Leibniz's Metaphysics: A Historical and Comparative Study 9781400879571

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STUDIES IN INTELLECTUAL HISTORY A N D THE HISTORY OF PHILOSOPHY General editors: M. A. Stewart and David Fate Norton This is a monograph series whose purpose is to foster improved standards of historical and textual scholarship in the history of philosophy and directly related disciplines. Priority is given to studies which significantly advance our understanding of past thinkers through the careful examination and interpretation of original sources, whether printed or manuscript. Major works and movements in philosophy often reflect interests and concerns characteristic of a particular age and upbringing, and seemingly timeless concepts may vary with the changing background of knowledge and belief which different writers assume in their readers. It is the general editors' assumption that a sensitivity to context not only does not detract from the philosophical interest or rigor of a commentary but is actually essential to it. They wish to encourage studies which present a broad view of a subject's contemporary context, and which make an informative use of philosophical, theological, political, scientific, literary, or other collateral materials, as appropriate to the particular case.

Labia's metaphysics

Other booh in the series Steven M . Nadler Arnauld and the Cartesian philosophy of ideas

Catherine Wilson

Leibniz's metaphysics A historical and comparative study

Princeton University Press Princeton, New Jersey

Copyright © Catherine Wilson 1989 Published by Princeton University Press 41 William Street, Princeton, New Jersey 08450 Library of Congress cataloguing in publication data

Wilson, Catherine. 1951Leibniz's metaphysics: a historical and comparative study/ Catherine Wilson. p.cm. — (Studies in intellectual history and the history of philosophy) Includes bibliographical references. ISBN 0-691-07359-7: $39.50 1. Leibniz. Gottfried Wilhelm. Freiherr von. 1646-1717Contributions in metaphysics. 2. Metaphysics — History — 17th century. I. Title. II. Series. B2599.M7W561989 1KT.92 — dc20 ISBN 0 71902788 8 hardback Printed in Great Britain

89-37831 CIP

Contents

Acknowledgements Abbreuiations Introduction I LAnpage, logic. encyclopedill 1 Erudition and systematization 2 Encyclopedias 3 Kircher, Lull, and the combinatorial art 4 Leibniz and the English language-projectors 5 Computation, thought, and the number characteristic 6 Substance and convention: Hobbes and Locke 7 The combinatorial universe II First philosophy 8 The modems 9 The New Physical Hypothesis 10 The Paris Notes: De summa rerum 11 Minds and their immortality 12 The reality of bodies 13 The confession of a philosopher 14 The continuum and its constituents 15 Leibniz's "system" before the Discourse III TIre Discourse on Metaphysics 16 Descartes and his successors 17 Metaphysics A: individual substance 18 Metaphysics B: matter and form 19 Metaphysics C: phenomenalism and the external world 20 Activity and passivity after Spinoza and Malebranche 21 Fate of the Discourse: Leibniz and Descartes

ix x 1

7 10 15 19 30 34 40 41 45 46

51 58 61 65 70 74

77 79 82 88 98 104 110 114

vi Contents IV Metaphysical foundations for natural science 22 Critique of Cartesian rationalism 23 Critique of physical atomism 24 Forces 25 Nature and natural law

121 122 131 138 145

V Atom, substance, send 26 Cudworth and the "Energy of Nature" 27 Cudworth, Sturm, and impressed forces 28 Teleology and pre-established harmony 29 Monads 30 Monads and matter 31 Souls and bodies 32 Monadic degree: the politics of nature

158 160 165 173 180 190 196 199

VI Leibnas theories of space, motion, and gravity 33 Zenonian reduction 34 Relativity and its consequences 35 Space as constructed from relations 36 Plenitude and gravity

203 204 205 217 224

VII Experience and the self: the New Essays 37 Personal identity 38 Minds and machines 39 Identity and responsibility 40 Moral motivation, powers, and "unease" 41 Knowledge and experience 42 Innateness and mind-writing 43 Theory of invention and self-criticism

234 238 243 249 255 260 264

VIII The problem of theodicy 44 Structural features of the theodicy problem 45 Creation and self-production 46 Malebranche: evil as a by-product of perfection 47 Part-whole relations 48 Perfection and progress 49 Justice and compensation 50 Reception and critique of the Theodicy IX Critical and compensatory metaphysics 51 Descriptive and revisionary metaphysics 52 Recovering the lost sense: Russell 53 Kant as a reader of Leibniz: methodological criticism 54 The pathology of the supersensible

232

268 272 275 281 288 290 293 296 304 307 311 314 320

Contents vii 55 Kant rewrites the Monadology $6 Epilogue

321 329

Works consulted Index

332 345

Take, for example, the rational form of a plant or an animal. If this were only an undifferentiated and not a diversified unity, it would not be a rational form at all, and what resulted would be merely material... So a face is not an undifferentiated mass, but there are nose and eyes, and the nose is not undifferentiated, but one part must be different from another... In the same way, there is also infinity in Mind, because it is at the same time a diversified unity . . . as a shape might contain within its outlines ever more outlines, it holds within it figures and forces and thoughts . . . as the whole living world divides into living beings . . . and these into ever smaller living beings and weaker forces, until it finally stops with indivisible Form. Plotinus, Enneads VI, 7,14.

To my parents

Acknowledgements

The Alexander von Humboldt-Stiftung furnished generous financial support during the writing of this book between 1984 and 1987, and the Research Office of the University of Oregon assisted with a summer grant. Albert Heinekamp of the Leibniz-Archiv in Hannover and Heinrich Schepers of the Leibniz-Forschungsstelle in Munster provided access to archival papers and pre-prints, and Jiirgen MittelstraB kindly made available the resources of the philosophy faculty at the University of Konstanz. My warm thanks are extended to each of them, as to the original readers of the manuscript for Manchester University Press and Princeton University Press and to Roger Fallon for their attention and efforts. My husband, Alexander Ruger, maintained the order of life and lent me the benefits of his expertise, thereby lightening the task immeasurably. Permission to quote and to draw on previously published material is gratefully acknowledged from the following sources: Kluwer Academic Publishers, for passages from G. W. Leibniz, Philosophical Papers and Letters, ed. L. E. Loemker; Cambridge University Press, for New Essays on Human Understanding, ed. J. Bennett and P. Remnant; Abaris Books for Malebranche, Dialogues on Metaphysics, ed. W. Doney; The Journal of Philosophy for the use of my own "Leibnizian Optimism" in vol. 80 (1983); Studies in History and Philosophy of Science, for "Leibniz and Atomism", in vo. 15 (1982); Studia Leibniliana for "De Ispa Natura: Sources of Leibniz's Doctrines of Force, Activity, and Natural Law", in vol. 19 (1987), and University Press of America for material from "The Combinatorial Universe".

Abbreviations

AK

Gottfried Wilhelm Leibniz: Samtliche Schriften und Briefe, ed. Deutsche Akademie der Wissenschaften (Darmstadt and Berlin: AkademieVerlag, 1923-). References are to series and volume. AT Oeuvres de Descartes, ed. J. Adam and P. Tannery, 12 vols (Paris: J. Vrin, 1974-86). CSM The Philosophical Writings of Descartes, tr. J. Cottingham, R. Stoothoff and D. Murdoch, 2 vols (Cambridge: Cambridge University Press, 1984-5). FH Leibniz: Theodicy: Essays on the Goodness of God, the Freedom of Man and the Origin of EmI, ed. A. Farrer, tr. E. M. Huggard (La Salle: Open Court, 1985). G Die Philosophischen Schriften von G. W. Uibniz, ed. C. I. Gerhardt, 7 vols (Berlin, 1875-90; repr. Hildesheim: Olms, 1962). GM G. W. Uibniz: Mathemalische Schriften, ed. C. I. Gerhardt, 7 vols (Berlin and Halle, 1849-63; repr. Hildesheim: Olms, 1962). HR Descartes: Philosophical Works, tr. and ed. E. S. Haldane and G. R. T. Ross, 2nd ed., 2 vols (Cambridge: Cambridge University Press, 1931). L Gottfried Wilhelm Lnbniz: Philosophical Papers and Utters, ed. and tr. L. Loemker, 2nd ed. (Dordrecht: D. Reidel, 1969). LB Leibniz Briefwechsel: as catalogued in E. Bodemann, Der Briefwechsel des Gottfried Wilhelm Leibniz (Hanover, 1889; repr. Hildesheim: Olms, 1966). LH Leibniz Handschriften: as catalogued in E. Bodemann, Die LeibnizHandschriften der Koniglichen offentlichen Bibliothek zu Hannover (Hanover, 1895; repr. Hildesheim: Olms, 1966). LO Malebranche: The Search After Truth, tr. T. M. Lennon and P. J. Olscamp (Columbus: Ohio State University Press, 1975). M Lsilmiz.· Discourse on Metaphysics and Correspondence with Arnauld, tr. G. R. Montgomery (La Salle: Open Court, 1902). MB G. W. Leibniz: Discourse on Metaphysics and Related Writings, fr. and ed. R. N. D. Martin and S. Brown (Manchester and New York: Manchester University Press, 1988). RB Leibniz: NewL·sayson Human Understanding, tr. and ed. P. Remnant and J. Bennett (Cambridge and New York: Cambridge University Press, 1981).

Introduction

Gottfried Wilhelm Leibniz was born in 1646 into an academic family. After showing a precocious talent for languages and poetry in childhood and early youth, he prepared for a legal career at the University of Leipzig. Passed over for a position owing to his lack of experience or to local intrigue, he withdrew to the University of Altdorf, where his talents were better appreciated. But he eventually rejected the offer of a professorship in law there and moved to Nuremberg to become the secretary of a secret chemical society. Meeting by chance - or prearrangement - the Baron von Boineburg, a minister of the Elector of Mainz, at a restaurant table, Leibniz accepted his offer of employment. The decision to earn his living as a cultural and political attache had both advantages and disadvantages. At the beginning of his career, Leibniz was able to move with ease through intellectual circles in Paris, London, Amsterdam, and Rome, and to overcome the deficiencies of his early education. Later, the role of court philosopher and historian drained his energies and compromised his freedom. Metaphysics was only one of Leibniz's interests, representing a small proportion of a ΝαώΙαβ of, according to his secretary, over a million pages. The scope of his occupations is astonishing, even for his own less specialized era, ranging from mathematics, linguistics, jurisprudence, and history to physics, psychology, and theology. His invention of the calculus and his disputes with Newton would have insured his fame in any case. But he is remembered primarily as the author of a curious system according to which the true constituents of the world are souls differentiated by the contents and clarity of their perceptions, each, as it were, alone with God and its own thoughts, but existing in a state of pre-established harmony with all of the rest. Why a theory which is so obviously false, which is

2 Introduction

probably the falsest theory in the history of philosophy, should be the basis of the fame of a great man was a question which Russell, at the beginning of this century, realized demanded an answer. The present study returns to this question, approaching it not by means of an examination of Leibniz's system understood as a collection of theses and principles, but developmentally and thematically. The governing assumption is that what the words of a philosopher removed from us by some three hundred years mean cannot be determined by an internal inspection of his texts. Such a method leaves too much undecided; in some cases it even assigns to the philosopher the opposite of what he intended, through a failure to recognize temporary concessions or those made for the sake of the argument. To resolve these indeterminacies - insofar as this is possible - we must have recourse to the principle of triangulation employed by surveyors, choosing some third object even if its location cannot be precisely fixed - as reference point. What a philosopher means to say can only be grasped in light of the choices actually open to him, and these are defined by his relation to past and present authors. We begin, accordingly, with a look at Leibniz's immersion in a set of studies belonging to some of the more eccentric aspects of the Renaissance, with its interest in codes, cryptography, machines, and logics, and follow him through his early period of confusion and indecisiveness as he learns physics and mathematics and attempts to answer fundamental questions about matter, minds, and motion. Leibniz's first attempt to put down his thoughts in organized form, the so-called Discourse on Metaphysics of 1686, is shown not to constitute a system at all, but a superposition of three independent system-fragments or semi-systems. It is a work both polemical and conciliatory, informed by natural philosophy, logic, and theology in equal measure, but it does not represent Leibniz's final scheme. It is only in the following two decades that the picture presented in the Monadology is worked out piece by piece, as Leibniz discards part of the Discourse and tries to come to terms with the implications of what is left. As is well known, Leibniz described two problems as labyrinths in which the human mind is caught: free-will and the composition of the continuum. As far as the first problem is concerned, my view is that he had no more to say here than any other determinist, though probably also no less. It was the second labyrinth which called forth

Introduction 3

his best efforts. Nearly every question to which he addressed himself was understood by Leibniz as, in one way or another, a version of the continuum problem. The problem may be put quite simply - are there atoms? If there are no atoms, what are things made of? If there are atoms, why is it that these things and not their parts are the atoms? Leibniz's first brush with this puzzle came through his confrontation with Gassendi's atomism and the problem of physical cohesion which it posed. If any extension is in principle divisible, a material atom must be the sum of its parts, held together by some glue or bond. But those parts must in turn be made up of smaller parts held together by some bond, and this to infinity. If there can be no such thing as a particle of infinite smallness, what did God bind together to create extended material objects? Once started on this train of thought in the 1670s, Leibniz finally reached the conclusion that there are atoms, but not material ones, and that matter, time, and space are benign illusions. The continuum cannot be composed; and so without immaterial atoms there would be nothing at all. This solution was then integrated with ideas about substance and perception which originated in entirely unrelated contexts: in logic and grammar, and in Leibniz's encounter with the post-Cartesian philosophy of Malebranche. The general features of this account have been understood since the beginning of the present century. What has not been explored is the relation of this solution to Leibniz's innovations in the theory of science and the philosophy of mind, and to the problematic optimism which furnishes the setting of all of his particular doctrines. For, despite the fact that he had no proper system, Leibniz was a clear, thorough, and coherent thinker. He is important not only on account of what some would consider to be his own excesses, but as a critic of some of the scientific fantasies of his age. The predominant one, which I have been forced to designate by the somewhat barbaric name of theo-mechanism, was represented for Leibniz by the teachings of the French occasionalists and the German philosophers Erhard Weigel and Johann Christian Sturm. Once sensitized to it, Leibniz - originally a theo-mechanist himself - began to detect its presence everywhere, not only in Gassendi, Malebranche, and Descartes, but in Boyle, Locke, and Newton. Each of these philosophers had either argued from problems in the foundations of

4 Introduction

physical science to the existence of God, or had seen God as performing a role in nature which assured its smooth operation despite foundational problems. The scholastic doctrine of continuous creation, which says that the world does not persist but is recreated from moment to moment in a slightly different configuration, is the central prop of this doctrine; it constitutes as well one response to the continuum problem. And the entire apparatus of Leibniz's metaphysics, with its forms, forces, natures, and continuities, is directed against this artifice. Sometimes Leibniz indicates that the overemphasis on divine agency is the first step to skepticism about religious matters and so needs correction. But his true commitment is to the idea of a self-sufficient physics. The actions of an object must follow from its nature; and if the scientific ontology of his day made this impossible, Leibniz was determined to rewrite it from the ground up. Thinking matter, universal attraction, supernatural immortality, arbitrariness in collision mechanics and soul-body relations, moral motivation as a momentary phenomenon - these conceptions serve one by one as the focus of his criticisms. The Leibniz who appears in these pages will be, it is hoped, a mixture of the familiar and the unfamiliar. He emerges as perhaps more of a Platonist, more of a disappointed Anglophile, more Spinoza-haunted than the literature has made him out. Despite his well-known eclecticism, he is correspondingly less apologetic, less reactionary, less keenly interested in reconciling Aristotle with the moderns, or theology with physics. Plotinus is perhaps his closest philosophical relative, both in the fineness of his analysis and in his vision of the hidden and multiple perfections of the world. Leibniz was fascinated by the idea of God, but his theology was, from the point of view of orthodox Augustinian Christianity, dubious. Preestablished harmony is ultimately a replacement for providence, not an extension of it, and Leibniz's theories of creation and of good and evil are too abstract and impersonal to meet orthodox requirements. His contemporaries were a good deal quicker to detect this than the modern commentator. The modern division of everybody into believers and unbelievers has flattened the distinctions and subtleties, the grades of heterodoxy and accommodation, of the late seventeenth century, and pitched Leibniz into the catch-all bin of devout physical scientists where he is required to endure the company of, among others, theo-mechanists.

Introduction 5

Leibniz always insisted on pushing his thinking farther, and this brought him deeper into the labyrinth, not out. He understood in principle that, although science sometimes moves forward by coming to grips with fundamental questions, it sometimes does better to ignore them. But he did not take this as applying to himself. The whole drift of post-Newtonian physical science, based on Newton's scheme of atoms-and-powers and proposing to solve the cohesion problem with short-range attractive forces, was opposed to reason; that it permitted the eighteenth-century chemist to proceed with his work would not have redeemed it in Leibniz's eyes. He knew that the idea of a solid, extended, undifferentiated material atom endowed with powers makes no sense - and indeed it does not. In the last chapter I have tried to address the problem of reading Leibniz in a post-Kantian era. For, when all is said and done, when the considerations which led Leibniz to his view of the world - the acts and moments of his philosophical development - are set out, the reader who does not think of philosophy as just a game of wits, even if it is partly that, must confess to a certain unease. Believing everything we do now, and believing especiaUy that the projection of moral values into physical theory constitutes an illusion, how should we deal with a philosopher who, while offering to separate the world into a kingdom of nature and a kingdom of grace, persists in linking the two together? What, the reader must wonder - particularly when away from desk or lectern, where his concern is to represent the thing in as convincing a light as possible - should he really make of this talk about immaterial living beings and their harmonious co-existence? One answer is that the survival of the Monadology shows us a good deal about the philosophical enterprise itself. This enterprise, except in rare cases, and even in moments of extreme self-consciousness, is always to some extent compensatory. That is to say, it does not describe our world, but the world as it should be. That which we ought not to do may be presented as that which we cannot do; that which is fairly straightforward may be presented as fascinatingly problematic. But in this respect, in its tacit recognition of a gap between ought and is, it is also implicitly critical, and the Monadology furnishes in this sense a model document. The survival of the work cannot however simply be put down to its connection with what Kant always calls the "interests of men",

6 Introduction

nor to its beauty and partial inscrutability as a literary work; as I try to show, the Monadology, like its parent the Discourse, is not one system but an oscillation between two. It has rather to do with the distinctively Leibnizian element of invention: the assemblage of materials left lying about by other philosophers into an edifice with an unmistakable character and style of its own. One might fear that, in proportion as it is successful, historical interpretation tends to reduce a philosopher to the sum of his influences, positive and negative. But every philosopher chooses his influences, deciding to whom he should pay attention and how. And once the borrowed and the adventitious, the inherited distinction and the opportunistic assimilation, have been pared away, only historical analysis is capable of showing the true originality of the subject. A more worrisome danger is that any general study of Leibniz's work runs the risk of prematurity. Much of what Leibniz wrote was not intended for public consumption and thus remains difficult to obtain, to decipher, and, in the absence of a long tradition of commentary, to understand. A study based on the exoteric writings which Leibniz either published or intended to publish cannot, as Russell and Couturat determined, fail to be based on and to promote serious misunderstandings. Since the end of the Second World War there has been a rapid production of new Leibniz texts, editions, and translations, and a surge of associated secondary literature, which have opened up a vast range of new material. Although this delivery of new texts is expected to continue well into the next century, lack of information is no longer the obstacle to productive research; the difficulty lies rather in the attempt to comprehend a vast and specialized literature. Without pretending to completeness, I have tried to balance the desirability of fresh texts against the availability of familiar ones, and to balance the use of Anglo-American secondary sources, typically more exact but often limited in the range of subjects they address, with the generally more subjective but often more penetrating scholarship of French and German commentators. For the ease of the reader, all quotations have been translated into English but can, in most cases, be easily checked against the originals.

I language, logic, encyclopedia

Sometimes a philosopher is struck by an idea which later comes to resemble a tune, once on everyone's lips, which he goes on hearing when the rest of his generation have forgotten it. This is the case with the metaphor of the labyrinth, which Leibniz used first in a conventional way to describe the condition of his era, and then in a particular and personal way to describe what he came to consider the most intractable of philosophical problems: the nature of the continuum, human freedom, and the true estimation of forces. "Considered with respect to the sciences which are directed to achieving our happiness," he writes, in an appeal for help and funds to construct an encyclopedia, "the human race appears to me comparable to a group of people who wander in confusion in the shadows without a guide or an order, without words or other signs for directing their movement... No mortal man is able to light the torch capable of banishing this darkness."1 The sects and their leaders are false flares, incapable of leading this ignorant army out of confusion, of handing it the thread of the labyrinth, of guiding it along the "pure and rippling stream of clear and simple knowledge".2 When Leibniz depicts the world as an intellectual labyrinth and his own philosophy as the thread of Ariadne - the thin, elusive, but also definitive means of escape - he is in all probability remembering Bacon, who, in the Preface to his unfinished Great Instauration, describes the universe as "framed like a labyrinth" to the eye of the human understanding, "presenting as it does on every side so many ambiguities of way, such deceitful resemblances of objects and signs, natures so irregular in their lines, and so knotted and entangled". The 1

Prkeptes pour avanctr les sciences et Its arts, G VII: 157. JWi/., p. 157.

2

8 language, logic, encyclopedia

"clue to the maze" or thread of the labyrinth can only take the form of "a method rightly ordered, which leads by an unbroken route through the woods of experience to the open ground of axioms".3 We observe here the employment of a few of the lavish set of images exemplifying the doomy, prophetic mood of the late Renaissance, the true context of Leibniz's first philosophical efforts. Reformers from the mid-sixteenth to the mid-seventeenth century draw their era as a wasteland, a disordered forest, a city built to no design, a band of men fighting underground in dark caves. They enter upon this scene with a plan: "I come into a forsaken house", van Helmont announces in his anti-scholastic Oriatrike, "to re-melt the dross that is to be swept out by me".4 Bacon sternly admits that "it may be thought a strange and harsh thing that we should at once and with one blow set aside all sciences and all authors ... relying on our own strength".5 Descartes's metaphors of darkness, chaos, wanderers "burning with desire", and urban renewal recur throughout the Rules for the Direction of the Mind and the Discourse on Method. These char-

acterizations, which form part of the established rhetoric of the early years of the scientific revolution, disappear by the end of the seventeenth century; for the "pathos of new beginnings"6 the Enlightenment has no taste and perhaps indeed no use. No one thinks it necessary any more to make a clean sweep, to doubt everything, to cast aside all books and all opinions, to pin the hopes of the world on a single wonderful scheme for mental regimentation. Unlike Bacon and Descartes, who hoped and prophesied but did not experience this transition, Leibniz begins with the suffocated zeal and single-minded obsession of the Renaissance reformer but ends as a radiant announcing angel. The cheerful panoramic expanses of the 3 Bacon, TAe Great lnstauration, Preface, Works, IV:18. Cf. ibid., p. 80. The Book of L. Fromond, Labyrinthus de compositione continui (1631) is often named as Leibniz's source of the metaphor, but Galileo uses the figure in the same connection in The Assayer of 1623 and Two New Sciences of 1638; cf. below, p. 59. On Ochin's description of the problem of free will as a labyrinth, see below p. 71, n. 90. The metaphor is, in any case, widespread and can be found in Comenius, Harvey and Descartes. On its significance for the baroque, see G. Hocke, Die Welt als ^yrinlh, passim. 4 Oriatrike or Physick Refined, p. 28. «Bacon, New Organon, Bk I, §122: Works, IV:108. 'See Blumenberg, Die Lesbarkeil der Well, p. 121, n. 11; and pp. 9lff. Cf. Kamlah, "Der Anfang der Vernunft bei Descartes - autobiographisch und historisch", for a critical view. Descartes, writing in the era of Gilbert, Galileo, and Kepler, among others, exaggerates his intellectual troubles.

Unguage, logic, encyclopedia 9

NewL·saysand the Theodicy impress the reader not only with their problematic metaphysical optimism, but with their justifiable intellectual optimism.7 Observed from the greatest distance at which its characters are still recognizable, this is how Leibniz's career appears to the historian: as a story of the escape from labyrinth and forest into broad fields and clear vistas. This judgement is however dependent on choice of scale, for, moving into the range where its details are visible, the commentator quickly becomes aware that Leibniz's relations to the theories and movements associated with the scientific and epistemological revolutions of the seventeenth century are less than fully clear-cut. If there is a point to classifying him as the rationalist successor of Descartes and Spinoza, it is nevertheless true that Leibniz was Descartes's most inventive and vigorous critic, and that he was not so much influenced as haunted by Spinoza. For these reasons, to begin with Leibniz as a philosopher set down amidst the controversies of modern philosophy, as the reader of Descartes, is to begin too late; it is, moreover, to miss the significance of an intellectual split which Leibniz recognized early in his life between the philosophical projects which had called up his first original efforts and the philosophical problems he encountered later when he left the enclosed world of the German universities for Paris and London. Leibniz was, of course, deeply unhappy about being recalled to Germany in 1676 after four years abroad which had formed him as mathematician and metaphysician. But Paris had held its own disappointments. In a letter written in 1679, he expresses to the Duke of Brunswick his distress at being forced to play two incompatible intellectual roles.8 Here in Germany, he complains, he has no one to talk to about geometry or arithmetic; everyone is mathematically too ignorant. But in Paris no one was interested in the scheme closest to his heart, the invention of a universal language and a reasoning calculus. Leibniz hopes, accordingly, that this distinctively non-Parisian enterprise will be looked upon favorably by the Duke. This letter confirms the suspicion that some of the clues to the origin and development of his metaphysics are tied to Leibniz's 7 Some doubts about Leibniz's relation to the Enlightenment are raised by Schneiders, "Leibniz-Thomasius-Wolff: Die Anfange der Aufklarung". «Letter to John Frederick, 29 March/8 April 1679, AK 1:11:155.

10 Language, logic, encyclopedia

early experiences with certain universalist linguistic, pedagogic, and moral-reform projects, projects associated with a set of names Erhard Weigel, Athanasius Kircher, John Bisterfeld, John Henry Alsted, George Dalgarno - standing outside the main lines of the development of modern philosophy. These philosophers had, in a sense, outlived their own era and could leave few progeny. Leibniz is perhaps their only significant descendant. They were out of touch: if they knew something of the new mechanical philosophy, they did not perceive many of its implications. They were directed towards moral and intellectual improvement, but their slant was esoteric. Kircher was interested in hieroglyphs, codes, Lullism, and thinking machines; Weigel in the application of Pythagorean notions of harmony and proportions to such subjects as economics, law, and morals; Bisterfeld and Alsted devoted themselves to bringing about world-harmony through logic and the systematization of knowledge; Dalgarno to artificial languages. Leibniz's first published treatise, De arte combinatoria of 1666, belongs to this tradition. It is a mathematical work in the Renaissance sense; that is to say, it employs elementary algebraical and numerical procedures, investing these procedures not only with a direct practical importance but one tied to moral and spiritual concerns. Later, Leibniz would all but repudiate the essay, calling it naive and uninformed, which, despite its great interest, it surely is. How far his thinking continued to be governed by the presuppositions of this curious work will nevertheless become clear.

1 Erudition and systematization The metaphors we have noted - forest, labyrinth, city, disordered army - are related to certain distinctive features of intellectual life in the first century-and-a-half of print. If such descriptions did not naturally occur to the medieval man of learning, this was not because the medieval mind was intrinsically orderly, conceiving of all facts, objects, and opinions as assigned a secure niche in a grand cosmological system. As Elizabeth Eisenstein has argued, such explanations confuse cause with effect. The intellectual serenity of the medieval world was an artifact whose character is better explained by the fact that the mechanisms for the transmission of

Erudition and systematization 1 1

knowledge in a scribal era worked effectively to reduce variety and inconsistency.9 With print came confusion and even resentment. A lament repeated from the time of Montaigne - from the beginning of the mass availability of printed literature - is that there are too many books, too many opinions, and that their sheer number and contradictoriness fatigue the reader and accuse the human race of incompetence. The flight from the written word is of course most spectacular in the case of Descartes, who, at first, finding himself placed at "one of the most celebrated schools of Europe", reports that he did not restrict himself to reading what they gave him, but "read everything including what is considered the most rare and curious" which fell into his hands. Disappointed in every field of endeavor, he says, "as soon as my age allowed me to escape the control of my teachers, I forsook entirely the study of letters".10 Leibniz too will adopt the stance of the book-weary in remarks intended for the occasional patron of the sciences, Louis XIV. Surveying all that has been done and written so far, he observes, we find a multitude of "beautiful discoveries", "solid and significant meditations", and "excellent minds" - but on the other side, "so many animosities and disagreements that a revival of barbarism is to be feared". For when so much of certain value can be recovered only with difficulty, he says, men grow cynical and weary and turn away from the search after truth, bored and repelled by "that horrible tower of books which grows higher every day".11 As in the case of the young Descartes, whose college allowed him the special privilege of roaming unrestrictedly through the library, we have to do here with the distinctive pathos of unsatisfied hungers. From his earliest years Leibniz read everything available to him, a habit which, unlike Descartes, he carried over into later life, when, as he cheerfully admitted, he read books, both good and bad, not always with full attention or careful regard for the true intention of the author, but in the hope of turning up something he could use. «See Eisenstein, The Printing Press as an Agent \bil, p. 394.

56 First philosophy

This opens the door to the true distinction between body and mind, which no one has explained heretofore. For every body is a momentary mind, or one lacking recollection, because it does not retain its own conatus and the other contrary one for longer than a moment. For two things are necessary for sensing pleasure or pain - action and reaction, opposition and then harmony ... Hence body lacks memory; it lacks the perception of its own actions and passions; it lacks thought.40 To be a body is to possess an array of instantaneous conatuses; to be a mind is to possess conatuses which endure without passing over into motion. Though Leibniz's theory of the mens momentanea is thus plainly borrowed from Hobbes, it is transformed in Leibniz's hands from the central prop of a materialistic philosophy to another statement in the "confession of nature". "I am struggling with some particular demonstrations on God and the mind", Leibniz writes to Oldenburg in 1671, "in which some marvellous things may be expressed, never uttered before, and yet perhaps conferring no ordinary illumination". 41 His plan, he explains, is to turn conatus theory to a demonstration of immortality; if the mind consists of a set of opposing endeavors each lasting more than a moment, it can never be destroyed by the impact of any other body. For, as Hobbes had shown, interaction can never destroy endeavors but only enhance or mask them. The Theory of Concrete Motion takes up where the first study leaves off. It presents the new physical hypothesis which Leibniz hopes will unify the phenomena of nature without giving offense either to Tychonians or to Copernicans. Leibniz begins with three types of matter: the solar globe, the terrestrial globe, and the intervening aether-filled space. The globes rotate, which preserves their shape, and the rotation of the solar globe produces a daily circulation of a luminous aether. Contact between the earth and aether produces an upward thrust, which Leibniz identifies with elasticity, and a downward thrust, which is gravity. 42 He goes on to give an interesting biblico-chemical account of creation. The aether, hovering over the waters like the spirit of God, "precipitates and sublimates", «°L 141; G IV:230. « Letter to Oldenburg, 11 March 1671: Oldenburg, Correspondence, VII:490f. «Cf. letter to Oldenburg, 29 April 1671: Oldenburg, Correspondence, VIII:26.

The New Physical Hypothesis 57 pervades the interior of everything without which it would be "inert dust, incoherent, dead".43 Next, bullae or corpuscles are formed, which materialize into ordinary particles with solidity and elasticity, which are "the true seeds of things, the fabric of forms,... the basis of bodies, the cause of firmness, the foundation of variety". Collected, figured, and intermingled, they are the ground of all phenomena. From here Leibniz goes on to suggest that he can explain with this apparatus colors, heat, magnetism, sympathies and antipathies, fermentation, explosion, the action of muscles, acid-alkali reactions, and even the chemists' principles of male and female, salt, sulphur, and mercury, "red" and "white".44 Bullae which are exhausted of air are female, alkali, and mercurial, "in the sense of the old chemists", while distended bullae are male, acidic, and sulphuric. Other qualities of bullae, their being ordinary or extraordinary, subtle, dense, soft or firm, correspond to such categories as perfect and imperfect, sterile and fruitful, animal, vegetable and mineral, and so on.45 Substantial forms are not needed, for "forms" are not entities but merely names for the internal structure and external relations of physical things. Nor, in addition to the bullae and their properties, is there a need for any directive principles such as the Paracelsian rector, the archeus of van Helmont, the "radical humor", "alcahest", or "nitric essence" of the chemists. His own theory, Leibniz states, reconciles chemistry and physics, explains impetus, collision, reflection, refraction, vibration, sound, fermentation, fire, and more, and renders all former obscurities clear and intelligible.46 He commends this work to Oldenburg, beseeching him to "dispose those distinguished men (to whom it is dedicated) to think well of this production by an unknown wanderer much preoccupied with other less agreeable studies".47 Oldenburg did his best, and the treatise was favorably regarded by the Royal Society, which agreed to publish both the abstract and concrete works.

"Theoria motus concreti, G IV:183f.; AK VI:II:225f. «Ibid., G IV-.202; AK VI:II:242. "Ibid., G IV:202ff. (cf. G IV:205); AK VI:II:242f. (cf. AK VI:II:245). «liid., G IV:219; AK VI:II:256f. 47 Letter to Oldenburg, 29 April 1671: Oldenburg, Correspondence, VIII:26.

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10 The Paris Notes: De Summa Rerum In the first part of 1673, Leibniz travelled to England, where he met Robert Boyle and other members of the Royal Society. One was the mathematician Pell, who, taking an interest in the young man and noting his naivety, kindly suggested a course of mathematical studies, which Leibniz diligently followed on his return to Paris. He had every reason to be grateful to the Society and especially to Oldenburg, who had not only smoothed the reception of the Hypothesis physica nova but had given him some friendly and excellent advice to the effect that he not attempt to present his design for a perpetual-motion machine to the Society. In Paris, where he remained until 1676, prolonging his stay even after the end of an unsuccessful diplomatic mission, 48 Leibniz made the acquaintance of a number of philosophers and mathematicians, most important among them Huygens and Malebranche. He had already been in contact with Malebranche's rival, Arnauld. Five years after the completion of the Hypothesis physica nova, Leibniz was no longer on firm ground with regard to fundamental physical theory. In the opening sections of the Theory of Abstract Motion, he had stated that a point has a magnitude less than any assignable one but greater than zero; a point is not without parts, but its parts have no distance between them. Points are unextended, but one may be greater than another, as Hobbes had argued by comparing the vertices of two unequal triangles. His analysis, Leibniz had announced to Oldenburg in 1671, "explains the hitherto unresolved difficulties of continuous composition, confirms the geometry of indivisibles and arithmetic of infinitesimals; ... shows that there is nothing in the realm of nature without parts; [and] that the parts of any continuum are in fact infinite". 4 9 These infinitesimal quantities, he thought, could form the fabric of the world, as Cavalieri's purely geometrical analysis indicated; the microscopical observations of Hooke and Kircher suggested to him that they had a physical realization, not simply as the "beginnings and ends" of motion, bodies, and spatial and temporal intervals, but in an infinite descending sequence of animate creatures: "Decay", he says in the «a On its purpose and results, see Aiton, Leibniz: Λ Biography, p. 40; Daville, "Le sejour de Leibniz a Paris" (Part I). 49 Letter to Oldenburg, 29 April 1671: Oldenburg, Correspondence, VIII:26.

Tlte Paris notes: De Summa Rerum 59

Theory of Concrete Motion, "is invasion by worms, dependent on an insensible fructification, ... and the animals in decaying things may be resolved again into still smaller animals and so on into infinity".50 Despite his boast to Oldenburg, Leibniz had not succeeded in resolving the difficulties of the composition of the continuum and in showing the set of qualities he ascribed to his points to be mutually consistent. An ingenious attempt to marry the notion of an infinitely divisible continuum with a theory of infinitesimal atoms had been advanced by Galileo in the Two New Sciences; here Salviati had tried to convince the Aristotelian Simplicio that he should admit that "a continuous quantity is built up out of absolutely indivisible atoms, especially since this method, perhaps better than any other, enables us to avoid many intricate labyrinths, such as cohesion in solids".51 Now Leibniz was no longer sure that this really was the way out of the labyrinth. Could a continuous quantity really be composed out of indivisibles in the mathematical case? If it could not, was matter composed of discrete solid units anyway as the Gassendists held, arguing that the mathematical problem of composing the continuum was irrelevant to the physical case?52 In that case, fluids were really a collection of particles, like flowing sand. Or did matter consist of an infinitely divisible fluid? In that case, particles were actually cohering fluids. Leibniz discusses this problem at some length in the Paris Notes, in a manner which is largely baffling because his conception of "philosophia prima" deliberately blurs the usual distinctions between issues in physics, epistemology, and philosophy of mind. After abandoning his youthful atomism, Leibniz seems to have been drawn towards the theory that fluidity is the basic state of matter and that the apparently solid corpuscles which take part in concrete chemical reactions are somehow derived from it.53 For motion to take place in a plenum, he thought - and Leibniz never admitted a vacuum - every part must be flexible; there can be no 50 Theoria motus concreti, AK VI:II:241; G IV:201. Cf. R. Hooke, Micrographia: or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses, London, 1665. On worms as agents of decay, see Kircher, ScruHnium physico-medicum; on Pascal and Leibniz, see Mahnke, Uneniliche Sphere, p. 26. 51 Galileo, Dialogues, pp. 47ff. On Aristotle's competing theory of points and continua in Physics V, 3, 226b ff., see Feyerabend, "Some Observations on Aristotle's Theory of Mathematics and the Continuum". "See Moll, Derjunge Leibniz, II:182ff. "Rivaud, "Textes inedites", p. 99.

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inflexible, unbreakable, or unbendable solids.54 On the other hand, he worried that if there existed only a continuous fluid, matter would be indistinguishable from space. His solution was to say that matter is both discontinuous and fluid and that God's sustaining activity is required to account for the appearance of solidity. Matter is, he observes first, only apparently continuous, for "taken without a cement" it can be reduced to a state of liquidity or pulverized. There are no parts in matter which are indissolubly cohesive, hence no atoms, yet matter is evidently distinguished from space by the fact that its parts can all be moved relative to one another. Though one might imagine, as Leibniz had earlier suggested to Hobbes, that apparently solid bodies preserve their integrity on account of the internal motions of their parts, he rejected this solution in 1676, returning to a theory of divine concurrence. Solid matter, he now thinks, consists of vortices of fluid particles, but these vortices must probably be sustained by an external source. Matter is "discrete being . . . united by motion or some mind". 55 Every mind, he goes on to speculate, is "implanted indissolubly in certain m a t t e r . . . Every mind has a vortex around it. All the mundane spheres are perhaps endowed with mind". 56 In a meditation set down a few months later, the point of assigning a mind to the vortices is clarified: "Any matter must be accompanied by something that retains the effect of that which precedes; namely a mind". 57 What is interesting about this explanation is that it is linked to a clearly stated version of the principle of variety, which says that there are no two things which are perfectly similar in the sense that they not only have all their properties in common but possess indistinguishable histories. Leibniz allows that two objects, for example two squares, might on the basis of their present appearance be indistinguishable. But something in their history, or in the manner in which they were produced, must differentiate them, and whatever this is must be "remembered" by them. 58 54 Ibid. 55 De arcanis sublimium vel de summa rerum, L 158; AK VI:III:474. The theory of minivortices was probably inspired by Malebranche. 56 Ibid., L 160; AK VI:III:476f. Cf. Aristotle, Physics V, 3, 227a ff. 57 Meditatio de principio individui, AK VI:III:490f. Cf. Parkinson, "Leibniz's De Summa Rerum", p. 138. s*Ibid., AK VI:III:490f.

Minds and their immoriality 61

Despite the plainness of Leibniz's general intentions in showing the dependence of the physical world on mind, all this sounds at first exceedingly obscure. But a good deal of light is again provided by reference back to the Catholic Demonstrations. Here Leibniz had attempted to argue that a "substance" was the union of a body with a mind. The argument was this: Substances are beings which are independent of other substances; a substance can "subsist within itself". Body, however, conceived as pure extension, cannot be considered a substance. For a substance, by definition, is a thing which acts, while an accident or an appearance is something which does not act. But body, considered as extension, has no principle of action within it, for no such body can set itself in motion. Human beings, by contrast, who are minds united to bodies, are substances, for they can act in virtue of the presence of a soul or a "concurring mind" attached to them. So too are ordinary inanimate bodies, but only insofar as they are in union with the "universal mind or God". Bodies not united to some mind are mere accidents or appearances.59 11 Minds and their immoriality A second recrudescence in the Paris Notes from the old Catholic Demonstrations is the set of speculations on the immortality of the soul. Earlier, Leibniz had attempted to construct a proof as follows. If the mind is indivisible and simple, it is immortal, for there is no way for it to be broken up or corrupted. The problem is only to prove that it is indivisible. If thought is awareness that we are sensing or have sensed something, then it is simple. If thinking were, however, just the occurrence of an image in the mind, we would have no grounds for saying that the mind is simple, for such an image itself has parts. But thought is "that 'something I know not what' which we perceive when we perceive that we think".60 This something Leibniz connects with the unity of consciousness. For if sensation were simply a mirroring of the external world, we should have no more reason to suppose that it involved an indivisible unity any more than the 59"On Transsubstantiation", L 116; AK VI:I:509. "The Immortality of the Human Mind Demonstrated in a Continuous Sorites", L 113; AK VH.-493. 60

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existence of a mirror, which, like the images it represents, can be broken into fragments. It is apparent that Leibniz had never believed, as Hobbes clearly had, that the conatus theory satisfactorily established materialism. He had objected to Hobbes in 1670 that the sustained conatus necessary for perception could not occur in nature without a new impress of motion, while the mind was able to keep active on its own. He had used this argument to deny that animals were conscious and to show that Hobbes had not succeeded in explaining human consciousness. "So I fear t h a t . . . we must say that in beasts there is no true sensation but only an apparent one . . . [just as there is no] pain in boiling water; and that true sensation such as we experience in ourselves cannot be explained by the motion of bodies alone". 61 The contrast between the unity, hence indestructibility, of the mind itself and of any machine which serves merely as a holder for a thought, is the theme of another section of the Paris Notes: intellectual memory consists not in what we sense but in that we sense - that we are those who sense. This is what we commonly call identity. This faculty in us is independent of externals. I do not see how a man or a mind can die or be extinguished while these reflections last... This sense of one's particular self is without other characters ... If this is the nature of mind, and it consists in the perception of itself, I do not see how it ever can be impeded or destroyed ... because the identity of the mind is not destroyed by any modifications and therefore is not destroyed by anything 62 The claim that this sense of self is immediate suggests that consciousness cannot consist in the Cartesian reading-off of brain traces. The notion that perception was something of the sort was already a problem for Descartes, who posited a consistent correlation, except in the case of "pure thought", between brain traces and experiences. But when thought was self-referential, it was paradoxical to suppose it was effected either by means of brain traces or without them. "By means of what traces should the [separated, Cartesian] soul remember that it existed and thought?", Leibniz asks accordingly.63 By means of what traces should even the embodied 61

Letter to Hobbes, 23 July 1670, L 107; G VII:574. De veritatibus, L 162 (my emphases); AK VI:III:509. On personality and immortality, see M. Wilson, "Leibniz: Self-consciousness and immortality". ""Zu Simon Fouchers Reponse", AK VI:III:319. 62

Minds and lheir immonality 63

soul, one might add, remember that it has thought, or think about its own thinking? It may well be, Leibniz realized, that I have a brain trace corresponding to my visual image of a certain perceptual manifold before me. But my awareness that I have this image is something distinct from this image. The hierarchical, recursive, and (Leibniz thinks) potentially infinite possibility of thinking-aboutwhat-one-has-been-thinking implies a machine of infinite complexity, containing an infinity of traces. To be sure, Leibniz will later argue that we are precisely such infinite, hence unmanufacturable and also immortal machines, containing both readable and illegible traces to infinity. In 1676, however, he has no basis for maintaining the immortality of organisms or organized machines; his arguments for personal immortality are drawn from observations on the experience of thinking alone. He is specifically concerned with criticizing Spinoza's claim that the mind is the "idea" of the body and loses its individuality with the destruction of the body.64 Leibniz had believed at the time of the Hypothesis physica nova that the true distinction between mind and body was explained by the distinction between momentary and persisting conatus without motion. At the same time, even in the moments when he insisted that persisting conatus itself requires the help of some extra-material principle, he was never drawn towards the Cartesian theory of an immaterial substance united with a material body and particularly closely united with the pineal gland. Instead, he at first treated the mind as another of the indivisibilia·. a point without parts, possessing a location but no dimensions. For if the mind has no location, he argued, it cannot have a sensory perspective, while if it is larger than a point "it is then a body and has parts among parts". But let the mind consist in a point, he says, "and it will be indivisible and indestructible, and from this will follow the truths of religion, providence, immortality, divinity, justice, predestination, and so on". 65 Just as all rays meet at a focus, so all visual, tactual, and auditory impressions from the nerves must converge at a point. This point-soul has a corporeal analogue, the "kernel", a notion perhaps derived from the chemical literature. "Cf. Spinoza, Ethics, Pt II, Prop. 16: tr. Curley, 1:463; pt V, Props. 21, 23: Curley, 1:607. «Letter to John Frederick, 21 May 1671, G 1:53; AK 1:11:108.

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My opinion is that every body, human as well as animal, vegetable, and mineral, has a kernel of its substance which is distinct from caput moriuum, as the chemists call it, from terra damnata and from phlegm. This kernel is so subtle that it remains in the ashes of the thing when it is burned and can draw itself into an invisible center. Thus one may use the ashes of plants for seeding; and in the fetus or fruit of the animal, the punctum saliens comprises this kernel of the whole body in itself.66 If a man is devoured by a beast, this kernel remains unassimilated; if he loses an arm, the kernel nevertheless retains a trace of it, and this explains his phantom sensations. Thus the kernel is a material, extended, reduced form of the body to which the point-soul has a particularly intimate relation. This geometrical analogy was revived again when Leibniz turned his attention in Paris to the disputed Cartesian theory of perception, which proposed that "corporeal images" on the surface of the brain are received by the mind as forms. This he found obscure. How can modifications in extension be received by the unextended mind? The connection cannot be a causal one; the best that can be said, he observes, is that there is some "rapport" between extended and unextended things. The arc of a circle is not identical with or caused by the angle, but is a measure of it. 67 The point may in this sense contain an "image" of the whole. Difficult though it is to summarize Leibniz's reflections on mind, matter, and motion through the end of the Paris period, several features stand out. We observe in the first instance the extreme distance separating Leibniz's theories from Descartes's; Leibniz shows a consistent preference for an Aristotelian conception of substance as a composite of matter and form, or matter and determining mind. Though he follows Hobbes's pioneering efforts to explain mental concepts by reference to physical minima, or the minima of movement and action, he becomes fully aware of the limitations of this approach. Like Hobbes, though, he is looking for an integrated theory of mind and physical activity. The Cartesian distinction between the subject-matters of natural philosophy and metaphysics mental substance and physical substance considered in isolation - and the subject-matter of ethics and psychology - the mind-body "Ibid., G I:53f.; AK I:!I:10Sf. ""Zu Simon Fouchers Roponse". AK VI:III:314.

The reality of bodies 65

composite, known through experience, but not metaphysically explicable - is foreign to him. 12 The reality of bodies

As we have noted, Leibniz held early on that body or extended matter without a concurring mind, either God's or the individual human mind, would be an accident or an appearance. Hallucinations are examples of such accidents or mere appearances. Their trademark is their ineffectuality: the hallucinated object is simply a modification of the mind, with no power to act. An hallucinated object offers no tactual resistance (Leibniz does not consider the case of tactual hallucinations, which would have undermined this theory), and this provides the grounds for saying it is unreal. These reflections draw on the problematic so clearly developed by Descartes and at issue in Paris during Leibniz's visit. Why should an experiencing subject suppose that in addition to appearances modifications of his own substance - there exist any other substances? To move beyond solipsism, Descartes reasoned, one needs to reflect on the causes of these appearances. It is true that I have a strong propensity to believe that these appearances in me are produced by a substance or substances outside of me. But this is no proof. There are three possibilities: I produce them myself; God or a demon produces them directly; or some substance or substances distinct from God, demon, and myself produces them. Following the well-known route, Descartes arrives at the conclusion that extended substance exists and is the cause of the appearances in him, with himself and God, but no demon, playing a supplementary role in the production of ideas.68 Leibniz's solution is a variant of this one. "Many things are experienced by me", and not simply "I think", is the true starting point of his epistemology. It is certain that there are appearances in me, he says, "but it does not follow that there are as many substances outside of me as there seem to be causes of these experiences, that is, just as many bodies. In no way can it be proved through natural reason that there are divisible or corporeal substances". 69 However, 68 "There is certainly further in me a certain passive faculty of perception . . . " Sixth Meditation, AT IX-1:63; HR 1:191; CSM 11:55. 69 Bodemann, Die Uibniz-Handschriften, p. 89; HoIz, tr., Kleine Schriften, p. 22.

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their variety seems to be an argument for their independence. "If there were nothing but mind, it would be remarkable that so many things are perceived in it". 70 As he writes to Foucher in 1675, we acknowledge that there must be some cause for the variations in our thoughts. On this basis we establish "particular beings or substances to [which] we ascribe some action, that is, from whose change we think that some change follows in us. So we make great strides in fabricating what we call matter or body". 71 At the same time - pushed to it by Foucher's skepticism - Leibniz admits that we cannot know that matter or body exists: all we can affirm with certainty, as he notes in De summa rerum, is that we sense, that we sense in congruence, and that something is the cause of this congruence. Perhaps it is not bodies themselves but God who is the source of the variety which appears to us. "If some invisible power were to take pleasure in giving us dreams that are well tied into our preceding life and in conformity with each other", we should not know it. What, then prevents our life "from being one long wellordered dream, about which we could be undeceived in a moment?" Clearly, we cannot resolve the question experientially: to understand the grounds of our experience, he tells Foucher, would require something like a "beatific vision".72 But, although we may ascribe some action to external things, the facts of perception ultimately lead back to God as the real source of perceptual variety. First, we cannot just suppose that there happen to be bodies which produce perceptions in us and leave it at that. There is no reason in bodies themselves why they should exist. We must conclude on this basis that something which exists necessarily, which is itself the grounds for its own existence and contains within itself "all the conditions of things", brings them into existence. 73 Second, as far as bodies are concerned, Leibniz argues - anticipating Berkeley that to exist means to be experienced. For, except in the case of God, we have no way of grasping the meaning of the term "existence" except by thinking of something sensed. To think of an unsensed body is to think of something which is too small or too far away to be "Parkinson, "Leibniz's De Summa Rerum", p. 139; AK VI:III:518. n Letter to Foucher, 1675, L 153; G:I:372. On Leibniz's relations with the antiCartesian Foucher, See S. Brown, Leibniz, pp. 39ff. " L e t t e r to Foucher, 1675, L 154; G 1:372. Cf. De Summa rerum, AK VI:III:511. " D e exisienlia, in HoIz, tr., Kleine Schriften, p. 17; AK VI:III:587.

The reality of bodies 67

seen, but which could, under the right conditions, be seen. From this premise he concludes that "unless there were a 'first experiencer' who was at the same time the cause of things, nothing would be experienced".74 The crucial difference between Leibniz's theory and Berkeley's is simply this: where Berkeley concludes that the existence of God is sufficient to explain perception without the assumption that there are material things, going so far as to argue that the notion of a material, active substance is a contradiction (and the basis of atheism), Leibniz embraces both arms of his dichotomy. It is here that we find the first traces of his later theory of "active matter", developed in an epistemological context without the help of a theory of physical force. Unable to decide whether being is something other than being perceived, he lays the groundwork of a theory of perception which remains permanently ambiguous on the question of the independent existence of "external" things. The "harmony of things demands", he says, "that there be something in bodies which itself acts".75 At the same time, it is God and God's perceptions which are the "ground of things" and the cause of our experiences. God is both the "aggregate of the requisites of all things" and "a perfect mind existing as a whole in the whole body of the world".76 In order to exist, then, a body must be both active and experienced by God. In one sense, the latter clause adds nothing new, for of course there cannot be any active bodies which God does not see. But it is precisely this clause which enables Leibniz to develop the theory of a harmony of perceptions, and the second theory would now seem to render the first superfluous. (It was for this reason that Malebranche, who held that we see all things in God, was not excessively worried about the difficulty of proving the existence of objects outside of the mind.) Leibniz later thought he had the solution: "matter" is inactive, "substance" is active, and all substances are capable of perceiving. But the difficulty was to fit these assumptions to the problem of the perception of something external. In any case, Leibniz had already begun to develop his ideas about totalities of perceptions in the mid-1670s. In a quite different context he had been struck by the analogy between perception and the •"Ibid., p. 19; AK V1:III:588. 75 Lx. cit. 7 *D« summa rerum, L 158; AK VI:III:474.

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representation of a city from different points of view. In 1671, when he had freed himself from forms and qualities and had determined that sensory qualities were to be explained as arising from their underlying mechanical causes, it struck him that the relation between essence and qualities, in Aristotelian terms, or internal texture and qualities, to use mechanical terms, or between the nature of a thing and its phenomena, to use his own terms, could be described "as the plan of a city, looked down upon from the top of a great tower placed upright in its midst, [which] differs from the almost infinite horizontal perspectives with which it delights the eyes of travellers who aproach it from one direction or another". 77 Though Leibniz only seldom avails himself of the terms, he is employing the distinction used in architectural drawings of the period between "ichnographic", or bird's-eye, and "scenographic", or lateral and perspectival, representation. The same city-image appears again in a note on metaphysics from December 1676. Here, however, the use made of it is different, in accord with the new emphasis on harmony. Leibniz is not attempting to explain the distinction between a thing and its qualities, but between God's mode of perception and our own. It is not in the least doubtful that God understands how we perceive things. If you want to give someone a complete idea of a city, you represent it in a number of different ways. And so God's intellect, which is similar to ours, understands how we know things; or rather, insofar as our intellect is a reflection of his, we may say that God's intellect is similar to ours and that God understands things as we do, with this difference: that he understands them simultaneously in an infinite number of ways, but we only in one.78 From a single ichnographic plan, all possible scenographs can be derived, while the scenographic plan obviously does not permit the derivation of a unique ichnograph. The infinity of scenographs are in this sense already contained in the ichnograph; in another sense they are not reducible to it at all, for every scenograph is different and unique. The analogy between the ichnograph-scenograph relation and the independent-dependent relation between God and particular minds clearly struck Leibniz as most beautiful and appropriate. To ""An Example of Demonstrations about the Nature of Corporeal Things Drawn from Phenomena" L 142; AK VI:1I:304. Cf. letter to Thomasius, L 97; G I:19f. "De menle, AK YI:I1I:400; cf. AK VI:III:523.

The reality of bodies 6 9

say that our particular minds exist in addition to God's is to say that God has judged it conducive to harmony "that there should somewhere be something that understands, i.e. some intellectual mirror or a reduplication of the world".79 That sensations do form a coherent system is evident both from reflection - waking experience permits stable habits and fulfilled expectations; we agree with other people for the most part about what we perceive - and a priori: God would not create an inharmonious totality of perceptions. We are, in a sense, as omniscient as God, for we too perceive the whole city, though not each of its parts with perfect distinctness. "A given mind perceives what happens in the whole world."80 Earlier, Leibniz had come close to actually identifying God not with the cause of the harmony of things, but with the harmony of things itself.81 How far he was prepared to move in this direction in 1676 is difficult to say. The notes in question were written during a period in which Leibniz was receiving information about Spinoza's metaphysics, but before he had actually read the Ethics and before the full implications of Spinoza's identification of God and the creation were impressed upon him and he felt the need to differentiate his own position. Against Spinoza, he asserts indignantly in his notes that "God is not a kind of imaginary metaphysical being, incapable of thought, will, and action as some make him". He must rather be "a definite substance, a person, a mind", who can "feel himself to act upon himself".82 But the language Leibniz employs does not always underwrite the personhood of God in any familiar sense. The origin of things from God, he speculates, is rather like the origin of properties from essences, or like the resolution of a number into all its various modes of factorial expression.83 God is the "subject of all absolute [affirmative] simple forms", while created objects correspond apparently to partial combinations of these simple forms.84 God, the mind of the world, is not a thing but a being. Like Spinoza, moreover, Leibniz denies the existence of miracles in the sense of impromptu deviations from the natural order, so that the thought, will, and "De summa rerum, L 158; AK VI:III:474. Parkinson, "Leibniz's De Summa Rerum", p. 139; AK VI:III:523. "Confessio philosophi, AK VI:ffl:129; Saame, tr., p. 66. »2 De summa rerum, L 158; AK VI:III:474f. 83 De origine rerum exformis, L 164; AK VI:III:518f. **Deformis simplicibus, L 163; AK VI:III:523. 80

70 First philosophy

action ascribed to God do not manifest themselves in divine intervention but in the natural course of things. "God has ordained things from the beginning", he says in the Paris Notes, "and whoever realizes this should be happy and contented".85 13 The confession of a philosopher

This happiness and contentment with things as they are is the moral of Leibniz's Confessio philosophi, a precursor of all the later writings on theodicy. The main interest of the work lies in the fact that it is an exposition of the Leibnizian doctrines of harmony and predestination, based on the principle of sufficient reason,»6 but without the logico-linguistic scaffolding of the Discourse's theory of individual substance. The existence of this essay casts doubt for this reason on Russell's view that the principle of sufficient reason follows from the theory of individual substance, for the latter is still nowhere in sight. The Confessio still operates with an ontology of events conceived of as a series, not with an ontology of individuals conceived of as a collection. This choice explains the fatalistic air attaching to the work despite its optimism, and explains as well why Leibniz was pained and astonished in 1686 to find the Discourse treated as a fatalistic system when the shift in ontology should have forestalled this interpretation. The dialogue, which is generally exploratory rather than polemical, begins with a discussion of the problem of Judas in the New Testament. Sin, it is pointed out, arises from capability and desire, this desire arising in turn from the temperament of the subject and the attraction for him of the object which tempts him. But all these things - desire, temperament, attraction, capability - come from God.87 Why then is God not responsible for sin? Why is it wrong to suppose that he wishes us harm and to hate him accordingly? The general form of answer given is that sin and evil follow not from God's will but from his understanding: "every relation, every proportion, every analogy, every proportionality stems from the nature of God, not his will, or what is the same thing, from the idea "Parkinson, "Leibniz's De Summa Rerum", p. 139; AK VI:III:477. MQmfessio philosophi, AK VI:III:118; Saame, tr., p. 40. "Ibid., AK VI:III:120; Saame, p. 46.

The confession of a philosopher 7 1

of things". 88 The "whole series of things" (tota rerum series) is, or proceeds from, a harmony which originates in the eternal and unchangeable ideas which are in God's understanding. 89 God is the only necessary being: "everything else which proceeds from the harmony of things, or the Existence of God, is itself contingent and only hypothetically necessary, although nothing happens just by chance, and everything according to fate, that is, from a particular reason of Providence". 90 God produces nothing through his will; his eternal and unchangeable ideas bring forth the harmony of things from themselves. If a certain sin had not occurred, the whole order would have been different, including the ultimate reason of that series, God himself. To the objection that this implies that sin is necessary, because it follows from the necessary existence of God, Leibniz provides two answers. The first is a statement of his theory of contingency. Though God's existence is necessary, and although the series of things follows from God's nature, no individual element of the series can be called necessary ioul coun, but only "hypothetically necessary". For none of these events, taken individually, has the ground of its existence within itself. Its negation does not imply a contradiction, though it is true at the same time that, had it not occurred, God's nature would have been different, which is impossible. Thus for Leibniz there are two distinct senses in which an event may be possible. An event is possible in the first sense if its description does not entail any inconsistency. An event is possible in the second sense if it is part of the series consistent with the nature of God. Not all events which are possible in the first sense are possible in the second. And some events which are impossible in the second sense are possible in the first. To be sure, the distinction between logical and hypothetical necessity does not lift the cloud, and Leibniz's second answer is addressed to determinism considered as a psychological, not as a logical, problem: what attitude is it appropriate to adopt towards the contingent, that is, the hypothetically necessary? According to his spokesman in the dialogue, "this inescapable labyrinth arises simply because ordinary language has twisted the words 'necessity', MJW(J., AK VI:ffl:122; Saame, p. 50. *>»«*., AK VI:III:131; Saame, p. 76.

72 F/rrf philosophy

'possibility', 'impossibility', 'will' and 'author' into confusion": there are some words which tend to frighten, disturb, irritate, embitter ... That's how it is if someone says 'Sin is necessary, God is its cause, God wants to damn some people, it was impossible to save Judas ...' and so on. Instead you should say, 'Because God is the ultimate ground of things, the sufficient reason for the universe, and because, from the grounds of the universe, only the most rational things, which are in accord with the highest beauty, that is with the universal harmony, are brought into being, and because it is part of the best chosen harmonies that an extremely confused chaos can suddenly be brought into order, pictures brought out of shadow, harmony made up of dissonances resolved of them ... so it follows that, if you assume God, sin follows'." The moral is that we should not be frightened and disturbed either by the fact of sin or by its predetermined existence. But what is this harmony of which it is a part? In its most general form, we are told, it is "similarity in variety". It begins with dissonant elements, dark shadows, odd numbers, and brings out of them harmonies, pictures, and even numbers. 92 At this point in the dialogue it is conceded that, although the re-normalization of the vocabulary of necessity and possibility may help to give the pessimist a new way of looking at the same facts, the solution to the problem of evil seems to be at the expense of free-will. What good is it to bring sin into harmony with the nature of God if free-will is sacrificed? "What can be made of human liberty", the objector asks, "if it depends on external causes . . . if a fateful chain links together our thoughts no less than the movement and collision of atoms?" 9 3 Leibniz's strategy here is to attack the claim that action depends on external causes. He takes advantage of Aristotle's definition of voluntary action, as that whose origin lies in the actor and not in some force external to him, 94 and defines a "free" action as one which (a) involves choice and (b) is voluntary or spontaneous in the Aristotelian sense: "someone is more spontaneous, the more his action flows from his nature, and the less it is altered from outside; n lbid., AK VI:III:126; Saame, p. 66. The source of the labyrinth metaphor is probably Bernard Ochin (1487-1564), author of labyrinlhus ...at libero et servo arbitrio, de dwina praenotione, destinations el liberate disputatio, Basle, 1561. Ochin promised a way out, but ended up resigned to the impossibility of any rational account of these topics. "Ibid. "Ibid., AK VI:III:132; Saame, p. 80. '4Cf. Aristotle, Nicomachean Ethics, 1110b.

The confession of a philosopher 73

and he is more free the more capacity for choice he has, that is, the more he can think with a pure and calm mind". 95 Free-will is just the "power of acting or refraining from action when all external requisites for the performance of the action are present". These characterizations at first appear to be pure sophistry; we have, after all, no capacity to choose the natures from which our actions flow, and whether we can think with a pure and calm mind depends, in turn, on our natures. Not all decisions taken with a pure and calm mind involve a freedom from external or even internal compulsion: the phenomenology of decision-making does not in any case seem to settle the ontological question. But Leibniz's challenge to his opponent is to explain clearly what he requires, in addition to spontaneity and choice defined in this manner, for the existence of true freedom. The anticipated answer is that it is required not only that the subject be able to do something or refrain from doing it, but that it be possible to say of someone who does the thing in question that it might have turned out that he did not do it, ceteris paribus. But this extra requirement is considered absurd by Leibniz. A power simply to do or refrain from doing something would be the power to act without a motivation, to act gratuituously. There is no reason this should be considered desirable. By 1676, perhaps under the influence of Malebranche, Leibniz began to identify harmony with simplicity and to think of the creation as determined by God's tendency to act, or simply to think, according to principles of maxima and minima. "God", he says in another fragment, acts by the simplest means. For among the infinity of possibilities, a few are the simplest, but the simplest which the most excel. Their reason for being is that there is nothing to determine the others. Just this is harmony; simplicity in multiplicity. In it consists beauty and pleasure. For things to exist is the same as for God to think of them as best or most harmonious.96 God thinks the optimally rich and simple world - our world - into being because it is the only one compatible with his nature.

«Gm/essio philosophi, AK VI:III:133; Saame, p. 82. «De existentia, tr. HoIz, Kleine Schriften, p. 19; AK VI:III:587f.

74 First philosophy 14 The continuum and its constituents

On his way back to Hanover from England in 1676, Leibniz pondered his characteristic and, to pass the time on board ship, composed a dialogue on time, change, and motion. He had been advised by Pell in 1673 to read Gregory of St Vincent, who discusses Zeno's paradoxes, and as soon as he began to study mathematics in earnest, the paradoxes of division were forcibly impressed upon him. In 1675 he discovered the algorithm for the calculus, which makes use of infinitesimal quantities - quantities which are smaller than any which can be assigned, but which are nevertheless something. This discovery naturally led him to wonder whether such quantities had any counterpart in nature, or whether they were simply mathematical fictions. He had for some years been prepared to accept the existence of a real infinite in nature. There exist infinitely many creatures and there is no smallest creature which does not contain smaller creatures within it. And originally he seems to have regarded this hypothesis as consistent with his interpretation of infinitesimal quantities: "Since we see that the hypothesis of infinites and infinitesimals turns out to be consistent in geometry", he notes, "this also increases the probability that it is true", 9 7 i.e. that such objects exist in nature. "The whole labyrinth of the continuum", he writes eagerly, "must be unravelled as soon as possible": We must see whether it can be demonstrated that there is something infinitely small yet not indivisible; from the existence of such a being there follow wonderful things about the infinite; namely if we assume creatures of another, infinitely small world, we will be infinite in comparison with them.98 The problem with this theory was, however, that it was necessary to begin with something continuous - a quantity of matter, a line segment. Then, by applying certain procedures - physical division or magnification in the physical case, the construction of Pascal's shrinking triangle in the mathematical case - one became aware that division proceeded without limit. But how did that continuous

97 De summa rerum, L 159; AK VI:III:475. On the historical background to the composition problem, see Heimsoeth, Atom, Seek, Monade.

•>*Loc. cii.

The continuum and its constituents 75

substance arise in the first place? If all extensa were infinitely divisible, what were they made of? A continuous line, Leibniz recognized, could not be generated from infinitesimals, if these were represented as extensionless points. Here he could employ a number of arguments, the most perspicuous of which involves drawing a line, and then drawing a diagonal which intersects it. New lines can now be dropped from each point on the diagonal to the first line. But the diagonal is clearly longer. How, then, can both lines be composed of the same number of points? Hence the continuum "cannot be either resolved into or constructed out of points".99 If, on the other hand, infinitesimals could not be represented as points, there seemed to be no hope whatsoever of composing the extended line segment from them. One might conclude that the composition of the mathematical continuum was an insoluble problem, but allow that the calculus was nevertheless a success in operation. Its employment was not, after all, dependent on the solution of the composition problem, for, in solving a problem, one begins with a given line segment. Outside the realm of pure mathematics, however, this instrumentalist approach was not very satisfactory. Certain metaphysical problems appear to presuppose a solution to the composition problem, notably the problems of change and motion. The dialogue Pacidius Philalethi begins accordingly with the problem of predication which is discussed in Plato's Phaedo. This puzzle is then perceived to lead rapidly into Zeno's paradoxes and so into the labyrinth of the continuum. How is it possible for something living to die? For what is dead cannot die, but neither can "is dead" be a property of something living. The proposed solution is to treat death and life as contiguous states, with contiguous things defined as those whose boundaries are adjacent, by contrast with continuous things, whose boundaries are the same. But, if their boundaries are merely adjacent, how can a thing leap over from life into death?100 It is quickly perceived by the participants in the dialogue that their problem can be regarded as another case of the basic problem of motion. If motion is the existence of a thing in two successive locations - call them A and B - what happens to the object when it "IbU., AK VI:III:549f. Cf. Aristotle's discussion in Physics V, 4, 228a ff. iooPacidius Philalethi, AK VI:ffl:535.

7 6 First philosophy

has left A but is not yet in B? The hopeful Charinus tries to solve this problem by proposing that successive locations are "points between which no third point can be interposed". From this definition he constructs a picture of time as an aggregate of densely packed moments, space an aggregate of densely packed points. But Pacidius, representing Leibniz himself, points out that this leads them "straight into the labyrinth". If space and time are aggregates of points, they must be aggregates of some number of points. But the case of the expansion of a triangle shows that no body can be assigned a determinate number of points. Leibniz-Pacidius now introduces a theory of continuous phenomena which is greeted by the others as amazing and wonderful. We must think, he says, of matter - and, by implication, space and time - as like a "tunic" or a "shell" which has an infinite number of folds, and within whose folds are folded still more. No matter how small a section of the tunic we examine, we will always find it folded and never flat. Thus bodies are extended and their parts are always extended - there are no non-extended parts and what we call a point is only the assigned end or limit of an extended body. No matter how small a piece of matter is taken, there are always material things to be found within it. Correspondingly, any temporal or spatial interval includes other temporal and spatial intervals within it ad infinitum.101 This theory, he thinks, should end all controversy between atomists and plenists, defenders of the priority of solids and defenders of liquids. But, as he acknowledges, this discovery does not seem to help much with the problem of motion. For if matter, space, and time are truly divisible without end, then an object can never get from A to B without passing through an infinite number of locations and requiring an infinite number of time intervals to do so. Charinus now tries to advance the suggestion that, as points are assigned to the continuum but do not compose it, a body in motion simply jumps from one assigned point to the next. But this, he is made to see, is absurd and leads to an infinite regress of jumps. Perhaps, he now ventures, these leaps are not absurd if we imagine them as infinitely small and as taking an infinitely short time.102 But here Pacidius refuses to follow him. He insists again that infinitely small indivisible temporal and spatial units are not to be employed in i»i Pacidius Philalethi, AK VI:III:555. IM Ibid., AK VI:III:564.

Leibniz's "system" before the Discourse 77

the foundations of physics. "I admit infinitely small times and spaces in geometry", he says, "for the sake of problem-solving. But it is not clear that they can be admitted in nature". 1 0 3 Here, infinitesimals are identified with indivisibles, and a strict separation between the practical tools of mathematics, which have the status of fictions, and the real world of nature is enunciated. The temporary solution to the problem of motion which Leibniz finally arrives at is, however, purely theo-mechanical, a revival of his earlier claim that God recreates a moving body in a series of locations. Here, he gives the theory a "new but beautiful" name - transcreation. 104 A body is annihilated at one assigned point and created at another. It is not the body itself which moves or is moved - indeed there turns out to be no such thing as motion, as it is ordinarily understood. Everyone is happy with this solution, which, it is observed, is not only consistent with perfect mechanism, but at the same time in conformity with the secret wisdom of Hermeticists and Pythagoreans.105 15 Leibniz's "system" before the Discourse

As is plain from the texts already considered, two of Leibniz's main principles, the principle of sufficient reason and the principle of variety, are announced by the late 1670s. The same is true of a number of his major themes - optimism, determinism, creation as the maximization of simplicity and diversity, the insubstantiality of matter without a mental principle, the harmony of perceptions, and the presence of infinite folds-within-folds in nature. The doctrine of contingency as compatible with necessity ex hypothesi has already been defended and two approaches to the problem of freedom articulated. Some fragments from the period point towards the theory of the pre-established harmony of mind and body. "If there were bodies without souls", Leibniz suggests, "everything would be the same: people would talk and write just as when they play".106 The sense of this enigmatic remark appears to be that people would in this case utter words without meaning them; mental activity is an optional accompaniment of speech and motion. i"Cf. his later letter to Bernoulli, 21 February 1699, L 514; GM 111:575. i°4Peri*iis Philalethi, AK VHII:567. io5 ibid., AK νΐ:ΠΙ:571. Perhaps a reference to Weigel? Cf. Ch. V. below, p. 171 f. io6De tnente, tr. HoIz, Kleine Schriften, p. 15.

78 First philosophy

But a philosophy is not constituted simply by themes and principles. One would be hard-pressed to call De summa rerutn or the Confessio philosophi statements of Leibniz's system. There are a number of reasons for skepticism on this score. First, Leibniz has not applied the predicate-in-subject principle, which plays such an important role in his logic, to ontological issues. Second, he has as yet no concept of force distinct from the Cartesian "quantity of motion" on one hand or Hobbes's unmeasurable conatus on the other.107 Third, he shows no awareness at this stage of the philosophical consequences of the relativity of motion, which he learned from Huygens during his Paris studies. Space is still treated as a substance in the Paris Notes; there is only a faint hint that it might be reduced to a set of perceptual relations, but this hint is left unconnected with the facts of relativity. Finally, the occasionalistic resolution of the composition problem in the Pacidius is not Leibniz's final word on the subject. The problem will ultimately lead him to the conclusion that all forms of extension which the mathematical sciences deal with - spatial, temporal, material - are metaphysically unreal, while "substances", which are real, are necessarily unextended. The only means of escape from the labyrinth, Leibniz will ultimately determine, depends upon carrying out the full implications of the break between mathematics and nature and extending it to a break between nature and metaphysics. In mathematics, and in nature, he comes to see, the line - or whole is prior to the part: the point is an imaginary entity given by an imaginary and indeed impossible process, that of carrying out an infinite process of division to a terminus. In metaphysics, however, the point is prior to the whole, for there can be no pluralities if there are no unities. So nature and metaphysics can never coincide: nature must be, at best, an image or appearance of metaphysical reality. But the clear articulation of these points is deferred until the 1690s.

107 Couturat argues that such a blank does not affect his thesis on the somewhat circular grounds that Leibniz's metaphysics has nothing to do with force. The analogy between force and metaphysical activity has for Leibniz, he claims, "only a negative and polemical value". See "Sur la metaphysique de Leibniz" pp. 4Of.

Ill The Discourse on Metaphysics

Leibniz wrote up the treatise later named the Discourse on Metaphysics and in 1686 sent a summary of its contents to the Cartesian Arnauld, to whom he had shown a copy of his Confessio philosophi more than ten years earlier. He was proud of the work and of the lengthy correspondence, mediated by Count Hessen-Rheinfels, which resulted. But he did not choose to publish either the treatise or the correspondence, so that, as far as the wider public was concerned, the Discourse did not exist. There are many theories purporting to explain the origins and intentions of the Discourse: some see it as part of the grand project of the Catholic Demonstrations, as the metaphysics which would furnish the basis of the universal church, and finally reconcile Catholics and Protestants;1 some see it as a sharp, opportunistic attack on the moderns,2 others primarily as a response to Malebranche.3 There is a basis for each of these claims. Above all, the work was a kind of probe, which came back with significant positive and negative results. Leibniz was, at the time of the essay, toying with the idea of becoming a Catholic, simply because the return of Protestants to Catholicism seemed a likelier possibility than an exodus of Catholics to Protestantism, and both Arnauld and Hessen-Rheinfels were eager to win him over. But Arnauld made clear from the start that the opinions expressed in the Discourse could not be tolerated by the Church, and urged him not only to modify them, but to give up 1

Loemker,"A Note on the Origin and Problem of Leibniz's Discourse of 1686", passim. 2 Notably Friedmann in LeibnizrfSpinoza, and to some extent Burgelin, Commenlaire du Discours de metaphysique. 3 Robinet, following a suggestion of Gueroult, in Malebranche et Leibniz, pp. 139ff., and other papers cited in the bibliography.

80 The Discourse on Metaphysics

metaphysical speculation. At first, Leibniz attempted to convince his correspondent that his views were not in the least dangerous and should not be a barrier to his being accepted into the faith. But he was forced in the end to recognize that his theory of individual substance was not the solution to the problems of faith and reason, but an aggravation of them. The Discourse is sometimes described as Leibniz's first coherent exposition of his philosophical system, on the assumption that the New System of the Nature and Communication of Substances of 1695 and the later Monadology are rewritten versions of the same thing. The letter to Burnett of 1697, in which he described himself as having made up his mind about twelve years ago, suggests that he arrived at his views in about 1685 and did not change them thereafter. But it is impossible to take this remark as conclusive. In other letters he admits to being radically undecided about certain basic philosophical issues; to Malebranche he wrote as late as 1700 that his thoughts were not yet fixed in an orderly system. 4 To be sure, many of the same themes are present throughout the sequence of texts: the uniqueness of substances, the harmony of perceptions, God as architect and lawgiver. But the key notion of "individual substance", which is Leibniz's major contribution in the first work, disappears in the second and third. The "metaphysical point" which takes its place in the New System and the "monad" of the Monadology do not mark simply a change in terminology, but a suppression of the logical determinism of the Discourse in favor of a determinism based on dynamical and biological notions. The description of the Discourse as a system is, moreover, somewhat exaggerated. To the reader who approaches it free of presuppositions, the treatise reveals not a single system, but three separate schemes or semi-systems, A, B, and C, seated in the general context of a theory of the nature and perfections of God. Metaphysics A is the theory of individual substance, based, as Russell and Couturat thought, upon Leibniz's logic of descriptions. Metaphysics B is the theory of bodies, or corporeal substances, scholastically inspired but given an extra dimension by Leibniz's theory of the vis viva. Metaphysics C, finally, the theory of the harmony of perceptions and actions, has strong affinities to the system of Malebranche. Further, 4

Letter to Malebranche, VJ January 1700, in Robinet, Malebranche el Leibniz, p. 344.

The Discourse on Metaphysics 81

although C, despite its independent origins, fits together well with A, and although A and B also show points of parallelism, the combination A, B, C ruins the attempt at coherence. Their incompatibility is the source not only of the notorious problem about relations, but of Leibniz's never-to-be-overcome indecision about perception. With good reason, he was unable to decide whether "perceives" is essentially a one-term or a two-term predicate, whether it consists in the modification of a conscious subject or in a relation between the subject and some external thing. The essay was composed at a time when Leibniz had been following with interest, and real or pretended disapproval, the extended quarrel between Arnauld and Malebranche, and he may have thought of himself as able to effect a compromise. In any case, in writing it he drew on his knowledge of Malebranche's Recherche de la verite (1674) and of his Traile de la nature et de la grace (1680). This is

apparent from an inspection of the work: in addition to the sections on perception and causation, section 5, which deals with divine perfection, is clearly Malebranchean in origin; and, in the course of the work, Leibniz addresses other issues of supreme importance to the older philosopher, such as the relation of miracles to laws of nature and the rationality of God's distribution of grace. Why he sent the treatise to Arnauld is a puzzling question, for he had good reason to expect a more favorable response from Malebranche. His earlier connections with Arnauld, his distrust of the mystical tone of Malebranche's writing, and his admiration for the logical acumen of Arnauld seem to have determined what proved to be perhaps the wrong decision. In addition to its promise to reconcile seemingly irreconcilable theological opinions, notably those having to do with the doctrines of election and grace, the work has a pronounced polemical intention. This is already apparent at section 2, in which Leibniz attacks those who claim that "there is in the works of God no goodness, or that the principles of goodness and beauty are arbitrary". And this polemical aspect helps to explain both the inclusion of and the curious split between metaphysics A and B. Leibniz's separate treatment of the topics of individual and corporeal substance corresponds in part to the traditional way of thinking about the creation: God creates both human souls and a world full of substances for them to experience. But this division also allows him to attack two fundamental doctrines

82 TAe Discourse on Metaphysics

of his modern opponents, Spinoza, Hobbes, Descartes, and their followers. To Spinoza's theory of the necessity and moral indifference of all events occurring in the world and all human actions, he will oppose his theory of contingency and divine choice. To Descartes's theory of matter as extension in three dimensions, he will oppose his theory of substantial forms. As he explains in an undated note: The disciples of Hobbes and Spinoza ... give out that good and evil pertain only to our judgements and are chimerical in the nature of things, and also that every possible good or evil can happen equally and indifferently without nature or God taking an interest... but we have established the foundations which destroy such a pernicious error in making clear that not all possibles can happen ... and that there are everywhere marks of order, choice and intelligence ... The artifice of God in the construction of the universe does not only exclude the void and atoms, but also every purely material substance, and every modification which consists only in figures and movements.5 The Discourse is thus firmly anchored in the controversies engendered by Cartesianism in its various lines of development. 16 Descartes and his successors

When Leibniz arrived in Paris in 1672, he had never studied Descartes's algebra, which he considered "too difficult"; he already owned a copy of Descartes's Opera Philosophica, but had given up on it. His progress in mathematics rapidly equipped him to reapproach the Geometry, and made this necessary if he wished to take his analytical work further. After his discovery of the calculus in 1675, he could rightly regard himself as having gone far beyond Descartes's own mathematical limits. And from about 1677 opposition to Descartes, nourished perhaps by a sense of mathematical superiority, became a focus of his intellectual organization. 6 At this time, Cartesianism, which had been a scandal in the first decade after Descartes's death, unleashing condemnations and prohibitions in Holland, Sweden, France, and Italy in the 1660s, was only gradually on its way to becoming acceptable and even orthodox 5

Bodemann, Die Leibniz-Handschriflen, pp. 62f. See the comments of Gerhardt, G 1:266.

6

Descartes and his successors 8 3

doctrine. 7 Originally, it had mainly signified adherence to such doctrines as the reduction of matter to pure extension, the universal applicability of mechanical explanations, the banishment of souls and forms from nature, and the existence of a God who, as Pascal put it, only gave a fillip to set the machine of the world in motion and then withdrew. It was this side of Descartes which had inspired Spinoza. But by emphasizing other Cartesian themes one could equally well develop a spiritualized form of the doctrine, and by the end of the century, thanks largely to the efforts of Malebranche, it had been transformed. It now came to signify the irreducibility of thought to a mechanical process, and the possibility of rationally demonstrating the existence of God and a future life. The same institutions which had been shocked by the doctrine to begin with (the Jesuits, for example, whom Descartes could not succeed in winning over during his lifetime) were eager, after the start of the new century, to turn him against the new threat of Locke's sensationalism. 8 Leibniz's own reception of Descartes follows a similar general pattern. The picture is nevertheless complicated by his strong ambivalence, and by his often varying assessment of the two philosophers who, on the face of it, had drawn such different conclusions from Descartes's premises. During his Paris stay, Leibniz actively sought out the Cartesian ΝαεΜαβ and was permitted by Clerselier, Descartes's executor, to copy out long passages from it, which he did with evident fascination. He was able to read the Rules for the Direction of the Mind in manuscript, along with the mystical-visionary Olympics. As a result, he could base his Descartes-critique as much on this inside information as on the published works. He quickly worked out a plan of attack. He would reveal Descartes as an unscrupulous man, an arch-deceiver, one who had pretended to pious thoughts but who had "fooled the world with agreeable words whose sense he corrupted, as he did with the 9 'existence of God' and the 'immortality of the soul' ". "I am careful not to say absolutely that [Descartes's doctrines] lead to atheism", he tells his young correspondent "Phillip", "but there are some suspect 10 things". In 1679 he singled out two doctrines as especially 7 Heilbron, Electricity in the 17th and 18th Centuries, p. 39. See also Dijksterhuis rf «/., eds, Descartes et Ie cartesianisme hollandais. 8 Spink, French Free-Thought, p. 239. «Letter to Molanus, c. 1679, G IV:300. 1 O Letter to Phillip, 1679, G IV:279.

84 The Discourse on Metaphysics pernicious. The first was that eternal truths depend on the will of God; the second, that matter takes on all forms of which it is capable in the course of time. The former claim, he says, is inconsistent with Descartes's belief in the certainty of what is perceived clearly and distinctly. But Descartes uses it nevertheless to try to prove that science does not need to take into account God's wisdom or purpose, but only to determine what he has actually willed. The second doctrine was one Leibniz returned to over and over, recognizing it for the face-saving maneuver it was. Descartes had wished to show that, even if the details of his cosmological theory were in fact false, matter set in motion and left to itself was capable of eventually producing the world as we see it, given any set of laws whatsoever. This stance, Leibniz rightly perceived, makes nonsense of the idea of physical law. To assert that all possibilities are eventually realized is to conceive of the unfolding of the world over time on analogy with successive throws of a set of dice. Furthermore, if the principle were true, it would follow, he thinks, that "there is nothing so absurd or bizarre and contrary to what we call justice that it has not happened and will not happen"." If everything which can happen does, nothing can be lawful or exceptional, good or bad. Descartes, he charges accordingly, destroys justice and wisdom, or understanding and will, leaving only a certain "limited power from which everything emanates, which deserves rather the name of nature than of God". He reads Descartes as having thought, but not said aloud, what Spinoza said openly. 12 Spinoza was of course the bete noire of the 1670s and 1680s; unlike Descartes he was not successfully rehabilitated until much later in the following century when, on better information, it was determined that he was not a hard-boiled materialist after all but a kind of pantheist. In the period in question, he was little read and less understood. His name, brought into the public eye in a book on radical sectarian movements in Holland by an adventurer named Stouppe in 1673, 13 came to stand for a package of morally and politically dangerous and repulsive doctrines. Though the purpose of "Letter to Phillip, January 1680, G IV:283. 11 IUd. See also Friedmann, Leibniz et Spinoza, pp. 117((. 13 Spink, French Free-Thought, p. 238. See also Jones, Spiritual Reformers, pp. llOff., on Spinoza's connection with the "Collegiants", a group combining Cartesian principles with Quakeristic ones.

Descartes and his successors 8 5

his Tractatus Theologico-Politicus was ostensibly to introduce a new form of biblical hermeneutics and to plead for liberty of conscience, the doctrine not inaccurately extracted from the work was that religion was a political tool for control of the mob and could be transcended by the philosopher. When the Ethics appeared after his death, the full extent of Spinoza's unorthodoxy became apparent, Spinoza did not distinguish between God and creation; God was the only substance, creatures his modes. He was a determinist in the physical and psychological realms; he denied personal immortality; his ethics was unchristian, half stoical, half eudaemonistic. Both Arnauld and Malebranche, whatever their disagreements, knew enough about Spinoza to know that they detested him and that his doctrines were false, without wishing or needing to read him. Malebranche reported that he had tried, but could not get past the first few pages. 14 Leibniz's response was entirely different and shows a curious parallel with his behavior towards Hobbes. Describing the Tractatus elsewhere as a "disgusting book" (though he had not yet read it), he promptly attempted to get in touch with its author, initiating a correspondence which he tried to keep secret by using messengers rather than the public post. 15 He offered to send Spinoza a copy of the Hypothesis physica nova, a gesture which called forth the corresponding offer of the Tractatus. He read the Tractatus in 1675-76 and annotated it carefully, without evident signs of alarm. In Paris he attempted to dig out from the mathematician Tschirnhaus, Spinoza's countryman, information about the unpublished Ethics.16 It was Spinoza who, given Leibniz's position as political attache and official defender of a Christian philosophy, was mistrustful; he cautioned Tschirnhaus to find out more about the intentions of his new friend - allegedly an admirer of the Tractatus - before revealing any information. Finally, on his way back from Paris to Hanover in 1676, "Spink, trench Free-Thought, pp. 238, 26Of. 15 Letter to Spinoza, 5 October 1671, in Spinoza, Opera, 11:177-8. Spinoza answered this letter, but the rest of the correspondence has been lost. 16 See G. Schuller, letter to Spinoza, 14 November 1675, in Spinoza, Opera, 11:235. Tschirnhaus wrote to Spinoza's amanuensis Schuller with lavish praise for Leibniz's moral and mental qualities. "Then he gets to the point", Schuller reported to Spinoza. "Leibniz deserves to see your book, which Tschirnhaus has told him nothing about. This Leibniz is a great admirer of the Tractatus Theologico-Politicus and once wrote you a letter about it, as you might remember".

86 The Discourse on Metaphysics Leibniz took a detour through England, where he remained only a week, perhaps to gain information from Oldenburg, an old correspondent of Spinoza's, before departing to spend four weeks in Amsterdam. How much time was spent with Spinoza himself, how much with his disciples, is not clear, but the two philosophers met each other at least once. Later, Leibniz said that he had forgotten most of the encounter, but he recalled that he had managed to show Spinoza his proof for the existence of God and to explain to him the falsity of Descartes's laws of motion. 17 The evidence is that he did not win from Spinoza the recognition that he hoped for and felt he deserved. Spinoza died in 1677, and his Opera Posthuma were published in January 1678. Leibniz received, read, and annotated a copy immediately, his hungry pursuit of the philosopher finally satisfied. But although his judgements immediately after Spinoza's death were balanced and moderate - he reported that he found many good thoughts, many opinions conformable with his own, these mainly on the passions - he now claimed to find the main propositions of the work unproved and dangerous. 18 Over time, his criticisms of Spinoza, like his criticisms of Descartes, became hardened into formula. But this did not reflect a settled mind. Spinoza was, in a sense, Leibniz's ghost. He was what Leibniz was afraid of being and saw himself as dangerously capable of becoming; the doctrine that God was in some way related to creatures as a whole to its parts, not as an extra item, was one which obsessed him. "If there had been no monads", he wrote to Bourguet once, "Spinoza would have been right". 19 The influence of this spectre, its demand to be exorcized, was so strong that in the NewL·saysLeibniz's spokesman Theophilus indicates that he had earlier fallen into the error of Spinozism, conceiving God as a pure power, before being saved by the New System, which also inspired him to change his name. There is some truth in this self-description, which is nevertheless mainly rhetorical. For as soon as he realized all of what Spinoza stood for, he was eager to dissociate himself. It was before he understood the doctrine fully, 17

Freudenthal, Spinoza, 11:270. See also Friedmann, Uibniz et Spinoza, p. 79. Letter to Justel, 4 February 1678, quoted in L. Stein, "Zwei ungedruckte Briefe", pp. 72f. "Letter to Bourguet, December 1714, G 111:575. 18

Descartes and his successors 87

when he was still dependent on Tschirnhaus's second-hand account, that its attractions sank in. The most superficial examination of the Ethics makes clear what Leibniz found fascinating and repellent. First, though Spinoza evidently regretted his open identification of God and created nature in the Tractatus, he stood by his claim that God is the immanent and not the transitive cause of the world.20 He goes on to say that there is nothing contingent in nature, "but all things have been derived from the necessity of the divine nature to exist and to produce an effect in a certain way". 21 God's intellect and will, assuming it is possible to speak of these things, can be nothing like ours: his and ours are no more similar to one another than the barking animal and the constellation called "the Dog", which simply share a name. 22 It is absurd to say that God does things for the sake of the good, or that there is any perfection or imperfection in his creation: "If God had willed it he could have brought it about that what is now the greatest perfection would have been the greatest imperfection and conversely God's power is his essence itself."23 Good and evil, Spinoza goes on to show, are subjective determina­ tions denoting only our assessment of the usefulness or impeding nature of a thing. 24 Guilt and remorse are thus feelings based in illusion, good for the masses but inappropriate for the philosopher; "he who repents what he has done is twice wretched", for he could not have done otherwise.25 Contingency and possibility denote nothing more than defects of our knowledge. "I have shown more clearly than the noon light", Spinoza announces, "that there is absolutely nothing on account of which [things] can be called contingent ... a thing's existence follows necessarily either from its essence and definition or from a given efficient cause".26 There are no non-existing essences, nothing which is only an idea in the mind of God but does not exist; the idea of the thing and the actual thing are the same, one considered under the attribute of thought, the "Letter to Oldenburg, G 1:129. Cf. Spinoza, Ethics, Pt L Prop. 18: Curley, 1:428. 2i EfAics, Pt I, Prop. 29: Curley, 1:433. "Jimi., Pt I, Prop. 17: Curley, 1:427. "Ibid., Pt I, Props. 33, 34: Curley, I:438f. 2«/ω., Pt IV, Defs 1, 2: Curley, 1:546. "Ibid., Pt IV, Prop. 54: Curley, 1:576. "•Ibid., Pt I, Prop. 33: Curley, 1:436.

88 The Discourse on Metaphysics other of extension.27 The effect of these prescriptions is both to display God as a pure power and at the same time to remove all traces of transcendence. Spinoza recognizes a necessitarianism on two levels. Everything which does happen must happen; and nothing which does not happen could happen. Human life is finite, brief, and limited by externals. "We are acted on insofar as we are a part of nature", he says; most of what happens to us "cannot be deduced from the laws of our nature alone". External powers infinitely surpass the power of a man to continue in existence, and our mortality is the proof of our absolute helplessness against the "infinite power of nature". 28 The suggestion that the Discourse is aimed at a distinct and identifiable philosophy is supported by its contents as well as the surrounding evidence. In a letter to Justel of 1678, Leibniz lists the following among the Spinozistic doctrines he dislikes: that there is only one substance, that creatures are modes or accidents of God, that the mind will not function as a personality after death, that everything works by a fatal necessity.29 These doctrines, together with the claim that the mind is the idea of the body, are precisely the ones criticized in the Discourse. And, in revising his original draft of the essay, Leibniz crossed out a reference to "Spinozists", who suppose that the goodness and intelligence ascribed to the work of God "are chimeras of human beings who think of God in human terms", replacing it by the vaguer expression "recent innovators".30 As long as no actual coterie can be identified as Leibniz's target here, it is tempting to speculate with Friedmann that the real target was, behind Spinoza, Descartes himself. 17 Metaphysics A: individual substance

In sections 8 and 13 of the Discourse, Leibniz discusses what he calls "individual concepts", or "individual substances", or simply "sub­ stances". Here he takes an historical figure, Alexander the Great, as an example of a substance: the discussion appears to presuppose the reality of persons, their bodies, their interactions with one another, "Ibid., Pt Π, Prop. 7: Curley, 1:451. "Ibid., Pt IV, Props. 2-4: Curley, I:548f. "Letter to Justel, in Stein, "Zwei ungedruckte Briefe". 5"LH Theo. HI, 1, noted by Friedmann.

Metaphysics A: individual substance 89

books of history, life and death, and so on. These individual substances, he goes on to explain, contain within themselves everything which has ever happened to them and everything which ever will happen to them. This follows, he thinks, from a consideration of the nature of true statements: there must, he says, "always be some foundation for the connection between the terms of a proposition, and this is found in their concepts". I have given a decisive reason, which, in my opinion, takes the place of a demonstration; this is that always, in every affirmative proposition, whether veritable, necessary or contingent, universal or singular, the concept of the predicate is comprised in some [way] in that of the subject. Either the predicate is in the subject or else I do not know what truth is.31 For a statement to be true, the notion or concept of the subject must contain the notion of the predicate, in precisely the way that the notion "cat" contains the notion "animal". Conversely, for a notion to be completely analyzed, all of the notions which it contains must be extracted from it. As Leibniz had earlier maintained in his logical writings, a complete analysis of the notion of gold is not simply the nominal definition which enables us to recognize it, but gives the sum total of its real, essential properties. Because, and only because, such an analysis is possible, given propositions about gold are true. Now he maintains that an individual person, like a natural kind, must also have a real, not merely nominal, definition. "Can it be denied", he asks in one of his letters, that everything, whether genus, species or individual has a" complete concept according to which God conceives of it (he who conceives of everything perfectly), a concept which involves or embraces all that can be said of the thing? And can it be denied that God is able to have such an individual conception of Adam or of Alexander that it shall embrace all the attributes, affections, accidents, and, in general, all the predicates of this subject? And finally since St. Thomas could maintain that every separate intelligence differed in kind from every other, what evil will there be in saying the same of every person and in conceiving individuals as final species .. .?32 The difference between the definition of a substance such as iron, gold, or water and the definition of a Leibnizian individual substance 3i Letter to Arnauld, 14 July 1686, M 132; G 11:56. "Letter to Hessen-Rheinfels, 1687, M 238; G 11:131.

90 The Discourse on Metaphysics such as Adam is that the definition of the individual substance is infinite. This truth is reciprocal with the truth that "there cannot be two individual things in nature which differ only numerically". 33 If two substances had only a finite number of predicates, those predicates might all happen to coincide, which is impossible. Conversely, if any analysis of two substances is carried out long enough, it will eventually reveal a difference between them. The principle of individuation has undergone some changes since its appearance in the Confessio philosophi. There, Leibniz had noted that two eggs may be so similar that not even an angel can tell them apart. Nevertheless, they are not one egg. They are distinguished by the fact that each can be pointed to separately. Qualitative identity or lack of intrinsic distinction is allowed for, so long as space, time, and movement can provide an extrinsic distinction. 34 By 1676, however, Leibniz had evidently come to believe the stronger thesis that all objects are qualitatively different. This principle appears to have nothing to do with his beliefs about the unreality of space and time, and probably antedates them considerably; it is substantiated rather on general metaphysical grounds. Two rectangles, Leibniz argues in De summa rerutn, one composed out of triangles, the other out of parallelograms, cannot be perfectly similar, for an effect must bear traces of its cause. 35 This principle now forces him to the conclusion that what are traditionally called substances are not one kind of thing at all; each sample is a collection of unique individuals. "Although gold or some other metal, or salt and many liquids", he says in the related paper "First Truths of Philosophy", "may be taken for homogeneous bodies, this can be admitted only as concerns the senses and not as if it were true in an exact sense". 36 The problem Leibniz now faced was in reconciling this theory of absolute differentiation with his logical proposition: namely, truth is that which can be demonstrated from identities by definitions, assuming these definitions are real and not merely nominal. 37 Clearly, this doctrine had an application in the case of ordinary substances. The real defining properties of substances should, given ""First Truths of Philosophy", in Couturat, ed., Opuscules et fragments, p. 520; L 268. ^Confessio philosophi, AK VI:III:147; Saame, tr., pp. 124f. 35 De principio individui, AK VI:III:490. 36 In Couturat, ed., Opuscules el fragments; p. 520; L 268. 37 Di veritalis primis, AK Vorausedition 1:115.

Metaphysics A: individual substance 91

real definitions, be actually demonstrable - the color, texture, and properties of gold actually following from its chemical structure, which is experimentally determined. But how could the same be said of individual substances? One might conceivably settle the question "Are all non-angelic spirits rational?" by appealing to a real characteristic, once the proper definitions for "angel", "spirit", and "rational" had been determined. But the idea of deciding, by any logical apparatus whatsoever, the question "Will Adam accept the apple?" in advance of his doing so seems absurd. Another philosopher might simply have decided that the truth about individuals cannot be determined by the fundamental proposition: it cannot consist after all in the inherence of the predicate in the subject. Decisively, Leibniz does not take this route. Instead he proceeds to separate the question of the actual inherence of predicates in subjects from their demonstrability. Whether a certain predicate is contained in a given subject is not demonstrable by anyone, including God, although it is knowable by God. As we have observed, in the Confessio Leibniz was as much of a determinist as Spinoza in the sense of holding that what happens happens inevitably. As R. M. Adams has pointed out, Leibniz had really once believed that human actions were necessary, though performed with will and reason. 3 8 Judas, he had argued in the Confessio, could not have done other than what he did; his actions are part of the whole, and the philosopher cannot wish that he had done otherwise, for these actions are part of the "whole series of things", which is identical with or proceeds directly from God's thought. Thus it was not surprising that Arnauld began his response by accusing Leibniz straightaway of maintaining that all that happens does so by "a necessity more than fatal". 39 As a bitter opponent of Calvinism as well as a foe of Spinoza, Arnauld could not have been expected to approve of a theory of predestination, whether or not the theory was, technically speaking, necessitarian. As we have also seen, Leibniz thought he could avoid this objection in the Confessio by distinguishing between hypothetical necessity and logical or "geometrical" necessity, and by redefining free actions as those done deliberately and spontaneously. By beginning with Μ Letter to Magnus Wedderkopf, May 1671, L 146f; AK II:I:117f. Quoted by Adams, "Leibniz's Theories of Contingency", pp. 244f. 3» Letter to Hessen-Rheinfels, 13 March 1686, M 73; G 11:15.

92 The Discourse on Metaphysics individual substances, he no doubt thought he had done even better, for here he had avoided depicting human beings as helplessly caught up in the toia series rerum. The notion that individual substances "have" all their predicates within them suggests that they are authors of their own destinies. Clearly, this did not satisfy Arnauld. It seems not to have occurred to Leibniz, moreover, that one might regard his theory as constricting not simply human freedom but divine freedom as well. Here too he offended his correspondent: Arnauld does not dispute that, in creating Adam, God knows everything that he will do; but he objects to Leibniz's claim that God knows this by intuiting the "intrinsic and necessary connection" between Adam and his life history. God does not, Arnauld thinks, need to examine the concept of Adam in order to see what he will do; and once he has decided to bring Adam into being, he is free to alter his destiny as he sees fit, not bound by the definition of a concept. 40 Leibniz angrily attempts to defend himself at this point by stating that it is "little consonant with God's dignity to conceive of him (with the pretext of assuring his freedom) like certain Socinians, as a human being who forms his resolutions according to circumstances". 41 Indeed he strengthens the apparent constraints on God, going so far as to introduce Malebranche's idea of God's indifference to the individual case and his aesthetics of parsimony. As Malebranche had insisted that God chooses a system of simple, fertile, and universal laws, whatever the results for particular people may be, Leibniz now insists that what happens to Adam must follow from an economical set of original specifications. There are, he states, "only a few primitive free decrees regulating the sequence of things which could be called the laws of the universe, and which, being joined to the free decree to create Adam, bring about the consequences. In very much the same w a y . . . but few hypotheses are called for to explain phenomena". 42 In fact, the Discourse is no more successful in reconciling freedom and determinism than the Confessio was. God's decision to bring the substance Adam into existence is, for Leibniz, the basis for the «o Ibid.

«Letter to Hessen-Rheinfels, 12 April 1686, M 78; G 11:23. ""Remarks upon Mr. Arnauld's letter concerning my proposition: that the individual concept of each person involves, once for all, all that will ever happen to him", May 1686, M 108; G 11:40.

Metaphysics A : individual substance 9 3

contingency of his existence and so the non-necessity of his actions; hence his freedom. That there is a non sequitur here, that God's choosing to create Adam cannot be constitutive of his free-will, is obvious. Nor does Leibniz's theory of possible worlds help him to meet the minimum logical condition of free-will, namely that it should have been possible for a given person to have done otherwise. For although Adam does not accept the apple in every possible world, there is no possible world in which Adam does not accept it. There are many possible worlds in which a substance resembling Adam in certain notable respects does not eat an apple which resembles the biblical one in certain notable respects. But Adam can exist only in one world, the actual one.43 Leibniz thus cannot avoid Arnauld's objection that he has no way of interpreting counterfactual conditionals involving individuals. Interestingly, though, he is a realist about possible worlds, Arnauld a skeptic. Although the latter would like a strong interpretation of counterfactuals, his wish to preserve the freedom of God leads him to deny the existence of possible individuals, so that he inadvertently aligns himself with Spinoza, showing the danger of not reading books one doesn't like: "these are chimeras which we construct ... pure possibilities are nothing else than the omnipotence of God".44 God, Arnauld thinks, creates certain natures. We can then go on to imagine "modifications" in these natures, in the forms of extended substances and the thoughts of thinking substances. But nonexisting substances, as opposed to non-actual modifications, are strictly impossible: "it is as little possible to conceive of several Adams as to conceive of several me's".45 This assertion is in part accepted by Leibniz, in part denied. It is correct to say that there is no more than one Adam and no more than one me in all possible worlds. It is incorrect to say that there are no merely possible substances, which could well be designated by names belonging to no actual beings. To the Arnauldian fear that uncreated possible individuals exist in some free realm outside the boundary of divine operation, Leibniz replies that these pure possibles are the only way of saving contingencies, "because if nothing is possible except what God has actually created «Letter to Hessen-Rheinfels, 12 April 1686, M 77f.; G 11:18. "Letter to Leibniz, 13 May 1686, M 97; G 11:30. "Locxil.

94 The Discourse on Metaphysics then what God has actually created would be necessary". 46 Here, Leibniz once again aligns himself with Malebranche, who regards the creation as a contemplative choice by God from the realm of pure possibilities. "God uncovers", Malebranche says, "in the infinite treasures of his wisdom an infinity of possible works, and, at the same time, sees the most perfect way of producing each of them". 47 But - and this point is repeated by Malebranche throughout his writings - God has no intentions with respect to individuals. It is the whole which is perfect, in virtue of its being regulated by laws which are simple, fruitful, and universal, even if these tend to the disadvantage of particular creatures. For Malebranche, if God punishes the sinner he has created for a sin which he has foreseen, this should not be understood as a vicious action but as an unavoidable by-product of the excellent plan of the whole. This is Leibniz's view as well, with the addition of his particular theory of identity: someone ... may say, how does it come about that this man will certainly commit this sin? The reply is easy; it is that otherwise he would not be this man. For God foresees from all time that there will be a certain Judas, whose idea or concept which God has contains this future free act. There remains then only this question: Why does Judas, a traitor, who is merely possible in the idea of God, actually exist? But to this question no answer can be expected here on earth .. .48 Here, Leibniz has recourse to his old paraphrase. The disturbing, troubling, embittering question "Why did God make Judas a traitor?", or "Why did God make me commit the shameful action?", is to be replaced with the question "Why was Judas (or I, a sinful person) admitted to existence rather than some possible individual who would not have committed the sinful action in question?" His point is that God has not, as it were, cast anyone in a bad role; we have no identities apart from our roles. Our actions proceed from ourselves; we have our reasons, our motives, perhaps even our satisfactions in our crimes. It is still sensible to ask why we were brought into existence at all; or why indeed God decided to create a world in which terrible things could happen; and why we should be punished outside «'"Remarks upon Mr. Arnauld's letter", M 116; G 11:45. i7 Traite de la nature ei de la grace, I:LV: Oeuvres, V:57. "Discourse, §30, L 322; G IV:455.

Metaphysics A: individual substance

95

of this life, as Christian doctrine implies. The answer to the first two questions is supplied, for Leibniz, by appeal to the harmony of things. The second question, however, will ultimately push him in the direction of denying that there is a philosophically significant break between life and death. Logical determinism is also Leibniz's recommended solution to the problem of grace (section 31). There were two outstanding problems which needed to be addressed. First, is the grace necessary for salvation dispensed on the basis of a person's works, or faith, or both, or is it given out according simply to the free will of God? If the former, it would seem that individuals can manipulate God; if the latter, salvation seems to be entirely arbitrary. Second, is grace always effective, or does its reception depend on the nature of the person involved? Leibniz argues here that God bestows both "ordinary" and "extraordinary" grace in accord with the faith and works of the person, but not on account of them, thereby making grace less arbitrary without compromising God's freedom. Here he departs from Malebranche's interesting theory that grace, like rain, falls on the just and unjust alike, on the proud and hard heart which resists it as well as on the well-prepared and tender heart, according to the simple, fertile, and universal laws which govern this realm. 49 But, like Malebranche, he is clear that God's foreknowledge encompasses the theological destiny of the individual. "God", says Malebranche, "before creating souls in order to unite them with bodies, foresees everything which will happen to them according to the general laws of nature and grace and everything they will do in all possible circumstances". 50 If Pierre has the misfortune to have a pagan for a father, or to grow up in a bad environment, or to busy himself with vicious occupations, he will infallibly end up in the ranks of the reprobate, though even here he is an ornament of the creation who enhances the beauty and greatness of the Church and is useful to God. 51 Nothing in the scheme of either Malebranche or Leibniz could have appealed to Arnauld, who insists on the absolutely free relationship obtaining between God and creatures, and it is difficult to see how such a reconciling move could have satisified either the proponents of works or the proponents of arbitrary election. i9

Traite de la nature et de la grace, I:XL: Oeuvres, V-AS. so Ibid., LLVlI: Oeuvres, V:60. si Loc.ci/.

96 The Discourse on Metaphysics Leibniz says at many points that it is the nature of an individual substance "to have so complete a concept that from it may be deduced all that can be attributed to it". Clearly, this deductive capability does not apply to mere humans, for then, as Leibniz says, "it would be as easy for us to become prophets as to be geometers". 52 I may consult with myself as to whether I am married or celibate and effectively determine the answer; I cannot consult with myself as to whether I shall undertake a certain journey. As a body contains "an infinity of sensible things", unknown through experience but revealed through the abstract consideration of bodies, the concept of a substance contains an infinity of indistinct predicates, unknown to the substance itself. My married state and the journey I shall take are both "written into" my concept, but one is written too indistinctly to be read. 53 After 1686, Leibniz introduced an important modification to this theory. Even though my concept is sufficient to assign a reason for my taking the journey, not even God can demonstrate that I shall do so, although he of course knows whether or not I shall. This view seems to be a development of the suggestion presented to Arnauld, that there is a difference between "complete" and "incomplete" concepts. 54 General concepts such as "circle" are incomplete, according to Leibniz. Their properties are accordingly necessary and demonstrable. Individual concepts are "complete", and their definitions are not only infinitely long but irreducible to finite length. In the same way, he explains later, no figure existing in nature can be described by a finite geometrical formula because of the infinite complexity of each. In the paper "On Freedom", Leibniz explains how, as he worried over the fatalistic implications of his theory, "a new and unexpected light arose at last ... where I least expected it, namely, from mathematical considerations of the nature of the infinite".55 To explain how the theory of the infinite reconciled divine omniscience with the contingent character of human actions, Leibniz requires the help of mathematical analogies. We remember from the 52

"Remarks upon M. Amauld's letter" M 116; G 11:53.

"he. tit M 106; G II:38f. 55 O n Freedom", L 264. The date cannot be 1679 as given: see De contingentia, in Grua, ed., Textes inediles, 1:302, n. 128.

Metaphysics A : individual substance 97 theory of the combinatorial characteristic that demonstration consists in the replacement of definitional equivalents. Suppose we are given two concepts Pi and Pi and wish to determine whether all Pis are also P2S. We need to take the characteristic numbers and determine whether n(Pi) is divisible by n(P2). Taking now the reduction of η (Pi) into its prime factors, we observe that some combination of these prime factors is equal to η(Ρί)· This enables us to prove the general proposition. "In contingent truths, however", Leibniz maintains, though the predicate inheres in the subject, we can never demonstrate this, nor can the proposition ever be reduced to an equation or an identity, but the analysis proceeds to infinity, only God being able to see, not the end of the analysis indeed, since there is no end, but the nexus of terms or the inclusion of the predicate in the subject, since he sees everything which is in the series.56 Does this imply that there could be no "characteristic numbers" for individual substances? Clearly, Leibniz can no longer afford to think of them according to the old multiplicative scheme; a substance now resembles the number which represents the summation of a series. God is able to see "not by demonstration - for this would involve a contradiction - but by an infallible vision", 57 that the term f is contained in this sum. But no identity can be constructed which reduces the individual to a finite set of terms including f. The object of God's creation is, according to metaphysics A, a collection of individuals. God does not really create substances in the scholastic sense, for the minima of apparently uniform substances are really distinct individuals. But here the purely combinatorial view of creation is given a tremendous lift by the doctrine of divine choice which Leibniz appropriates from Malebranche. "My principle", he was prepared to state in 1676, " . . . is that whatever can exist and is compatible with other things does exist, because the reason for existing in preference to other possibles cannot be limited by any other consideration than that not all things are compatible". 58 But

56 O n Freedom", L 265. This proposal is discussed at length by Resetter in "The Infinite Analysis of Contingent Truths" Leibniz's Metaphysics of Nature, pp. 42-55. " O n Freedom", L 265. 5»"Two Notations for Discussion with Spinoza", L 169; AK VI:III:58lf.

98 The Discourse on Metaphysics this theory is obviously powerless against Spinoza's claim that what exists is neither good nor bad except in light of human interests. Why should the maximum number of substances also be, objectively speaking, the best, from the moral point of view? Leibniz has no answer here; he can only echo Malebranche's claim that efficiency is beauty, as he does in section 5. But even if efficiency is beautiful, it does not follow that the beauty that the philosopher seeks is just efficiency, and this problem pursues Leibniz well into the pages of the Theodicy. 18 Metaphysics B: matter and form Leibniz developed metaphysics B not in the context of problems about definition, predestination, choice, and contingency, but as a critique of the Cartesian conception of substance as pure extension. Here, he was in no position to be helped by Malebranche, and he reaches, self-consciously and somewhat apologetically, back to the pre-modern doctrine of substantial forms, which he describes as "not so far from the truth, or so ridiculous, as our modern philosophers commonly imagine". "I was", he says, "for a long time convinced of the emptiness of these beings to which I am at last compelled to return in spite of myself and as [though] by force". 59 Descartes had arrived at his theory of the unique subjectindependent status of extension by considering how far qualities can be subtracted from matter without making it the case that nothing material is there. "What then did I know so distinctly in this piece of wax?", he asks, considering a fragment which has melted, lost its taste, color, and smell. "It could certainly be nothing of all that the senses brought to my notice, since all these things which fall under taste, smell, sight, touch, and hearing, are found to be changed, and yet the same wax remains". 60 These qualities Descartes goes on to describe as confused and obscure, by contrast with the qualities of extension, movement, duration, and number. 61 "As to other things such as light, colours, sounds, scents, tastes, heat, cold and the other tactile qualities, they are thought by me with so much obscurity and

"Dixourse, §-XI, L 3011; G IV:435:MB49. Descartes, Second Meditation, AT VIII:30f.; HR 1:154; CSM 11:20. «Descartes, Third Meditation, AT VIII:43; HR 1:164; CSM 11:30. 60

Metaphysics B: matter and form 99

confusion that I do not even know if they are true or false, i.e. whether [they] are actually the ideas of real objects or not". 62 Descartes resolves his doubts on two levels. On the first level, he tries to reassure the conservative reader, or the conservative tendencies of every reader, that this confusion is benign. God is not a deceiver, and the existence of a world as the senses perceive it need not be doubted. The Sixth Meditation restores everything taken away in the Second, leaving only the new certainty that a person has an immortal thinking component in addition to his mortal extended component. On the second level, Descartes communicates to the more adventurous reader that to see the world aright one must really abandon common-sense notions of objects and their properties. The "spontaneous inclination" which impels us to believe that sensory equalities and ideas in general proceed from sources which "resemble" them is, after all, deceptive; and even if God does not exactly deceive us, he offers at any rate the possibility of a more accurate reading of nature to those who take the trouble to think out the truth about the nature of sensation - although the Meditations avoid going into detail on this subject. To one who has done so, the sensory qualities of taste, color, scent, heat, and so on, retain their subjective character and the dubious status assigned to them in the Second Meditation. Their causes consist in the impact on the nerves and brain of extended particles. God has nevertheless joined the mind to the bodily machine in such a way that certain ideas are regularly produced as a result of this impact. Leibniz now carries this argument in an unexpected direction, insisting that Cartesian extension is as mind-dependent, hence as unreal, as color, heat, taste, and so on. The nature of body, he maintains, cannot consist in size, figure, and motion alone, for these properties possess something "imaginary and relative to our perceptions" in the same way as the others. What arguments does he offer for this claim? In the letter to Arnauld of 9 October 1687, he attempts to justify the point. "Matter", he says, has not even those precise and determined qualities which can enable it to pass as a determined being ... because figure itself, which is the essence of a limited extended mass, is never, strictly speaking, perfectly determined in the state of nature because of the actually infinite division of the parts of matter: «Loc.cii.

100 The Discourse on Metaphysics there is never a globe without inequalities, never a straight line without an intermingling of curves, never a curve of a certain finite nature without an intermixture of some other ... so that far from the figure being a constitutive element in the body, it is not a quality at all real and determined outside of the thought. Never can an exact surface be assigned to any body as could be done if there were atoms; I can say the same thing of size and of motion, namely, that these qualities or predicates are phenomena like colors and sounds, and although they involve a more distinct knowledge they cannot hold up under a final analysis.*3 If there were atoms, Leibniz thinks, material bodies would have precisely determinable edges. But this is inconceivable. Only ideal bodies, such as the circle considered in abstracto, have a precisely determinable surface. For any mathematical curve that we specify as defining the edge of a material body, closer inspection will show that the material body at some point contains irregularities which deviate from the curve. 64 Shape is a mathematical notion which applies only by approximation to the physical world. The same argument might be applied to size: for any length we succeed in determining, closer examination will show a material body to be larger or smaller. If we magnify the point of coincidence of object and measuring instrument we shall always observe it to be less than perfect. Hence magnitude and figure cannot constitute properties of bodies as they are in themselves. For Descartes, it was important to establish the existence of a substance with precisely determinable properties which did not depend upon contingent facts about the human sensory apparatus. This assumption underwrites his attempt to construct a science on foundations other than bare sensory observation. Leibniz, by contrast, can treat the possibility of such a science as a foregone conclusion. He does not doubt that a Cartesian science is possible; that the essential pattern of explanation in natural science is mechanistic and requires reference to unobservables. As he says in the Discourse, explanation by means of efficient causes - the flow of fluids and mechanical organization - is in fact "profounder and in 63

Letter to Arnauld, 9 October 1687, M 222; G II:118f. The argument that apparently homogeneous physical bodies will always appear heterogeneous if viewed with a microscope was usually regarded as an argument for atomism. Walter Charleton uses it, as does J. Jungius; see, on the latter, Meinel, "Early Seventeenth-Century Atomism", p. 84. 64

Metaphysics B: matter and form 1 0 1

some ways . . . more immediate" than the more superficial explanation in terms of purpose. 65 The victory over Aristotelian physics assured, nothing, as far as Leibniz was concerned, was now to be gained by insisting that substance was simply what could be handled geometrically. Leibniz has no intention, in the context of Metaphysics B, of denying that there are bodies composed of non-Cartesian matter, a composite of primary matter and form. "The reality of bodies", he states elsewhere, hearkening back to the Catholic Demonstrations, "does not consist in mass, but in the force of acting and suffering", 66 and this force must be treated as a "form". In a paper from the same year as the Discourse he asks: What must we then add [to pure extension] in order to complete the concept of body? Nothing except what the senses themselves testify to. They inform us at once of three things: first, that we observe, and that what we observe is a variety of things, composite or extended. Consequently, action has to be added to the notion of extension or variety. Therefore body is extended activity, and a substance may be said to be extended if we hold that every substance is active and every active thing is called a substance.67 Why does it follow from the fact that we perceive many things that what we perceive is active? The only reasonable answer is that extension is what is common both to phantasms and to real bodies. If the variety which we observe is a sign of the non-phantasmal character of what we perceive, then what we perceive must be active as well as extended. This epistemological argument is complemented by the famous physical argument given in section 17. Here Leibniz tries to show, on the basis of a thought experiment, that real bodies possess "force" which cannot be identified with the product of their size and speed. But it is not that force - the vis viva - which makes bodies real rather than phantasms. The vis viva, as becomes clear in the later dynamical writings, is only a surface manifestation of the primitive activity of a substance. Two more arguments which Leibniz employed at this time against the identification of substance and extension are of particular ^Discourse, §22, L 317; G IV:4481; MB66. ^Specimen inventorum, AK Vorausedition 111:488; G VII:3i4. 67 O n the True Method of Philosophy and Theology", in Wiener, tr. and ed., Selections, p. 64; AK Vl:ffl:158.

102 The Discourse on Metaphysics significance. Both are related to the problems of change, predication, and composition discussed in the Pacidius Philalethi. In the Discourse, the laconic comment is made that if the properties of matter alone could characterize body, none would ever subsist longer than a moment. 68 How is this to be understood? Leibniz's point appears to be that it is impossible to distinguish between the successive recreation of body N in a number of different places, and the successive creation of a series of bodies Ni-N n which are qualitatively similar, if that body is supposed to be purely material. Only an object which is ensouled can escape the occasionalist reduction to mere sequentiality. This argument we will consider more closely in later chapters. For now it is sufficient to remark that, for Leibniz, if anything is the subject of change, and if the world is not simply a succession of momentary instantiations of properties, these subjects or substances must be something like persons. Here, metaphysics B joins hands briefly with metaphysics A. A second argument, one much loved by Leibniz, is based not on the Heraclitean problem of identity and change, but on Zeno's divisionand-composition paradoxes. Thus: For the substance of bodies there is required something which lacks extension; otherwise there would be no principle to account for the reality of the phenomena or for true unity. There would always be a plurality of bodies, never one body alone; and therefore there could not, in truth, be many. By a similar argument Cordemoy proved the existence of atoms. But since these have been excluded, there remains only something that lacks extension, something like the soul, which was once called a form or species.69 Whether anything at all exists, in other words, cannot depend upon how something else is put together. For there to be many things there must be single things - "thises". But no material atom can be a "this", as he explains to Arnauld. In calling the atom "one thing", according to Leibniz, I am grouping together a set of parts which happen to be in spatial contiguity and cohesive with one another. But these parts might just as well not have been together in this state, and they may not endure in this configuration for more than

^Discourse, §12, L 309f.; G IV:436; MBSO. »"First Truths", in Couturat, ed., Opuscules el fragments, p. 523; L 270. See Heimsoeth, Atom, Seek, Monade, pp. 339f. 6

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an instant. They are no more one thing than the herd of cattle which similarly exhibits cohesion and contiguity of parts. The true "thises" are indivisible; they do not possess parts which may form parts of other "thises"; their unity does not come from the spatio-temporal accident of their being found together and being related by motion, or whatever the cause of cohesion is. 70 A person, an animal, even a plant, is a true "this"; its parts cannot come together to form another person, plant, or animal. We do not call the thing one in virtue of the fact that its parts are contiguous or cohesive, but in virtue of the fact that one life is here. Thus, for there to be substance at all there must be "animated machines whose soul or substantial form [constitutes] the substantial unity independently of the external union of contact". 71 This is a new twist on the cohesion problems of the 1670s, and is perhaps inspired by Aristotle's discussion of the different kinds of bond present in continuous substances. 72 The argument is in any case rejected by Arnauld, who points out that the concept of unity admits of various degrees of precision and should not be taken as absolute. Granted that there is a special kind of unity present only in "intelligent natures", he argues, we should recognize that a watch, a church, a horse, an orange, all possess more unity than a pile of stones or a bag of coins in virtue of the fact that their parts "work together for a similar purpose". 73 The issue is, he thinks, the consequence of presumptive verbal legislation on the part of Leibniz. Why should Leibniz be entitled to define substance as that which is a "real unity", rather than sticking with the traditional definition of substance, namely, that which is not a manner of being of another substance? It is obviously the case, he insists, that a block of marble is not a mode of being of another substance. So why not allow it the status of a substance?

"Letter to Arnauld, 28 November/8 December 1686, M 162; G 11:74. Cf. Cordemoy, Six Discours sur la distinction et la union du corps et de lame: Oeuvres, p. 96; and Prost, Atomisme et occasionalisms ch. VI, esp. pp. 47ff. "Letter to Arnauld, 28 November/8 December 1686, M 162; G 11:74. 72 Cf. Physics, ed. Ross, V, 3, 227a: "Continuity belongs to things that naturally in virtue of their mutual contact form a unity. And in whatever way that which holds them together is one, so too will the whole be one, e.g. by a rivet or glue or contact or organic union". "Letter to Leibniz, 4 March 1687, M 179; G 11:89. Cf. letter to Arnauld, 9 October 1687, M 223; G 11:119.

104 The Discourse on Metaphysics What Arnauld does not realize, with his brisk pragmatic approach, is that Leibniz does not consider the thesis that a block of marble is merely a mode of being of another substance as an hypothesis which is obviously and trivially false, but as one which is both alluring and dangerous. It is just Spinozism: if Spinoza is right, he thinks, the block of marble is as insubstantial as the rainbow - a mere aspect of God's thought. And if this is all the block of marble amounts to, what is to prevent us from saying that the person too is only a mode of the divine substance? Leibniz is placed in a difficult position by Arnauld's challenge. He wishes to deny that a purely material, purely extended, inactive, unensouled object could be anything but an appearance. On the other hand, if he allows that inanimate things are only appearances, he has conceded too much already to Spinoza. So he has no choice but to assert that seemingly inanimate things are really animate. Either all matter is animated or it is simply a dream, of ours or of God's. Thus blocks of marble, piles of wood, stones, etc., must be full of living creatures, and by dividing one of them far enough we will eventually reach its living atoms, the micro-organisms of which it is composed. Metaphysics A tells us that a block of marble is actually a collection of unique individuals, not a homogeneous substance, and so metaphysics A and metaphysics B here join hands again for a moment. The "concurrent mind" of 1668, which made inanimate bodies substances, has fallen away, and the same work is now done by "forms". 19 Metaphysics C: phenomenalism ana the external world

Despite their very different origins and the very different character of the arguments meant to establish them, metaphysics A and metaphysics B thus show several points of rattachement. But the picture is complicated considerably by Leibniz's desire to introduce a third scheme, in the form of the quasi-Malebranchean theories of perception and causation of sections 9,14 and 15. Here, the reader's assumption that individual substances are either normal historical agents, or large and small animals and perhaps plants, is abruptly violated. The ordinary world is rejected in favor of what Leibniz calls the "universal system of phenomena". He now claims that "each substance is a world apart, independent of everything else outside of itself except God", and that "all our phenomena, that is to say, all the

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105

things that can ever happen to us, are only the results of our own being".74 If everything in the world were destroyed except myself and God, he asserts, my experiences would not be other than what they will be if this does not occur. "Nothing can in fact happen to us except thoughts and perceptions, and all our future thoughts and perceptions are only the consequences, however contingent they may be, of our preceding ones". 7S This is a radical way indeed of countering Spinoza's claim that we are infinitely weak against the power of external things. These claims might be made to look more innocuous than they are by taking into account the original meaning of phenomena - what appears. To say that God creates only phenomena is not necessarily to say that God creates simply intra-mental presentations, but that he creates appearances, which, as in the case of the "celestial phen­ omena", may well be "outside" the observer. Unfortunately, Cartesianism had forced a clarification here: in addition to objects outside of us there are only mental presentations within us. Leibniz must be aware of this, and as a result his claims resemble, with one important difference, the theory of perception developed by Malebranche in the Recherche de la verite of 1674.

In Chapter II, we saw Leibniz wavering between two hypotheses the first being that God is the cause of our mental presentations of bodies, and the second that bodies, which contain something active, are themselves the cause. Malebranche himself, as a consequence of his broader doctrine of the causal inefficacy of created things, held that neither external objects nor the soul itself could produce its ideas or its sensory experiences. Without the assistance of God, men are deaf, dumb, blind, and as powerless to move themselves as logs or stones. It is not merely a metaphorical truth that in God we live, move, and have our being, Malebranche thinks: this is a scientific fact. On the occasion of looking at a sensible object, he explains, we have both a sensory impression of the object and an idea. God acts on us to produce the former, but the idea of the object we have by 76 participating in his idea. The objects outside of us thus play a purely incidental "occasional" role, and Malebranche admitted Μ Discourse, §14, L 312; G IV:440 M B 54. "Locci't. ^Recherche de la verite, 111:11:V: Oeuvres, 1:445. Cf. Eckircissement X: Oeuvres, HI:147ff. S e e Yolton, Perceptual Acquaintance from Descartes to Reid, p p . 42ff.

106 The Discourse on Metaphysics candidly that he knew of no way of proving that such objects exist: it was left to Berkeley to draw the obvious conclusions here. The similarity between Malebranche's description of perception, as involving open channels of communication with God but no actual contact with the world, is not accidentally similar to the mystic's description of states of ecstacy. In this connection, Leibniz himself frequently mentions St Theresa, who describes the soul, when in a state of mystical communion with God, as "dead to the things of the world" and as living, seeing, and understanding in him. That this feature of exceptional states of consciousness should be brought down to apply to the humdrum perceptual experience of everyday does not trouble either philosopher. Although Leibniz shows himself in other contexts somewhat mistrustful of the more visionary episodes in Malebranche's writing, he can say straightforwardly in section 28 that God is the "only immediate object of our perceptions and . . . we see things through him". [F]or example, when we see the sun and stars, it is God who has given to us and preserves in us the ideas of them and who determines us, through his ordinary concourse, actually to think of them at the moment when our senses are set in a certain manner, in conformity with the laws which he has established.77 But, as he goes on to explain in the following section, he cannot approve of the position of "certain able philosophers" who hold that we think and perceive in or through the mind of God and not with our own ideas. Backtracking on his position somewhat, Leibniz states that the soul has, in addition to its passive capacity of being affected by God and so of expressing "all possible and actual beings" along with God himself, "an active power by virtue of which it has always had, within its own nature, marks of the future production of this thought". 7 8 Where, on Malebranche's theory, it is as though each soul were alone with God, on Leibniz's each soul appears to be alone 79 with itself. Note that this theory does not follow directly from the definition "Discourse, §28, L 321; G IV:453; MB 72. ™ Discourse, §29, L 321; G IV.454; MB72-3. Cf. Malebranche's treatment in the Recherche, 1:1:11, Oeuvres, I:45f; and the later Entretiens sur la metaphysique ei sur la mart (1688), VII: Oeuvres, ΧΠ:165. " S e e Mondadori, "Solipsistic Perception".

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of individual substance. From the claim that the concept of Adam contains the sum total of his predicates, it does not follow that the soul of Adam contains all his experiences. It follows that it is now true of Adam that he will perceive such-and-such in the future; but this does not show us that his perceptions are not produced by something external to himself. The containment analogy is nevertheless a forceful one, and establishes a connection between Leibniz's A and C metaphysics. At this point, Leibniz implicitly calls in his multiplicity of individual substances, by showing how these solipsistically-perceiving souls together form a system. Holding in abeyance the Cartesian question whether the phenomena we experience "are anything outside of us and whether others perceive them also", Leibniz now indicates that it is possible sequences of perceptual experience, mere perspectival loci, which are truly primitive. He depicts God as having created in the beginning certain experiential perspectives whose sum total constitutes the phenomenal world: as God turns the universal system of phenomena which he has seen fit to produce in order to manifest his glory, on all sides and in all ways, so to speak, and examines every aspect of the world in every possible manner, there is no relation which escapes his omniscience, and there thus results from each perspective of the universe, as it is seen from a certain position, a substance which expresses the universe in conformity to that perspective, if God sees fit to render his thought effective and to produce that substance.80 Metaphysics A and C, taken together, imply that each substance is dreaming up a world of other substances - producing them from its own depths - and that these dreams are congruent, there being after all many substances, and form together a harmonic system. Now, if each substance is only dreaming up its own world, then the postulated harmony is apparent only to God and explains nothing about the experiences of any particular substance. Leibniz, however, sometimes seems to hold that the theory of pre-established harmony explains something about our conception of a common world, inhabited by many substances together. He gives, for example, the following analogy: as a number of people can agree to meet together on a certain day and in a certain place, though each possesses his own ««Discourse, §14, L 31lf.; G IV:436; MB 53.

108 The Discourse on Metaphysics means of measuring time and arrives from a different direction, "so a number of spectators believe they see the same thing and are in fact in agreement about it, although each one sees and speaks of it 81 according to the measure of his own point of view". There is, in the case of perception, an empirical agreement which needs philosophical explanation - the fact, for example, that two people may designate an object appearing in a similar but not identical spot in the visual field of each, in a public language, as "that". But this agreement cannot possibly be explained by the theory of harmonizing solipsistic perceptions. Leibniz's problem presupposes the notion of a common external object of reference, while his solution takes it away. Metaphysics B supplies that common world and offers a theory of the distinction between private mental phenomena and real substances; metaphysics C destroys the distinction and removes that world. It is the tension between them which leads to the notorious problems about relations. Leibniz appears on one hand to believe that every object is related to every other: every individual substance expresses the whole universe in its m a n n e r . 8 2 At the same time he asserts t h a t substances have "no purely extrinsic denominations which have no basis at all in the subject itself", and that "whenever the denomination of a thing is changed, some variation has to occur in the thing itself".83 Now, it would be natural to treat the assertion that each substance expresses all the rest as meaning that if substances Si ... Sn exist in the same universe, then a complete description of Si will include propositions describing its relations to S2-S„, for example its being larger or smaller than each one, or so many kilometers distant. Thus, information about relations is duplicated many times over, as information about the city is duplicated in the various perspective drawings that are made of it. The problem now is that the relations of a thing to other things appear to be prime examples of "external" denominations which cannot be reduced to "internal" qualities of the subject itself. If y moves ten feet farther away from χ so that it is now twenty feet away, how can this be said to involve a variation in χ itself, except in ^Discourse §14, L 312; G IV:439; MB 53-4. '^Discourse §14, L 312; G IV:440; MB 54. 83 "First Truths", in Couturat, ed., Opuscules et fragments, p. 520; L 268.

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the trivial sense that it is now false to say of χ that it is only ten feet from y? The problem has its logico-linguistic parallel. If truths can be expressed as statements in which the subject contains the predicate, what explains the truth of the statement that χ is to the right of y ? Leibniz insists, albeit somewhat later, that relations are ideal but are founded in the intrinsic denominations of things. 8 4 We are presented with the strange theory that Solomon is real and that it is true that he has a father; that David is also real and that it is true that he has a son; while that Solomon is the son of David is "a mere mental thing". There are two possibilities of interpretation here. Either Leibniz thought that propositions involving extrinsic denominations could, by analysis, be reduced to subject-predicate form, on the grounds that all truths are reducible to this form, 8 5 or he thought that there are no true statements about a thing which are relational. Now, Leibniz gives no formula for converting relational statements into plain subject-predicate form. And, indeed, any attempt to make "being-a-Solomon-father" and "being-a-David-son" into intrinsic predicates - ordinary adjectives - would seem doomed to failure. For to say that "David is a Solomon-father" is to say, not just that he is the father of some Solomon, even one with an infinite list of properties, but that he is the father of that particular one. If, on the other hand, Leibniz thought that relations are mere mental things in the sense that no two things are really related to each other in any way, then it is thoroughly unclear how every object in the universe could express every other. The crux of the problem seems again to lie in Leibniz's theory of perception, together with his principle of absolute qualitative individuation. This principle implies that there cannot be two otherwise identical objects which can be distinguished only relationally. For example, there cannot be two identical clouds, one on my right and one on my left. Relational characteristics do not help to distinguish a substance, and Leibniz may well have slid from this premise to the conclusion that relational differences are not, after all, real differences, and from there to the conclusion that relations are not real. 84

Letter to des Bosses, 21 April 1714, L 609; G 11:486. According to the usual interpretation, at any rate; cf. "First Truths", Couturat, p. 518; L 267f. 85

110 The Discourse on Metaphysics However, this analysis does not help us with the Leibnizian paradox that no one becomes a widower in India on the death of his wife in England without some real change occurring in him. 8 6 Perhaps the trivial truth that if x's relation to y changes, then something about χ changes seemed to Leibniz a deep truth, when he considered his substances not as robust historical actors but as points of view or classes of perception. Then, according to the principle that we are never affected by external objects, that "nothing can happen to us except our perceptions", it follows that the Englishman's wife's death must register at least unconsciously with him: otherwise it would not have happened. But now, according to the principle that we are alone with our perceptions, or at best with God, the Englishman's experience of subconsciously registering his wife's death does not depend at all on his wife. The natural desire of the critic is to turn all this around: the existence of relations is a refutation of Leibniz's claim that nothing can happen to us except our perceptions. Not only can a man be made a father without perceiving it, but a man cannot be made a father, no matter what the status of his perceptions, unless some other entity comes into the world which is his child. To summarize: the theory that nothing in our experience requires us to posit the existence of real relations is tenable only if one has already accepted the premise that nothing happens to us except what we experience, and the best reason to doubt this premise is that it does not fit the case of relations. Leibniz's theory of the unreality of relations can be given no sound interpretation, no matter whether one treats it as belonging with metaphysics A and the theory of definitions, or with metaphysics C and the theory of solipsistic perception. 20 Activity and passivity after Spinoza and Makbrancfu Leibniz's denial that substances can act upon each other cannot be construed as a full endorsement of Malebranche's thesis of the inefficacy of created things. It is true that he is aware of the difficulties in conceiving causal interaction clearly and distinctly, difficulties which Malebranche uses to support his claim that the only active agent is God, and we will be concerned with these in the next 84

G VII:321. See the discussion by Parkinson, Logic and Reality, pp. 36f.

Activity and passivity after Spinoza and Malebranche 111

chapters. But his theory that each substance is the source of its own phenomena is incompatible with Malebranche's theory of the utter passivity of creatures. Substances are, for Leibniz, active even if not interactive. The denial of interaction and the presentation of the soul as a system closed in on itself was an exceptionally effective defense against Spinoza, for if nothing happens to us except our phenomena, we cannot die; the external forces of disruption or even of gradual decay have nothing to fasten on to. But Leibniz needed some formula to replace ordinary empirical talk about the transeunt actions and passions of individuals when metaphysical truth is at issue, and, interestingly, he appears to derive inspiration precisely from Spinoza's discussion of activity and passivity as they relate to intellectual understanding. At any rate, his claim that "the action of one finite substance upon another consists in ... the increase of degree of its expression together with the diminution of the expression of the other"87 is similar to Spinoza's theory that activity consists in the possession of clear and distinct ideas, passivity in the possession of confused ones; the evidence for it appears to be drawn from the phenomenology of the emotions. According to Leibniz, for a substances to act is for it to "improve and enlarge itself"; for a subject to be acted upon is for it to suffer some degree of limitation and pain. Thus, a creature is active and undertakes movement for its own betterment and increases thereby its expression of the universe, while a creature is passive or suffers punishment by limiting its movement and perception or suffering their restriction. Note that the theory is not intended to apply, for example, to an ordinary case of collision in which an "active" billiard ball sets a "passive" one into motion; Leibniz assures us that we can continue to speak of one as acting upon the other, rather as good Copernicans speak of the sun as coming up and going down. "One billiard ball" is metaphysically inexact anyway. But wherever individual substances and hence souls are directly involved, as they are in the case of voluntary action and perception, it is important to introduce this new conception. "One has good reason to say", he insists, "that my will is the cause of this movement of my arm and that an interruption in the continuity of the matter of my body is the *7Discounx, §15, L 312; G IV:440; MB 56. Cf. Spinoza, Eikics, Pt V, Prop. 3: Curley, 1:598.

112 The Discourse on Metaphysics cause of the pain, for the one expresses distinctly what the other expresses more confusedly". 88 Pain is thus the confused expression of something distinctly expressed by the interruption of bodily continuity; the will expresses distinctly what a movement of the body expresses only approximately or indistinctly. Finally, we ascribe to ourselves, he says, those phenomena which we express more perfectly. 89 This we must take to mean that we ascribe sensations which we experience distinctly to our own persons, despite the fact that we express the entire universe. Is the relation between mind and body natural or supernatural? For Malebranche the answer to this important question is plainly the latter; for Descartes, despite some unclearness, it is evidently the former. Mind-body interaction, though impossible to explain theoretically, Descartes argues, is experienced by everyone and is obviously possible and so, we may conclude, natural. Leibniz, as we have seen, never accepted the Cartesian theory of two substances. Nevertheless, he cannot avoid facing the problem of how physiology is related to sensation. The theory of pre-established harmony which is supposed to answer the question is stated only sketchily in the Discourse but given greater elaboration again in the correspondence. "Whatever is expressed in the body by a movement or by a change of position, is perhaps expressed in the soul by a sense of pain". 9 0 This expression is not, however, simply a relation between a bodily state (for example, injury to tissue) and a mental one (pain), but extends through a whole series of intermediate states: The nerves and membranes are for us the parts which are more sensitive than the others and it is, perhaps, only through them that we perceive what seems to happen to the others, because the movements of the nerves, or of 91 the liquids in them, imitate the impressions better and confuse them less .. . As long as the direction of imputed causation and hence distinctness of expression is supposed to run from bodily state to experience, this attempt to explain the role of the nerves cannot be considered entirely successful. For if the nerves are, loosely speaking, the causes »8Letter to Arnauld (draft), 28 November/8 December 1686, M 154; G 11:71. 89 Discourse, §15, L 313; G IV:440; MB 56. '"Letter to Arnauld (draft), 28 November/8 December 1686 M152; G 11:70. «ι Letter to Arnauld, 30 April 1687, M 181; G H:90f.

Activity and passivity after Spinoza and MaUbranche 113

of experiences, they must express the state of the world more distinctly than the soul itself. But what is interesting here is Leibniz's attempt to introduce continuity and hence true naturalness into the mind-body relation. Rather than an inexplicable leap from bodily state to mental state, we have a sequence of expressions covering the state of the body, the nerves, the membranes of the brain, unconscious sensations, and finally conscious sensations. Again, however, there is a conflict with the analysis of causation; for an unconscious sensation standing farther towards the "active" side of the pseudo-causal chain ought to express the universe more distinctly than the pseudo-passive conscious sensation. Arnauld finds all this puzzling. He attacks the theory on two fronts, as an explanation of sensation and as an explanation of voluntary action, taking particular exception to the claim that my relation to my own body is privileged in that my soul expresses more distinctly what takes place in its body than what takes place anywhere else. 92 How, he asks, can the soul be supposed to have more knowledge of the movement of lymph in the lymphatic ducts than of the movement of the satellites of Saturn? How can a body set itself in motion at precisely the time when the mind wills it to move? Leibniz replies that the movement of the lymph is in fact perceived better than the movement of the satellites, though it is perceived only indistinctly. This is only because of habituation, or the inability to distinguish bodily sensations from one another; at the beginning of an illness, for example, a small alteration of the lymphatic circulation might lead to powerful subjective symptoms. The satellites of Jupiter and Saturn are known "only in accordance with a motion which is produced within the eye", and small changes here might well be undetectable. 93 The second question is more troublesome. It is true, he concedes, that stationary bodies cannot set themselves into motion. But there are no absolutely stationary bodies. A body could be reduced to perfect repose only by a miracle, and it would then indeed require a new miracle to set it in motion. But the initiation of motion in, for example, a motionless sleeper who suddenly wakes and lifts his head, only apparently involves an abrupt transition from repose to movement; on a deeper «Letter to Leibniz, 18 August 1687, M 203; G 11:105. 93 Letter to Arnauld, 9 October 1687, M 213; G 11:113.

114 The Discourse on Metaphysics analysis, what must be involved is the redetermination of a certain tendency to motion already active in the body.94 21 Fate of the Discourse: Leibniz and Descartes Leibniz concluded his exposition and defence believing, no doubt, that he had succeeded in addressing the major issues of the day: mechanism, miracles, predestination, the nature of substance, the distribution of grace, and the perfections of God. He had also hoped to undermine Arnauld's Cartesianism by pointing out the errors of the Cartesians on the equation of substance and extension, and to suggest means of reconciling some of Arnauld's disputes with Malebranche. Unfortunately, the Discourse must have appeared to Arnauld to contain all the disagreeable features of Malebranche's philosophy - his doctrine of ideas, his determinism, and his conception of God as obliged to act in particular simple, uniform, intelligible ways - together with a new scandal, Leibniz's theory of logico-conceptual predestination. Malebranche's critics had accused him of the Pelagian heresy. They took his claim that God acts only according to general laws, and wishes for the salvation of all, to imply that, even without particular gifts of grace, natural man was not so depraved that he could not earn salvation by his own efforts. Leibniz's theory was open to the same charge, as he recognized. 95 A substance does what it can and what it is bound to do: it is not susceptible to unforeseen intrusions, even from God himself. In making salvation dependent in any way on the worth of the individual, not arbitrary and inscrutable, he was indeed, even if unintentionally, going against Augustinian orthodoxy. By the end of his correspondence with Leibniz, Arnauld is clearly somewhat frustrated. To Hessen-Rheinfels, he describes Leibniz as holding "a good many very strange opinions" in natural philosophy, "some of which appear to be hardly tenable". 96 He indicates that he has tried to convey this to Leibniz without hurting his feelings, and repeats his suggestion that Leibniz ought to give up philosophical M

ftW.,M217;GII:115f. "M. Arnauld thought when he first saw it that it diminished the role of grace and supported the Pelagians". Letter to rHopital (unfinished), 12/22 July 1695; given in Robinet, Malebranche et Leibniz, pp. 318f. «Letter to Hessen-Rheinfels, 31 August 1687, M 209; GH:110. ,5

FaIc of the Discourse: Leibniz and Descartes 115

speculations until his conversion to Catholicism is accomplished. "There are numberless problems", he had told him "which are not to be solved before one has faith and will not be solved in life without faith". 97 Leibniz reacted indignantly, accusing Arnauld in turn of intolerance. "[Is] it not", he asks, "to repulse men by a useless and untimely strictness, to condemn so easily all kinds of opinions which have nothing to do with faith?" 98 If the DUcourse had been intended as the basis of a metaphysics acceptable to Protestants and Catholics alike, this remark would reveal Leibniz as desperate indeed, ready to wash his hands of the whole project. And, despite his great eagerness later to prove the compatibility of his monadology with any number of theological opinions, it is difficult to believe that Leibniz ever applied himself with the same ingenuousness to the reconciliation of philosophy with theology. Arnauld had misunderstood nothing. The old harmony theory, the immanentist substructure of the Confessio, is not fully lost behind Leibniz's attempt in the Discourse to introduce a transcendent God of choice, creation, reward and punishment. In a curious way, Leibniz seems as unable as Spinoza to hold sin against the individual. For Spinoza, it was impossible to say that Adam's sin was an imperfection, wrong in itself, or contrary to the will of God. "[I]t is as impossible for something to happen contrary to His will as it would be for something to happen contrary to His intellect." 99 The problem of why God ordained that Adam would eat the apple, then forbade him to, then punished him when he did, is, according to Spinoza, not to be solved by philosophical distinctions but by a better biblical hermeneutics. The point of telling the story of prohibition and punishment is to convey to the unsophisticated the true meaning of the story, which is Adam's discovery of death. To be sure, Leibniz did not possess Spinoza's radical theory of biblical interpretation, his repugnance towards the very idea of sin, or his sophistication in handling the story of the expulsion from Paradise. But his acceptance of Adam's sin insofar as it constitutes part of the world-order, an acceptance re-expressed as the conformity of this sin with God's plans, is part of a rationalism not easily reconciled with Christian «Letter to Hessen-Rheinfels, 12 April 1686, M 74; G II:15f. «Letter to Hessen-Rheinfels, n.d., M 238; G 11:131. "Letter to Willem van Blijnbergh, 5 January 1665: Curley, I:358f.

116 The Discourse on Metaphysics teachings about evil, which find its cause in the wayward, autonomous impulses of men qua men against God. Leibniz's speciestheory appears to efface the generality of sin, as well as its particularity. It is clear that Leibniz, freed of his early extreme provincialism in matters of religion, was privately attempting at the time of the Confessio and through the late seventies to recast relations between God and the world, soul and body. Tschirnhaus could report that in the Paris period he had found Leibniz "free from the usual prejudices of theology . . . without being led by the affections, he simply followed the dictates of reason". 1^o Perhaps Leibniz did not regard these experiments as altogether successful; but he made them, and they were not particularly consistent with orthodoxy. "The soul acts, somehow, in the body", he writes: So God in the world: not by way of miracles, but through mechanical laws, so that if per impossible minds were destroyed, and the laws of nature remained, it would still be as though there were minds, and books could even be read and written by human machines in no respect intelligent. We cannot know if this can take place... Souls do not act in bodies irregularly, nor God in nature .. .101 These are free and astonishing speculations; if God never acts irregularly in nature, as Malebranche had all but declared and as Spinoza explicitly maintained, little of orthodox theological dogma can survive. Like the philosopher he refused to read, Malebranche thought ordinary people believed that there are two forces in the world, Nature and God, and that God can reveal himself only by acting against Nature. To the true philosopher, however, he reveals himself in the ordinary course of events. 102 Malebranche's official parallelism, his recognition of a realm of grace existing alongside a realm of nature, is thus a provocative rather than a defensive move in the seventeenth-century context, and the same is true of Leibniz's. For the purposes of advancing his own anti-occasionalist views, Leibniz later resorted to the implied formula "Malebranchism is Spinozism", with the intention of being

iG. Schuller, Letter to Spinoza, 14 November 1675; Spinoza, Opera, 11:235. ioiBodemann, Die Leibniz-Handschriflen, p. 89. 102 TmUede la natureetdelagrace, I:XXI (Addition): Oeuvres, V:34f.

Fate of the Discourse: Leibniz and Descartes 117

somewhat shocking. But he had captured an important truth and was more bound up in it himself than the accusation suggests. Leibniz's judgements of Spinoza in the following years were sometimes surprisingly mild. He defended, for example, Spinoza's resistance to becoming a convert to Catholicism.103 By contrast, his attitude towards Descartes was characterized by a nearly surreal exaggeration, which reached a peak in the immediate post-Discourse period. His animus was curbed only in the late 1690s, when the Cartesian Henry Sylvain Regis, having intercepted a letter, denounced Leibniz publicly in the Journal des savants for having "wished to found his reputation on the ruins of Descartes", as was clear, he explained, "from the alliances he has formed and from the fragments he injects from time to time in the Journal de France".104 Regis advised him (maintaining that this was also the secret opinion of his best friends) to avoid metaphysics, which he did not understand, and to stick to mathematics, for which he admittedly had a good head. He saw through Leibniz's strategy of implying guilt-by-association, stating that the difference between Descartes and Spinoza was "as night and day". This denunciation appears to have had a sobering effect. At any rate Leibniz was deeply hurt, and his anti-Descartes campaign came to an end. Leibniz's actions are best explained by reference to what Robert Westman has aptly called the "Cartesian Syndrome", the difficulty of establishing a philosophical identity in the post-Cartesian era. 105 Like Huygens and Newton, Leibniz, at different times in his life, rang every chord between hero-worship and contempt, recognizing all the while that Descartes had entirely altered the old meaning of philosophy. "I know of no one", he writes, "who had views as comprehensive as his, joined to a penetration and a depth as great as his own". Descartes's genius, he says, has been more useful to the 103

Friedmann, Leibniz et Spinoza, pp. 92f. Reflexions sur une lettre de Monsieur Leibnits... dans laquelle il pretend faire voir que Us principes de la Philosophie de Monsieur Descartes renfermenl des consequences contraires a la Religion et β Ia piet G IV:333. 10S "If we collectively examine the biographies of Huygens, Henry More, Leibniz, Newton and others," Westman observes, "we find that each in his own way 'discovered' Descartes, each was initially overwhelmed by the power and coherence of Descartes's system, and then . . . each sought to destroy and rebuild it. We might call this general pattern of reactions the 'Cartesian Syndrome'". "Huygens and the Problem of Cartesianism", p. 99. 104

118 The Discourse on Metaphysics human race than all the erudition of "those grammarians". 106 Probably no theorist of the seventeenth century, certainly not any of the "Cartesians", was capable of studying Descartes with the same focussed attention as Leibniz himself, who for that reason could not bear being thought of as a Cartesian. Some of his summary judgements are, accordingly, utterly absurd; some are deep. He was acute, for example, in recognizing the problematic character of Descartes's recourse to clear and distinct ideas. There can be no standard, inter-subjective means of measuring the clarity and distinctness of a thought. He saw the celebrated Cartesian method as nothing more than an attempted legitimization of the nearly pathological self-confidence of its author. Vision, as he says, drawing on his private knowledge of Descartes's highly egotistical versions of mystical experiences in his youth, makes visonaries. The four Rules of Descartes's Discourse on Method are not rules of the sort which could help anyone out, but mere hand-waving - equivalent to the injunction "Be and do as you should and you will get what you want". 107 According to Leibniz, an example of the pitfalls of Cartesian illuminism is the set of proofs for the existence of God in the Third Meditation. Descartes's argument that nothing less than God can be the cause of his idea of God is "too short and violent", as is his use of the ontological argument. Perhaps, he argues, Descartes thinks he has an idea of God when he really only attaches some vague image to certain predicates. Now, it is true, Leibniz says, that we often indulge in such "blind" or symbolic thinking, using a name or an image or a short description to stand for a full concept. In mathematics, blind reasoning is essential; we think with unanalyzed symbols. But such thought is only secure when the concepts employed are demonstrably free of contradiction. And the idea of "the most perfect being", no less than the idea of "the most rapid speed", may contain a contradiction. So may the idea of a "non-extended substance", for all Descartes knows. He has proved that we may doubt the corporeality of the soul, but not that mind and body are distinct substances. 108 Leibniz's own fascination with the syllogism, his dedication to the systematization of existing knowledge, his concern for the "order of 106

Remarques sur labrege it la vie Ae Mons. des Cartes, G IV:324. M A K quaedam G.G.L circa vilam ei doclrinam Cariesii, G IV:329. ^letier Io Sophie, n.d., G IV:293ff.

107 w

Fate of the Discourse: Leibniz and Descartes 119

materials" in the scholastic sense, made him distrust Descartes's attempt to dispense with these procedures. 109 Given the novelty of his own discovery of the calculus, this is at first hard to understand. But he and Descartes attached entirely different kinds of significance to their mathematical discoveries. For Descartes, the discovery of his own stupendous mathematical talent in his geometrization of algebra gave him the confidence to reject an entire body of learning, to see, in the unfolding of a long chain of consequences from the analysis of a problem, the possibility of a new form of metaphysical reasoning based on intuitively clear steps and having nothing to do with the old logic. For Leibniz, the discovery of the calculus was a hint, a shadow, of something he considered far greater, a comprehensive and universal logic broader in scope than mathematics itself. He did not perceive the possibility of doing without the old logic but wanted to bring it to an undreamed-of perfection. We can thus concur with Friedmann, who found Descartes the true object of Leibniz's jealousy and animosity, Spinoza only a convenient weapon. Eventually, Leibniz would succeed in criticizing not only Descartes's theology, but his cosmology, his philosophy of science, his ethics, his theory of method, his mathematics, his scientific relationships, and his morals. Descartes, he tells us, plagiarized from Aristotle, Democritus and Leucippus, Kepler, Snell, Fermat, Vieta, and Harvey without the slightest acknowledgement, pretending to have arrived at his views through an unaided intellect stripped bare of external influences. 110 He tells us in his autobiography that he spent his time soldiering, not shut up in libraries, but he writes in the "collegiate style". 111 He mishandled his scientific relationships, quarreled with other mathematicians, exploited his disciple Regius, and used his translator Schooten "as his creature". 112 The logician Jungius was far superior to him in philosophical depth, and it is a tragic accident of history that one became famous while the other remained obscure. It is fortunate that the relation between Descartes and Leibniz is not, for example, that w *Notae ... circa vitam et doctrinant Cartesii, G IV:328ff. See Belaval, Leibniz, critique de Descartes, esp. pp. 23ff., and Hacking, "Leibniz and Descartes: Proof and Eternal Truths", on the conflict between Cartesian "intuitionism" and Leibnizian "formalism". no Letter to Molanus, n.d., G IV:304ff. wlbid., G IV:307. ul Remarques sur I'abrege de la vie de htons. des Cartes, G IV:321f.

120 The Discourse on Metaphysics of Democritus and Diogenes Laertius, and that we have sources other than Leibniz's notes, for the following judgement from a letter to Molanus is not untypical: Descartes himself had a rather bounded intelligence; he excelled above all in speculation, but never discovered anything concrete or practically worthwhile. His Meditations are too abstract, like his metaphysics and his geometry; or too fanciful, like his physics. Only his hyperbolic magnifyingglasses, with which he promised us we could see animals on the moon and all the tiniest parts of creatures, were a useful invention, but unfortunately he could never get anyone to execute the design. And besides, the advantage of the hyperbola is really not so great as he thought.. .113

i » G IV:298.

IV Metaphysical foundations for natural science

After the debacle of the Discourse, Leibniz could see that the «introduction of substantial forms via a theory of animated substance was going to prove more difficult than he had hoped; the intellectual climate was perhaps more favorable to Cartesianism than he had suspected. After 1686, he returned in any event to a study of Descartes, finishing the collection of annotations to the Principles of Philosophy by 1690. Meanwhile, on a diplomatic trip to Rome, he had encountered Isaac Newton's Mathematical Principles of Natural Philosophy, which prompted him to push forward his own physical theories in opposition to it, an impulse which resulted in the Specimen Dynamicum of 1695. Both studies forced him to clarify his position with respect to the problems of force, activity, natural law, and the form of scientific knowledge in general. Leibniz had always thought of physics as the antechamber of metaphysics; important truths about God and the soul were to be extracted from the study of matter and motion. But this union of theology and empirical science became increasingly indirect, as Leibniz moved farther away from the position of philosophers who insisted on giving God a significant role to play in the establishment and maintenance of the laws of nature, or in mechanical interaction. Whether the issue was atomism, gravity, or causal interaction, his aim was to reconstruct physics around the notion of the powers of a substance - in the particular Leibnizian sense of "power" as something "between the mere capability of acting and action itself"1 rather than, with a good number of his distinguished contemporaries, the power of God. In reintroducing forms and powers, 1

O n the Correction of Metaphysics and the Concept of Substance" (1694), L 433; G IV:469.

122 Metaphysical foundations for natural science

Leibniz was only superficially taking a backward step, or continuing with his early project of reconciling physics and theology. In a deeper sense, he was liberating physics from its entrapment in theology. This is true despite the fact that he did so ad majorem gloriam Dei, and that the work involved retrieving certain discarded concepts. 22 Critique of Cartesian rationalism To understand this "correction", and with it Leibniz's opposition to the scientific procedures of both Descartes and Newton, it is important to grasp the point of his contrast between "geometrical necessity" and "metaphysical reasons". Leibniz tried persistently to show that a purely geometrical science of nature - a designation which, he thought, characterized not only the Cartesian kinematics, a science of motion without forces, but the Newtonian so-called dynamics as well - was impossible or incomplete. Cartesian science, which operated with the notions of res extensa and motion alone, left too much open; it did not decisively limit the possibilities. Newton, in turn, had called upon forces in addition to matter and motion, but he had failed in Leibniz's view to ground these forces metaphysically, to give them a philosophical justification. Leibniz's frequent appeal to principles to justify his doctrines - to the principle of sufficient reason and the principle of the identity of indiscernibles to show why space and time are unreal and why there can be no atoms; to the law of continuity to show why the Cartesian rules of motion are unsound - can produce the impression that these principles, springing straight from a faculty of pure reason, were applied in a dubious way to the subject-matter of science. Perhaps nature is interested in such principles, the critic may feel, but then again perhaps it does not care for them and produces indiscernibles or discontinuities in abundance. If so, a science based on a priori principles stands no better chance of success than one which is not, and perhaps a worse chance. But the impression of apriorism in Leibniz's work is somewhat misleading. It is true that his criticisms often depend on thought experiments. But they are also, he thinks, repeatedly confirmed by experience: a science which ignores them typically turns out, judged on independent grounds, to be wrong. His objections to the equation of matter with extension and to atomism itself depend upon principles of a much lower order of generality.

Critique of Cariesian rationalism 123

Indeed, Leibniz was in many ways a critic of scientific rationalism. A confusion between geometry and physics lay at the heart, he thought, of the unsatisfactory theory of hypotheses shared by Descartes and Spinoza. Both declare that it is a matter of indifference how we explain physical effects so long as we derive them in an orderly fashion from hypotheses; what counts is the structure of the argument. Spinoza ties this claim directly to the geometric nature of the external world. If one wishes to investigate a parabola, he says, it does not matter how this curve was generated, whether sliced from a cone or described by the motion of two lines, or in any other way. "Similarly", he continues, "we are permitted to assume any hypothesis we please to explain the features of nature, provided that we deduce all the Phenomena of nature from it by Mathematical consequences".2 For Leibniz, who, as we have seen, believed that even mathematical figures are distinguished by their origins, the analogy between a phenomenon in nature and a geometrical object is entirely misconceived. To investigate a parabola is to determine what further properties can be inferred from its definition, where to investigate a natural phenomenon is to determine how it comes about. We are not permitted to assume any hypothesis we please, because the task is precisely the determination of the correct explanation out of the multiplicity of possible explanations. Descartes had, as he told his readers, adopted the geometrical approach to phenomena to avoid the obscurities of the scholastics when it came to assigning causes. The early mechanical philosophers complained persistently that they could not understand the scholastics' explanations when these were phrased in terms of "natures" and their distinctive "virtues" or "faculties". To say that rocks are formed in the bowels of the earth by a "fossilizing virtue" is to leave their formation as puzzling as ever. But neither Descartes nor Boyle, an equally powerful opponent of scholastic physics, ever achieves the terse formulation of Moliere. The usual objection against explanations phrased in terms of faculties and powers is not that they are ridiculously tautological but that they are unsuited to our intelligence. As Descartes argues, we understand mathematical concepts (size, shape, motion, speed) and the mathematical arguments 2

Spinoza, "Descartes's Principles of Philosophy", Pt III, Curley, 1:296.

124 Metaphysical foundations for natural science

which take their relations into account; we do not understand the language of powers and virtues, except in a confused and subjective way. We know nothing about the "natures" of the objects God has created. Physics should for this reason be conducted without reference to them, and without reference to God's plans or his principles of design, which we know nothing about either. If nature were to take any form other than that proposed by the mechanicomathematical philosophy it would be essentially unknowable. But it is knowable - for God is not a deceiver; hence this philosophy is true.3 With this claim Descartes stumbled against the old problem of the underdetermination of all theories depending upon unobservables; for the magnitude, figure, and motion of the parts which explain observed effects are not open to direct inspection. If one is concerned simply to save the phenomena, any number of hypotheses will serve equally well. But if the philosopher professes an indifference to the true nature and relations of the unobservables involved, then it is hard to see how he can claim to have explained the phenomena any better than the scholastics with their specially selected powers and virtues. If, on the other hand, he believes he has an indirect means of arriving at an understanding of the unobservables and their relations, he must justify this claim. Descartes's handling of this problem betrayed the defects of his method. Comparing nature at one point to a coded message, he states that the first code we try out which gives a sensible reading - that is, the first hypothesis we locate from which the phenomena can be deduced - is to be accepted; there is no reason to look further.4 That other keys might deliver the same message makes no difference. The only real criterion for the acceptability of an hypothesis is, according to Descartes, its ability to account for many phenomena simultaneously. This condition, he thought, was sufficient to remove the charge of circularity from his own procedures and to differentiate them from the procedures of the scholastics, who proposed a separate explanation for each phenomenon. As the discussion at the end of his Principles continues, however, it becomes clear that Descartes is actually torn between two views: the first, that we can never possess real as opposed to 3 I take this to be the general agenda of the Meditations: see Caton, The Origin of Subjectimty, esp. pp. lOff. * Principles, IV:205: AT IX-2:323f.; HR 1:301; CSM 1:290.

Critique of Cariesian rationalism 125

"moral" certainty about the truth of any physical hypothesis because of the possibility of a multiplicity of keys to the code;5 the second, that it is within the power of a genius of his own stamp to hit immediately on the right one.6 Even if he had taken up his principles at random, Descartes boasts, everyone would have to admit that "it could hardly happen that so much would be coherent if they were false". " Both alternatives, the claim that the adoption of any phenomenasaving hypothesis is justifiable and the claim that some exceptionally capable physicists are able to hit on the uniquely correct hypothesis by intuition, seemed undesirable to Leibniz. Despite his leaning towards a radical coherence theory of truth in broad questions of epistemology of the sort raised by Foucher, he believed that a via media between the Cartesian alternatives was necessary, and that it lay in the acknowledgement of certain principles of choice for discriminating amongst hypotheses. Some of these principles are objective; by applying them one is capable of constructing a physics which mirrors God's thought. Others are conventional; by applying these one arrives at a hypothesis which is convenient for certain ends, but which does not represent the whole truth of the matter. As exaggerated claims are often made about Leibniz's realism or antirealism in the philosophy of science, it is important to distinguish these principles and their specific realms of application. First, on the objective side, physics must take into account certain "architectonic" principles of construction which Descartes's ban on talk about final causes had made impossible. Solutions of optical and mechanical problems are subject to constraints deriving from such considerations. In this context, Leibniz regularly assumes that we do have insight into the ways of God or the principles upon which the world is constructed. It is not simply by convention that we adopt the simplest or most elegant statement of the laws of reflection and refraction, or the laws of collision. Nature herself chooses a minimum path, producing the greatest effect with the least effort. Second, physics must not ascribe to objects powers and properties which do not follow from their natures, even if such ascriptions bring Hbid., IV:204: AT IX-2:322; HR 1:300; CSM 1:289. *lbil, IV:205: AT IX-2-.323; HR 1:301; CSM 1:290. 'he. cit.

126 Metaphysical foundations for natural science

the phenomena into order. We can know, Leibniz will later argue, that gravity or the power of attraction is not a natural property of physical masses, for nothing in the concept of mass can explain it. The suggestion that God can, if he wishes, superadd a non-natural power to physical masses is unacceptable. God does not tamper with the natures of created things. In both cases, Leibniz appears to speak as a realist about the status of laws, objects, and their powers, and this realism is not in the least offset by his belief that matter and motion are themselves not entirely real. By contrast, when it comes to problems involving the ascription of motion or rest, such as the question of heliocentric v. geocentric astronomy, the choice of hypothesis is dictated purely by convenience and economy of description. It is not that such problems belong to a more superficial level of knowledge than mechanics and optics. Rather, because God's perspective on the world embraces the totality of all possible perspectives, it makes no sense to suppose that architectonic considerations can determine which objects are absolutely at rest, which in motion. That a particular object is at rest is true for an observer in a particular reference frame, false for other observers: there is no need of, and no possibility of, any more objective determination of matters. We decide that the boat is moving and that we are standing still, or that the earth moves and the sun stands still, simply because the resulting description of the phenomena is simpler for the purposes which concern us. Finally, corpuscular explanations of phenomena, though convenient, are highly approximate, because the world is actually a plenum. Here, Leibniz argues as an anti-realist or even an instrumentalist, who fully accepts the consequences of claims about the equivalence of hypotheses and believes in explanatory fictions. There is accordingly no point to designating his philosophy of science as realistic or anti-realistic tout court. The application of the first principle takes a number of forms. Leibniz is able to show in the "Critical Thoughts", for example, that Descartes's laws of motion require three unrelated graphs for the representation of the collision of two bodies of equal size moving at different speeds in different directions. A single continuous curve, he discovers, is actually adequate to the representation of every case. "All these incoherent rules", he says, "are already excluded in advance of a full understanding of the matter or of the discovery of the kind of

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line [curve] involved". 8 This unembarassed apriorism amounts to the claim that we do possess insight into the aims of God or the characteristics of nature, which exclude over-complex hypotheses even if, lacking a full understanding of the matter, we have not proved that they do not account for the phenomena. Choice of the simplest hypothesis here is more than mere convention, for Leibniz is confident that a full understanding of the matter will confirm empirically the choice of the simpler or more elegant curve, or the solution to the problem which involves the determination of a maximum effect with minimum effort. We shall return to some of the problems with this form of apriorism in the chapter on Leibnizian optimism. As the focus here is Leibniz's rejection of Cartesian philosophy of science, it is useful to ask why Descartes had accepted these rules, with ail their oddities, which patently conflicted with experience as well as with the desire for simplicity. For he goes so far as to insist in his suppressed Treatise on Light that these laws would hold good in all worlds, not simply on earth. In Leibnizian terms, this means that they are necessary, and it is at first difficult to see why Descartes should have committed himself to what was in any case a strong claim. As we have seen, a failure to conform to experimental observation was not, for Descartes, for Hobbes, or for the Leibniz of the Theory of Abstract Motion, a reason for abandoning a theory; and, pace Hume, the laws of collision mechanics are not to be derived by experimentation with billiard balls on tables. The Galilean contrast between the senses and reason, which had served so well in the defense of the Copernican system, could always be cited as an example of the limits of empiricism. This pattern of thought is evident in the treatment of Descartes's much-disputed Fourth Rule of Motion, which states that a body at rest can never be moved by a smaller body in motion. 9 This seemed evident to Descartes for bodies treated geometrically, where resistance is simply measured by weight. Even if one body contained more quantity of motion mv than another, Descartes did not believe that the lighter body would transfer this motion; it would simply rebound against its immovable opponent and conserve mo by this alternative means. Descartes believed, in other words, that ""Critical Thoughts", 11:53, L 403; G IV:384. «Principles, 11:49: AT IX-2:90f.

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"movement" and "rest" were both positive states of a body, each resisting the other. To decide which of two bodies will win in a confrontation between movement and rest, one can only have recourse to their masses.10 Rule Four, finally, can even be regarded as a special case of Rule Two, which states that in a collision between a smaller and a larger body moving at the same speed, the smaller will change direction, both continuing with their original speed. Cancelling out the motion of the larger body, it appears as though the smaller body ought simply to rebound, continuing in the opposite direction. As Descartes well knew, experience provides many examples contrary to Rule Four. He himself attempts to disarm objections by considering the case of a large vessel in water which is easily set in motion by a smaller tugboat. The ship, he explains, is in a fluid medium, pressed on all sides by masses of water and thus motionless. The push from the tugboat is simply added to the pressure from one direction, and the total body acting on the ship is now greater than the ship. The ambient aether, or particles of subtle matter, has the same effect on ordinary bodies. In a void, however. Rule Four would hold good just as it stands.11 But the fact that he was able to explain away the apparent evidence against the rule does not fully explain why Descartes was so committed to it in the first place. He must have recognized the difficulty inherent in maintaining that the resistance exercised by a body increases mysteriously with the size of the body which collides with it, before suddenly vanishing altogether when the two bodies reach equal size. But he saw two crucial features of his world-system as depending on the truth of the rule. If it were false, he realized, the fine particles of his aether, which filled all of space and transmitted light mechanically to our eyes, would lose all their motion to the massive stable objects which they continually bombarded; the vortices would lose their power to drag the planets around, and the world would come to a standstill.12 Second, if the rule were false, he had no good explanation for cohesion. As things stood, he could suppose that a bar of iron retains its bar-like form because one part 10 See the "Extrait de la vie de R. P. Malebranche", in Malebranche, Oeuvres, XVII1:19. Cf. Recherche de la verite, VlMXK, Oeuvres, 11:444. "Principles, 11:56: AT IX-2:95f. 12 As explained again by Malebranche, Recherche de la verite, VI:II:IX, Oeuvres, II:447f.

Critique of Cartesian rationalism 129

can be set in motion relative to another part only by a superior mass which is then sufficient to break it. Initially, in the Recherche de la virile, Malebranche rejected Rule Four but accepted its relative. Rule Two, along with Descartes's claim for the conservation of mv.13 He points out that Rule Four, along with Rules Five, Six, and Seven, requires a force of rest which is proportional to the size of the attacking body and thus a kind of occult knowledge on the part of the resisting body. His revisions went unchallenged until Leibniz published his "Brief Demonstration of a Notable Error of Descartes" in 1684. Malebranche conceded in 1688 and retracted his revised rules, insisting nonetheless on maintaining the Cartesian conservation of mv. Leibniz remained dissatisfied, and continued to urge Malebranche privately to dispatch Cartesian physics wholesale. 14 As Leibniz had realized, Rule Two is as problematic as Rule Four. When two bodies of equal size collide, they rebound in opposite directions. If we increase the size of one ever so slightly, its direction is suddenly reversed. This is incompatible with the principle which Leibniz enunciates as follows: When the difference between two instances in a given series or that which is presupposed can be diminished until it becomes smaller than any given quantity whatever, the corresponding difference in what is sought or in their results must of necessity also be diminished or become less than any given quantity whatever.15 Each body must possess both a tendency to be reflected and a tendency to push the other body before it. If one body is now infinitesimally larger than the other, it will be reflected only a little less, the other pushed a little more. Malebranche, Leibniz notes shrewdly, was less troubled by the peculiarities of the Cartesian laws than he should have been because he was an occasionalist. "Father Malebranche admits in a way that there is some difficulty in them,

™lbid., Oemres, 11:444. "Letter to Malebranche, 13/23 March 1699, G 1:356. Cf. Malebranche, Oeuvres, XVII-1:15. See also Robinet, Malebranche el Leibniz, pp. 337f. On the reasons for Malebranche's resistance, see Costabel, Leibniz and Dynamics, p. 59. 15 "Letter of Mr. Leibniz on a General Principle Useful in Explaining the Laws of Nature through a Consideration of the Divine Wisdom; to Serve as a Reply to the Response of the Rev. Father Malebranche", L 351; G 111:52, Cf. "Critical Thoughts", 11:45, L 397f; G IV:376.

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but he continues to believe that since the laws of motion depend on the good pleasure of God, God could therefore have established laws as irregular as these".16 Leibniz admits that the principle of continuity may be violated or may appear to be violated in certain cases: a small spark falling into a mass of gunpowder can destroy an entire city.17 But this discrepancy disappears when we have given a full account of the situation, in which case it is clear that the laws of nature which explain it fall under the principle. He is willing to extend it even to the problem of sensation. In the New Essays, for example, he notes that the Cartesians, as well as Locke, "regard it as arbitrary" what perceptions we have of the qualities of color and warmth, "as if God had given them to the soul according to his good pleasure, without concern for any essential relation between perceptions and their objects. This is a view", he says, "which surprises me and appears unworthy of the wisdom of the author of things". There must be a relation of continuity between the motions in bodies which correspond to these qualities and the "insensible parts" of sensible perceptions.18 The analogy is made explicit: the falsity of the Cartesian Rule Two is held to support the theory of insensible perceptions: "To think otherwise is to be ignorant of the immeasurable fineness of things, which always and everywhere involves actual infinity".19 Leibniz's criticism of Descartes's Rules is an example of the complex interplay between metaphysical principle and experiential data. Historically, it is difficult to say whether Malebranche himself was moved more by Leibniz's appeals to a stronger notion of order or by Mariotte's experimental determinations, using a clever apparatus, of the true collision rules. But even if it took Mariotte to budge him, this hardly saves the case for a Humean empiricism. Clearly, such higher-order principles as the principle of continuity are not applied in indiscriminate and dogmatic fashion to the data, and Leibniz's complaints about the irregularity of Descartes's Rules are fully justified. Leibniz's rationalism, moreover, if rationalism is just the adherence to such principles, must be distinguished from Descartes's; the one rejects, the latter accepts, the claim that the laws of motion wftirf., L 352; G III:53f. "Ibid., L 353; G 111:54. '«Nno Essays, RB 56f.; AK VI:VI:56f. "Loc. cii.

Critique of physical atomism 131

are available only to reason because they cannot apply to the empirical case. When Leibniz rejected the presuppositions of the Theory of Abstract Motion, he was rejecting rationalism in the Cartesian sense. Rather than a set of weakly rational laws whose evident inconsistency is mitigated by claims about the omnipotent and inscrutable will of God, and whose empirical failure is referred to the complications of the real world, Leibniz insists on strongly rational laws, supported only by the wisdom of God and consistent with phenomena. "In the true theory of motion", as he says, "there is remarkable agreement between theory and experience". 23 Critique of physical atomism Our second example of the complex interplay between principle and data is the often-repeated claim, based on remarks in the LeibnizClarke correspondence and elsewhere,20 that Leibniz rejected physical atomism because it implied the existence of a vacuum, this being incompatible with the principle of plenitude; or that he rejected it because it implied the existence of many identical objects, this being incompatible with his theory of the identity of indiscernibles. In fact, Leibniz's anti-atomic stance is developed at a lower level. For numerous reasons he defends a fluid plenum theory against atoms though how his theory of mini-vortices was intended to square with the theory of an infinite descending chain of organisms is wholly unclear. The immaterial atom or monad at which he eventually arrives in his metaphysical reasoning is thus not the direct competitor of the material atom, and he never abandoned his theory of perfect fluids even after he had evolved the monadology. When considering the status of corpuscular theories of matter in the late seventeenth century, it is important neither to overestimate nor to underestimate their attractions. It is equally important to distinguish between the reasons for believing (a) that the change and variety of the visible world depend upon the properties of insensible particles, and the reasons for believing (b) that these particles are solid, indivisible, hard, and denumerable - between corpuscularianism in general and atomism in particular, even if the distinction was not always regarded as significant by the participants 20 See, for example, Leibniz's "RS." to the lVth Letter to Clarke, L 691; G VII:378.

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in the controversies over atoms. For Leibniz's position is that the facts cited to prove (a) can be accounted for by another hypothesis, namely that the universe is full of miniature whirling vortices, while (b) is pure speculation about entities which turn out, on analysis, to be impossible objects. Chemistry had provided the best set of arguments for (a) against the Aristotelian apparatus of forms and qualities; for dramatic changes of color, smell, and consistency took place apparently as a result of mechanical operations alone. The variation of qualities in objects whose parts were arranged differently had always been a compelling argument against the Aristotelian theory of matter and form, and Bacon and Boyle revived it with enthusiasm. But it provided no good arguments for (b), and neither of these men could be called a frank atomist. There is even some doubt whether Gassendi, the rehabilitator of Epicurus, actually fitted the billing. Bacon, after toying with atomism, came to believe in a range of immaterial chemical spirits responsible for most important physical changes; Gassendi as well refused to proclaim the reducibility of chemistry to physics. Boyle carefully avoided taking sides. But atomism in the narrower sense, the belief in discrete material units of limited variety, was supported by several considerations. The alphabet analogy discussed by Aristotle in his critique of the ancient atomists, and by most later atomists, suggested that the invisibilia of the world should be treated on analogy with letters: as a small number of the latter can be combined to say everything that can be said, so a small number of atomic types should suffice to produce limitless effects. The invisibila should also be indestructible if they are the true primary constituents of things; translated into simple terms, this meant that they must be very hard. Other than shape, hardness, and a capacity for being moved, however, the theoretical atom needed no other properties. The notion that atoms are arranged in the void could explain the difference in weight-volume ratios between different substances more intelligibly than the theory of "condensation" and "rarefaction". One might argue as Clarke did against Leibniz, employing Newtonian "pore theory": Either there are or there are not perfectly solid particles of matter. If there are, then their parts, "taken of equal figure and dimensions . . . , are physical atoms perfectly alike". If not, there is no matter at all in the universe, for, "the farther the division and subdivision of the parts of

Critique of physical atomism 133

any body is carried, before you arrive at parts perfectly solid and without pores, the greater is the proportion of pores to solid matter"; so that if the division is carried on ad infinitum, according to Clarke's triumphant argument, "it will follow that all bodies consist of pores only, without any matter at all; which is a manifest absurdity".21 But the vacuum which they brought with them was not half so attractive as atoms themselves, and some philosophers who defended the theory of insensible particles on the grounds supplied under (a) rejected (b) for that reason. Descartes, for one, doubted that there could be a vacuum in nature: "Two bodies must touch", as he says, "when there is nothing between them".22 When we measure an empty room, his point is, we are not measuring an extent of nothingness but simply matter-as-usual, though matter of a form too subtle to be perceived. Once again, the peculiar arguments Descartes gives for the equivalence of matter and extension conceal his true grounds for maintaining this theory, which have to do with the tenability of other doctrines, notably his theory of light. He is concerned to demonstrate that light reaches us from the stars in the form of a mechanical disturbance, which requires pressure in an intervening medium.23 This theory, which is the basis of his analysis of vision, is the crux of his entire attack on forms or occult qualities. A true void would have vindicated at least the theory of visual species. The Cartesian denial of the void was in any case dealt a serious blow by Guericke's experiments with the air pump and his success in emptying the air from a bowl consisting of two hemispheres so that its halves could not be pulled apart even by powerful draft-horses. Plenists argued that the Guericke bowl was still full after the air had been pumped out, an aether subtle enough to penetrate glass or metal having rushed in to take its place. Guericke pointed out to Leibniz, as he no doubt pointed out to many others, that if the aether were subtle enough to penetrate glass it ought already to have been in the glass. But an aether which can be shut out by no container, he says, is no different from empty space.24 For Guericke, the void had its own beauty; it was the theater of the virtus mundanae - electricity "L 719, n. 24. ^Principles, 11:18, IV:206: AT IX-2:72f., 324. "Treatise on Light, Ch. IV: AT XI:16ff.; CSM I:8Sff. "Letter to Leibniz, 6/16 June 1671, G I:95f.

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and magnetism, the attractive power of the sun. A material aether, however fine, was always de trop; it could only create a drag interfering, among other things, with the motion of the planets. From as early as 1671, Leibniz sided on this issue with the plenists. Though he had once allowed that space was simply a "primary extended being . . . which contains nothing but three dimensions and is the universal locus of all things", 2S he claims against Guericke that if space is simply length, breadth, and depth, it cannot serve as a medium of transmission for any of the mundane virtues. 26 Today, he tells Guericke, with all due respect to Kircher and Gilbert, we don't approve of this talk of virtues and qualities; we require a semblance, but only a semblance, of action at a distance to explain cosmological effects; hence we must suppose the emission of a space-filling aether from the sun. 27 But this does not mean that matter is the same thing as extension. The problem with Descartes, Leibniz had already realized, is that he cannot explain why two portions of matter cannot occupy the same space. There is no reason why a substance possessing only the property of being measurable should exclude another substance whose only property is that of being measurable. Indeed movement, or a state of tension or effort, appears to be the fundamental characteristic which distinguishes matter from space, "for if everything were at rest, God himself would be unable to distinguish matter from nothing". 28 If all motion in the world were to stop, the world would disappear. Thus Leibniz turns the Cartesian argument on its head and accepts - with all its problems - the all-pervading material, and thus resistant aether. The properties of matter which distinguish it from extension must be referred either to movement, as in the case of its apparent "solidity", or to force, as in the case of its "resistance". Leibniz saw clear differences between his plenum and Descartes's. This is why he treats Descartes in the "Critical Thoughts" as an atomist despite himself who did not take seriously the consequences of his own theory of infinite divisibility. Either Descartes's extended

"Letter to Thomasius, 20/30 April 1669, L 100; G 1:24. " L e t t e r to Guericke, 1671, G 1:98. "ibid., G 1:99. 28 Proposition» quaedam physkae, AK VI:HI:56.

Critique of physical atomism 135 plenum collapses into mere space, or it must be interpreted as a fluid 29 "divided into parts smaller than any given quantity". In the latter case, there can be no perfectly hard, incompressible, inelastic bodies, and the continuity of matter must be taken as a mere appearance, like the pseudo-continuity of poured sand. This theory is essentially the one Leibniz will defend later against the atomist Hartsoeker. In the "Critical Thoughts", Leibniz attempts to establish these whirling liquid vortices in place of Cartesian particles by appealing to the problem of cohesion. Even if you hold, he says, "as do certain thinkers, that there are no parts in the continuum before actual division, it follows either that this does not prevent separation, namely, when a further reason is added which tends to produce an actual division . . . or that no continuum can ever be broken into parts." 3 0 Matter looks continuous but must consist of infinitesimally small parts whose cohesion can only be explained through motion. "I believe that matter itself, which is homogeneous and equally divisible throughout, is differentiated by motion alone . . . Thus a vigorous jet of water will prevent anything from breaking into its own path from without with more force than the same water at rest". 3 1 We learn from the case of the magnet, he continues, by means of an "elegant experiment" that things which in themselves are separate and, so to speak, sand without lime, can acquire some firmness by motion alone. When iron filings are placed near a magnet, they suddenly become connected like a rope and form filaments ... It is no doubt also by some kind of magnetism, that is, by an internal co-ordinated motion, that other parts of certain bodies are linked together .. . 3 2 Fluid bodies are characterized by the disorganized quality of their internal motions, solids by the concurrent or patterned quality. The solidity of a body is thus only apparent: "moving rapidly, like a jet of water or the spokes of a wheel", the particles "simulate one ""Critical Thoughts", 11:33-5. "What Descartes says here is most beautiful and worthy of his genius ... Yet he does not seem to have weighed sufficiently the importance of this last conclusion", namely that matter is not only infinitely divisible in principle, but in fact infinitely divided. L 393; G IV:370. *>"Critical Thoughts", 11:54-5, L 405f.; G IV:387. η Ibid., L 407; G IV:388f. nlbid., L 407; G IV:388.

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continuous solid".33 This theory is confirmed by observation, Leibniz claims. Water freezes when the agitation produced by heat does not disrupt the harmonic movement of water particles, while the motes in a sunbeam illustrate the normal agitated state. A body which appears to be at rest is one in which the sum of the direction of internal motions is effectively null; in a fluid there is "equally unhindered motion everywhere and in all directions". 34 For a piece of matter to cohere, then, all its parts - and there are an infinite number of them - must be in motion. This account clearly excludes atoms, and in his later correspondence with Hartsoeker, whose solid, simple, homogeneous, hard, inert atoms floated in a kind of spiritual broth, Leibniz reproduced many of the objections he had turned against Descartes's corpuscles. Perfectly hard atoms cannot obey the laws of nature. For, if the atom is not compressible, and thus composite, it cannot be elastic, and cannot rebound after collision.35 A related difficulty is "firmness". If the reason for the indestructibility of the atom is its infinite firmness - and no finite degree of firmness would seem to guarantee this - then all bodies, as composites of atoms, should be infinitely firm as well, which is absurd. But what, then, accounts for the differing degrees of firmness and elasticity in actual bodies? As Leibniz says to Hartsoeker: To explain the firmness which we experience we don't need a primitive and insurmountable firmness, which we don't experience, don't know how to experience, and which can never be inferred from our experience ... why stick to something so miraculous and so extraordinary with no appearance of reason? You might as well have: primitive heat, indeed primitive cold, primitive evil, primitive shadows, light and opacity, primitive density and rarity, primitive weight or attraction ... You might as well even have, he continues, "'illuminative' or 'resonative' qualities... in short, all the faculties of the old doctors". 36 For the defender of atomism, or even its half-substitute Cartesian corpuscularianism, the prospect of having an entity which could fulfill a role designed for it in the general scheme of mechanism - that "JhVi., 11:56-7, L 408; G IV:389. >*Loc.cU. "Letter to Hartsoeker, 8 February 1712, G 111:534. «Jii Essays, RB 212; AK VI:VI:212. Cf. p. 68. 130 True Intellectual System, p. 55. ™i AT VII:80; HR I:192ff.; CSM II:S6ff.

198 Atom, substance, soul

Leibniz tries now to explain the soul's concern for its body by insisting that the body is always with us. Perception and feeling are the permanent capacities of a creature and will not be erased by death. General considerations of harmony require, moreover, that only one mind, God's, exist independently of matter. The particular sensory organs of a creature are what differentiate its perceptions from those of another and give sense to the notion of a multiplicity of perspectives on the world, some superior, some inferior. In the Monadology we are told that "since . . . the universe is regulated with perfect order, there must also be an order in the being which represents it, that is to say, in the perceptions of the soul and therefore also in the body.. .".132 The importance of this doctrine is spelled out better in the Theodicy: The operation of spiritual automata, that is of souls, is not mechanical, but it contains in the highest degree all that is beautiful in mechanism. The movements which are developed in bodies are concentrated in the soul by representation as in an ideal world, which expresses the laws of the actual world and their consequences, but with this difference from the perfect ideal world which is in God, that most of the perceptions in the other substances are only confused.133 Were there souls without bodies, not only would "all that is beautiful in mechanism" not apply, but the soul would have no standpoint in the world. Thus Leibniz sometimes treats the soul as analogous to a lens. What it represents clearly, and what only in a blurred fashion, depends not only on its intrinsic quality but on where it is placed. Finally, the principle is associated with Leibniz's claim that created minds and souls cannot reason without symbols. The basis for this claim is unclear. Descartes states that the brain cannot be involved in pure operations of the understanding, but only in imagination and perception; he believed it possible for himself to add two and two, even if incorrectly, before being certain that he had a body. 134 Apparently, the fact that symbols possess shape and size and are in this sense corporeal makes Leibniz think that they must be related to a corporeal organ of thought. If so, then contrary to Descartes' view, disembodied spirits cannot conduct demonstrations. If they also «2 Monadology, % 63, L 649; G VI:618. ^Theodicy, §403, FH 365; G VI:3S6. »< Reply to Objections V, AT VII:358; HR 11:212; CSM 11:248.

Monadic degree: the politics of nature 1 9 9

cannot perceive, imagine, or feel, this diminishes the attractiveness of the state of disembodied existence considerably. 32 Monadic degree; the politics of nature It is impossible to say whether Leibniz's second reading of Cudworth at the end of 1703 took place in time to influence his treatment of Locke. But the claims that perception is essentially confused cognition, that the mind possesses an internal creative power, that there is a hierarchy of existence, that not all thinking is conscious, in short, many of the great themes of the New Essays On Human Understanding, are to be found in Cudworth's True Intellectual System. "The Rational Soul", Cudworth says there, echoing Plotinus, "is itself an Active and Bubbling fountain of Thoughts; that perpetual and Restless Desire, which is as Natural and Essential to us as our very Life".135 Like Leibniz, who was impressed by the inventions of the sleeping mind, Cudworth observes that the soul in sleep or dreams "frames Interlocutory Discourses bewixt itself and other Persons, in a long Series with Coherent Sence and Apt Connexions" 136 - this is to count as evidence for the active power of the unconscious. Leibniz may have been struck by Cudworth's discussion of the sleeping geometer and the sleeping musician, who possess their theorems, knowledge, and songs even when unconscious. The Cartesians, he says, who suppose that the essence of the soul consists in cogitation, "cannot in any way render it probable, that the Souls of Men in profound Sleeps, Lethargies, and Apoplexies as also of Embryo's in the Womb ... must cease to have any Being". Thus, he continues, it must be granted that "Clear and Express Consciousness is not Essential to Life".137 The Cartesian who does not admit this 13S

True Intellectual System, p. 846.

ι»ΐω., p. 161. 137 Ibid., p. 160. The sleeping musician is a figure of Henry More's from the earlier Antidote Against Atheism (1653), I:V: "Suppose a skilful Musician fallen asleep in the field upon the grasse, during which time he shall not so much as dream any thing concerning his musical faculty, so that in one sense that is no actual skill or Notion nor representation of any thing musicall in him, but his friend sitting by him ... jogs him and awakes him, and desires him to sing this or the other song, telling him two or three words of the beginning . . . , he presently takes it out of his mouth, and sings the whole song upon so slight and slender intimation: So the Mind of man being jogg'd and awakened by the impulses of outward objects is stirred up into a more full and clear conception of what was but imperfectly hinted to her from externall occasions". In

Patrides, Cambridge Platonists, p. 2 2 3 .

200 Atom, substance, soul recognizes accordingly " n o . . . Scale or Ladder in Nature, no such Climbing Stairs of Entity and Perfection", but only "One Flat and Level" universe. 138 This reference to natural hierarchies carried inevitable political overtones, as all discussions of nature, natural law, and the natural order did for the seventeenth-century philosopher. It was no accident that Hobbes, the voluntarist in metaphysics, materialist in physics, and conventionalist in philosophy of language, denied the natural right of kings and presented a picture of justice as a convention established by competing atomistic interests. A natural community founded on noblesse oblige and obedience, formed by creatures and their creator, is no longer the appropriate model, as far as he is concerned, for civil relations. Hobbes's view comes up for criticism in due course in Cudworth's attack on "Modern Atheistic Politicians" who try to "Make Justice by Art where there is none by Nature ...by Renouncing and Transferring mens Right, by Will and Words". Such pacts and convenants, Cudworth says, are nothing but "Words and Breath; and therefore can have no Force to Oblige".139 But if civil societies are not founded upon such artificial, magical, and therefore, inefficacious procedures, nor upon pure violence and thralldom, there must be some "Naturall Vinculum" to hold a society together, obliging subjects to obey and rulers to act for the good of their subjects. The model, Cudworth announces, is the civitas dei: Had not God and Nature made a City; were there not a Natural Conciliation of all Rational Creatures,... men could neither by Art, or Political Enchantment, nor yet by Force, have made any firm Cities or Polities. The Civil Sovereign is no Leviathan, no Beast, but a God Il have said ye are Gods:) he reigns not in meer Brutish Force and Fear, but in Natural Justice and Conscience .. . 140

The notion of a natural vinculum and a natural hierachy is captured as well in the Monadology's doctrine of the relation obtaining between God and creatures. First, there are objective relationships of superiority and inferiority within the cosmos. "Not only is there life everywhere", the "Principles of Nature and of Grace" informs us, "but there are also infinite degrees of it in the monads, some of which

138 Xfui Intellectual System, p . 160. 139 True Intellectual System (Contents). "OJW., p . 896.

Monadic degree: the politics of nature 201 141

dominate more or less over others". Monadic superiority appears to consist above all in the clarity of perceptions of the monad, which depends on the sophistication of the mechanisms of the body associated with it. Such acuity is associated with memory, "a perception of which there remains a kind of echo for a long time".142 But in addition to perception and memory, which it shares with the animal, the human soul possesses what Cudworth called "Duplicity" and what Leibniz terms "apperception". The human soul rises up to "reflective acts which enable us to think of what is called I and to consider this or that to be in us".143 The lowest degree of development belongs, then, to those simple living beings which have neither distinguishable perception nor memory, the next to beasts with "distinct phenomena" and memory but without knowledge of necessary and eternal truths. Knowledge of these truths is associated with self-consciousness. For the material of these truths - the notions of the simple, the compound, being, substance we discover within ourselves. This self-consciousness is ultimately the basis of the civil "natural vinculum"; for memory implies responsibility for good and evil and the justifiability of punishment and reward. The hierarchy itself implies, moreoever, the reciprocality and naturalness of the relationship between God and subjects, a thesis disputed or ridiculed by Hobbes and Spinoza. It would be wrong however to state that Leibniz is only reinforcing the traditional picture of political authority as a version of divine and paternal authority. Cudworth, for example, who is outraged by the idea - which he thinks follows from Hobbes's theory of artificial justice - that one who tortures and murders his parents has done something wrong only in the sense that it is unconventional, is led by a series of steps to the declaration that the civil sovereign is "no Beast, but a God". It is difficult to imagine that Leibniz was under any illusion about the moral qualities of the leaders of his time; he assuredly was not tempted to ascribe divinity to them. In suggesting that civil relations were mirrored in the intelligible realm of the monads, Leibniz was perhaps not so much glorifying the former as criticizing them. The picture of a community of spirits is less an 141

"Principles of Nature and of Grace", §4, L 637; G VI:599. ™Loc.cit. !"Monadology, §30, L 646; G VI:612.

202 Atom, substance, soul

attempt to justify the European slalus quo, which in any case did not form a single hierarchy, than to express the conditions of an ideal society in which rank and power of action is strictly correlated with goodness and with clarity of perception. Hobbes and Locke did nevertheless succeed in demystifying and naturalizing political philosophy, and their analysis of civil society as founded upon agreement, enforcement, and contract - the political correlates of atomism, voluntarism, and conventionalism - appears to have been a precondition of the political gains associated with the Enlightenment. Leibniz's views have more in common with Romantic political theories, which stressed the social bond, rather than the management of power relations, as the proper foundation of the state. This was inspiring in its own way, but turned out to be liable to abuse in ways he probably could not have foreseen.

VI hibnizs theories of space, motion, and gravity

We have seen in the last chapter that the possibility that there exist only unextended monads and their perceptions was one Leibniz could not, and indeed had reasons for not wishing to, defend consistently. That continuous matter must be a kind of illusion he did not doubt. But, as long as he thought in Cartesian terms of perceptions "within" corresponding to objects "without", he could not avoid heaping up his metaphysical points at a set of locations and having them looked at, as though they were physical objects. When he tried to free himself from this picture and to think in terms of a harmonic ensemble of perceptions with nothing either within or without, hence no correspondence, he made bodies and forces redundant. So Leibniz hung suspended in the middle, leaning now to a form of idealism in which the objects of experience were mere phantasmata, now to a form of realism in which monads formed the last line of defense against that view. The theory of well-foundedness did not solve a problem but only tagged it. To understand Leibniz's theories of space, time, and motion, insofar as it is actually possible to do so, it is essential to remember that here again it is a question of two entirely unrelated points of departure. First, like all continuous phenomena which cannot be composed, space, time, and motion must be illusory. Second, motion, as Leibniz learned from Huygens, could be determined only relative to a designated observer. Putting these insights together, Leibniz came to the conclusion that space and time must be relative to observers too, and that this must, in some way, compensate for their illusory nature.

204 Leibniz's theories of spaa, motion, and gravity

33 Zenonian reduction Leibniz had been interested in Zeno's paradoxes at least since his reading Gregory of St Vincent's works during his studies in Paris. Gregory had purported to show geometrically how Zeno's hare might catch up to and overtake the tortoise, 1 thus apparently providing a solid solution to the problem of the composition of the continuum. Galileo, as we observed in Chapter II, had also made a tentative effort at solving it, and Leibniz originally agreed that the spatial, temporal, and material continua were composed of unextended positive quantities from which nothing could be removed. But when exactly he decided that, in effect, Zeno was right and the continuum cannot be composed at all, and matter and motion were unreal, is unclear: there is a gap of ten years between the Pacidius and the Discourse. Almost certainly, he was entertaining this solution in the early 1680s, for he says in the extraordinary pre-Discourse esoteric fragment of 1683, Mira de natura substantiae corporae, that neither extension nor motion is distinctly conceived; when we try to do so, we become trapped once more in the old labyrinth. We must say instead, he remarks, that there is perhaps nothing real in motion except a hidden force, nothing real in extension either, but only a principle of limitation or passion and one of action. 2 "The conclusions which can be drawn from Zeno's arguments", he would claim in 1698, a propos of Bayle's dictionary article "Zeno", thereby making the ancient sceptic himself a harbinger of the New System, "agree better with my system than any other, for what is real in extension and movement consists of nothing but the foundation of order and the regular sequence of phenomena and perceptions". We conceive of extension in conceiving an order in coexistences, but we should not conceive of it, any more than of space, in the nature of a substance. The same is true of time, which presents to the mind only an order in changes. As for motion, that which is real in it is force or power, namely, something in the present state which carries with it a change for the future. The rest is only phenomena and relations.3 1 OpUsgeometricum quadrature circuit et sedionum coni, (2 vols, Antwerp, 1647). Leibniz later characterized this solution as "doubtful": Grua, ed., Textes inedites, 1:42. 2 JWiVe de natura substantiae corporeae (1683?), AK Vorausedition 11:294. ^"Clarification of the Difficulties which Mr. Bayle has found in the New System of the Union of Soul and Body", L 496; G IV:523.

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And this was the insight which, he said later to Father Tolemei, allowed him to escape from the labyrinth.4 The argument here draws on Zeno's "arrow parodox". Zeno claims that an arrow flying through the air, in virtue of the fact that it is found at each instant at a particular location, does not really move. "Motion", Leibniz repeats in the L·sai de Dynamique, "is a transient thing which never exists, strictly speaking, seeing that its parts are never all together. But it is force (which is the cause of motion) that truly exists".5 "Its parts are never all together" means that motion is a succession of instants, consisting in the occupation of certain places at certain assignable times. It is thus only a kind of convention which allows us to treat a succession of appearances as the movement of a thing, rather like the convention according to which we call a pile of gravel a thing. By contrast, Leibniz thinks, the notion of force can be identified without making its definition dependent on time, for "a given force can produce a certain limited effect which it can never exceed whatever time be allowed to it. Let a spring uncoil itself suddenly or gradually, it will not raise a greater weight to the same height, nor the same weight to a greater height".6 What Zeno did not see, he thinks, is that although motion is unreal or phenomenal, its phenomenality presupposes the existence of something real. As he expresses it in the New Essays, motion is an "image" of force, as matter is an "image" of substance.7 34 Relativity and its consequences

We come now to the second strand of Leibniz's theory of motion. Leibniz had been concerned with the problem of true and apparent motion since his Paris days and had corresponded with Huygens at some length on the subject. What he says to the Newtonian Samuel Clarke in the correspondence of 1715-16 depends on a previous thrashing-out of these issues with Huygens, who was trying himself to understand how far the implications of Galilean relativity could be extended. 4 This declaration occurs in the letter to Father Tolomei of 17 December 1705, G VII:467. See Cassirer, Leibniz' System, pp. 522ff., for discussion and further references. s Essai de dynamique (1692), text reproduced in Costabel, Leibniz and Dynamics, p. 131. ^ Ibid., p. 129. 'RB 21Of.; AK VI:VI:210.

206 Leibniz s theories of space, motion, and gravity

In reading the Clarke correspondence, one may again be troubled by the extreme abstractness of the discussion, the ready flight to principles in the place of a careful consideration of examples. Why does Leibniz, for example, ignore Newton's bucket experiment, supposed to deliver the coup it grace to denials of absolute motion? Why does Newton-Clarke in turn fail to explain how the determination of absolute circular motion could bear on the problem of determining absolute linear motion? To explain how Leibniz and Newton manage to draw antithetical conclusions from the same body of data concerning relativity and the determination of "true motions", it is necessary to look behind these thought experiments at certain more fundamental ones. If Zeno's paradoxes provided reason for thinking that motion was metaphysically unreal, the principle of Galilean relativity provided Leibniz with reason for thinking that no empirical observation could establish anything except a change of relations and never the true subject of motion. Nevertheless, Leibniz operated intermittently with a somewhat puzzling notion of "real motion", which he thought could be assigned on the basis of force or autokinesis. "When a number of bodies change their position with respect to each other" he notes briefly in the Discourse, "it is impossible, merely from a consideration of these changes, to determine to which bodies motion ought to be ascribed and which should be regarded as at rest But the force", he continues, "or the immediate cause of these changes is something more real, and there is a sufficient basis for ascribing it to one body rather than to another. This, therefore, is also the way to learn to which body the motion preferably belongs". 8 These reflections follow from Huygens's effort to perfect the statement of Galilean relativity, applied in a partial and inconsistent manner by Descartes. Suppose, Leibniz argues in the Specimen Dynamicum, that people are being transported in a large ship (assumed to be closed, or at least so constructed that the passengers cannot observe external things), and the ship moves at a great velocity, yet smoothly and without acceleration, they will have no principle by which to discern whether the ship is at rest or in motion (on the basis, that is, of what is happening within the ship), even if they play ball or carry out other motions.9 'Discourse, §18, L 315; G IV:444; MB 60. ^Specimen Dynamicum, L 450; GM VI:253.

Relativity and its consequences 207

From this observation, Leibniz appeared to draw three consequences: (a) uniform motion is undetectable by experiments performed in a closed environment where no change of relative position can be observed: it generates no effects which could inform us that it is occurring; (b) uniform motion is detectable if there is perceptual access to the environment, because the observer will note a perceptual change in relations. But (c), though an observer with perceptual access to the environment can determine that movement is occurring, he cannot tell from the phenomena alone who or what is moving and at what velocity. Suppose people in the hold of a ship observe the shape of a large fish first at the left, then at the right, of their underwater porthole. They have reason to think that something is moving, but they cannot say whether they are at rest and the object is moving from left to right, or whether they are moving from right to left past a stationary object, or whether both they and the object are in motion. AU such hypotheses about motion are equivalent. Huygens had argued further that the laws of motion should hold good for observers in any "inertial" frame of reference who are themselves moving with a uniform velocity or at rest, a requirement grossly violated by Descartes's system.10 They must be stated in such a way that, whatever hypothesis about motion is selected, the conservation of speed and direction holds good.11 We assign motion, Leibniz now thinks, either by appealing to dynamical considerations or by taking the simplest hypothesis. Interestingly, he identifies the choice of the Copernican over the Ptolemaic hypothesis about celestial motion as dependent purely upon the simplicity of one relative to the other, as though no dynamical considerations could be considered relevant. He does not mention either Kepler's or Newton's attempt to connect the true system of motions with a dynamical basis, namely, the "motive" or "attractive" power of the sun. Though he should be sympathetic to such attempts, he disapproves of the particular forces involved. Although Huygens states that "all motion and rest of bodies is relative" and that "without mutual reference nothing can be said to 10 Huygens, Dc motu corporum ex percussione (1654), Appendix I, pts V, VI; Oeuvres, XVI:104f. ii Descartes implicitly recognizes this when he defines motion as translation from the vicinity of one body to the vicinity of others (Principles, 11:28, AT IX-2:78; Philosophical Writings, 1:234); but he does not apply it in his treatment of the laws of collision.

208 Leibniz's theories (ή spaa, motion, and gravity

be moved or at rest", 12 and although he had presumably communicated this view to Leibniz in Paris, he had once believed that one important phenomenon did provide a means of determining the "absolute subject" of motion, namely, uniform circular motion, which generated a centrifugal force and observable effects. Consider the case of a rotating disk in a field of objects. Although the disk does not change its relation to any of these objects, it is nevertheless in motion. But we ascribe motion, Huygens points out, on the basis of a change in relations, not of the body as a whole relative to other bodies, but of its parts relative to other bodies.13 For this reason various hypotheses may again be considered equivalent. The appearances will be the same for a disembodied mind watching a rotating disk, or being carried around the edge of a stationary disk.14 Thus circular motion, like straight-line motion, can evidently be detected only by a conscious being who notes a change in relations. Suppose, however, that what is rotating is not the edge of a disk but a bucket full of water, and that the observer is not an angel but an ordinary human being. Then it should be apparent from extrarelational considerations which is in motion: if the bucket rotates, the water will rise towards the edge; if the observer rotates, he will feel certain sensations. Huygens anticipates this objection, arguing that these effects derive from the presence of bonds or obstacles. Without these bonds, it is as impossible to assign absolute circular motion as it is to assign absolute linear motion. But, assuming a bond, for example a rope connecting the catapult to the hand, or some obstacle, for example the sides of a bucket of water, or a body being whirled around the edge of the disk, then the cohesion of the parts will generate tension, a deflection of the water, or a sensation. Circular motion, Huygens finally determined, giving up the position he had first disputed with Leibniz, is only "relative [motion] of parts excited in contrary directions but constrained on account of some bond or connection".15 He eventually realized, according to his account of his conversion, that the effects supposedly generated by circular motion 12 "Pieces et Fragments concernant la Question ... de 'Movement Absolu'" (1688), Oeuvres XVI:222f., quoted by H. Stein, "Some Philosophical Prehistory of General Relativity", p. 45. " H . Stein, ibid., p. 45. "Ibid., p. 48. "IbU., p. 48.

Relativity and its consequences 209

were only pseudo-effects, belonging not to motion considered in itself but to motion in a world of bonds and obstacles. Apparently, it was Leibniz himself, although he later indicated that at some point both he and Huygens had believed in absolute motion, who had first tried unsuccessfully to bring Huygens around to this point of view.16 In any event, by 1687, when Newton tried to explain absolute motion by appealing to the forces generated by a rotating bucket full of water in the Eighth Definition of his Principia, Leibniz and Huygens had both come to the conclusion that "circular motion has no advantages in this respect".17 Both theorists rejected the moral of Newton's bucket experiments. Newton's thought experiment was an attempt to break the equivalence of hypotheses by exhibiting the effect noted above, the dip of water in a rotating bucket, which cannot be explained by any relative motion. For, according to the terms of the experiment, the effect occurs both when the water is not in motion relative to the bucket and when it is.18 The only conclusion to draw, Newton said, is that the reason for the dip is the motion of the water relative to absolute space. It should now be clear why Leibniz appears utterly indifferent to this argument. In the Clarke correspondence he ignores it, not because he has no good answer, but because he had already discussed these issues with Huygens and the two had long been in agreement that circular motion possesses no advantages. Leibniz claims, in a variant of the Huygens argument, that because circular motions are compounded of infinitesimal straight-line motions they cannot escape the general sweep of Galilean relativity.19 Leibniz is unmoved by the point that a true deformation of the body is observed as a result of the force, which the observer cannot cause to disappear simply by changing his frame of reference: Newton, he no doubt "See his letter to Burnett, 8/18 May 1697. "He [Huygens] and I were both of the opinion of Mr. Newton on absolute movement, and for the same reasons having to do with centrifugal force which he alleged, but when Mr. Newton's book appeared, we had already both changed our minds even without having communicated with one another as we found out later". G 111:205. "Letter to Huygens, 4/14 September 1694, L 419; GM 11:193. 18 Newton, Mathematical Principles of Natural Philosophy, General Scholium, Def. 4: Motte-Cajori, tr., I:10f. "Dynamica, 11:111:19, GM VI:507f., quoted by H. Stein, "Some Philosophical Prehistory", p. 4.

210 Leibniz's theories of spaa, motion, and gravity

thought, as Huygens seems to have agreed, confused the ideal theory of motion with the complicated physical case. If an angelic intelligence observes the movement of geometrical disks, rather than physical buckets, no forces or effects are evident. In the real world of cohering objects, the situation may be otherwise, but we are not in this case dealing with the pure phenomenon of motion. Here Leibniz seems to clutch at the old distinction between the theory of abstract and the theory of concrete motion, the distinction he had rejected for the case of collision mechanics. Newton was, to be sure, aware of the implications of Galilean relativity and considered it compatible with his dynamics. Yet he rejects the Leibniz-Huygens notion of an abstract theory of motion which cannot be elicited from phenomena. The task of mathematical philosophy is, as he says explicitly, to "collect" true motions from apparent, from the phenomena themselves. For Newton, as Howard Stein stresses, it is a foregone conclusion that there must be a distinction between "absolute space", that which "in its own nature, without relation to anything external, remains always similar and unmovable", as well as "absolute motion", defined as "the translation of a body from one absolute place into another", and the corresponding "common" or relational notions. 20 The problem is simply to find a means of distinguishing one from the other. So Newton argues that the common way of determining motion, according to perceived changes in relations, cannot be the only way. If it were, two conclusions would follow. First, mechanics, which requires the notion of uniform movement in a straight line, could not be articulated. Second, God would not possess a complete knowledge of the universe; Descartes's loosely relativistic idea of motion has this implication. For example, if the place of the Planet Jupiter a year ago be sought, by what criterion, I ask, can the Cartesian Philosopher describe it? Not by the positions of the particles of the fluid matter, for the positions of these particles have changed greatly since a year ago. Nor can he describe it by the 20Newton, Mathematical Principles, General Scholium, Defs 1-4: Motte-Cajori, tr., I:6f. Stein argues that Newton's absolutism is directed against Descartes and serves the theological aim of both maintaining the literal sense of "the sacred writings" and upholding the "purity of mathematical and philosophical truths": "Newtonian SpaceTime", pp. 289f.

Relativity and its consequences 2 1 1

positions of the Sun and fixed stars for [various disturbances] change both the magnitude and positions of the stars so much, that perhaps they do not suffice to designate the place sought for but with an error of several miles— Truly there are no bodies in the world whose relative positions remain unchanged with the passage of time. And so there is no basis from which we can now designate a place that was in time past... And so ... it is manifest according to Descartes's doctrine that, of the place of any moving body, not God himself (a new state of things holding) could describe it accurately.21 It follows, Newton says, that, according to Descartes, no length of space traversed can be assigned; that a moving body can have no determinate speed, that no space was passed over and no direction of movement can be assigned - in short, that the laws of mechanics cannot be stated. "So it is necessary", he concludes, "that the determination of places, and therefore of local motion, be referred to some immobile being". Even Descartes, he notes, implicitly recognizes this, for his vortices must spin relative to some extension distinct from bodies.22 For Newton, it makes sense to assert that not simply the earth but the totality of objects in the universe is moved in some direction, even though there are no possible phenomena which could bring a non-divine observer to announce this occurrence. If absolute rotation, and thus absolute acceleration, exist, then, he thinks, absolute motion and absolute velocity must also exist, whether or not any human being can measure or even detect them. It is indeed because no non-divine observer can determine absolute movement that it is necessary to suppose that a divine observer can. Unlike Leibniz, Newton does regard God as having a special mode of appreciation of spatial relations. God is capable of evaluating the movement of the whole; he does not have to consider competing hypotheses about movement like the common observer and to choose between them. He can simply see whether or not any object in the universe, or the universe itself, is stationary or moved through space. This conception he tries to express by saying that space is God's "sensorium". What does this mean? The sensorium of a human being, which is supposed to supply the analogy, is the non-spatial, non-extended mind "in" which three-dimensional space "outside" is represented. 21 Tr. Stein, op.cit., p. 269f. "ftai., p. 270.

212 Leibniz's theories of space, motion, and gravity

We see things "in" space, on Newton's account, because external objects act on our nerves and brain to produce in an unknown way three-dimensional spatial pictures "in" our sensoria.23 Though Leibniz appears to interpret the expression "sensorium" as referring to a part of the brain, or at any rate something in the head, this does not seem to be what Newton meant: either Leibniz was deliberately misrepresenting, or else he honestly did not understand what Newton intended. The question is whether Newton knew what he meant. We should take the term to mean, perhaps, the same as "visual field", understanding the visual field however as something present in the mind of the observer, not as a chunk of external space. Our "little" sensoria are limited: that is to say, we cannot see everything or even very much at one time. God's great sensorium differs from our little sensoria in two ways. First, there is no causal story to be told. In God's mind all of space is pictured, without its being the case that this picture originates somewhere else. Second, God's sensorium is infinite and panoramic. We may thus think of absolute space as what God sees, as what is within the infinite panoramic visual field of God. Now clearly, just as we can determine when something in our visual field has moved without needing to judge the change of relation relative to any other object, God too simply sees when something in his visual field has moved. Nothing can, of course, move out of his visual field - as objects can disappear altogether from our little sensoria - because it is infinite. Leibniz tries now to show that the idea of a divine sensorium cannot be coherently made out. To do so, he must now appeal to principles and thought experiments, largely ignoring empirical considerations. So he calls, for example, on the principle of the identity of indiscernibles. One point seems to be this: if God's sensorium were a container with edges, it would make sense to speak of God as observing the universe as a whole being moved around within it. But if there are no boundaries to God's infinite visual field, hence no changing relations between object and border, God himself could not detect such motion; hence no such motion can exist. To say that God can cause the whole universe to move forward in a right line or in 23 On this image in Newton, see Buchdahl, "Comment on 'Newton's Achievement in Dynamics'", p. 140; and Bernstein, "Leibniz and the Sensorium Dei".

Rektivity and ife consequences 213

any other line, he says to Clarke, "without otherwise making any alteration in it", is "chimerical".24 The perceptual problem has its counterpart in action. It follows now that if the whole universe cannot be moved relative to absolute space, neither can a particular object such as Jupiter be moved relative to absolute space; hence absolute space cannot exist. And if space is not the embodiment of the divine visual field and not a substance, it can be no more than "an order of the existence of things observed as existing together".25 Leibniz's addressing the matter in this way disguises an objection which Clarke might well have made: one may turn around a chair in a room, so that its former eastern arm is now its western arm; why can one not turn the universe as a whole around in space? Why can we not imagine that God causes the universe to become a rigid body with this chair at its center, and that the whole is then simply revolved around its axis? Surely Leibniz would not deny that the power of God could cause the various parts of the universe to cohere into one lump, and the objection that there could be no sufficient reason for God to do so seems irrelevant. Here Leibniz's response would have to be that what is false of the whole ("can be turned around in absolute space") is also false of the part; and that some property of the part ("has been reversed in local space") cannot be a property of the whole. "Turned around in space" always means, in this case, local, relational space and can only be understood by reference to surrounding external objects, which are lacking if we are required to imagine that everything has been congealed into a single lump. The upshot is: either God cannot cause the universe to congeal into a solid lump which he then rotates, or, if he can make it into one lump, it will no longer be anything movable. As long as Leibniz and Clarke restrict themselves to uniform motion, Leibniz has the old advantage of the Galilean equivalence of hypotheses. But Clarke raises again the question of acceleration and the Newtonian forces. This is the substance of what he regards as his key objection, "the argument to which no argument has been given". Suppose, he says, God were to set the universe as a whole in motion, and then suddenly bring it to a halt. A shock would evidently result on this sudden braking action, despite the fact that the universe was "IVth Letter to Clarke, L 688; G VIL373. "ViA Letter to Ckrh, L 700; G VII:395.

214 Leibniz's theories of space, motion, and gravity

in motion relative to nothing other than absolute space. This proves, moreoever, he claims, that even the uniform motion of the universe through empty space is real, though imperceptible, because its cessation would be perceptible. 26 (The argument resembles Leibniz's own claim that we are faintly aware of the motion of the lymph in our lymph glands, because we would notice it if it suddenly ceased.) 27 Leibniz's answer consists first in simply denying the premise. God could not set the universe as a whole in motion, for the reasons he has already stated. But he goes on to make a surprising concession. Nothing in the bucket experiment, he says, "can prove the reality of space in itself". However, I grant that there is a difference between an absolute true motion of a body and a mere relative change of its situation with respect to another body. For when the immediate cause of the change is in the body, that body is truly in motion Tis true that, exactly speaking, there is not any one body that is perfectly and entirely at rest, but we will frame an abstract notion of rest by considering the thing mathematically.28 "Thus", he concludes, "I have left nothing unanswered of what has been alleged for the absolute reality of space". We can frame a "mathematical" notion of true motion, but this notion should not be thought to entail the "absolute reality of space". This is very puzzling, for, on Newton's view, absolute true motion, which he also calls "mathematical", just means motion through absolute space. It is thus unclear from what Leibniz says whether he (a) agrees that, abstractly speaking, true motion can be defined as motion through absolute space, even if no possible world - including ours - exists in absolute space; or (b) denies that the abstract definition of absolute motion requires reference to absolute space. He appears indeed to embrace both positions. No one, including God, he implies, can apply the mathematical theory of absolute motion to the case in nature, since in order to do so one must not simply define absolute rest, but actually locate a body which is at absolute rest. Newton thought he could uphold his claim that "the center of the system of the world", the center of gravity of the sun 26

JViZi Letter to Leibniz, L 693; G VII:384. Cf. letter to Arnauld, 9 October 1687, L 339; G 11:113. 28 VM Letter to Clarh, L 706; G VII:404. 27

Relativity and its consequences 215

and planets, was at rest. 29 But Leibniz denies that we can say this of any particular thing in the universe. Thus, even if everything in the universe were in uniform real motion (a view Leibniz actually seems to hold!), there could be no fixed reference point for determining the absolute degree of motion of anything at all. In this case, he is not denying that some apparently stationary things are really moving, and vice versa; he is denying that any being, including God, can estimate this motion precisely. But he also refuses to make the Newtonian connection between true motion and absolute space, which his "abstract", though hardly mathematical, conception of true motion as motion which has its source in the moving body does not require. On this interpretation, God can identify absolute motion, but such motion does not involve translation in absolute space. In the end, Leibniz's refusal to draw the Newtonian moral from the bucket experiment depended not only on the principles stated so dramatically in the correspondence with Clarke, but on his perception of Newton's arguments as "geometrical". He was committed in advance to the position that no set of observations could determine the true subject of motion, just as Newton was committed to the claim that some set of observations must be able to do so. For Leibniz, such experiments, which reveal only the translation of bodies relative to others, always remained at the surface. He was determined at all costs to maintain the distinction between metaphysical truth and the approximate, common, relativistic notions of physical science. From the propositions that (a) hypotheses about motions drawn from phenomena are equivalent, and (b) each body must have a certain motive force, Leibniz drew his favorite conclusion, "that there is something more in nature than what geometry can determine about it". This, he says, "is not the least important of the many arguments which I use to prove that besides extension and its variations, which are purely geometrical things, we must recognize something higher, namely, force". 30 Leibniz could not afford to recognize any demonstration of true motion from the phenomena or "geometry", which was what Newton's bucket experiment threatened. For this would have shown 29

H. Stein, "Newtonian Space-Time", p. 265. Letter to Huygens, 2/12 June 1694, L 418; GM 11:184. See also Theodicy, §347, FH 333; G VI:320f. 30

216 Leibniz's theories of space, motion, and gravity

that force was not, after all, the bridge from physics to metaphysics; we should not have been compelled to recognize "something higher". Force could, in this case, begin and end happily as a physical notion, demonstrated from the phenomena and applying to the phenomena. Second, Leibniz saw the principle of Galilean relativity as a beautiful example of the non-necessitarian but orderly character of physical law, and his desire to state the equivalence of hypotheses in as general a form as possible was fed by his search for continuity in the statement of those laws. Conversely, with this bridge in place, the requirements of divine power and divine knowledge which Newton and Clarke insist upon were of no importance. For Leibniz, it does not matter that God has no superior means of detecting motion different from ours. For Newton, it would be a defect on God's part if it were impossible for him to determine the absolute position of Jupiter a year ago. For Leibniz, this inability does not constitute any kind of failure. The term "the absolute position of Jupiter a year ago" is, as far as he is concerned, a kind of non-referring expression. God knows where Jupiter is in every conceivable frame of reference, relative to other objects. He does not see each object in its absolute location at all times, as Leibniz's early ascription to God of ichnographic perception seemed to imply. Rather, his perception embraces the totality of all possible finite points of view, or systems of objects, in relation to each other. But if the world is composed of non-material, non-spatial entities, as the late doctrine implies, it cannot be viewed by God from a perspective-free location by contrast with the sum total of perspectival locations. Curiously enough, it is Newton who assumes the right to Leibniz's old city-metaphor. Explaining himself to Huygens, Leibniz says that motion must have a subject, and it is his inability to identify a unique subject which pushes him to the claim that movement and space consist solely in changes of relation and in the totality of possible changes in relations. At the same time there is a strong counter-movement in his thinking which pushes him to link true motion with the exercise of force, which, he believes, can be assigned to a subject. This situation leaves it unclear whether the notion of "true motion" reaches up to the phenomena at any point, or whether all determinations are to be made, according to the relational view, on the basis of simplicity of hypotheses. Does the awareness of its own activity on the part of an

Space as construded from relations 2 1 7

ensouled subject, in other words, count for anything? If I feel myself to be struggling through shallow water, is this an infallible indication that I am truly moving? Or would Leibniz insist that I have only chosen the simplest hypothesis - that I am moving, and not the ocean floor, and that nothing, not even kinaesthetic sensations, can 'break the general law of equivalences'? Leibniz might have maintained that such sensations are authoritative, while denying that awareness of such true motion was awareness of motion relative to absolute space. 35 Spaa as constructed from relations

Some, though not all, of Leibniz's readers are puzzled by his failure to distinguish between, one one hand, questions about the properties of space and time and, on the other hand, questions about the basis of our perception of duration, extension, and movement - between, in other words, ontology and epistemology. A causal realist about space and time would, for example, claim that we are situated within real space and time and that they act upon us to produce the experiences of space and time in the same way that the material objects amongst which we live causally induce in us perceptions of themselves. But such a realist might well hold to a relative rather than an absolute notion of space and time. Conversely, a philosopher who, like Kant, regards spatio-temporal properties not as causally active properties of "things in themselves", but as qualities of experiences, may well believe that this experienced space is absolute, as Kant himself did. In the Clarke correspondence, Leibniz appears to move too rapidly from the non-epistemological facts about Galilean relativity to epistemological theses about the fictionality of space, ignoring the distinction just outlined. This state of affairs points up the radical nature of Leibniz's theory; he is not merely concerned to defend a relative theory of space and time in the sense that even a causal realist might, but to argue that space and time are fictions which the mind constructs. But where the Galilean arguments showed only that particular examples of motion may be "constructed" in various ways, not all of which can simultaneously be in effect, that a moving consciousness may construct for itself a hypothesis of rest and vice versa, by attending to other "moving" and "stationary" objects, these arguments do not

218 Leibniz's theories of space, motion, and gravity

show that motion and rest are mental inventions. It is clear, however, that Leibniz's claim that space and time are only well-founded phenomena requires some further step. Nothing in Galileo's arguments, in other words, implies that Zeno was right or even half-right to argue that motion was unreal. Leibniz believed that if he were to reject the concept of space as the divine visual field, the image which gives Newton's theory its content, he would owe some further account of the meaning of the term. It is impossible, he thinks, to derive the true changes in spatial location from the apparent, but it is possible to show how, from the data of qualitative changes in perception, the observer comes to invent a fiction: the fiction of a three-dimensional arena for these changes with certain definite locations within it. Like the term "mass", such notions enter into the statement of physical laws while remaining on the surface. Thus the term "mathematical" assumes for Leibniz the opposite value to the one it had for Newton. The critical concept here is of course this alleged "feigning". When Newton described space as the sensorium of God, one might interpret this as "feigning" too: as simply an image or metaphor corresponding to a certain mathematical description of a space with certain properties. It does not follow from either the metaphor or the possibility of defining this space mathematically that it must be Leibniz's dreaded unthing "unthing" - a something that is nothing. For Leibniz, in the end, though he detests the metaphor, accepts the necessity of thinking, for the sake of physics, of a uniform threedimensional space. This shows once more that the true issue between Newton and Leibniz is not the "ontological status" of space as thing or unthing, but the problem of access to that space. For Leibniz, it is essential that it be "cut off", unreachable through experiment, merely thought. Suppose, he says, we "feign" that a certain number of fixed bodies have undergone no change - perhaps the fixed stars, or the streets of a city. We then consider the existents which have undergone some change, and speak of x, for example, as occupying now the same "place" which y occupied a moment ago. This means simply that the perspective of χ is now qualitatively the same as that which y had a certain time ago, assuming that the other elements have undergone no change. Considering the set of all possible "places", we form the abstract notion of space, which "shows that in order to have an idea

Space as constructed from relations 2 1 9

of place, and consequently of space, it is sufficient to consider these relations and the rules of their changes, without needing to fancy any absolute reality out of the things whose situation we consider". "In like manner", he goes on, the mind can fancy to itself an order made up of genealogical lines whose bigness would consist only in the number of generations wherein every person would have his place; and if to this one should add the fiction of a metempsychosis and bring in the same human souls again, the persons in those lines might change place; he who was a father or grandfather might become a son or a grandson, etc. And yet those genealogical places, lines, and spaces, though they should express real truths, would only be ideal things.31 These genealogical lines, though they could even be measured on any genealogical chart to determine the number of generations since a given one, do not correspond to anything in reality. What is real are the qualitative statements, for example, "X is the father of Y" and Y is the sister of Z". AU that is contained in the table could be expressed non-pictorially in such a way that there would be nothing to count or measure. In the same way, Leibniz may have thought, one could express all the truths we currently express by assigning spatial locations, by stating what objects are present in the visual field of each particular object. The question is, what does this procedure actually give us? It is difficult to see that Leibniz has shown how to eliminate spatially descriptive terms from a metaphysically exact language; all that can be hoped for is a set of statements phrased in terms of x's being above, below, to the right of, to the left of, farther than or nearer than y, given from the perspective of each perceiving substance. Moreover, the "construction" of space in this manner from perceptual changes and relations seems to depend on the reality of extended physical objects and observers who can watch them change places. This solution was good enough for the Discourse on Metaphysics, for Leibniz at that time believed that individual and corporeal substances, with the property of extension and with the power of action, were the basic inhabitants of the universe. When, however, he was tempted to give up the reality of anything except unextended monads, this solution became problematic. For there were no longer 3i Vth Letter to Clarke, L 704; G VII:401.

220 Leibniz's theories of space, motion, and gravity

any changes in the relation of objects to observe. Space and time had to be grounded in the perceptions of monads; but unless the monads perceived other things in the full transitive sense, Leibniz could not claim to be explaining the "well-foundedness" of space and time, but only the subjective impression of extension and duration. If the analogy is to serve, some list of statements about what each monad perceives must "give" space and time in exactly the way that a set of statements about family relationships gives a genealogical tree with built-in distance relations. Leibniz had already suggested in the Discourse that the relations of near and far could be referred to the intensity of perceptions. In the "Metaphysical Foundations of Mathematics", he tries to show how "near" and "far" may be defined in terms of the complexity or simplicity of the forms between two objects; two points are nearer if the straight line joining them is shorter.32 But here "things", not classes of perceptions, are assumed, and the real problem is not touched. There is no difficulty in imagining how the perceptions of each monad might effectively and uniquely "express" its location qualitatively: Ian Hacking, for one, has shown how this might be done.33 But this leaves us with a set of translation rules from color sensations (in Hacking's example) into spatial locations, not a set of construction rules. Ballard, who holds the theory of inter-monadic perception disputed in the previous chapter, suggests in a similar vein that "just as we regard our notions of material substances as resulting from a confused state of perception of mental substances, so likewise we may regard the relation of space and time between these material bodies as resulting from a confused awareness of the point of view of mental substances".34 But it is this notion of "point of view" or situs itself which we are trying to explain. Leibniz was clearer than his interpreters about the radical nature of his proposal: "There is no spatial or absolute nearness or distance between monads", he says. "And to say that they are crowded together in a point or disseminated in space is to use certain fictions of our mind when we seek to visualize freely what can only be understood".35 "L:667;GMVII:18. 33 In "A Leibnizian Space". •""Leibniz's Theory of Space and Time", p. 65. «Letter to des Bosses, 16 June 1712, L 604; G II:450f.: quoted in H. Stein, "Some Philosophical Prehistory", p. 30, n.2.

Space as constructed from relations 2 2 1

The problem Leibniz faced here was one which has since led many philosophers to suspect that it makes no sense to talk about deriving statements about spatial relations from statements about non-spatial qualities. Kant came early in life to the conclusion that there was no hope of trying to do so and referred the problem accordingly to the "mystery of our sensibility". The Transcendental Aesthetic says, formally, that space is a transcendental condition of sensibility; informally, this means simply that we possess a not-furtherexplicable-space-constructing-perceptual-faculty, which happens to be organized along Newtonian lines.36 Kant thereby evades causal realism about perception of space, while endorsing its absolute character. Kant is, moreoever, shrewd in his identification of the locus of Leibniz's confusion between ontological and epistemological que­ stions. He reads Leibniz as having interpreted an epistemological principle, the identity of indiscernibles, which really applies only to concepts or definitions, as a hard fact about things in themselves, and as having been led consequently to the view that, since space and time play no role in the individuation of objects, they must be "unreal". 37 Historically, this account does not conform to our understanding of how Leibniz's views actually developed, but as a reconstruction of the final state of his thinking it is accurate. For Kant himself, the discovery of incongruent counterparts ultimately showed that Newton was wrong to think of space as capable of existing independently of all human or humanoid 38 perceptions. Left and right do not pertain to a divine observer, but only to human ones. But originally he proposed to use it to trap Leibniz in the following fork: either Leibniz should admit, contrary to his principle, that there are indiscernible non-identicals, for example a universe consisting of exactly one right-handed glove and a universe consisting of exactly one left-handed glove, or he should admit that spatial orientation is a discriminating feature, even though (as Kant ^Critique of Pure Reason, B33ff./Al9ff., Kemp Smith, pp. 65f. To be sure, Kant does not describe it this way, but as a non-discursive β priori representation which necessarily underlies outer appearances. ν Nova Dilucidatio (1755), Pt II, Prop. 12; cf. Critique of Pure Reason A272/B328, Kemp Smith, p. 283. 38 See Earman, "Kant, Incongruous Counterparts, and the Nature of Space". Kant does not seem interested in God's role as perceiver of Newtonian space.

222 Leibniz's theories of space, motion, and gravity

thought) it involves relations only to absolute space and not to any other object. Kant took Leibniz to be arguing that, insofar as they were not identical, a left-handed object and a right-handed object could be distinguished conceptually by some set of specifications. A distinct enough conception of a right-handed glove would reveal it as a different sort of object from a left-handed glove. This was what he meant by his enigmatic remark that Leibniz took things-inthemselves for appearances and that he regarded perception as a confused form of intellection. 39 But no set of specifications, he thought, whether internal, having to do with the relation of the parts of the hand to one another, or external, having to do with the relation of the hand to any other object, could reveal this difference.40 Had Leibniz recognized that no such differentiating conception of a perceptual object is possible or necessary, he would not have been forced into having to say that the gloves are indiscernible from each other even though one cannot be substituted for the other. Kant's argument might appear to hit somewhat wide of the mark here, for Leibniz might have replied that any two empirical objects such as gloves cannot really be identical throughout their warp and woof, while denying that right-handed and left-handed gloves in general have differentiating concepts. Had Kant challenged him to say whether a single glove in empty space was right-handed, lefthanded, or neither, Leibniz could easily have replied that it was neither, for two universes, one containing a right-handed glove and one a left-handed glove, would indeed be descriptively indistinguishable. But he would not have known what to say about nonempirical objects such as congruent triangles, nor how to answer the question whether the glove which remains in an otherwise empty universe after its right-handed mate has been withdrawn retains its orientation or loses it. Where Kant teaches that space and time are psychological predicates which apply nevertheless to objects rather than perceptions, Leibniz sought a middle way between causal realism 39

Critique of Pure Reason, A264/B320, Kemp Smith, pp. 278f. The problem of incongruent counterparts in its various forms is to be found in Kant's "Von dem ersten Grunde des Unterschiedes der Gegenden im Raume" (1768); also in the Prolegomena (1783), §13, A56, tr. Beck, pp. 33f.; and in the Metaphysical Foundations of Natural Science, Ch. 1, Expl. 2, obs. 3, tr. Ellington, pp. 23f. 40

Space as constructed from relations 2 2 3

about space and time and a Zenonian theory according to which they are pure illusion by looking to the notion of well-foundedness. Like Kant, he wished to avoid the realist's picture of actual space as responsible for the subjective idea of space; at the same time he could not take the spatiality of perception as simply a fact about the perceiving consciousness. The solution which is hinted at, but never developed, is that there is some way in which, from non-spatial data, both the mathematical notion of space and perceptual space may be constructed. The mathematical space in which objects are supposed to exist and to perform their motions is constructed from the imaginary and mathematical notions of point, line, and plane. A single solipsistic mind could easily arrive at this notion by considering its perceptions. A line results from the imagination's conceiving the path of a point, a surface from the path of a line; a filled space or solid is the path of a surface.41 Such a construction appears, to be sure, to presuppose a Kantian spatial faculty of representation. But it might still be possible for this mind to construct a phenomenological space for itself, not from mathematical concepts but from sensations which are not in themselves spatial. Now, according to Leibniz, we know that blind men are capable of learning and contributing to geometry; they can learn the basic concepts by touch; they know what it means to say that two objects are near or distant, behind or in front of one another, that they are in a plane or a three-dimensional space.42 But the kind of experimentation which leads to the acquisition of these concepts, Leibniz might well have argued, consists only in the reception of some pattern of qualitatively different sensations. To take a simple example, "farther", for a blind geometer, might simply be associated with a feeling of strain in the muscles, "nearer" with a relaxation of strain, "up" and "down" with sensations of resistance or enhancement of voluntary movement. In a similar way, Berkeley argues that the third dimension is not directly perceived but constructed from visual clues; it is well-founded in God, if not in things themselves. If this is the sort of constructive process Leibniz has in mind, then for us to form a geometrical and visual-kinaesthetic notion of space, it is not required that three-dimensional space exist, 41

"Metaphysical Foundations of Mathematics" L 668; GM VII.-21. "New Essays, RB 137; AK VI:VI:137.

224 hibniz's theories of space, motion, and gravity

or that it be in any sense an innate idea of ours. All that is required, although we have no idea how to analyze this at present, is a patterned occurrence of sensations, in virtue of which the conception formed would be well-founded rather than unfounded. What would be the properties of such a constructed space - absolute or relative is again a separate question. Whether Leibniz in turn would have favored such an interpretation of his enigmatic claims is a further question; we have been concerned here mainly with attempting to distinguish the various senses in which Leibniz considered space, time, and motion to be unreal, or fictitious, or created by the mind. 36 Plenitude and gravity As I have tried to argue, Leibniz's rejection of Newtonian space, though not his own theory of space in its broad and ill-defined entirety, depended largely upon the interpretation placed on actual experiments and thought experiments. The principles of plenitude, sufficient reason, and the identity of indiscernibles, which assume so aggressive a role in the Clarke correspondence, could, Leibniz thought, be regarded as confirmed by experience in this sense, rather than as a priori legislation. His rejection of the Newtonian force of attraction, and of the Newtonian void through which it operated, was, in the same way, less categorical than it at first appears. Just as Leibniz wished to reconstitute the Newtonian idea of "true motion", although he had no very clear idea how this was to be done, so he wished to reconstitute Newton's theory of celestial mechanics as an abbreviated version of the truth. Still, there is no denying the powerful emotional impression which Newton's vacuum theory made upon him. The Cartesian hypothesis of a perfect, inertia-less fluid pervading the whole universe was one which Leibniz was willing to employ, even knowing it to be false. He was also willing to consider atoms-and-the-void in the explanation of particular effects, as we have seen, so long as one recognized that atoms too were useful fictions. But he could not tolerate too many of these fictions at once. The Newtonian picture of a world largely emptied of matter, in which forces acted from one region of space to another, he found frightening and repulsive. It was no doubt disagreeable enough for Leibniz to encounter Newton's surmise, in the Queries appended to the second edition of the Opticks in 1704,

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that God had, in the beginning, most likely formed matter in hard, massy particles; Leibniz had arguments enough against this common heresy, good enough for "mere physical scientists". Far worse was the rumour that Newton considered the universe to be mainly void, a new and bizarre view Leibniz appears to have learned about from Newton's sometime disciple, the Swiss mathematician Fatio de Duillier. He (Fatio) believes, Leibniz reports, "that matter fills only a very small part of space and that bodies are open structures like skeletons to permit easy passage".43 Such a world must necessarily be saturated with forces acting at a distance, for such bodies can rarely if ever touch each other. But why would God create a world of attractions, repulsions, and void, rather than a world of creatures? For Newton this vision appears to have been beatific; for Leibniz it was simply unthinkable. Though a friend of forces, Leibniz was a friend only of metaphysical forces, those which could be understood on analogy with the efforts of autokinetic, Aristotelian subjects. Like the question of absolute space, the gravity question, which forms a kind of addendum to the Clarke correspondence, was an old issue with Leibniz. From the days of the Hypothesis physica nova, Leibniz remained faithful to aether theory. The sun, he thought, was ultimately responsible for the motion of the planets, but through the pressure of a light-bearing aether radiating outwards from it, not a force pulling things in. He posited "harmonic vortices" of aethereal matter, which should precisely account for Kepler's observation that the velocity of a planet is inversely proportional to the square of its distance from the sun. From the observation that the planetary orbits are elliptical, Leibniz says, together with the hypothesis of vortices, we can derive the rule that "gravitation" is reciprocally proportional to the square of the distance;44 the hypothesis of an attractive force and that of mechanical vortices are kinematically equivalent. Thus he employs essentially the same facts as Newton, who, from the assumption of an attractive force and the inertial motion of a planet, derives the elliptical orbits; however, he orders those facts «Letter to Huygens, 12/22 June 1694, L 417; GM 11:183. u Tentamen de motuum coelestium causis (1689), GM VI:144-61. Huygens, himself once a Cartesian, tried unsuccessfully to persuade him to give it up: see his letter to Leibniz, 12 January 1693, GM 111:150. For a crisp summary of the inconclusiveness of Newton's explanation of the planetary orbits by means of his theory of universal attraction, see Heilbron, Electricity in the 17th and 18th Centuries, p. 47.

226 Leibniz's theories of spaa, motion, and gravity

differently. Gravity does not play a causal role in determining the shape of the orbit: Leibniz assumes this as given, and proves only that gravity, a pseudo-effect, must assume different values at different distances, as though it were produced by an attractive force radiating out from the sun. 45 Vortices or rotations, Leibniz argues, should form naturally in a fluid medium, which minimizes their interference. This rotating light matter tends to depart from the center, which forces down "less agitated", non-rotating, heavier bodies. By this means, pressure outwards is curiously transformed into a tendency inwards: the centrifugal pull of matter can be considered as rays of attraction leaving the center as compared with the bodies which they make approach that center. The analogy of nature may lead us to believe that there is something approaching this in the nature of the solar system - that the planets tend toward the sun for a similar reason and that their attractions are in the ratio of the inverse squares of their distances, as in illumination.46 As a result, there is an analogy, as Gilbert maintained, between the earth and a magnet, even though no body actually possesses an attractive power. Leibniz was clearly impressed by the analogy between illumination and gravity, both of which appear to be governed by the inverse-square law. However, these gravity rays are not to be interpreted realistically, despite the "analogy of nature"; they are only a mathematical device for representing a mechanical situation. At times, Leibniz was inclined to stress the common ground between his own theory and Newton's. He had initially no objection to speaking of "attractions", and even claimed priority for their discovery. "We agree and maintain with them, and have maintained even before they published their view", he wrote to Bourguet in the year before his death, "that the great globes of our system, having a certain magnitude, attract each other". 47 He hoped to be able to explain Newtonian attraction as a special case of a theory not only compatible with mechanics but fuller in its implications. Indeed the alternative to the Newtonian theory is not implausible. Leibniz «Letter to Arnauld, 23 March 1690, L 361; G 11.137. «Letter to Huygens, 16/26 September 1692, L 415; GM II:142f. "Letter to Bourguet, 5 August 1715, L 663; G 111:580. Cf. the letter to Huygens of 1/11 April 1692, GM 11:133.

Plenitude and gravity 227

argues that we can know only that the planets move both as though they experienced a combined motion towards the center and a tangential motion, and as though they were carried by a subtle matter. Where Newton's theory unifies the phenomena of weight, terrestrial gravity, and planetary motion, his own theory is meant in turn to unify the celestial patterns with the phenomena of the roundness of water drops, the formation of the planetary globes, and the direction of their orbits. As he explains in 1692: The reason why I cannot abandon this deferent matter, even after learning Mr. Newton's explanation, is among other things, that I find that all the planets move somewhat in the same direction and in a single region, a thing which applies even to the satellites of Jupiter and Saturn. Without this deferent matter, on the other hand, nothing would prevent the planets from going in every direction.48 Given this single fact, there was, as far as Leibniz was concerned, no empirical advantage and a distinct disadvantage to Newton's theory, which he considered otherwise as mathematically and kinematically equivalent. Later, however, and perhaps earlier in his private notes, Leibniz attempted to minimize the equivalences he had earlier so tolerantly emphasized. He argued that the theory was old hat. As far as he was concerned, Descartes himself had settled the issue by showing how absurd it was of the mathematician Roberval to propose it. He quotes with approval Descartes's remark that such attraction requires us to suppose that the universe is full of intelligent beings who know their own masses, the masses of every other object, and their distances from every object, in order to calculate the degree of pull they must exert. 49 A second, somewhat ingenuous-seeming argument is that Newtonian attraction requires us to ascribe real circular, hence "unnatural", motion to bodies, whereas all mechanical motion is propagated in straight lines.50 In the last years of his life, Leibniz was no longer interested in reconciling Newton's version with his own, or in insisting that they were two aspects of the same explanation, but in showing Newton up as a benighted occultist. He was well aware of the two accounts of «Letter to Huygens, 16/26 September 1692, L 415; GM II:142f. "Bodemann, Die Leibniz-Handschriften, p. 57. 5°Mro Essays, Preface, RB 66; AK VI:VI:66.

228 Leibniz's theories of space, motion, and gravity

gravity which Newton himself was drawn to, and rejected both. He in turn maintained a position which Newton, after a brief flirtation, abandoned. The first possibility was that gravity should be considered a primitive power of matter, not essential to it but bestowed on it by God at the Creation. It was, in other words, a "superadded power". This seems to have been Locke's reading of Newton.51 The second possibility was that there should be an underlying mechanical explanation. At one time, Newton had been open to this possibility; he once wrote politely to Leibniz that he would be "far from objecting" were someone to account for gravity by means of the action of a subtle matter. Yet it was reported that Newton and Halley had laughed at Fatio's attempted mechanical explanation,52 and Newton gave up his own attempts to construct pressure-based models after a certain point. He gave them up, however, not simply because of the difficulty of constructing a suitable one, but because the third possibility, that gravity was an active principle and neither a property of matter nor a superadded power, was the one closest to his theological conception of God as a space-pervading power.53 It was this theory which Leibniz found occult, perhaps shrewdly perceiving Newton's mystical leanings, his interest in Boehme's nature-philosophy, in Henry More's extended all-pervading God, the vital principles of the Cambridge Platonists, and in the quasi-spiritual agents of alchemical theory. In a letter to Burnett of 1700, Leibniz had observed that Newton had "explained so well many phenomena of nature in supposing a gravity or attraction from matter upon matter". His generally favorable attitude towards Newton at this stage is demonstrated by his expressed annoyance with Newton's reluctance to publish his si See his letter to Stillingfleet (2nd Reply to the Bishop of Worcester 1698), Worts, IV:463ff. "See Newton's letter to Leibniz, 16 October 1693, The Correspondence of Isaac Newton, ed. Turnbull et al., 111:286; cf. Correspondence, 111:191. 53 As argued originally by Burtt, Metaphysical Foundations, pp. 143ff. See also Koyre, From the Closed World to the Infinite Universe, ch. 6, and Leibniz's own Anliharbarus physicus, which assigns to the pathetic category of "renovators of scholastic qualities" everyone whose doctrines he disapproves of, equating Newtonian gravity, elemental chemistry, hylarchic powers, plastic natures, Galenic humours, operative ideas, sympathy and antipathy, and Paracelsian archei (G VII:337-344). Cudworth's own attack on (preNewtonian) gravity is based on his perception of it as part and parcel of atomology; he describes it as "an Asylum, a Sanctuary, a refuge for ... Ignorance". True Intellectual System, p. 668.

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book on colors, the Opticks; Leibniz thinks he is under an obligation to do so for the public good. "His first work", the Mathematical Principles, Leibniz says, "has already contributed much to what concerns religion and piety". This is clear, he thinks, from the consequences Locke has extracted from it.54 What he meant by this unexpected and soon-to-be-contradicted declaration is explained by a letter written two years earlier. "I am happy to see", he says there to Burnett, "that people are moving away from a too materialistic philosophy, which tries to explain everything in bodies by simple modifications of matter, and that one no longer goes to the extremes of those who deny all feeling to beasts and imagine that the action of bodies is to be referred to God". M. Locke, he notes, has retracted what he formerly said in his Essat/, persuaded by his reading of "the excellent M. Newton" that it is false that matter can only act by impulsion. Although Huygens does not share his opinion, he notes, Newton's ideas are "not to be scorned".ss Similarly, the tone Leibniz adopts to Huygens in the late 1690s when he is discussing Newton's theories is entirely different from the formalized, hardened, denunciatory rhetoric with which he hammers Clarke some twenty years later. In direct contradiction to what he had told Burnett, Leibniz now accuses the English of dreadful impieties, and rejects all nonmechanical, non-impulsive forms of action. To Clarke's suggestion that Newtonian attraction between spatially separated bodies is entirely non-miraculous in virtue of being constant and regular, though accomplished "invisibly and intangibly" by non-mechanical means, Leibniz replies that to the terms invisible and intangible Clarke might well have added "inexplicable, unintelligible, precarious, groundless and unexampled".56 "A body", he states, "is never moved naturally except by another body which impels it by touching it, and afterwards it advances until it is stopped by another body which touches it. Every other operation on bodies is either miraculous or imaginary".57 What had happened in the meantime? There are many explanations, which have yet to be systematically weighed and ««Letter to Thomas Burnett, 2/13 February 1700, G 111:262. ss Letter to Thomas Burnett, 1698, G 111:228. 5« Vth Letter to Clarke, L 716; G VII:418. "Ibid., L 702; G VII:398.

230 Leibniz's theories of space, motion, and graoity

evaluated before a clear picture of the history of Leibniz-Newton and, not incidentally, Leibniz-Locke relations emerges. Noting the artificial battle-lines of the Leibniz-Clarke correspondence, some students of the case have come to the conclusion that the controversy was less a scientific than a political and emotional controversy - or indeed that so-called scientific controversies are mainly political and emotional. 5 8 No doubt they are partly right; the fury produced by the dispute over who had a right to be considered the inventor of the calculus, and the last-ditch political maneuvering which consumed Leibniz's last years, had a role to play. Once an Anglophile, a protege of Oldenburg, an admirer of Boyle and Dalgarno, later of the Cambridge Platonists, Leibniz was rebuffed by Locke, and never succeeded in establishing good relations with the English after his first youth, as his brutal treatment by the Royal Society in the calculus affair demonstrated. 5 9 Moreover, Leibniz was still trying and failing to gain recognition for the New System, by 1715 no longer new and fresh as it had been in the 1690s, but old and beleaguered. Around the turn of the century, he appears in fact to reach a kind of accommodation with Descartes which shows up in the appreciative remarks in the New L·says. His capacity for painting his opponents in unflattering colors is now engaged by Newton and Locke, and he depicts Newton's world as either the disguised vision of a materialistic atheist or the dream of a magician. To his atomic skeletons in the void, Newton had indeed added a wondrous assortment of active powers beyond the force of gravitation. These quasi-divine agents were, like the plastic natures of the Cambridge Platonists, God's intermediaries: they conserved the universe, kept the planets in motion, warmed the bodies of men and animals; and without them the entire universe would, Newton said, "grow cold and freeze . . . and all putrefaction, generation, vege­ 60 tation and life . . . cease". Here Newton was indeed teetering on the edge of a dangerous dialectic. Leibniz could accuse him both of embracing a form of non-mechanistic super-materialism, which 58 O n the political motives behind the Leibniz-Clarke correspondence, see Shapin, "Of Gods and Kings". 59 O n the mishandling of the calculus affair, which reached a peak in 1712, see Aiton, Leibniz: Λ Biography, pp. 337f. *°Opticks (4th ed., London, 1730), Bk III, Query 31; in Thayer, Newton's Philosophy of Nature, p. 175.

Plenitude and gravity 231

effectively replaced God with the active powers of nature (the same accusation of "Stratonian atheism" levied by Bayle against the Platonists), and of being the author of a theo-mechanical system featuring a lazy, sporadic, and willful miracle-worker for a God.61 Both pictures contrasted with the Leibnizian preference for a system informed by a spiritual presence which nevertheless did not act in it. The Newton of Laplace, who exhibits a flawless clock designed by a mathematical deus absconditus, was not Newton as Leibniz perceived him, and indeed this popular picture of Newton actually fits his rival a good deal better.62

"llnd Letter to Clarke, L 678f.; G VII:357. After the Acts of Toleration and of Freedom of the Press in 1689 and 1694, England became the radiant center of unorthodoxies, a development Leibniz was ready to exploit ad homines. See the opening statements of his first letter to Clarke, L:67S, G VII:34S. 62 As Koyre, loc. cit., first pointed out.

VII Experience and the self: the N e w Essays

The New hsays on Human Understanding is undoubtedly Leibniz's best composition: the richest, the most tightly argued, the most fertile in its application to contemporary philosophical problems. Before he finished it in 1704 he had already reviewed Locke'sL·sayConcerning Human Understanding several times since the appearance of a preview in 1688, and was aware of the changes from edition to edition.1 His own book was written up quickly, after he had a chance in 1703 to study Pierre Coste's translation, and he seems to have intended to publish it. What prevented him from doing so after Locke's death in 1704 was perhaps an observation of the nihil mortui rule. It is also possible that his friendship with Lady Masham, who had been Locke's warm admirer and was much grieved by his death, strengthened his scruples in the matter.2 Had he actually resolved to publish it, the NewL·saysmight have emerged as a different document, for it is in many ways a curious work, hardly a book at all. Though the commentary form itself is nothing new, this example of it is particularly unusual. Its wide deviations from the material of the text bear out Leibniz's confession that he did not always read with the aim of understanding, but rather with the aim of finding something he could use. Like the Theodicy, the book is a flurried unpacking of mental souvenirs by a man who has

1

ThIs preview appeared in 1688 in LeClerc's Bibliotheque choisie. Leibniz began to take more systematic notes probably from 1696 on; see his letter to Burnett, 7/17 March 1696, G 111:176. 2 See her letter to Leibniz, 24 November 1704: ".. .one that had been my Freind above half my life time. Mr. Locke I meane... who... has supplyd to me the Plan of a Father and Brother ... [has] left... to my Son ... a legacie in money of a value seldom givn by any to such as are in no way related" (G 111:365).

Experience and the self: the N e w Essays 233

forgotten almost nothing of what he has read or heard. Not only does the author seize on every one of Locke's own digressions, he introduces his own at every opportunity. The work is full of misreadings, red herrings, irrelevancies, associations leading off into personal recollection or anecdote. At the same time these formal defects convey a sense of authenticity. Leibniz had often tried the experiment of internalizing a philosophical interlocutor, a procedure which normally succeeds no better than a game of chess against oneself. His best dialogues, the Confessio, the Pacidius, and those on Malebranchean themes, are nevertheless successful examples of the form. But a real interlocutor, one in whose mouth words cannot be put, brings a good deal more than an invented one, and, at the same time, opens up the possibility of radical misunderstanding, not possible when the author is talking to himself. It is perhaps the sense that the New Essays is not a proper book which has encouraged commentators to treat Leibniz as no match for Locke.3 Some charge him with failing to grasp the merits of Locke's theories; others suppose that its mild and ingratiating tone indicates that Leibniz was genuinely bowled over by the Essay and prepared to make significant concessions to its author. It is true that Leibniz over-interpreted Locke. Accustomed perhaps to continental subtlety, to the ignorance-as-weapon approach of writers like Pierre Bayle, Leibniz found it difficult to believe that when Locke said he did not know about an issue he really did not know. He increasingly took Locke's epistemological statements about the limits of knowledge as a cover for radical metaphysical doctrines, and the polite interest of the earlier reviews gave way to harsh condemnation. As he wrote to Malebranche in 1711, "I have tried in passing [in the Theodicy] to combat certain philosophes relaches, like M. Locke and M. Ie Clerc and their type, who have false and base ideas of man, of the soul, of the understanding and even of God, and who treat as chimerical anything which goes beyond their popular and superficial notions".4 Even taking into account the lapse of time and the expectations of the addressee, this is unusually frank and disapproving language for Leibniz. Whether or not Jolley is right to say that his motives in the 3

This is generally the impression conveyed by Jolley's otherwise excellent study,

Leibniz and Locke.

* Letter to Malebranche, 1711, G 1:361.

234 Experience and the self: the N e w Essays

work are frankly theological,5 there is no doubt that he was deeply offended by what he took to be highly casual assumptions behind Locke's views on personal identity, moral motivation, and the origins of ideas. We will concentrate on these topics in this chapter, attempting to bring out both the interest, and sometimes the strength of Leibniz's theories and their connection with his metaphysical doctrines. 37 Personal identity "If mass were the essence of the human substance", Leibniz had stated in Mira de natura suhstantiae corporeae, "it would be impossible to explain how a man remains the same".6 Aware, at least since his reading of Locke's correspondence with Stillingfleet, of the former's somewhat timid and hedging interest in the possibility of "thinking matter", Leibniz brings this issue to the forefront of the discussions. He succeeds in mounting a forceful attack on Locke's view that consciousness and not "substance" can provide an adequate theory of identity, raising the same doubts about Lockean psychological atoms, event-memories, or experiences, as he had about material atoms. It is not, he concludes, a parcel of matter which establishes identity, "nor is it what we call I; rather, it is the soul".7 As a number of studies have made clear, Locke has several aims in expounding a theory of personal identity in Book II, Chapter 27 of the Essay. One is to explain how the soul can be immortal even if there is no such thing as Cartesian immaterial substance. Another is to encourage legal reforms which will shield certain categories of people from what he considers unjust punishment. His theory is too familiar to need much exposition, but its central points are worth repeating. The identity of a person is constituted, according to Locke, first by his immediate intuition of himself, second by what he can remember of his own life.8 Actual memory of an event is sufficient for its having been an action or experience of his; potential memory is s

Jolley makes a far better case for Locke's theological motivations in his cryptoSocinianism than for Leibniz's. The question of the latter's real theological commitments is a complex one; see my Introduction and below, Ch. VIII, pp. 298ff. See also S. Brown, Leibniz, pp. 188f. 6

Mira de natura suhstantiae corporeae, AK Vorausedition 11:294. NfU) Essays, RB 2 4 1 ; AK VI:VI:241. *Essay Concerning Human Understanding, Bk II, C h . 27, § § 1 1 , 20. 7

Personal identity 235

a necessary condition.9 It is sometimes said that the first condition is circular, on the grounds that there is no way of distinguishing between memories and fantasies-with-the-feel-of-memories except by referring to the facts of identity. But we may leave this objection aside for the moment - not all circular analyses are for that reason useless. More immediately problematic is Locke's negative formulation of his theory. "Suppose", he says, "I wholly lose the memory of some parts of my Life, beyond a possibility of retrieving them, so that perhaps I shall never be conscious of them again". Am I the same person who did those things? No, Locke says, I am the same man, but "the self same Person [is] no longer in that Man".10 Souls, he says, are "indifferent" to the parcels of matter with which they may be united,11 so that any person, or indeed no person at all, may be conjoined with a given man at any time. Where identity-conditions for "man" are formally the same as identity-conditions for "horse" or "pear tree" and have to do with the persistence of the same "continued life",12 identity-conditions for persons depend upon consciousness. To find out which person we have, we must investigate what is inside his consciousness. These assumptions furnish Locke with material for his many puzzle cases involving alleged exchanges of consciousness between one man and another, or even between man and beast, and are the basis of his curious theory of immortality as involving what Robert Herbert terms "gapinclusive existence".13 Let us first consider what is so persuasive about this account. To begin with, what might be called the "sense of self" seems to be connected with available memories, with the ability to recall hardships endured, obstacles overcome, triumphs achieved, interesting sensations, experiences, storms of feeling, and so forth. There might exist beings for whom the sense of self involved only premonitions and expectations about the future rather than memories of the past; but even so, this sense would be given content only in the images and descriptions associated with these •>Loc. cit.

1° Essay, 11:27:20. "IHi., 11:27:14, 27. 12 Ibid., 11:27:10. "See Herbert, Paradox and Identity in Theology, pp. 129ff.

236

Experience and the self: the New Essays

expectations. Thus it is easy to understand the appeal of Locke's theory: take away my memories or expectations, and what is left which could possibly distinguish me from other "selves" similarly deprived? Second, it is difficult not to agree with Locke that moral responsibility requires a memory of the actions for which one is allegedly responsible. A person is only "concerned and accountable", Locke urges (arousing immediate sympathy on this point), for what consciousness presents to him. Transfer the problem of temporal justice to the extra-mundane realm of divine justice, and the consequences appear writ large. Once the social fabric and all utilitarian considerations are eliminated, how could it be good and just to punish a sensitive being for something he could not remember having done? 14 Locke's theory is not meant to imply that I did not do any of the things I have forgotten that I did and so am not responsible for having done them. It is for this reason that Locke speaks of the loss of memory for "some parts of my Life", rather than for certain events.15 The excusing memory disturbance must be one which wipes out all memories, not a selective capacity for forgetting unpleasant occurrences. "Cannot" has here a modal force. It is not enough for me simply not to remember my lying and cheating of yesterday for them not to be mine; it must be the case that it has become impossible for me to remember them; they have not been stored up in any form in which they might be retrieved for me, even by God. So Locke indicates that on the day of final judgement everyone shall "receive according to his doings, the secrets of all Hearts [being] laid open". 16 This does not seem to mean that drunks, amnesiacs, and sleep-walkers, precisely the people Locke wishes to protect, will be restored to a memory of their actions: no such restoration is possible. The merely self-absorbed and lazy will, however, be restored to a memory of theirs. Locke argues that to focus attention on metaphysical identity of substance is to look in the wrong place; for such identity, to the "Essay, 11:27:26. ι5 Ibid., 11:27:20. 16 ItUi., 11:27:26. Cf. 11:27:2. In his correspondence with Molyneux, however, Locke shows a good deal of indecision about the moral and legal responsibility of drunkards. Cf. Works, IX:327ff.

Persona/ identity 237 extent that we can understand what it involves, is not sufficient for personal identity, nor is it necessary. As long as consciousness is "self to it self now", and as far back as memory reaches, a change of substance will no more make it two than a change of clothes makes a man another. 1 7 Happiness and misery, he points out, are "that, for which every one is concerned for himself, not mattering what becomes of any Substance, not joined to, or affected with that conscious­ ness". 1 8 Although he allows that it is "more probable" that "this consciousness is annexed to, and the Affection of, one individual immaterial Substance", 1 9 the whole thrust of his discussion is against it, and he takes pains to develop a theory of immortality which can accommodate its falsity. His view is, as stated, that "the union or separation of such a Spiritual Substance would make no variation of personal Identity". 2 0 O n this account, the person-man composite is essentially an organic machine, a temporary unity as destructible as a pear tree, to which God has joined consciousness as a superadded power. Having considered the possibility discussed by some of the Newtonians that gravity was simply a superadded power implanted by God directly in matter, Locke hit on the idea that, in the same way, God might just join thinking to matter directly, rather than creating "thinking substance" and joining this in turn to matter. Thought should count in this case as a "power" of suitably organized matter rather than as an essential property of thinking substance. 2 1 At death, the bodily machine ceases to function and may in fact be physically dispersed; consciousness is extinguished. For a time the person literally does not exist. At the Resurrection, however, God restores the body and returns to it its power of thought, together with the memories possessed by the former person. This and nothing more is all that is required for the resurrection of the person. 2 2 So all the problems of the occupation of thinking substance in the interim between death and resurrection are avoided. " Essay, 11:27:10. Cf. 11:27:23. "IbU., 11:27:18. "Ibid., 11:27:25. Cf. IV:3:6. Μ Ibid., 11:27:25. 21 See especially the Second Reply to the Bishop of Worcester, in WorL·, IV:460ff., and Essay, IV:3 :6, on gravity, thinking matter, and superadded powers; on Locke's suggestions, see also Yolton, Thinking Matter, pp. 14-20. "Second Reply, Works, IV:303ff.

238 L·perience and the self: the N e w Essays

38 Minds and machines Leibniz objects to this scheme on a number of grounds. The first parallels his objection to the Newtonians' superaddition of the power of gravity. "To speak of sheerly 'giving' or 'granting' powers is to return to the bare faculties of the Scholastics, and to entertain a picture of little subsistent beings which can fly in and out like pigeons with a dovecote". 23 Powers must be rooted in the nature of substances. 24 Hence a person with the attribute of consciousness cannot essentially be a machine with this added property, but must be a substance which can, according to its nature, also be conscious. Now Locke, of course, does not say that people are machines with the power of thought. He thinks of them as a kind of organic life, better organized than a mere machine, with the power of thought. He does not envision God superadding this power to something equivalent to a lawn-mower or a water-mill. But this point is necessarily lost on Leibniz, who recognizes only two kinds of empirical object: beings by aggregation and real, ensouled ones. If God could somehow attach consciousness to a machine by a miracle, then, Leibniz concedes, Locke would be right. 25 We should then have to say that the identity of this being is given to us qualitatively, in terms of its mental contents; for whether the "same machine" were present or not would not suffice fully to determine the case. Imagine that God has given consciousness to some nonanthropoid machine, say, a water-mill. We should then be able to entertain Locke's hypothesis that the soul of Socrates had come to inhabit this mill, a hypothesis which it would make sense to test by checking memories. The same principle should then hold if we suppose that the machine is of the human type. The question "Which person is this?" does in this case reduce to the question "Which consciousness is this?". Suppose, however, that there are, in addition to machines, certain more-than-mechanical unities. Then, according to Leibniz, the relevant question is no longer whether the same consciousness is present, but whether the same more-than"New Essays, RB 379; AK VLVL379. 24 See Leibniz's Preface to the New Essays, RB 66; AK VI:VI:66: "it is not at God's arbitrary discretion to attach this or that quality haphazardly to substances. He will never give them any which are not natural to them, that is, which cannot arise from their nature as explicable modifications". "New Essays, RB 236; AK VI:VI:236.

Minis and machines 239

mechanical unity is present. It might look here as though Leibniz is simply asserting that the presence of the same organic body - the same "man" - is what determines identity, so that Locke's distinction is after all gratuitous. But for Locke organic bodies are destructible, where for Leibniz more-than-mechanical unities are not. On Locke's view, if God annihilates a consciousness and breaks up the parcel of matter with which it was associated, there is no longer a person. On Leibniz's view, God might annihilate a consciousness and break up its body, but an unconscious more-than-mechanical unity would persist. In fact, this is what ordinary death entails. The organism persists; its organs are "merely enveloped and reduced to a small volume", with the cessation not of all functions but only some of the more noticeable ones, such as breathing, heartbeat, digestion, and sensation. 26 Leibniz's arguments for natural immortality are, as we have indicated, based on the evidence of Swammerdam against Harvey that there is no new production of forms but only growth. Symmetry now dictates for Leibniz that there is no destruction of forms but only shrinkage and reduction. The reasonableness of the hypothesis, where this is founded upon the best scientific observation of the day, gives way to certainty in the "Principles of Nature and of Grace", where Leibniz states that, "speaking as natural scientists", we can be sure that "souls cannot fail to awake from the state of stupor into which death . . . may place them". 27 The result is that, in pressing the advantages of natural, scientific immortality over revealed and miraculous immortality, he inadvertently implies that the best way to save religion is to destroy it: For in our day especially, when many people have scant respect for pure revelation and miracles, it is infinitely more useful to religion and morality to show that souls are naturally immortal, and that it would be miraculous if they were not, than to maintain that it is of their nature to die but that, thanks to a miraculous grace resting solely on God's promise, they will not die. It has long been known that those who have sought to destroy natural religion and reduce everything to revelation ... have been under suspicion, and not always without reason. But our author is not one of these .. .28 26

"Reflections on the Doctrine of a Single Universal Spirit", L 557f.; G VI:533. ""Principles of Nature and of Grace", §12, L 640; G VI.-604. 16 NeWL·says,RB 68; AK VI:VI:68. Cassirer, too, notes Leibniz's effort to detach his theory of immortality from its basis in revealed religion: Leibniz System, p. 417.

240 Experience and the self: the New Essays

These are, in any case, pointed remarks. As Leibniz knew, Locke's view, despite his hedging on the question of the soul's immateriality, was that its immortality could be known only through revelation. So his further comment, to the effect that Locke's sincerity is as great as his philosophical insight, must be taken as purely sarcastic. Philosophically, Locke is unable to appreciate the difference between reviving a person from death and making a copy of that person. If, on the Day of Judgement, God reconstitutes bodies and attaches the memories of certain no-longer-existing persons to them, is this sufficient for speaking of the continuation of life in the hereafter? For Leibniz it is not; I am no more identical with that «fabricated person that I am with a being qualitatively identical with me but existing right now on another planet. 29 Locke would presumably protest that his theory of resurrection need not imply that God creates counterparts rather than re-creating individuals. The divine intention may be one thing when dedicated to restoring a defunct individual, another when dedicated to copying him. This distinction is not on the face of it absurd. If a house falls down, one may restore it by putting its parts back together in the old way. Even if it has burned down to the ground and must subsequently be rebuilt with new materials, it could be argued that this need not involve mere copying; I could think of myself as putting doors, walls, and windows back on the ground where they once stood. But it is difficult to apply this analogy. As on Locke's theory a person has no essential material constituents but consists wholly of mental contents, there is not even a "ground" to build these back up on, so that, even for God, reproduction in the sense of copying seems to be the only real possibility. In the end, Locke's machine-with-the-power-of-thought cannot, according to Leibniz, escape the reduction to the merely serial or sequential which was the downfall of the Cartesian conceptions of matter and motion. Earlier, in the correspondence with Arnauld, Leibniz had tried to make the fact of personal identity count in favor of his logical conception of substance, constructing the following argument: Let a certain straight line, ABC, represent a certain time, and let there be a "New Essays, RB 245; AK VI:VI:245.

Minds and machines 241

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 BC. Now since people suppose that it is the same individual substance which perdures, or that it is the same me which exists in time AB while in Paris and which continues to exist in the time BC when in Germany, it must needs be that there should be some reason why we can veritably say that I perdure ... for, if there were no reason, it would be quite right to say that it was another .. . 3 0 "To be sure", he continues, "my inner experience convinces me a posteriori of this identity but there must also be some reason a priori". This reason is then, he suggests, to be found in the fact that the attributes belonging to each time period are predicates of the same subject. 31 An analogous argument can be mounted in terms of experiences and their subjects rather than grammatical subjects and predicates, more in keeping with Leibniz's later metaphysics. Suppose that, as in the example above, we are considering two possibly identical individuals with different experiences at times ti and t„. How can we distinguish between a succession of two individuals with a succession of properties existing at times ti through t n and a single person with changing properties existing over the whole period? On Locke's theory we cannot distinguish the two cases even with the help of memory. Even though there should exist at ti a consciousness which remembers inter alia living in a garret in Paris, and there should exist at t n a consciousness which remembers inter alia living in a garret in Paris, and even if it were possible to compare these memories and take note of their qualitative identity, this would be at once too strong and too weak to establish identity of persons. Two entirely different people might possess qualitatively identical memories of a Paris attic; or one person's memory might alter qualitatively. One might say: the two people are identical only if the same attic at a particular time in its existence is the basis for both memories. I am, in this case, no other than the person who experienced the things which are responsible for my remembering them. But here we are supposing the possibility of objective reference to an item persisting over time. If Leibniz is right, however, personal identity is a clearer, ""Remarks upon M. Arnauld's letter". May 1686, M 112; G 11:43; MB 129. η LK. CU.

242 Experience and the self: the New Essays

more fundamental notion than physical-object identity. It is only of myself that I can say "I know that it has been in existence for some time". This is indeed what the claim that the self is a substance amounts to. Λ posteriori, we have no good reason to suppose that aggregates have any more identity than a conventional, functional one. Accordingly, we need seek no a priori reason why this chair or boat remains this one. So long as the new one serves the same purposes as the old, it does not matter if God substitutes a new one every five seconds. But a posteriori I cannot (pace Hume) consider myself an aggregate of conscious states, for it would matter if God were to substitute a new one every five seconds. The a priori fact which Leibniz thinks explains this is my substantiality. Some commentators have been puzzled by the fact that Leibniz appears to ascribe to Locke the view that men could be apparent identities without being real ones. 3 2 Is this not the very distinction Locke's theory is supposed to obliterate? Thinking you are the same person as χ and really being the same person as χ are the same for Locke, if your thinking involves memories. They conclude that Leibniz has somehow failed to grasp the argument. But Leibniz is not confused here. He has simply picked up Locke's ill-considered remark that a change of substance cannot make a change of person any more than a change of clothes. A person, Leibniz would say, does not have a certain substance as he has a certain wardrobe; he is one. God could remove the clothes of memory from one substance and put them on to another, but it is inconceivable that God could remove the substance of one person and insert it into another. When Leibniz appears to concede that such a transfer could occur "through God's absolute power", he means - in accord with his strict anti-voluntarism - that such a transfer could not occur. As it is memories, not substances, which are like clothes, even Locke is forced to prise the consciousness of S's deeds and experiences off the deeds and experiences themselves. He must admit that my mental contents may be deceptive; I may be clothed in someone else's memories. Leibniz's point might be put as follows: the question "Why does M believe that she is Noah's wife?" might be answered by saying that she has a memory-impression of herself as having loaded animals into the Ark in the distant past. But the same "Nfio Essays, RB 236; AK VI:VI:236.

Identity and responsibility 243 statement would not be an explanation of why she is Noah's wife, as Locke seems to assert. Normally, Leibniz argues, apparent identity is associated with real; the person whose consciousness is full of deeds and experiences which he represents to himself in the first person is typically the author of those deeds and the subject of those experiences. God could make it happen that there was no relation at all between the contents of a person's consciousness and what that person had actually done: this would be unusual and abnormal. But we should not conclude in this case that the person actually was another, even if the contents of his consciousness happened to fit the history ascribed to another "man" better. This shows that we do have a conception of real identity, distinct from the psychologically based apparent identity, even if the two are usually found together. If a person senses himself to be the one who did such-and-such, Leibniz argues, he cannot in the normal course of things be mistaken.33 But this is not to say that his being the one who did such-and-such is nothing other than his sensing himself to have done so. There is an obvious analogy here in the theory of perception. When a person in good health in broad daylight has the impression of a green square in front of him, there is usually a green square to be seen. But this is not to say that there being a green square in front of him consists in nothing more than his having the impression of there being one. The "sense of self" is for Locke a kind of awareness, like the sense of something green's being in front of one, with no true object. For Leibniz, by contrast, being aware of myself is like seeing something green. On the basis of my conscious impressions I make a judgement, which is practically always right, not by definition, but in the same way that perceptual judgements are practically always right. 39 Identity and responsibility To Locke's claim that moral responsibility must be associated with memory of our actions, Leibniz responds with a number of distinctions. He appears at first to accept this claim, indeed to have anticipated it. However, it emerges later that he interprets the 33

Lx. cit.

244 Experience and the self: the New Essays

relationship between memory and responsibility in a broader sense, so that he would not require, for a person to be morally responsible for having φ-ed, that he must remember himself φ-ing. Already in the Discourse we find a bond established between consciousness, memory, and responsibility. The soul, according to Leibniz, knows what it is and is "able to say this little word T which means so much". This knowledge and this ability give it a moral identity beyond its metaphysical identity. They furnish not only a justification for punishment and reward, but a motivation for good behavior. For, without memory of one's previous life, immortality could not be rewarding, or - as Leibniz points out elsewhere - punish­ ing. 3 4 Without memory, he states, "immortality would be worthless". He offers the following example to Arnauld: Suppose some private man should suddenly become King of China, but only on condition that he forget what he had been, just as if he were being born anew; would it not be the same practically, or so far as discernible effects are concerned, if he were annihilated and a King of China created at the same instant in his place? This particular man has no reason whatever to desire this.« Note that Leibniz does not draw the Lockean conclusion that the individual in question has been extinguished and a new King of China has come into being. Moral identity is a more restrictive notion than metaphysical identity. He simply points to the limitations on motivation. We can now observe how Leibniz's and Locke's descriptions of a certain type of case first run parallel, then diverge. Both begin by describing cases in which, despite the existence of a prima facie identity, the subjects - Locke's drunkards and amnesiacs, Leibniz's king - do not appear to fulfill the psychological precondi­ tions for a full moral or prudential identity. Faced with this situation, Locke responds by denying that the prima facie identity was after all real in any sense. He redefines real identity here to mean moral identity with appropriate preconditions. Leibniz takes another tack. From the same contrast, he draws the conclusion that my real identity may not be simply given to me. I may need to discover it. His eye is firmly fixed on the real case and its Μ Discourse, §34, L 325; G IV:460; MB 80. 3S bx. cit.

Identity and responsibility 2 4 5

asymmetries, not on Locke's spectacular puzzle cases. Although real people do suddenly or gradually forget their pasts, they do not very readily acquire new ones. Society has thus evolved means, formal and informal, of establishing who people are and filling them in about their pasts; it has not needed to evolve so many ways of proving to them who they are not. So the "baby in the cradle" was surely I, although I discover this only by hearing anecdotes, seeing photographs, and so on. Moreover, it may be necessary for me to discover my moral identity, or even for it to be established for me despite my protests. This is of course the theme of the Oedipus story. In the terms of Locke's account, it would be impossible to say that Oedipus is guilty of murdering his father. He remembers an event, meeting somebody at the crossroads, and makes a discovery about the identity of the man involved. But he does not remember that he killed his father. If he had lived out his life in ignorance, God would have been justified only in punishing him for the action of killing an old man in a fit of temper, not for killing his father. It would have been cruel of God to bring forward the relevant facts only on the Day of Judgement, since they are, in the classic version of the story if not in its Freudian reconstruction, not "secrets of the heart" of Oedipus. Recall the modal formulation of Locke's criterion: Oedipus cannot remember killing his father and seducing his mother, not because he has repressed these events, but because for me to remember that I have φ-ed implies that I was once aware of ψ-ing, and Oedipus took his father and mother for perfect strangers. For Leibniz, because there is real, non-psychological identity, the unwilling discovery of moral identity is possible. I may be taught that 36 I am the subject to whom certain predicates apply. The difference between the amnesiac who is taught his name, and how to read and write, and gradually comes to understand who he is, and the man who wakes up as King of China consists in the fact that for the latter there is no way to learn or discover his true identity: who is there who could teach him of it? To Locke's point that such instruction could then only be based on the recognition of sameness of man, not of person, and is thus unsatisfactory, Leibniz, since he will not concede that men are machines with consciousness, must reply that *New Essays, RB 236f.; AK VI:VI:236f.

246 Experience and the self: the New Essays the subject who is so instructed is recognized as a more-thanmechanical unity. It is true that he does not say by what external criteria we could distinguish an amnesiac person from, say, a deprogrammed machine. But clearly the only injustice in practice that could arise from making the false identification here would involve taking a guilty person for a machine and failing to punish him, a possibility so remote that it is not worth considering. Leibniz's approach to punishment is fully pragmatic. He agrees with Locke that we do not punish madmen who have no memory of their actions. However, this is not because we suppose that two persons are involved, and that there is no moral identity, but because we do not believe that punishment will do any good. But if punishment is effective, as it may be in the case of sleep-walking, it is worth a try. 37 Because consciousness does not present to me a temporal interval densely packed with experiences, according to Leibniz, consciousness cannot in principle present to me endurance through time as a subject. This is ultimately why personal identity is a metaphysical notion arrived at by reflection and not a psychological notion arrived at by introspection. The self is like the infinitely-folded tunic of the Pacidius dialogue of 1676. An experience is like a point; it is assigned to a moment in the continuous existence of the subject. But this continuous existence is not made up of any definite number of experiences; for between two consecutive experiences a third could always be interposed, even if it is not immediately available to consciousness. The "mediating bond" of my life thus does not consist in the dense packing of experiences: this would be like trying to compose a line out of pencil dots. It consists rather in the possibility of infinite interposition. The line, or life, is prior to its points. For this reason, it is not necessary that I should now possess a complete panorama of my experiences and actions for them to be mine. Forgotten intervals, nights, days, whole years, are perfectly compatible with the continuity of the subject. "It is sufficient", Leibniz states, "that between one state and a neighboring (or just a nearby) one there be a mediating bond of consciousness, even if this has a jump or forgotten interval mixed into it". 38 But what kind of mediating bond is present in this case? »ftU., RB 243; AK VI:VI:243. " M , RB 236; AK VI:Vi:236.

Identify and responsibilify 247

Suppose that I no longer have any conscious memories pertaining to the calendar year 1964 and cannot retrieve any voluntarily, though I have some pertaining to the year before and the year after. Why do I nevertheless conceive of myself as having persisted through this entire year? Leibniz's view appears to be this: Suppose we define a point Pm as "accessible" to me if and only if I can now remember something that happened at Pm or another point Pn is accessible to me, at which point Pm was accessible to me. Then I have existed at all points which are accessible to me, and, knowing that I cannot compose the continuum in any case, I must conceive myself as having existed during all intervals between those points. My imagination, one might say, produces a continuous phenomenon from these discrete points. I cannot, of course, suppose that the initial point of my existence is accessible to me; but this does not matter, for we are concerned here only with what I could discover unaided. Everything that happened before the first accessible point I must discover with the help of others. That there are unremembered experiences in infinite number between any two remembered experiences indicates to Leibniz that all memories are in principle recoverable, all points in principle accessible. There is nothing which, in Locke's modal sense, cannot be remembered; there are only memories so dim that they are never noticed. So, in reply to one of Locke's puzzle cases, Leibniz maintains that an immaterial being or spirit cannot 'be stripped of all' perception of its past existence. It retains impressions of everything which has previously happened to it, and it even has presentiments of everything which will happen to it; but these states of mind are mostly too minute to be distinguishable and for one to be aware of them, although they may perhaps grow some day".39 This point allows Leibniz finally to reject the assumption behind Locke's puzzle cases, namely, that souls are indifferent to the particles of matter with which they are united. For Leibniz, the question whether Socrates has been reborn as the mayor of an English town, or the soul of the Roman emperor has passed into a hog, can always be answered decisively in the negative. For a being could not possess both the perceptual situs or perspectival location of Socrates and simultaneously that of the mayor of Casterbridge, or of II

39Ibid., RB 239; AK VI:VI:239.

248 Experience and the self: the New Essays

the emperor and a beast. In supposing that it is simply that "I" - what is immediately available to consciousness - which could be transferred to a new parcel of matter, Locke has mistaken this I of immediate apperceptual awareness for the soul, unaware that the latter is the richer concept. Curiously, however, Leibniz is willing to consider one fantastic case. If, he says, "a parrot were the transformed daughter of a king and revealed itself as such by speaking, no doubt the father and mother would caress it as their daughter and would believe that they had her back though concealed in that alien form".40 But we are to understand this example not as involving the flight of a human consciousness into the body of a parrot but as the transformation of a human body into a bird's body. This would be extraordinary, but it does not involve incoherent philosophical principles and makes the tender concern of the parents understandable. In closing this section, we should take note of a weakness of both positions, though the weakness is less pronounced in Leibniz's case because he stresses not simply the establishment but the discovery of moral identity. The insistence that memory is tied to moral identity disguises the fact that my memory may represent me as intertwined with events in variously colored ways. The subject determines his role not simply from the data of his immediate consciousness, nor simply from the facts he is told by others, but in accord with his particular moral temperament, in a way which can always be the subject of an evaluation which is itself moral and hence underdetermined. The corrective efforts of society, as Leibniz realizes, are needed to adjust the subject's sometimes erroneous conception of what he is or what he has done. But self-correction has a role to play here. A person who has in fact done something out of ignorance, inconsistent with his aims and values, and who has forgotten the whole episode, may nevertheless come to acknowledge his part in the ensuing disaster, taking full responsibility upon himself. Such a case may involve moral delusion, a drastic overestimation of his actual role in the theater of the world, but it need not. Conversely, a person may underestimate his responsibilities, insisting that, although he will accept a certain description of the event in which he figures as an unwitting accomplice, he will not 40lbid., RB 235; AK VI:VI:235.

Moral motivation, powers, and "unease" 249

adopt any view of himself as agent. Again, his stance is open to criticism. In both cases, facts about memory and consciousness cannot settle the question, which is one of the rightness or wrongness of his stance towards the event. 40 Moral motivation, powers, and "unease"

There is a strong tendency for seventeenth-century philosophers to address ethical questions in terms of inter-mental causality. How can the mind resist impulses stirred up by the senses? Accordingly it is in his section on "Powers" that Locke addresses the question of the springs of moral and amoral action. "What moves the mind", he asks, "in every particular instance, to determine its general power of directing, to this or that particular Motion or Rest?" 41 The answer, he says, must be disquiet or "unease", and this proposal occasions one of the most eloquent and original sections of the L·say (quoted nearly in full, with deserved admiration, by Leibniz), in which the pronouncement of the moralist that the will is moved by its perception of the good is set against the facts of human cravings, despairs, and compulsions. "Who is there, that has not felt in Desire, what the Wise-man says of hope . . . that it being deferr'd makes ihe Heart sick?"42 Locke continues: Let a Man be never so well perswaded of the advantages of virtue, that it is as necessary to a Man, who has any great aims in this World, or hopes in the next, as food to life: yet till he hungers and thirsts afterrighteousness;till he feels an uneasiness in the want of it, his will will not be determin'd to any action in pursuit of this confessed greater good ... [L]et a Drunkard see, that his Health decays, his Estate wastes; Discredit and Diseases, and the want of all things, even of his beloved Drink, attends him in the course he follows .. .43 In the intervals between his drinking hours, he takes resolutions to pursue the sovereign good, but "when the uneasiness to miss his accustomed delight returns" to torment him, it determines the will against all his resolutions, bearing out the motto from Ovid, Video

"Essay, 11:21:29. «ftirf., 11:21:32 i3 lbid., 11:21:35.

250 Experience and the self: the New Essays meliora prohoque, deteriora sequor - "I see and esteem the better, I follow

the worse".44 Locke's argument here actually divides into two parts which are both addressed by Leibniz. The first is that events occurring in the future cannot exert a motivational effect: only what is now happening possesses that power. The second is that to be motivated is to be suffering pain. Taking action is always pain-reducing and never pleasure-enhancing. These two claims are supposed to entail that a person cannot subject himself to painful deprivations in the present merely to insure some future good for himself. Leibniz is hardly eager to concede that a human being can be a victim of irresistible compulsions, as Locke's example implies. Sometimes, clever techniques of self-management will do the trick; or the adoption of distracting hobbies will help get one's mind off the obsession: "To dangerous interests we will oppose innocent ones like farming or gardening; we will avoid idleness, will collect curiosities, both natural and artificial, will carry out experiments and inquiries ... engage in useful and agreeable conversation or reading .. .".45 Again Leibniz seems to be missing the point. Locke has produced an astonishing theory which turns the problem of akrasia on its head. The problem is not to explain how one can do what one perceives to be the worse alternative, but how one can ever act in a prudent fashion at all and sacrifice the goods of the moment. This question is in turn closely connected with the issue of personal identity. If my being is composed of momentary states of consciousness, is given by what I am aware of at this moment, Locke's conclusion appears to follow automatically. No promise of future good, however durable, can outweigh the urgings of the slightest present discomfort; for it is inconceivable that I should now submit myself to pain simply in order that a different consciousness, even one which would remember my present sacrifice, should experience pleasure. But if my existence is really limited to what self perceives as itself now, I should not even be able to consider the diminishment of my present pleasure - for it would not be my diminishment, but that of another being. This shows that prudential concern for the future must always be present; the dissipated man in "Ibid. "New Essays, RB 187; AK V1:VI:187.

Moral motivation, powers, and "unease" 2 5 1

the throes of an intoxicated ecstacy is not indifferent to it, for he would like to prolong this pleasure if only for an instant. Like Baudelaire's character, he is willing to undergo an eternity of punishment at some future time if only his next moments may be exquisitely agreeable. The impossibility of eliminating this concern gives Leibniz enough of an opening to be able to concede a great deal to Locke, without however arriving at the latter's pessimistic conclusions. Everyone acts only according to his present perceptions, he agrees. And "if there were only the present, one would have to settle for the perfections which it offered, i.e. for present pleasure". As soon as Locke observes that, "were the Pleasure of Drinking accompanied, the very moment a Man takes off his Glass, with that sick Stomach and aking Head which ... are sure to follow not many hours after" he would never let wine touch his lips,46 he has identified the problem. Though motivation logically must reach beyond the moment if I can desire the continuation of my present ease and take steps to prevent its disruption, it may not extend far. Even presupposing the most acute discomfort, a gap of eight hours between action and consequence may be too much to comprehend; how much more difficult is a gap of months or years, with effects unknown. This is the basis of Locke's dramatic attempt at generalization. Present goods, he thinks, always carry the advantage, as Objects, near our view, are apt to be thought greater, than those of a larger size, that are more remote". But, as Leibniz observes, Locke's distance rule does not always hold, and the conclusion that akrasia is the normal, non-paradoxical state, prudential action the absurdity, does not follow. "The effect which a visible thing has on our eyesight is", he argues, "inversely proportional, more or less, to its distance from us, but the same does not hold for the effect on our minds and imaginations of things in the future". 47 A small interval of time may completely hide the future from us, as though events behaved according to the geometrical rules of curved spaces rather than flat. But even a great distance may not diminish the effect of the object if conditions are right. The future may exert an effect over-proportional to its distance if a person's «Essay, 11:21:63. "New Essays, RB 202; AK VI:VI:202.

252 Experience and the self: fhe New Essays

image of it is sufficiently strong, or "through his having made a policy and practice of being guided by the mere name or some other arbitrary symbol of the future without any image or natural sign of i f . 48

When an object is out of sight, it does not exert its usual effect directly, but only through a representation: a symbol, an image, a name, which in turn may be either natural or conventional. The concept of sobriety, the images of illness and discomfort, take the place of the experienced effect of alcohol. Weakness of the will is no mystery; but neither is prudential action inexplicable. In proportion as real feeling is reduced to symbolic representation, it tends to lose in strength. But this is not to say that it is strengthless: The neglect of things that are truly good arises largely from the fact that, on topics and in circumstances where our senses are not much engaged, our thoughts are for the most part what we might call "blind" ... I mean that they are empty of perception and sensibility, and consist in the wholly unaided use of symbols, as happens with those who calculate algebraically with only intermittent attention to the geometrical figures which are being dealt with ... [T]his sort of knowledge cannot influence us - something livelier is needed if we are to be moved. Yet this is how people usually think about God, virtue, happiness .. .49 Blind thinking is, as Leibniz had long ago discovered, indispensable to mathematical invention: the capacity to manipulate a symbolism without possessing at every moment an intuitive idea of what it represents is the distinctive contribution a symbolic language makes to thought. But what is good for mathematics is bad for ethics. And, as the beasts do not reason, neither do they possess a moral sense: a beast may be ineffectual or energetic providing for itself, but it cannot be either akrasic or prudential. For both qualities imply the possibility of blind thought. How does this square with Locke's assertions about unease? By a process of redefinition it might seem as though only thoughts which are not so blind that they fail to produce unease can exert a motivating power. This is the second strand of the argument: motivation is discomfort. Leibniz does not wish to concede this point

"Ibid., RB 204; AK VI:VI:204. "Ibid., RB 185f.; AK VI:VI:185f.

Moral motivation, powers, and "unease" 2 5 3

either, for it entails the curious conclusion that we are wretched so long as we are actively pursuing our own good, and content only when we cease to do so. To Locke's "unease" he therefore opposes a milder version of unconscious disquiet: What usually drives us are those minute insensible perceptions which could be called sufferings that we cannot become aware of, if the notion of suffering did not involve awareness Far from such disquiet's being inconsistent with happiness, I find that it is essential to the happiness of created beings; their happiness never consists in complete attainment, which would make them insensate and stupified, but in continual and uninterrupted progress towards greater goods .. .50 Nature, he says, "has given us the spurs of desire in the form of the rudiments or elements of suffering, semi-suffering one might s a y . . . This lets us enjoy the advantage of evil without enduring its inconveniences . . . This account of tiny aids, imperceptible little escapes and releases of a thwarted endeavour . . . provides a somewhat more distinct knowledge of our inevitably confused ideas of pleasure and pain". 51 Socrates' itching paradox of pain and pleasure from the Phaedo is solved by proposing that infinitesimal pains and their infinitesimal reliefs follow upon one another so rapidly that the effect is a true mixture, which cannot occur when pain and pleasure are intensive enough to be fully present to consciousness. Simultaneously, Leibniz offers a model of psychophysiological homeostasis, for which there may be no precedents. O u r natures are always seeking equilibrium, attaining it momentarily and being thrust out of it by new stimuli. The German word for the balance of a clock, Leibniz tells us, is Unruhe, restlessness: and one can take that for a model of how it is in our bodies, which can never be perfectly at their ease. For if one's body were at ease, some new effect of objects - some small change in the sense-organs, and in the viscera and bodily cavities - would at once alter the balance and compel those parts of the body to exert some tiny effort to get back into the best state possible; with the result that there is a perpetual conflict which makes up, so to speak, the disquiet of our clock.52 softirf., RB 188f; AK VI:VI:188f. si Ibid., RB 165; AK VI:VI:16S. 52jf>«/., RB 166; AK VI:VI:166.

254 Experience and the self: the N e w Essays

This image in fact provides Leibniz with a general account of human action as resulting from the summation of various conflicting and reinforcing inclinations: the eventual result of all these impulses is the prevailing effort, which makes a full volition. 53 This account, with its obvious analogies to the conatus theory of the 1670s, applies the principle of sufficient reason to human actions. "Free beings", Leibniz asserts bluntly elsewhere, "do not act in an undetermined way". A strange passage takes account of this difficulty: If by "necessity" we understood a man's being inevitably determined, as could be foreseen by a perfect Mind provided with a complete knowledge of everything going on outside and inside that man, then, since thoughts are as determined as the movements which they represent, it is certain that every free act would be necessary .. .54 However, he goes on to insist, only geometrical and metaphysical reasons necessitate; physical and moral ones "incline without necessitating". This is an evasive locution: are physical and moral reasons in fact sufficient to determine action, one wants to know, or do they produce a mere leaning in a certain direction? Anything less than full determination would seem to imply what Leibniz calls an "utterly imaginary and futile freedom of equilibrium"; ss if a pure will did exist, it would have to be capable of willing against all determinations, even those produced by reason - and how should such a will be of use to morality? Leibniz appeals to the conventional idea that the will is free when it is moved more by reason than by feeling. But he seems to be of two minds about whether our thinking itself, and so moral decision, is free. Bayle had expressed himself skeptically in his Dictionary article "Averroes", indicating that no one can create ex nihilo even in his own mind. How, he asks there, can a man form for himself the picture of a rose in his mind, when the same man could not sew two stitches? "Does it not appear on the contrary that this mental portrait is in itself a work more difficult than tracing on canvas the shape of a flower?" Doesn't experience provide more evidence of the servitude of the will than of its dominion? One could not will to love an enemy,

"Ibid., RB 192; AK VI:VI:192. s*lbid., RB 178; AK VI:VI:178. 55 IW., RB 180; AK.VI.VI:180.

Knowledge and experience 2 5 5

to hate a mistress, or to scorn a fine sonnet of one's own, even if "there were a hundred pistoles to be gained and [one] ardently desired to gain these hundred pistoles". 56 To this Leibniz will reply in the Theodicy that, although we do not form our own ideas, "they form themselves through us, not in consequence of our will, but in accordance with our nature and that of things", as the foetus forms itself in the animal. 57 Such thoughts are, then, determined but natural; they fit the thinker. But what of thoughts which do not seem to fit the thinker? In the New Essays, Leibniz takes account of those "flying thoughts" odd ideas, weird images, strange impulses - which come unbidden or as though one had "a magic lantern, with which one can make figures appear on the wall by turning something on the inside", and "which provide upright people with moments of moral unease, and provide much work for casuists and directors of conscience". 58 But the mind, he thinks, is able to say Stop!, and to good effect. And elsewhere he tells Locke that "in so far as a man wills vigorously, he determines his thoughts by his own choice instead of being determined and swept along by involuntary perceptions". 59 Thus he seems resolved to maintain an empirical thesis about the power of the pure will in the midst of a metaphysical theory which denies it. 4 1 Knowledge and experience

The question whether the soul at first is "completely blank like a writing tablet on which nothing has as yet been written" 60 is, for Leibniz, an issue of paramount importance between himself and Locke. In keeping with his general approach, he reads Locke's theory not simply as a contribution to theory of knowledge or psychology, but once again as a metaphysical doctrine with ethical consequences. In this he is not entirely unjustified, for Locke's denial of innate ideas was deployed both in his political theory and, as Leibniz's essay of 1700 points out, in his campaign against "enthusiasm". Locke attempts to discredit those people who think they have been instructed by their consciences in the knowledge of radical social and ^Theodicy, §401, FH 363; G VI:354f. "Ibid., §403, FH 364; G VI:3S6. 5«Nra> Essays, RB 177; AK VI:VI:177. "Ibid., RB 180; AK VI:VI:180. « M . , Preface, RB 48, AK VI:VI:48.

256 Experience and the self: the N e w Essays

religious truths - people who find within themselves a divinely sanctioned injunction to rebel against social norms. Leibniz, who seems to consider visionaries mainly as curious or pitiful, but not as dangerous, finds Locke's wholesale rejection of innate ideas and the "natural light" too extreme. For, without such a notion, as he points out in his review essay, Locke cannot distinguish between necessary truths, which are, as Plato thought, recalled as a result of experience, and those which have their ground in experience per se.61 That such a distinction sits uncomfortably with the old theory of metaphysics A to the effect that all our thoughts proceed from ourselves, without being caused by anything external, should no longer be too surprising, given the complexity of the cross-currents to which it was subjected from the beginning. That the tabula rasa theory could not be considered morally neutral was clear to critics like Cudworth, who had attacked Hobbes's mechanical theory of mental activity, and it was perhaps through him that Leibniz arrived at his strongly metaphysical reading of Locke's epistemological doctrines. According to the rejected view, all knowledge is obtained by a mechanical process of interaction with the environment, so that the so-called truths of reason are either themselves obtained by a process of stamping, in the same manner as sensory impressions, or they are not substantive truths but, like Locke's famous "oyster is oyster", nonsense accidentally generated by the symbolism. There is in either case, technically speaking, no room for a higher-level critical, correcting, or inventive function of reason. "Had we no Mastery at all over our Thoughts, but they were all like Tennis Balls", Cudworth says, "Bandied and Struck upon us, as it were by Rackets from without, then could we not steadily and constantly carry on any Designs and Purposes of Life".62 Cudworth sees connections between the tabula theory, "atomology", and hedonism. According to the "Democritick and Epicurean Atheist", he reports, 'all Knowledge and Understanding is Really the same thing with Sense".63 Those like Hobbes, who think of sensation as the result of a pressure from bodies, take imagination and thinking to be no more than "the 61 Philosophischer Versuch, betreffend den menschlichen Verstand, in Guhrauer, ed., Deutsche Schriften, 11:330. 62 True Intellectual System, pp. 845f. Here he follows the lead of Henry More: cf. More, An Antidote Against Atheism, I:v, in Patrides, Cambridge Platonists, pp. 222ff. 63 True Intellectual System, p. 851.

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Reliques and Remainders of those Motions of Sense formerly made and Conserved afterwards in the Brain".64 But, Cudworth points out, sensations and passions cannot be true or false, but only more or less obscurely or clearly felt. To admit that judgements may be false is to admit that the mind can do more than suffer experience passively: "We conclude therefore. That since there is such a thing as Error or Fake Judgement, all Cogitations of the Mind cannot be meer Passions; but there must be something of Self Activity in the Soul it Self".65 The Epicureans endeavor to Depreciate and Undervalue Knowledge or Understanding, as a thing which hath not any Higher Degree of Perfection or Entity in it, than is in Dead and Senseless Matter. It being according to them, but a Passion from Singular Bodies Existing without, and therefore both Junior and Inferior to t h e m . . . at best but a Thin and Evanid Image of Sensibles, or rather an Image of those Images of Sense; a mere Whiffling and Phantastick thing .. . 66

Locke had, to be sure, allowed for a process of "reflection" which might have met Cudworth's demands for some principle of "selfActivity" in the mind, just as Leibniz's concession that even necessary truths need to be excited in the mind by sensory experience might well have met Locke's demands. How far apart these two positions really are is thus clear only from the philosophical setting in which they are embedded. Like Cudworth, Leibniz assumes that there is a firm alliance between materialism and sensationalism. "Does the soul have windows?", he asks; "is it similar to writing-tablets, or like wax? Clearly, those who take this view of the soul are treating it as fundamentally corporeal". 67 The admission that human beings, unlike machines, are conscious, he points out, does not count for much, if this consciousness does nothing more than enable the pressure of external objects to be represented as sensations. There is in this case a brain which has the power to become conscious of the motions within it, but, as far as he is concerned, no mind. It is now apparent to him that his best strategy for refuting this view is to try "hoc. cit. "True Intellectual System, p. 852. «!(«