke, argue that the classifications which suit our convenience have no real basis in nature and are arbitrary from her point of view (9). Thus, despite the fact that early eighteenth century natural history classified things as belonging to three main kingdoms, it could draw no fixed boundary between the living and the non-living. At the observational level, a strict and deep distinction between the three kingdoms was difficult to maintain: Foucault is right to suggest that it was not difference. but interconvertibility and analogy which stood out. As Newton sees it, "Eggs grow from insensible magnitudes, and change into Animals; Tadpoles into Frogs; and Worms into Flies. All Birds, beasts and Fishes. Insects, Trees, and other Vegetables, with their several parts, grow out of Water and watry Tinctures and Salts, and by Putrefaction return again in watry Substances. And Water standing a few days in the open Air, yields a Tincture, which ... by standing longer yields a Sediment and a Spirit,

(X) "It is usual to divide things in nature into thrl'l' dasses: minerals. which arc recognized as capable of growth but nol of movement or feeling. vegetables. which arc capable of growth and susceptible to sensation; and animals. which are capable of spontaneous movement. As for life and the threshold it establishes. these can be made to slide from one end of the scale to the other. according to the criteria one adopts." M. FOUCAULT. The Order of Things. p. 160. (9) IIJid .. p. 138ff. Cf. LOCKE. Essay Concerning Hllman Understanding. ed. P.H . Nidditch. Oxford. Clarendon. 1975. Bk III. Ch. 5. in fact the doctrine that categories are "made by the Mind. but very arbitrarily ... without Patterns or reference to any real Existence. applies to names of "mixed modes" not to names of "substances"; but a similar doctrine applies in the latter case; see ibid., III: 6:8. See also F. JACOB, The Logic of Life. p.46f.

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but before Putrefaction is fit Nourishment for Animals and Vegetables." (10) Examples of ambiguity and cross-referencing between the three kingdoms were multiple. Fossils have the shape of ferns or leaves; and these "stony plants" might be confused with corals; mineral solutions make "trees" and grow into stalactites; mineral deposition in the "veins" of mines was impossible to distinguish from mineral growth. Corruption and corrosion, rust and mildew seem to be equivalent processes. Water vapour on the windowpane freezes overnight and assumes the form of a plant: it is uncertain whether we have to do with a trick of nature, a self-citation, a common principle of generation, as Digby