The Bloomsbury Companion to Leibniz 9781472531513, 1472531515

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The Bloomsbury Companion to Leibniz

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Bloomsbury Companions The Bloomsbury Companions series is a major series of single volume companions to key research fields in the humanities aimed at postgraduate students, scholars and libraries. Each companion offers a comprehensive reference resource giving an overview of key topics, research areas, new directions and a manageable guide to beginning or developing research in the field. A distinctive feature of the series is that each companion provides practical guidance on advanced study and research in the field, including research methods and subject-specific resources. Titles currently available in the series: Aesthetics, edited by Anna Christina Ribeiro Aristotle, edited by Claudia Baracchi Continental Philosophy, edited by John Mullarkey and Beth Lord Epistemology, edited by Andrew Cullison Ethics, edited by Christian Miller Existentialism, edited by Jack Reynolds, Felicity Joseph and Ashley Woodward Hegel, edited by Allegra de Laurentiis and Jeffrey Edwards Heidegger, edited by Francois Raffoul and Eric Sean Nelson Hobbes, edited by S.A. Lloyd Hume, edited by Alan Bailey and Dan O’Brien Kant, edited by Gary Banham, Dennis Schulting and Nigel Hems Leibniz, edited by Brendan Look Locke, edited by S.-J. Savonious-Wroth, Paul Schuurman and Jonathan Walmsley Metaphysics, edited by Robert W. Barnard and Neil A. Manson Philosophical Logic, edited by Leon Horsten and Richard Pettigrew Philosophy of Language, edited by Manuel Garcia-Carpintero and Max Kolbel Philosophy of Mind, edited by James Garvey Philosophy of Science, edited by Steven French and Juha Saatsi Plato, edited by Gerald A. Press Pragmatism, edited by Sami Pihlström Socrates, edited by John Bussanich and Nicholas D. Smith Spinoza, edited by Wiep van Bunge

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THE BLOOMSBURY COMPANION TO LEIBNIZ

Brandon C. Look

LON DON • N E W DE L H I • N E W YOR K • SY DN EY

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Bloomsbury Academic An imprint of Bloomsbury Publishing Plc 50 Bedford Square London WC1B 3DP UK

1385 Broadway New York NY 10018 USA

www.bloomsbury.com Bloomsbury is a registered trade mark of Bloomsbury Publishing Plc First published as The Continuum Companion to Leibniz 2011 © Brandon C. Look and contributors, 2011, 2014 Brandon C. Look has asserted his right under the Copyright, Designs and Patents Act, 1988, to be identified as the Editor of this work. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage or retrieval system, without prior permission in writing from the publishers. No responsibility for loss caused to any individual or organization acting on or refraining from action as a result of the material in this publication can be accepted by Bloomsbury or the authors. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. eIsBN: 978-1-47253-151-3 Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. Typeset by Newgen Knowledge Works (P) Ltd., Chennai, India

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CONTENTS

List of Contributors

vii

PART I: LEIBNIZ’S TIMES AND PHILOSOPHICAL PRECURSORS 1. INTRODUCTION: LEIBNIZ’S LIFE AND WORKS

1

BRANDON C.

LOOK (UNIVERSITY OF KENTUCKY, USA)

3

2. DESCARTES AND LEIBNIZ PAULINE PHEMISTER (UNIVERSITY OF EDINBURGH, UK)

16

3. LEIBNIZ AND HOBBES PHILIP BEELEY (UNIVERSITY OF OXFORD, UK)

32

4. LEIBNIZ’S FASCINATION WITH SPINOZA URSULA GOLDENBAUM (EMORY UNIVERSITY, USA)

51

5. MALEBRANCHE AND LEIBNIZ SEAN GREENBERG (UNIVERSITY OF CALIFORNIA, USA)

68

PART II: LEIBNIZ’S PHILOSOPHY

87

6. LEIBNIZ’S METAPHYSICS: THE PATH TO MONADOLOGY BRANDON C. LOOK (UNIVERSITY OF KENTUCKY, USA) 7. LOGICAL THEORY IN LEIBNIZ

89

SAMUEL LEVEY (DARTMOUTH

COLLEGE, USA) 8. LEIBNIZ’S THEORY OF COGNITION

110 MARTHA BOLTON (RUTGERS

UNIVERSITY, USA) 9. LEIBNIZ’S THEORY OF MODALITY

136 OHAD NACHTOMY (BAR-ILAN

UNIVERSITY, ISRAEL)

159

10. LEIBNIZ’S THEORY OF CAUSATION BRANDON C. LOOK (UNIVERSITY OF KENTUCKY, USA)

174

11. LEIBNIZ’S PHILOSOPHICAL THEOLOGY MARTIN LIN (RUTGERS UNIVERSITY, USA)

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CONTENTS 12. LEIBNIZ ON FREE

WILL JACK DAVIDSON (TEXAS LUTHERAN

UNIVERSITY, USA)

208

13. LEIBNIZ’S MORAL PHILOSOPHY

GREGORY BROWN (UNIVERSITY OF

HOUSTON, USA)

223

14. LEIBNIZ’S CONTRIBUTION TO NATURAL PHILOSOPHY FRANÇOIS DUCHESNEAU (UNIVERSITY OF MONTRÉAL, CANADA)

239

15. LEIBNIZ AND THE LIFE SCIENCES JUSTIN E. H. SMITH (UNIVERSITY OF PARIS 7, FRANCE) 16. LEIBNIZIAN MATHEMATICS

259 DOUGLAS M. JESSEPH (UNIVERSITY OF

SOUTH FLORIDA, USA)

275

PART III: THE AFTERMATH

287

17. KANT, THE LEIBNIZIANS AND LEIBNIZ ANJA JAUERNIG (UNIVERSITY OF PITTSBURGH, USA)

289

Bibliography

310

Index of Names

331

vi

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LIST OF CONTRIBUTORS Philip Beeley Research Fellow, Faculty of History University of Oxford Oxford UK Martha Brandt Bolton Professor of Philosophy, Department of Philosophy Rutgers, the State University of New Jersey New Brunswick, NJ USA Gregory Brown Professor of Philosophy, Department of Philosophy University of Houston Houston, TX USA Jack D. Davidson Assistant Professor of Philosophy, Department of Philosophy Texas Lutheran University Seguin, TX USA François Duchesneau Professor of Philosophy, Department of Philosophy University of Montréal Montréal Canada Ursula Goldenbaum Associate Professor of Philosophy, Department of Philosophy Emory University Atlanta, GA USA

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Sean Greenberg Associate Professor of Philosophy, Department of Philosophy University of California, Irvine Irvine, CA USA Douglas Jesseph Professor of Philosophy, Department of Philosophy University of South Florida Tampa, FL USA Anja Jauernig Associate Professor of Philosophy, Department of Philosophy University of Pittsburgh Pittsburgh, PA USA Samuel Levey Associate Professor of Philosophy, Philosophy Department Dartmouth College Hanover, NH USA Martin Lin Associate Professor of Philosophy, Department of Philosophy Rutgers, the State University of New Jersey New Brunswick, NJ USA

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LIST OF CONTRIBUTORS Brandon C. Look Professor of Philosophy, Department of Philosophy University of Kentucky Lexington, KY USA

Pauline Phemister Reader, School of Philosophy, Psychology and Language Sciences University of Edinburgh Edinburgh UK

Ohad Nachtomy Associate Professor of Philosophy, Philosophy Department Bar-Ilan University Ramat-Gan Israel

Justin E. H. Smith University Professor of the History and Philosophy of Science Department of the History and Philosophy of Science University of Paris 7 (Denis Diderot) Paris France

viii

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PART I: LEIBNIZ’S TIMES AND PHILOSOPHICAL PRECURSORS

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1 INTRODUCTION: LEIBNIZ’S LIFE AND WORKS

Rather than living a life of ascetic, contemplative or philosophical withdrawal, Leibniz sought out a life of engagement with the world as he found it, and in two important ways. First, he sought actively to reconcile the opposing forces that he saw before him: balancing political interests, unifying Protestants and Catholics, and combining the insights of the ‘moderns’ and the ‘ancients’ in philosophy. Second, he attempted to contribute to the commonwealth of learning, or the republic of letters, in those fields of human knowledge where he had something to say, and he had something to say in almost every field.

Gottfried Wilhelm Leibniz was born into a world of conflict and intellectual revolution. The Thirty Years War, which was caused by the religious intolerance of Protestants and Catholics and the power politics of European nations and which had convulsed and destroyed much of the German Empire, killing approximately one-third of its inhabitants (Wedgwood, 1938, pp. 516), was drawing to a close. Galileo Galilei had died four years earlier in Florence while under house arrest for his publications advocating the heliocentric system of the universe. René Descartes had just published his Meditations on First Philosophy and Principles of Philosophy, which would fundamentally alter the trajectory of metaphysics and natural philosophy, just as his earlier work in analytical geometry changed the field of mathematics. Thomas Hobbes was at work on what would become the Leviathan, which would fundamentally alter political theory and conceptions of morality. William Harvey had published his short but important work on the circulation of blood and the workings of the heart; Evangelista Torricelli had finished his experiments on air pressure and vacuums. And, in Amsterdam, a teenage Baruch Spinoza was certainly puzzling over his readings in the Torah.

LEIPZIG CHILDHOOD AND EDUCATION Leibniz was a child of the legal and academic circles of Leipzig. His father, Friedrich Leibniz, was born in the nearby town of Altenburg in the German Electorate of Saxony in 1597 to a civil servant and his wife. At the age of 20, he matriculated at the University of Leipzig, which he was never to leave. He earned his Master’s degree by 1622, became involved in 3

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LIFE AND WORKS age of fifteen, he enrolled in the local university. But the University of Leipzig was, like the city itself, relatively conservative. The ‘modern’ philosophy of Descartes, Galileo, Gassendi, Hobbes and others had not made a great impact there – or anywhere in German-speaking lands. Consequently, Leibniz’s philosophical education was chiefly scholastic in its nature, though with a heavy mix of Renaissance humanism. His most important teacher in Leipzig was Jacob Thomasius, who instilled in him a respect for ancient philosophy, especially Aristotle, and who supervised his first philosophical treatise, De principio individui (On the Principle of Individuation). With the De principio individui, Leibniz was awarded his Bachelor’s degree in philosophy in 1663, shortly before his seventeenth birthday. Immediately after completing this baccalaureate, Leibniz spent one semester at the University of Jena, where he studied with Erhard Weigel, who impressed upon Leibniz the possibility of harmonizing disparate philosophies in an eclectic mix (Mercer 2001, pp. 38–9). One semester in Jena was enough for Leibniz, however; he returned to Leipzig for the following semester and received his Master’s degree in philosophy in 1664. At this point, Leibniz changed the focus of his studies to the field more in keeping with his family’s history: law. He took a Bachelor’s degree in law in 1665 before moving on to Altdorf, where he received his Juris Doctor degree in February 1667. While in Altdorf Leibniz published in 1666 the remarkably original Dissertatio de arte combinatoria (Dissertation on the Art of Combinations), a work that sketched a plan for a ‘universal characteristic’ and logical calculus, a subject that would occupy him for much of the rest of his life. Although Leibniz was offered a position on the faculty of law upon the completion of his Doctorate, he had a different future in mind. Leibniz’s own descriptions of his early philosophical development deserve some

the university’s administration as an actuary, and in 1640 was elected to the chair of moral philosophy; along the way, he also served as dean of the faculty four times and as the university’s notary (Antognazza, 2009, p. 29). While professionally Friedrich Leibniz was successful, personally he was perhaps less so. His first wife died in 1634, leaving him with a young daughter and son, and his second wife died nine years later after eight years of a childless marriage. In 1644, however, Friedrich married his third wife, Catherina, the 23-year-old daughter of his former colleague, the professor of law, Wilhelm Schmuck. Two years later, on 1 July 1646, their first child, Gottfried Wilhelm Leibniz was born. The young Leibniz could not have known his father well, for Friedrich died in 1652 when Leibniz was only six years old. Yet Leibniz’s few memories of his father were connected with the world of books and learning; in his own autobiographical sketch, for example, Leibniz writes of how he and his father read works of sacred and profane history (Pertz 4, p. 165). After the death of Friedrich Leibniz, Catharina never remarried and by all reports dedicated herself to raising Leibniz and his younger sister, Anna Catharina. And this care included granting her son virtually free access to the family’s library. According to Leibniz himself, he was largely an autodidact, learning to read Latin largely by himself and spending time with works of history and poetry (Pertz 4, pp. 166–7, 173). As Leibniz says, ‘Before I even entered a school class . . . , I was deep into the historians and poets, since I had begun to read the poets almost as soon as I could read, and in verse I found great pleasure and importance’ (GP VII, 506). Of course, Leibniz’s education was not entirely self-directed. As one would expect for a boy of his age and station, he was sent to one of the principal Latin schools of the city, and at the 4

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LIFE AND WORKS by their way of writing, which requires a great deal of meditation . . . Yet nearly all of what I know of the metaphysical and physical meditations of Descartes has come from reading a number of books written in a little more casual style that report his opinions. (GP I, 371)

consideration. In a famous piece of selfmythologizing, Leibniz writes the following to Nicolas Rémond late in his life: . . . I have tried to uncover and unite the truth buried and scattered under the opinions of all the different philosophical sects, and I believe I have added something of my own which takes a few steps forward. The circumstances under which my studies proceeded from my earliest youth have given me some facility in this. I discovered Aristotle as a lad, and even the Scholastics did not repel me; even now I do not regret this. But then Plato too, and Plotinus, gave me some satisfaction, not to mention other ancient thinkers whom I consulted later. After finishing the trivial schools, I fell upon the moderns, and I recall walking in a grove on the outskirts of Leipzig called the Rosental, at the age of fifteen, and deliberating whether to preserve substantial forms or not. Mechanism finally prevailed and led me to apply myself to mathematics. . . . (GP III, 606/L 654–5)

In other words, at the age of fifteen, Leibniz could not have had much of an understanding of what constituted modern philosophy or the mechanical philosophy. And his desire to turn to mathematics would be more than a decade away of being close to being fulfilled. What Leibniz’s letter to Rémond tells us more than anything else, however, is that he wished to be a player in the philosophical arena, that he was happy to bring together the thought of the ancients and the moderns, and that he saw a way forward in the mechanical philosophy.

FROM FRANKFURT AND MAINZ TO PARIS

Now, there are a number of reasons to be mildly sceptical about this picture. As Leibniz says in a letter to Simon Foucher in 1675, he did not truly understand the moderns until after his youthful excursions in the Leipzig parks.

Rather than going down the path of an academic, Leibniz opted for a life of active engagement in the world of political affairs. This was made possible through Baron Johann Christian von Boineburg, who had met Leibniz in 1667 and formed a very favourable opinion of him. Writing to his former teacher Hermann Conring in 1668, Boineburg says the following of the young Leibniz: ‘He is a twenty-two-year-old doctor in law: very learned, a good philosopher, committed, able and prompt in speculative reasoning . . . He is certainly a man of great knowledge, of disciplined judgement, and of great capacity for work. He lives now in Mainz, not without my support’ (quoted in

I admit that I have not yet been able to read [Descartes’s] writings with the care that I wished to bring to them. And my friends know that, as it turned out, I read nearly all the other new philosophers before I read him – Bacon and Gassendi first fell into my hands, their familiar and easy style being more fitting for a person who wants to read everything. It is true that I glanced at Galileo and Descartes, but, since I have only recently become a geometer, I was soon repelled 5

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LIFE AND WORKS a diplomatic mission to Paris, the intellectual center of Europe. As Leibniz wrote in 1675, ‘Paris is a place where you can achieve distinction only with difficulty. You find there, in all fields of knowledge, the most learned men of the age, and you need much work and a little determination to establish a reputation there’ (A I, i, 491). But establish a reputation Leibniz did. In all, he was able to stay in Paris for four years (with two brief trips to London), and in this time he met many of the most important thinkers of the period: the philosophers Antoine Arnauld and Nicolas Malebranche, and, most importantly, the Dutch mathematician and physicist, Christiaan Huygens. It was he, ‘the great Huygenius’ (as John Locke was to call him in the Dedicatory Epistle to his Essay Concerning Human Understanding), who tutored Leibniz in the developments in philosophy, physics and mathematics. Moreover, Leibniz was not only able to converse with some of the greatest minds of the seventeenth century while in Paris, he was also able to read and study the unpublished manuscripts of Descartes and Pascal. And, according to Leibniz, it was while reading the mathematical manuscripts of Pascal that he began to conceive what was eventually to become his differential calculus and his work on infinite series. In this time, Leibniz also designed a calculating machine able to perform addition, subtraction, multiplication and division. And his trip to London in 1673 was meant in part to present his designs to the Royal Society, which must have been impressed because Leibniz was voted a member of the Society. It is safe to say that this period was the single most important period in his intellectual life, for it was not until this period that he truly began to understand mathematics and the modern philosophers. Indeed, one has only to look at his writings in this period to see

Antognazza, 2009, p. 86). Boineburg, a Protestant convert to Catholicism, was minister to Philipp von Schönborn, the Elector of Mainz, and he was able to secure a position for Leibniz in the court. Leibniz produced a series of works in law and political briefs for his employer and became ever more engaged in European politics. At the same time, Leibniz engaged in other more philosophical work and produced writings that combined his philosophical interests with his political aspirations. For example, in Mainz, Leibniz composed a series of works in philosophical theology, the Catholic Demonstrations, which manifest Leibniz’s lifelong irenicist tendencies: in this case, in their attempt to provide a basis and justification for the reconciliation of Protestantism and Catholicism. He also turned to philosophy of law in his Elementa Juris Naturalis (Elements of Natural Law), which was part of a project of legal reform in the Holy Roman Empire and in which he argued, among other things, that the first principles of law and justice are essentially identical to those of theology, since God is the lawgiver for the world. Leibniz also turned his mind to natural philosophy, having finally been able to study some of the works of the moderns; the result was a two-part treatise in 1671, the Hypothesis physica nova (New Physical Hypothesis). The first part, theTheoria motus abstracti (Theory of Abstract Motion), was dedicated to the Académie des Sciences de Paris, and the second part, theTheoria motus concreti (Theory of Concrete Motion), was dedicated to the Royal Society in London. These works, however, were not likely to impress their audiences, for, given his circumstances, Leibniz could not but produce amateurish works in the field. This changed, however, in 1672, when Leibniz was sent by the Elector of Mainz on 6

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LIFE AND WORKS tual death, and spoke with him ‘several times and at length’ (A II, i, 568). Their discussions indeed seem to have been relatively farranging: Leibniz reports that they spoke of Spinoza’s metaphysics, which Leibniz found to be ‘strange and full of paradoxes’ (A II, i, 568), of Leibniz’s own proof of the existence of God, and of Dutch politics, including the murders of the De Witt brothers. Leibniz arrived in Hanover in December 1676 and found, in Johann Friedrich, an amiable and supportive employer, committed to intellectual pursuits. Like his employer in Mainz, Johann Friedrich was a convert to Catholicism; nevertheless, he did not impose his confession upon the largely Lutheran population of Hanover. In fact, for Leibniz, he was an exemplar of religious toleration. While Leibniz admired the person of Johann Friedrich, he was not perfectly satisfied with his position. It was his understanding that he would be a counsellor in the Hanoverian court, yet he found himself largely relegated to the position of court librarian. Indeed, after he had done so much in the court of Mainz and after he had accomplished so much philosophically in Paris, he was clearly disappointed to have such a modest position. But over the years his engagement and responsibilities grew. Although Leibniz had good relations with Johann Friedrich, they were short-lived. The Duke died three years after Leibniz began his employment in the court, and his brother Ernst August came to power. Ernst August and his successor, his son, Georg Ludwig, had little interest in philosophy or the sciences. It was Leibniz’s good fortune, however, that the women in the family, Ernst August’s wife, Sophie, and Georg Ludwig’s sister, Sophie Charlotte, were very intelligent and deeply interested in the world of the intellect and enjoyed conversing with

that an incredibly brilliant young man has become a deep and profound philosopher. At the beginning of his stay in Paris, he penned his Confessio philosophi (Confession of a Philosopher), which offers insight into his still early thought on the problem of evil. But in short pieces published in the twentieth century under the title De summa rerum, for example, one sees Leibniz wrestling with a host of issues in metaphysics in deep and interesting ways. In this period, he makes his first truly important steps toward fundamentally altering mathematics with the discovery of the calculus in 1675, and his metaphysics (arguably) starts to take on the form that it will have when he reaches his maturity. By the time he left Paris, Leibniz had the opportunity to become a member of the Académie des Sciences – on the condition that he convert to Catholicism, which he refused. (He was finally made a foreign member of the Académie – without conversion – in 1700.)

HANOVER UNDER JOHANN FRIEDRICH AND ERNST AUGUST, 1676–98 During Leibniz’s stay in Paris, his patron, Boineburg, and his nominal employer, the Elector of Mainz, died in rapid succession, causing Leibniz to try to secure more stable employment. Eventually, he found a new position in the court of Duke Johann Friedrich of Brunswick, who ruled in Hanover and whom Leibniz had met in Mainz several years earlier. Although Leibniz tried to stay on in Paris as long as possible, he was given an ultimatum in the autumn of 1676 and grudgingly decamped. On the way to Hanover, however, he stopped in Holland to meet Spinoza, just months before Spinoza’s even7

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LIFE AND WORKS and philosophical projects. Most notably in the practical realm, Ernst August turned to Leibniz with an engineering task: to drain the silver mines in the nearby Harz Mountains. This was of great importance to the duchy, since approximately half of all the silver in the Holy Roman Empire came from the Harz Mountains. Leibniz devised an elaborate system of mills and pumps to keep the shafts free of water and debris, and he travelled often between Hanover and the mines throughout the decade to supervise construction. Unfortunately, his proposed solution met with delays and ultimate failure. At the same time, however, he had much more luck with his projects in mathematics and philosophy. Indeed, this was a period of extraordinary productivity for Leibniz, as the most recent volumes of his collected philosophical writings attest. In 1684 Leibniz published a short piece laying out the basics of the calculus, the Nova methodus pro maximis et minimis (New Method for Maxima and Minima). While Leibniz had every right to be proud of his important work, this paper would set the stage for a rather acrimonious debate decades later with Isaac Newton over who had first discovered the calculus. In the same year, Leibniz produced his first mature philosophical publication with his Meditationes de cognitione, veritate et ideis (Meditations on Knowledge, Truth and Ideas). And in 1686 he finished the composition of his Discours de métaphysique (Discourse on Metaphysics), a work of great insight and importance, which carries within it the seeds of all his later work in metaphysics. In between these works are notes, essays and scribbles dealing with logic, modality, epistemology, language, metaphysics, physics and much more. Moreover, it was in this period that Leibniz engaged in his first truly important extended philosophical correspondence – with Arnauld. The correspondence

Leibniz. Ernst August, in particular, was primarily concerned with increasing his political power, and to this end engaged Leibniz in a task that was to be a burden for the rest of Leibniz’s life: writing a history of the royal house. There were very important consequences for this project, for it was Ernst August’s aim to raise his duchy to the ranks of an imperial electorate, and, if it could be shown that the House of Hanover had more important connections in its past, then its imperial position could be strengthened. Leibniz was eventually able to give the duke what he wanted; his archival researches showed a connection between Ernst August’s duchy and the famed and important Este family. This fact, combined with Ernst August’s decision to adopt primogeniture, after generations of split inheritance among children had divided territories and eroded political power, led ultimately to Ernst August’s achieving the position of ninth Elector of the Holy Roman Empire. Moreover, his son would achieve an even greater elevation of power, which was also due to a small degree to Leibniz. The English Parliament’s Act of Settlement had declared that there were to be no Catholic successors to the throne after the rule of King William III and Queen Anne. Ernst August’s wife, Sophie, as granddaughter of James I and daughter of Elizabeth Stuart, was the last Protestant heir of the last Protestant ruler, and she and her heirs were the choice of Parliament to succeed to the throne. Apparently, however, Sophie was not keen on these prospects, and Leibniz, among others, used his close relationship to convince her to accede. Thus, upon the death of Queen Anne, it was Georg Ludwig who became King George I of England. The 1680s saw Leibniz direct his energies to an enormous range of practical, scientific 8

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LIFE AND WORKS way to understanding Leibniz completely. Equally important to Leibniz during his travels, he sought out and conversed with leading scholars and scientists along the way, including the anatomist Marcello Malpighi and the Franciscan priest and professor of philosophy Michael Angelo Fardella. The latter advocated a unique blend of Cartesianism and Platonism, and in notes of their discussions Leibniz leaves interesting and important clues about the development of his conception of substance (see FC 317–23/AG 101–5). We saw above how Leibniz described his move away from scholastic philosophy and towards the mechanical philosophy of the ‘moderns’ while just a boy of fifteen. In the same letter, he went on to explain his development after his conversion to mechanism:

was occasioned by Leibniz’s sending a précis of his Discourse on Metaphysics to Arnauld through an intermediary and Arnauld’s strong reaction to §13 of the Discourse. In order to acquire historical material necessary for writing the history of the House of Hanover, Leibniz travelled from 1687 to 1690 through southern Germany, Austria and Italy. When he was not scouring libraries for archival nuggets, he continued his philosophical, mathematical and scientific research. Two works in natural philosophy stand out in this brief period of travel. First, upon reading a review of Newton’s Principia in the journal Acta Eruditorum Leibniz hurried to publish his Tentamen de motuum caelestium causis (Essay on the Causes of Celestial Motion), in which he sought to provide an answer to the question that Newton so studiously avoided – what is the cause of gravitational attraction? Second, Leibniz expended great efforts on a huge work in physics: the Dynamica de potentia et legibus naturae coporeae (Dynamics, on the Powers and Laws of Corporeal Nature). Though he never published this work in his lifetime, certain aspects of his thought did see the light of day in his publication in 1695 of the Specimen Dynamicum (Specimen of Dynamics). Moreover, he began a work in geology and natural history which was to act as a kind of preface to his history of the House of Hanover. In it, the Protogaea, Leibniz sketched the history of the formation of the earth, based in part on geological inquiries and fossil studies. Finally, it is now thought that it was while in Italy that Leibniz composed the short piece known to us as Primary Truths (see A VI, iv, 1643–9/AG 30–4), which in lapidary prose lays out the Leibnizian system so clearly that if one understands this text well one has gone a long

[W]hen I looked for the ultimate reasons for mechanism, and even for the laws of motion, I was greatly surprised to see that they could not be found in mathematics but that I should have to return to metaphysics. This led me back to entelechies, and from the material to the formal, and at last brought me to understand, after many corrections and forward steps in my thinking, that monads or simple substances are the only true substances and that material things are only phenomena, though well founded and well connected. Of this, Plato, and even the later Academics and the sceptics too, had caught some glimpses . . . I flatter myself to have penetrated into the harmony of these different realms and to have seen that both sides are right provided that they do not clash with each other; that everything in nature happens mechanically and at the same time metaphysically but that the source of mechanics is metaphysics. (GP III, 606/L 655) 9

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LIFE AND WORKS the Acta Eruditorum, of the first part of his Specimen Dynamicum (mentioned earlier). Moreover, 1695 also saw the publication in the French Journal des Savants of his Système nouveau de la nature et de la communication des substances, aussi bien que de l’union qu’il y a entre l’âme et le corps (New System of Nature and of the Communication of Substances, as well as of the Union of Mind and Body). Although Leibniz had argued for his ‘hypothesis of concomitance’ in the Discourse on Metaphysics, it is here that one first finds Leibniz’s theory of the ‘pre-established harmony’ of mind and body. Despite the anonymous publication, Leibniz was quickly identified as the author, and he began a series of exchanges with scholars about his answer to the burning problem of the mindbody relation. Finally, in 1698 Leibniz published in the Acta Eruditorum his De ipsa natura (On Nature Itself), in which he again examined fundamental metaphysical issues and first employed the term ‘monads’. While Leibniz may not have had as much time as he wanted to pursue his intellectual projects, he still accomplished a great deal of importance in this period.

Much of Leibniz’s return to metaphysics happened in the 1680s; one sees it in the metaphysical treatises mentioned above. While it remains a vexed question in Leibnizian scholarship whether his commitment to idealism and phenomenalism per se began here or in the 1690s or even later, the preponderance of the evidence does suggest that in the 1680s, at the very least, Leibniz moved ‘from the material to the formal’ and held that material things were only phenomena. After a period of travel and intellectual exchange, Leibniz found life in Hanover vexing, especially since he did not have the freedom to work on the projects that truly interested him. I cannot say how remarkably distracted I am. I dig up various things from archives, inspect old records, and gather unpublished manuscripts. From these things I try to shed light on the history of Brunswick. But I have so many new things in mathematics, so many thoughts in philosophy, so many other literary observations, which I do not want to lose, that I am at a loss for where to begin. I almost feel like that line from Ovid: inopem me copia fecit (abundance has made me poor). (D VI, 1, 59) Nevertheless, the 1690s saw Leibniz begin to publish some of his most important philosophical works. In 1694, he published his De primae philosophiae emendatione, et de notione substantiae (On the Correction of Metaphysics and of the Concept of Substance) in the principal academic journal of Germany, the Acta Eruditorum. This short piece is notable because it ties the notion of substance closely to Leibniz’s notion of force, making dynamics itself central to metaphysics. The following year Leibniz went further down this path with the publication, again in

HANOVER UNDER GEORG LUDWIG, 1698–1716 Leibniz’s employer of almost twenty years, Ernst August, died in 1698, and his son Georg Ludwig assumed rule of the Electorate of Hanover. While Leibniz’s relations with the father had been strained at times, those with the son were worse. On the other hand, Leibniz had developed a close and affectionate relationship with Georg Ludwig’s sister, Sophie Charlotte, who became the Electress of Brandenburg in 1688 and, upon the elevation 10

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LIFE AND WORKS mother in Hanover. She was only 36. Writing to Lady Masham months after the death, Leibniz, who had been in Berlin at the time, says,

of Brandenburg-Prussia to a kingdom, Queen of Prussia in 1701. In fact, Leibniz spent a great deal of time in the late 1690s and the early part of the new century travelling between Hanover and Berlin, between mother, Sophie, and daughter, Sophie Charlotte. In Berlin, Leibniz conversed regularly with Sophie Charlotte on many philosophical matters, but he also attended to his pet project, the establishment of an academy of sciences on the model of the Royal Society of England and the French Académie des Sciences. The year 1700 saw Leibniz not only named a foreign member of the Académie but also given permission from Sophie Charlotte’s husband, Friedrich, to create his Academy of Sciences. Thus, in between writing the history of the House of Hanover and working on his own projects in philosophy, science and mathematics, Leibniz devoted himself to assembling scholars and scientists and arranging for the support of their work. But Leibniz’s own work was not without significance. He began a detailed study of John Locke’s Essay concerning Human Understanding, the Nouveaux Essays (New Essays), which he shelved after Locke’s death and which was not published until 1765. (The clear debate between rationalist and empiricist positions had a deep effect on Kant, whose picture of Leibnizianism was a caricature.) In answer to probing questions from Sophie Charlotte, he penned in 1702 the short essay Sur ce qui passe les sens et la matière (On What is Independent of Sense and Matter). He also became engaged in important philosophical correspondences with, among others, the Dutch Cartesian philosopher, Burcher de Volder, and the Jesuit philosopher and theologian, Bartholomew des Bosses. Leibniz experienced a great loss, however, in 1705, when Sophie Charlotte died unexpectedly of pneumonia, while visiting her

The death of the Queen of Prussia has caused a long interruption in my correspondence and my thoughts (meditations). This great princess had an infinite kindness for me. She liked to be informed of my speculations; she even deepened them . . . There may have never been a queen so accomplished and so philosophical at the same time. You may judge, Madam, what pleasure I would have had to be around such a princess and to be encouraged by the ardor that she had for the knowledge of the truth. When she left for Hanover, I was to follow her shortly thereafter, for she did me the honor of asking for me often. But what was my surprise, and that of all of Berlin, when we learned of her death! For me in particular it was like being struck by lightning . . . I thought I would fall ill, since sentiment does not depend upon reason. I have been so distraught by this death, but I am coming back to myself and my friends. (GP III, 366–7) Leibniz came back to himself and his friends by, among other things, turning to an issue that had been the subject of much discussion between him and Sophie Charlotte: the problem of evil. According to Leibniz, while on his visits to Berlin, the two spoke often of the works of Pierre Bayle, and it was Sophie Charlotte who urged him to write down his reflections: My book, entitled Essais de Théodicée sur la Bonté de Dieu, la liberté de l’homme, et l’origine du mal (Essays on Theodicy: On the Goodness of God, the Freedom of Man, and the Origin of Evil) will be 11

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LIFE AND WORKS what I put in the journals of Leipzig, Paris and Holland. In the journal of Leipzig, I adapted myself to the language of the School; in the others I adapted myself rather to the style of the Cartesians; and in this latest piece I try to express myself in a manner that can be understood by those who are not yet too well accustomed to the style of either. (GP III, 624)

published shortly in Amsterdam by Jacques Troyel. The greater part of this work had been down on scraps of paper, when I found myself with the late Queen of Prussia, where these matters were often discussed on the occasion of the Dictionnaire and other works of Bayle, which one was often reading there. I was in the habit of responding to the objections of Bayle in our discussions and of showing the queen that they were not as strong as some people, less favourable to religion, would like to make believe. Her Majesty ordered me fairly often to put my responses into writing so that one could consider them with more attention. After the death of this great princess, I reassembled these pieces and expanded upon them at the urging of friends who knew of them, and I made of them the work of which I have just spoken. (GP VI, 9–10)

For students of Leibniz, this passage raises a very important set of questions. What is the relation between the Principles of Nature and Grace and Monadology, on the one hand, and his more scholarly presentations of his system in learned journals? How do all of these publications compare with what Leibniz was writing for a select few philosophers in private correspondence? Suffice it to say, one should be careful in basing one’s interpretation of Leibniz’s metaphysics solely on these popular pieces, especially when one compares these works with, for example, his correspondence with Des Bosses, in which Leibniz can be seen to be wrestling with deep problems in his metaphysics. Nevertheless, these popular essays proved to be important historically, for they determined how Leibniz was understood for several generations after his death. Sadly, Leibniz’s final years were largely frustrating, physically and intellectually. As one might expect, his health was declining; his attacks of gout and arthritis becoming more regular. In 1714, in quick succession, the dowager Electress Sophie died, followed by Queen Anne of England, and thus the throne of England was passed to Elector Georg Ludwig, who became King George I of England. Leibniz had hoped to follow the court to London, but that was not to be. His application to be the royal historian in England was rejected, and he was instructed

Leibniz’s Theodicy was published in 1710 and quickly established itself as an important work in the European intellectual landscape. Unfortunately, it would also be the only book-length publication of Leibniz’s life. In the second decade of the eighteenth century, Leibniz worked to distill his complex metaphysical thoughts into brief essays suitable for popular consumption. The results were his two well-known essays, Principes de la Nature et de la Grace (Principles of Nature and Grace), and the untitled piece, now known as his Monadology, both composed in 1714. The former study Leibniz sent to Rémond in France, with the hope of making his philosophy better known to a wider reading public, writing the following: I hoped that this little paper would contribute to making my meditations better understood, by combining it with 12

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LIFE AND WORKS to stay in Hanover and finish his historical work (Gädeke, 1994, p. 73). And, even worse from Leibniz’s point of view, he became engaged in an acrimonious dispute with Isaac Newton over the priority of the discovery of the calculus. As already mentioned, Leibniz had published his discoveries in 1684, three years prior to the publication of Newton’s Principia. Newton claimed, however, that he had sent a letter to Leibniz in the 1670s, in which he said that he had discovered a new method of finding tangents to curves and gave a hint at the solution. Newton charged him with intellectual dishonesty, and Leibniz was deeply stung. (As it turns out, most historians of mathematics are charitable in their interpretations, claiming that Newton and Leibniz discovered the calculus independently, with Newton first in the actual discovery, Leibniz first in publication. In other words, for all intents and purposes, it was a tie.) The dispute with Newton took a positive turn of sorts, however, for Leibniz became engaged in a proxy war with Newton’s friend and collaborator, Samuel Clarke. The result, the Leibniz–Clarke correspondence, contains some of Leibniz’s deepest reflections on the nature of space and time as well as important insights into his views on natural religion. Leibniz died in his bed on 14 November 1716 in Hanover. The next day his remains were transferred to the Neustädter Church, where they were interred. (A sandstone plaque with the words ‘Ossa Leibnitii’ [‘The Bones of Leibniz’] was erected in the church and can still be seen there.) Leibniz’s official funeral several weeks later was poorly attended by the remaining members of court, and this is certainly because he seemed to have been appreciated in Hanover only by Sophie and Sophie Charlotte, who preceded him in death.

THE PERSON Leibniz often expressed his feeling of physical and intellectual isolation while in Hanover and often seemed vexed by the demands of his official duties. To counteract the feeling of isolation and, more important, to learn of the latest developments in philosophy and science, Leibniz created an enormous network of correspondents. In fact, over the course of his life, he exchanged letters with over 1,100 different people; his Nachlass contains over 15,000 letters. Moreover, despite the myriad demands placed on Leibniz as librarian, then historian, and counsellor at the court of Hanover, he was able to complete work that is in its breadth, depth and sheer quantity staggering. Leibniz has suffered from a rather poor description of his character. According to Russell, he ‘was one of the supreme intellects of all time, but as a human being he was not admirable’ (Russell, 1945, p. 581). He spent too much of his intellectual energies trying to please princes and patrons; he was too enamoured of power and wealth. And in a recent popular book, The Courtier and the Heretic (Stewart, 2007), Leibniz is clearly condemned for not living the pure life of the philosopher – that is, for not being more like Spinoza. As always, such judgements say as much, if not more, about the person doing the judging. Certainly, Spinoza lived a life worthy of a true philosopher: as Nietzsche suggested, he took the ascetic ideals of poverty, humility and chastity and turned them to his own purposes. Leibniz, on the other hand, while chaste, certainly did not care to live a life of poverty and humility. Nor did he choose the life of a professor – something that he could easily have done. Instead, he chose a life dedicated to his credo: Theoria cum praxi (theory with practice). He chose a life of political 13

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LIFE AND WORKS If Leibniz does not live up to the expectations of Bertrand Russell, so be it. But if we choose to trust Eckhart’s description and contemplate Leibniz’s life of engagement, there is every reason to believe that Leibniz was indeed an admirable person.

engagement at the highest level available to him, and he sought constantly to make real changes in the lives of people around him. This took many forms, as has been shown. There were Leibniz’s practical projects in engineering (draining the mines in the Harz Mountains) and in commerce and trade (he planned to import and to cultivate silkworms and mulberry trees in order to establish a domestic European silk trade). There were his legal and political projects: drawing up plans to divert France’s political and military power away from central Europe and towards the Near East; providing the historical and legal arguments for the elevation of the Duchy of Hanover to an Electorate; to making the case for the accession of the House of Hanover to the English throne upon the death of Queen Anne. And even Russell’s judgement of the person seems rather harsh when one considers what those who knew him well said of him. For example, his former secretary Johann Georg Eckhart (who is perhaps not completely trustworthy) wrote the following:

UNDERSTANDING LEIBNIZ As T.S. Eliot correctly observed, ‘Leibniz’s originality is in direct, not inverse ratio to his erudition’ (Eliot, 1916, p. 568). Indeed, Leibniz should be understood in terms of his relations to other philosophers, for much of his work is a reaction to important issues that were debated in his life. Thus, there are essays in this volume that seek to establish the philosophies of and Leibniz’s reactions to his most important contemporary philosophers: Pauline Phemister writes of Descartes’s philosophy and its role in the development of Leibniz’s ideas; Philip Beeley examines Leibniz’s relation to Hobbes; Ursula Goldenbaum explores Leibniz’s fascination with Spinoza; and Sean Greenberg shows the core of Malebranche’s philosophy and Leibniz’s critical reaction to it. Moreover, although interest in Leibniz is now principally philosophical, this biographical introduction has tried to suggest that Leibniz’s work was incredibly sweeping in its scope. Upon Leibniz’s death, the secretary of the Académie des Sciences in Paris, Bernard le Bouvier de Fontenelle, wrote a long eulogy for Leibniz. In it, Fontenelle famously likened Leibniz to a charioteer who could simultaneously control up to eight horses – in this case, the sciences, history, mathematics, metaphysics, theology, logic and so on. In this volume, therefore, the

[Leibniz] liked women and lost track of time when he was able to converse with them. Indeed, he knew how to act in conversation so that one would not have taken him for a philosopher at all. He was often at court, often dined there, and was certainly an ornament of the royal table. Her Royal Highness used to call him her walking encyclopedia because nothing came up which he did not discuss in depth. He spoke with soldiers, courtiers and statesmen, artists and the like as if he were one of their profession; so everyone liked him, except those people who did not understand such behaviour. He spoke well of everyone, saw the bright side of everything, and even indulged his enemies . . . (Eckhart 1982, pp. 198–9)

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LIFE AND WORKS modality (Nachtomy), logic (Levey), causation (Look), his theory of free will (Davidson), and moral theory (Brown). How Leibniz was subsequently understood, how his philosophy became the ‘Leibnizian’ philosophy of eighteenth-century Germany, how this impacted his great successor, Immanuel Kant, are the subjects of Anja Jauernig’s concluding essay.

reader will find essays that address a number of Leibniz’s concerns outside philosophy narrowly conceived: Douglas Jesseph writes about Leibniz’s mathematics; François Duchesneau about his physics; and Justin Smith about his concern with the life sciences. More straightforwardly philosophical topics are addressed in essays on Leibniz’s metaphysics (Look), philosophical theology (Lin), his theory of cognition (Bolton), his account of

Brandon C. Look

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2 DESCARTES AND LEIBNIZ

overestimated, ranging across eighteenthcentury French materialism, nineteenthcentury German phenomenology and twentieth-century Anglo-American analytic reductionism. Focusing on his own experience and armed with his ‘method of doubt’, Descartes found in his mind’s act of thinking the single indubitable Archimedean point he sought: clear and distinct knowledge of his own existence. Seeing here a link between knowledge and the clarity and distinctness of our ideas, Descartes went on to restore, for instance, his knowledge of God’s existence and to argue that mind and body are really distinct substances capable of existing independently of each other. All the same, he tempered his mind-body dualism by insisting that mind and body are substantially united and towards the end of his life, he strove to explicate this union in The Passions of the Soul. The Passions of the Soul, composed for Princess Elizabeth of Bohemia and published in 1649, was the last of his works to be published in Descartes’s lifetime. His authorship was then made known, but in his earliest foray into print, he had been more circumspect, publishing his Discourse on the Method anonymously in 1637. Attached to the Discourse were essays showing the application of the method in optics, meteorology and

Eclectic appropriations and reworkings of ancient, mediaeval and renaissance thought abound in the writings of Leibniz and are rarely accompanied by outright criticism of views he did not positively endorse. Generally, he acknowledged his agreement respectfully and chose simply to disregard, rather than openly refute, points of contention. The same cannot be said of his relations to his near and actual contemporaries. With them, although he sometimes noted his agreement, his more common policy was to highlight contrasts with his own views and offer detailed reasons for his opposition. Openly critical of figures such as Benedict de Spinoza (1632–77), Nicolas Malebranche (1638– 1715) and John Locke (1632–1704), for the most part, Leibniz’s critical quill is directed against the ‘father of modern philosophy’, René Descartes. Descartes (1596–1650) was educated at the Jesuit collège, La Flèche, where he was schooled in classics and Aristotelianism (Gaukroger, 1995, pp. 48–61) and went on to develop one of the most original and farreaching systems of philosophy, as well as making noteworthy contributions to the study of optics, mathematics and natural philosophy. Best known today as an epistemologist and metaphysical dualist, his influence in the history of philosophy cannot be 16

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DESCARTES AND LEIBNIZ Cartesians, Géraud de Cordemoy (1622–84), had published his The Distinction of the body and the soul in six discourses, in order to be useful for the clarification of physics (Le Discernement du corps et de l’âme en six discours pour servir à l’éclaircissement de la physique) in 1666. Here, defending Cartesian dualism of mind and body, Cordemoy advanced occasionalism over interactionism to explain their relation. Other prominent Cartesians, such as Arnold Geulincx (1624–69), Louis de la Forge (1632–66) and Nicolas Malebranche followed Cordemoy in advocating both mind-body dualism and occasionalism. The latter’s Treatise of Nature and Grace, published in 1680, set the scene for what would become an acrimonious public controversy, ostensibly on the nature of ideas but fundamentally on opposing views concerning the grace of God. The controversy was with Antoine Arnauld (1612–94), co-author with Pierre Nicole of the PortRoyal Logic, or the Art of Thinking (1662) and author of the fourth set of objections to Descartes’s Meditations on First Philosophy, who was both one of Descartes’s staunchest promoters and astutest critics. It was within this climate that Leibniz sought to situate his own thought, clarifying points of agreement, as well as, and more importantly, his often subtle, and always substantial, areas of disagreement with Descartes. On the whole, he appreciated what Descartes had achieved, describing his philosophy as the ‘antechamber’ to the true philosophy (to Christian Philipp, early December 1679: GP IV, 282/L 272; to Nicolas Rémond, 10 January 1714: GP III, 607/L 655). In contrast, Descartes’s followers failed to gain Leibniz’s respect. He believed they had been led astray by too great faith ‘in the genius of others’, while Descartes had only been ‘led astray by too great faith in his own genius’

geometry. Prior to this, Descartes had decided against publication of a two-part treatise – ‘The World’ and ‘Treatise on Man’ – fearing condemnation similar to that meted out to Galileo in 1633. In 1641, however, the Meditations on First Philosophy were published under Descartes’s name, together with six sets of objections from contemporaries and Descartes’s replies, a seventh set of objections and replies being added to the second edition in 1642. These were followed in 1644 with the publication of the four-part Principles of Philosophy in which Descartes outlined his metaphysics and physics before setting out his views on the natures of the universe and of the earth. The work incorporated some material from the previously abandoned ‘The World’ and would presumably have included material also from the ‘Treatise on Man’ had Descartes fulfilled his initial plan for the work to contain a further two parts, on animal and plant life and on man respectively. Leibniz’s initial introduction to Descartes’s thought was second-hand. In a letter to Simon Foucher in 1675 he admitted that what he knew at that time ‘of the metaphysical and physical meditations of Descartes has come almost entirely from the reading of a number of books written in a more popular style which report his opinions’ (A II, i, 247/L 153). But while in Paris during the winter of 1675–6 and into the following spring, Leibniz made notes on Descartes’s Principles of Philosophy and was also granted access to many of Descartes’s unpublished manuscripts by Descartes’s literary executor, Claude Clerselier (Antognazza, 2009, p. 167). By the end of 1679, Leibniz reported to Christian Philipp that he had considered Descartes’s philosophy ‘with attention’ (GP IV, 281). By this time, Cartesianism had established itself as a major intellectual force in early modern northern Europe. One of the leading 17

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DESCARTES AND LEIBNIZ and theology. Particular points of contention included attitudes towards scepticism, the nature of ideas, the value and place of final causes in ethics and science, the essences of substance, mind and body, animal souls, and mind-body relations. Here, we begin by addressing methodological and epistemological issues, especially those concerning the nature and role of clear and distinct ideas. We then attend to metaphysical and natural philosophical questions on the nature, existence and relations of mind or soul and body.

(A Brief Demonstration of a Notable Error of Descartes: GM VI, 119/L 298). It was excessive pride in his own abilities, rather than unreflective adherence to others’ thought, that had prevented Descartes proceeding beyond the antechamber to truth. As well as accusing Descartes of being more concerned with his own reputation and legacy than with truth, Leibniz charged him with not following his thought through to its logical conclusions. Thus we find that even when Leibniz himself employed Descartes’s arguments – as for instance, his cogito and dream arguments – he extended Descartes’s reasoning and drew different conclusions (to Simon Foucher, 1675: GP I, 372–3/L 153–4; Critical Thoughts, I.7: GP IV, 357/L 385). Even when their views converged, Leibniz adopted various strategies to distance himself from the Cartesians. Sometimes he offered alternative reasons to make good the deficiencies he found in Descartes’s demonstrations, for instance against the vacuum and material atomism or in favour of unlimited extension, the homogeneity of matter, and the differentiation of bodies by shape and motion. At other times, he declared the Cartesian position in need of revision or extension, as was the case with Descartes’s doctrine of clear and distinct ideas, the promotion of mechanistic explanation of phenomena and mind-body dualism. And occasionally, as in the case of Descartes’s first and second laws of motion and his claim that bodies contain within them a plurality of motions, he acknowledged their truth, but refused to credit Descartes with their discovery, claiming they had been discovered earlier by others who had sometimes developed them further than had Descartes. Leibniz’s critical concerns extended to Descartes’s methodology, physics, geometry, logic and epistemology, metaphysics, ethics

EPISTEMOLOGY AND METHODOLOGY In the second part of his Discourse on the Method, Descartes outlined four rules that constitute his method, the first of which is to accept as true whatever he perceives so clearly and distinctly that he finds it absolutely beyond doubt (AT VI, 18/CSM I, 120). We shall present Leibniz’s reaction to Descartes’s first rule below, but first, it is worth noting Descartes’s strategy when clear and distinct ideas are absent. In these cases, Descartes adopted a rather unusual stance: he decided to count as actually false not only what he could prove to be false, but also anything upon which he could cast even the slightest degree of doubt. Hoping to break his habit of accepting as absolutely true preconceived, but only highly probable, opinions, he proposed the following: to turn my will in completely the opposite direction and deceive myself, by pretending for a time that these former opinions are utterly false and imaginary. I shall do this until the weight of preconceived opinion is counter-balanced and the distorting influence of habit no longer 18

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DESCARTES AND LEIBNIZ prevents my judgement from perceiving things correctly. (Meditation One: AT VII, 22/CSM II, 15)

ideas. In the first two Meditations, Descartes went in search of a truth that satisfied his first methodological rule and which he could accept as true because he perceived it so clearly and distinctly that he could not doubt it. Extending sceptical doubt to its hyperbolic limit, he finally reached the absolutely indubitable truth, namely, ‘that this proposition, I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind’ (AT VII, 25/CSM II, 17). He then went on in Meditation Three to appeal to the existence of a non-deceitful God in order to guarantee that the relation between clarity-distinctness and truth that was so evident in the singular case of his own existence as a thinking thing is not an isolated case, but is instead a particular instance of the ‘general rule’ that all that he perceives ‘very clearly and distinctly is true’ (AT VII, 35/CSM II, 24). Somewhat overstating his case, Leibniz declared Descartes’s first rule to be ‘deceptive in infinite ways’ (A new method for learning and teaching jurisprudence, 1667: A VI, i, 280/L 88). He justified this judgement in later revision notes (1697–1700), observing that Descartes’s first rule ‘proves, not existence, but only possibility’ (A VI, i, 280n/L 91n9). What can be clearly and distinctly conceived is indeed possible for it contains no contradiction, but not everything that is possible is also actual. Moreover, because he had not provided precise criteria for what it means for something to be perceived clearly and distinctly, Descartes had rendered his first rule useless (ibid.). The criticism is repeated in 1692 in Leibniz’s Critical Thoughts on the General Part of the Principles of Descartes (I.43, 45, 46: GP IV, 363/L 389), his most detailed critique of the first two parts of Descartes’s Principles of Philosophy, which he seems to have intended not for general distribution, but simply for

The strategy, Leibniz believed, backfired and led Descartes away from, rather than towards, truth. Before Descartes’s desired rebalancing could be effected, the method had led him to regard minds as immaterial, non-extended thinking substances and bodies, in contrast, as non-thinking, extended substances, with the further consequence that each might then be considered as separable and really distinct from the other (Meditation Six: AT VII, 78/CSM II, 54). Descartes had established in Meditation Two that the existence of the soul, at least when it is thinking, is beyond doubt whereas the existence of the body (res extensa) is not beyond doubt. Then, by treating as actually false what is merely doubtful, he had persuaded himself that corporeal things do not exist. Since corporeal things do not exist, while the soul undoubtedly does exist, he concluded that the soul is definitely not a corporeal thing (Critical Thoughts, I.8: GP IV, 357–8/L 385). The conclusion would follow if it really were the case that bodies do not exist. However, the assumption that they do not exist has arisen only through Descartes’s error-inducing strategy of taking what is merely dubitable to be actually false and Descartes himself will prove, in Meditation Six, that bodies do exist. The mere uncertainty in Meditation Two that attaches to the existence of the body is not sufficient, according to Leibniz, to establish the non-corporeality of the soul (ibid.). Descartes’s argument shows only that the corporeality of the soul is itself questionable: it does not show that it is actually false. Leibniz was equally critical of Descartes’s positive attitude towards clear and distinct 19

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DESCARTES AND LEIBNIZ 374/L 154). On the other hand, even with an infallible demonstration of God’s necessary existence, we could still not be absolutely assured that everything that we take to be true is actually true. There are other possible sources of human error, such as human sin (Critical Thoughts, I.13: GP IV, 358/L 386) or the ‘lack of attention and memory’ that give rise to a ‘weakness of the human mind’ that ‘cannot be completely overcome’ (Critical Thoughts, I.5: GP IV, 356/L 384). Besides, even were God’s existence sufficient to guarantee the truth of those things that we perceive so clearly and distinctly that we find it psychologically impossible to doubt, sure and absolute infallible proof of God’s existence is not forthcoming and cannot be provided by appeal to our clear and distinct ideas. Leibniz’s statement of the classic problem of the Cartesian Circle (namely, that proof of God’s existence is needed in order to guarantee the truth of clear and distinct ideas, including that of the clear and distinct ideas that are needed in the proof of God’s existence) is concise and to the point: if hyperbolic doubt about the truth of our most clearly and distinctly perceived ideas ‘could once be justly raised, it would straightaway be insuperable; it would always confront Descartes himself and anyone else, however evident the assertions they presented by them’ (Critical Thoughts, I.13: GP IV, 358/L 385). Descartes’s hyperbolic doubt is allpervasive and stops the Cartesian project in its tracks. Given his disapproval of Cartesian hyperbolic doubt, Leibniz was content nevertheless to accept the link between the clarity and distinctness of ideas and their truth. It is not for this reason, therefore, that Leibniz thought that Descartes’s proofs of God’s existence are inconclusive. Rather, it is the absence of any clear and distinct idea of God that explains

distribution among Cartesians in the hope of eliciting responses from those of Descartes’s followers who had not come under the spell of their master to such an extent that they had lost their capacity for independent and critical reasoning (to Christiaan Huygens, 16/26 September 1692: GM II,146/L 416). Leibniz had already attempted to remedy the deficiencies in Descartes’s account of clear and distinct ideas eight years earlier in a paper to which he often referred in later years, his Meditations on Knowledge, Truth, and Ideas, published in the Acta Eruditorum in 1684. His account there does not in essence conflict with Descartes’s, but it is more nuanced and builds upon Descartes’s account by helpfully differentiating ideas that are merely clear and distinct (in which elements sufficient to distinguish the idea from others are identified) from ideas that are clear, distinct and adequate (in which all the elements are themselves also distinctly perceived). Leibniz also objected to Descartes’s appeal to the necessary existence of a benevolent and non-deceiving God as the supreme guarantor of the truth of our clear and distinct ideas. In his First Meditation, Descartes had raised doubt to hyperbolic levels by proposing that ‘some malicious demon of the utmost power and cunning has employed all his energies in order to deceive me’ (AT VII, 22/CSM II, 15). Although Descartes’s knowledge of his own existence survives the malicious demon hypothesis, ‘metaphysical’ doubt with respect to the rest of human knowledge can be removed only by proving the existence of a non-deceiving God (Meditation Three: AT VII, 36/CSM II, 25). Leibniz regarded a divine guarantee as both unnecessary and impossible to obtain. Even if God does not exist, some truth is still attainable (Critical Thoughts, I.13: GP IV, 358/L 386; see also letter to Simon Foucher, 1675: GP I, 20

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DESCARTES AND LEIBNIZ the cosmological proof of God in Meditation Three (AT VII, 45–7/CSM II, 31–3). There, appealing to the scholastic maxim that the cause of an idea must possess a degree of ‘formal’ reality (that is, actuality) equivalent to the idea’s ‘objective’ reality (effectively its representational content), Descartes had argued that his idea of God, as representative of an absolutely necessary being, possesses the highest degree of objective reality and can only have been brought about in him by the one truly necessary being, namely God. Leibniz, however, rightly observed that in arguing from the presence of the idea of God in his mind to the existence of the real God as the only possible source of his idea, Descartes had merely assumed that he does in fact have an idea of God (Critical Thoughts, I.20: GP IV, 360/L 387). Indeed, Descartes’s argument assumes even more than this: it requires that his idea of God is ‘utterly clear and distinct, and contains in itself more objective reality than any other idea’ (AT VII, 46/CSM II, 31). In short, his argument rests on the premise that God has provided us with such a clear and distinct idea of himself as an infinite and perfect being that there can be no doubt whatsoever that we could neither have produced this idea by ourselves by combining aspects derived from our own experience, nor have been given it by some other being, greater than ourselves, but nonetheless to some extent imperfect. Leibniz too, in the first draft of the Critical Thoughts, admitted to having an innate idea of God (GP IV, 360n/L 410–11n9), but his idea differs from Descartes’s in important respects. Although both men accepted God as the transcendent creator of the world, Leibniz regarded Descartes’s notion of God as erroneous and, more importantly, as dangerously atheistic. The problem lay with the implicit determinism Leibniz discerned in

Descartes’s failure. In his ontological argument in Meditation Five, Descartes argued that the existence of God follows necessarily from the essence of God as the most perfect being: the perfect being would not be perfect if it did not exist (AT VII, 65–9/CSM II, 45–7). Leibniz held that the ontological argument can succeed in deducing the necessity of God’s existence from God’s essence only if a prior proof of God’s possibility is given, that is, if it is first shown that it is in fact possible for a most perfect being to exist (Critical Thoughts, I.14: GP IV, 359/L 386; see also That a most perfect being exists: GP VII, 262/L 168; to Arnold Eckhard, summer 1677: GP I, 269/L 180). Since Descartes provided no such proof, his ontological argument is incomplete and leaves open the possibility that the idea of a perfect being is, like the idea of the greatest motion, superficially intelligible, but on closer examination, evidently self-contradictory (Critical Thoughts, I.18: GP IV, 360/L 387). The conjunction of the individually intelligible ideas – ‘being’, ‘perfection’ and ‘greatest’ – might be an impossible combination and the description ‘being with the greatest perfection’ refer to something impossible and internally incoherent (Meditations on Knowledge, Truth and Ideas: GP IV, 424/L 292). To attain absolute certainty, Descartes would have needed an idea of God that was so clear and distinct that from it, the non-contradictoriness of the combination of the ideas of being, perfection and greatest could be demonstrated. It is evident, however, that Descartes’s idea of God’s essence is not sufficiently clear and distinct for him to be able to establish its non-contradictoriness. Consequently, his ontological proof falls short of the degree of certainty he awards it. An insufficiently clear and distinct idea of God also blights Descartes’s first version of 21

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DESCARTES AND LEIBNIZ goodness, truth and justice are such . . . only because God has established them by a free act of his will . . . For if things are good or evil only as the result of God’s will, the good cannot be a motive of his will, being posterior to his will. His will, then, would be a certain absolute decree, without any reason . . . (GP IV, 284/L 273/)

Descartes’s thought. Descartes had argued in the demonstration of article 47 in Part III of his Principles of Philosophy that everything happens in accordance with unchanging laws of nature and that ‘by the operation of these laws matter must successively assume all the forms of which it is capable’ (AT VIII, 101/ CSM I, 257). However, Leibniz took exception to this view on the ground that ‘if matter takes on, successively, all possible forms, it follows that nothing can be imagined so absurd, so bizarre, so contrary to what we call justice, that it would not have happened and will not some day happen’ (to Christian Philipp, January 1680: GP IV, 283/L 273). He was quick to associate Descartes’s determinism with similar doctrines in Spinoza – for whom, too, all that does happen, happens necessarily and all that does not happen, is impossible – and in Hobbes whom he reports as holding that ‘everything that is possible is either past or present or future’ (ibid.). Leibniz was appalled by these strict determinist doctrines, for if matter itself assumes all possible forms, then over time, everything becomes necessary and nothing is subject to God’s free choice. In Leibniz’s opinion, ‘there will be no place for trust in providence if God produces everything and makes no choice among possible beings’ (ibid.). ‘The true philosophy,’ wrote Leibniz in the same letter to Christian Philipp, obviously anticipating the philosophy he hoped to develop, ‘must give us an entirely different concept of God’s perfection, one that will be of use in both physics and ethics’ (GP IV, 284/L 273). Descartes had advanced a voluntaristic account according to which God is the final arbitrator, determining even the eternal, necessary truths of mathematics and morals (for discussion, see Gaukroger, 1995, pp. 205–9). Leibniz objected that it is very strange indeed to propose as Descartes had done that,

For the voluntarist, God’s will itself is arbitrary for there are no rules, logical or ethical, to guide his thought and action. No reason can be given for moral claims other than the fact that God decreed them. Applying this to the act of creation, we find that Descartes’s God could not have been guided by any inherent goodness to create the world as he did, for goodness, under voluntarism, is simply whatever God has decreed is so. Obviously Descartes’s God creates a good world, but God does not create it because it is good, or even because it is the best; rather, it is good simply because God has created it. Any world that God created would therefore count as a good world, even if it contained only greed and injustice rather than charity and justice. Leibniz, on the other hand, insisted that the true philosophy must deny that God acts in such an arbitrary fashion if it is to do justice to God’s perfection. Leibniz’s God compared the overall goodness of each possible world with the goal of creating the best, basing his decision on criteria of perfection and goodness that he understands, but which are not dependent on his will. Thus, God permits his free choice to be influenced by final causes. According to Leibniz, a god who was not guided by final causes would have neither will nor understanding: For what kind of a will (good God!) is that which has not the Good as object or motive? What is more this God will not 22

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DESCARTES AND LEIBNIZ qualities – magnitude, figure, and motion’ (Confession of Nature against Atheists, 1669: GP IV, 106/L 110; see also Critical Thoughts, II.64: GP IV, 390–1/L 409), when it comes to the general question why bodies operate by the laws of nature that obtain in this world rather than by some other laws of nature, the mechanical philosophy is impotent. The laws themselves are explicable only by reference to the intelligent will of God: they issue from God’s wise and informed choice of the best possible world, based on final considerations of perfection, beauty, order and goodness that are not dependent on God’s will and that are accessible to both divine and human understanding.

even have understanding. For if truth itself depends only on the will of God and not on the nature of things, and the understanding being necessarily BEFORE the will . . . , the understanding of God will be before the truth of things and consequently will not have truth for its object. (To Christian Philipp, January 1680: GP IV, 285/Duncan, 1890, p. 4) For Leibniz, final causes are essential both in physics and ethics. Ethics requires not only that God acts in accordance with final causes, but also that individual creatures act in pursuit of ends or goals that they perceive as the best. True freedom resides in acting rationally and in choosing that which one knows to be the best option. That is to say, we act most freely when our ends coincide with God’s. It is not enough merely to be able not to do something (‘to affirm or deny, to pursue or avoid’) or to suspend judgement when there is insufficient evidence, as Descartes had proposed (Meditation Four: AT VII, 57/CSM II, 40; AT VII, 59–60/CSM II, 41). And final causes are needed in physics in order to explain the laws of nature. Descartes had proposed that ‘we shall entirely banish from our philosophy the search for final causes’ (Principles of Philosophy, I.28: AT IXB, 15/CSM I, 202). After all, in his view, the laws of nature rest on God’s arbitrary, voluntaristic will, and it is therefore vain for us to search for an intelligible explanation of them. But for Leibniz, intelligible explanation is possible so long as final causes are not entirely rejected. Although he appreciated the value of excluding final causes and God from explanations of the operations of particular natural phenomena – and indeed advised that ‘so far as can be done, everything should be derived from the nature of body and its primary

METAPHYSICS AND PHYSICS (I) MIND AND SOUL Descartes had argued for a real distinction between mind and body, whereby each is a complete substance, capable of existing independently of the other (Meditation Six: AT VII, 78/CSM II, 54). His argument made use of conclusions drawn from the cogito and wax arguments in Meditation Two. There, Descartes had concluded that he is a ‘thinking thing’, res cogitans. ‘Thought’ constitutes the essence of his mind, for, he explained, this alone is inseparable from me . . . For it could be that were I totally to cease from thinking, I should totally cease to exist. At present, I am not admitting anything except what is necessarily true. I am, then, in the strict sense, only a thing that thinks; that is, I am a mind, or intelligence, or intellect, or reason . . . a thinking thing. (AT VII, 27/CSM II, 18) 23

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DESCARTES AND LEIBNIZ could not doubt unless one existed. However, he also thought that Descartes should have gone further. He ought not to have been content to rest with a proof of the existence of his mind as a thinking thing. He should have enquired further into the nature of the thoughts that this thinking thing thinks. Had he done so, he would have been far less inclined, as we shall see below, to doubt the existence of the body and consequently, less inclined to maintain the real distinction and possible separation of mind and body. As essences and as conditions for the possibility of other attributes, those of thought and extension hold a privileged position, being the ‘principal’ attributes of mind and body respectively (Principles of Philosophy, I.53: AT VIIIA, 25/CSM I, 210–11). Once again, Leibniz took issue with Descartes’s position (Critical Thoughts, I.63: GP IV, 365/L 390). With respect to thought, the attribute is too general and abstract to constitute the essence of any particular mind. Each substance must have an essence that is peculiar to itself that constitutes its individual unique identity. The true essences of substances are infinitely complex and cannot be explained in words or at least certainly not in few words (Critical Thoughts, I.52: GP IV, 364/L 390). Moreover, as an activity of the mind, thinking is only one among many other mental activities. The true essences of substances are forces (On the Correction of Metaphysics and the Concept of Substance: GP IV, 469/L 433), responsible for the actualization, by means of appetitions, of the sequence of perceptions, including particular thoughts, that comprises an individual mind or soul. Self-consciousness is the key feature of the Cartesian res cogitans. It is in being conscious of the ‘I’ that the mind or soul knows that it exists. Two consequences are often thought to follow from this. First, Descartes has been

The essence of body, on the other hand, resides in its being extended. Body is an extended thing, a res extensa, for no matter how many changes a piece of wax or any other body may undergo, so long as it remains a body, it is extended (AT VII, 31/ CSM II, 20–1). Descartes then reasoned in Meditation Six for the real distinction of mind and body: given that God can bring about whatever can be clearly and distinctly understood, and given that mind can be clearly and distinctly understood without reference to body and body can be distinctly understood without reference to mind, it follows that God can create mind and body as separate, independent substances (Wilson, 1976). Leibniz believed that Descartes’s separation of soul and body had been reinforced by Descartes’s mistaken conception of death as the separation of the soul from the body: With the common people, they [Cartesians] have confused a long stupor with death, properly speaking, which made them fall again into the Scholastic prejudice of completely separated souls, and they have even confirmed unsound minds in the belief in the mortality of souls. (Mon. §14: GP VI, 609/AG 214) On his side, however, Leibniz viewed death only as a state whereby the soul enters into an extended period of obscure perception. In death, the soul is not thereby separated from its body. Indeed, soul and body are naturally inseparable, even in death. Thus they are not at all distinct substances in the Cartesian sense. All the same, Leibniz agreed wholeheartedly with Descartes that the very act of thinking itself proves indubitably the existence of the mind that is thinking: even in doubting one’s own existence, it is evident that one 24

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DESCARTES AND LEIBNIZ the fact of animal sensation does entail that animals have souls. Furthermore, attributing basic feeling to all living creatures, even those that are infinitesimally small, Leibniz envisaged souls, in the form of entelechies or substantial forms, far beyond the animal kingdom and throughout the material world. All living things, even microscopic organisms, have soul-like entelechies or substantial forms and are as naturally inseparable from their organic bodies as are human souls, a view which led Leibniz to an account of the extended world radically opposed to that of Descartes.

credited with holding that the mind is always conscious of its thoughts (for discussion, see Clark, 2003, pp. 187–9). Second, in denying self-consciousness to animals, Descartes also denied them souls. Leibniz’s opposition to both points is clear. He held that minds and souls must have insensible perceptions of which they are not conscious, but which serve as components of their conscious and self-conscious perceptions. For instance, when we hear the sound of the sea, our conscious perception is composed of insensible perceptions of each individual wave (DM 33: GP IV, 459/AG 65). Furthermore, Leibniz accused Descartes and his followers of failing to acknowledge a distinction between perception (‘[t]he passing state which involves and represents a multitude in the unity or in the simple substance’) and ‘apperception or consciousness’ in which the perceiver is aware that he or she is perceiving something (Mon. §14: GP VI, 608/AG 214). He then attributed their denial of animal souls to their failure to make this distinction. They ‘took no account of the perceptions that we do not apperceive’ and this led them to ‘believe that minds alone are monads and that there are no animal souls or other entelechies’ (ibid.). According to Leibniz, the Cartesians denied animals feelings and consequently also denied animal souls (to Arnauld, 9 October 1687: GP II, 113/L 340). But the situation is more complex, for Descartes did admit that animals have feelings and sensations. However, unlike Leibniz, Descartes conceived such perceptions as arising purely from the activity of the material brain (Cottingham, 1998) and saw no need to grant them souls. Leibniz, on the other hand, considered perception as an activity of the soul that is not explicable in terms of the mechanical workings of the brain (Mon. 17). For him, therefore, and contrary to Descartes,

(II) BODY After doubting the existence of body in Meditation One and even persuading himself of its non-existence in Meditation Two, Descartes eventually proved in Meditation Six that external bodies do exist. His proof appealed to the notion of a non-deceiving God who arranges that nature should teach us, by means of our sensations of pain and pleasure, not only that bodies exist, but also that some are beneficial and others harmful, and that we have a special relation to our own bodies to which we are ‘not merely present’ but so ‘very closely joined’ that the mind and the body together ‘form a unit’ (AT VII, 80–81/ CSM II, 56). Leibniz thought that Descartes could have proven the existence of bodies through a simple expansion of his cogito argument in Meditation Two. That I think suffices to establish the existence of my mind, but my thoughts also have varied content: I think many things. Descartes stopped short with the fact of his thinking, but should have gone on to consider what he was thinking about. He would then have been led to conclude that there is, in addition to his own mind, an external world of bodies. 25

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DESCARTES AND LEIBNIZ adventitious and fictitious, as well as innate, ideas (Meditation Three: AT VII, 37–8/CSM II, 26). From this point on, Leibniz would conceive individual substances as so completely independent of each other that nothing in the life of one would be altered even were all the rest to be annihilated. All the soul’s perceptions arise spontaneously from its own nature and would do so even if bodies did not exist. Even so, Leibniz did not abandon his new version of Descartes’s cogito. In his 1692 Critical Thoughts, he again insisted that the soul’s thinking many things shows that ‘I am affected in various ways’ (I.7: GP IV, 357/L 385). Variety in the soul’s perceptions may still serve as evidence of the existence of bodies because it is the nature of the soul to represent in itself all the changes that occur in the physical world. Leibniz’s revision does not prove conclusively that bodies exist. It remains possible that God creates souls that he knows will have perceptions of bodies (or, as in occasionalism, creates souls and then gives them perceptions that seem to be of bodies, even though God has not actually created any bodies at all. Nonetheless, Leibniz believed he had made an advance on Descartes. The latter had sought, and failed, to provide absolute certainty of the existence of the physical world (Critical Thoughts, II.1: GP IV, 366–7/L 391–2). Leibniz, however, had only ever sought, and successfully provided, moral certainty of the existence of a world outside us, grounded in the ordered nature of the appearances of bodies (to Foucher, 1675: GP I, 373/L 154), their consistency with each other and with principles of reason. This is sufficient to allow prediction of future events from past, but it is ‘vain to ask for anything more from sensible experience’ (Critical Thoughts, I.4: GP IV, 356/L 384).

The conclusion does not follow automatically. After all, as Leibniz recognized, the variety in our thoughts only shows that there is some cause of the variety of my thoughts. Leibniz did think, however, that it is possible to demonstrate that the cause of this variety must lie in something external to the mind (to Foucher, 1675: GP I, 372/L 153). The undeniable fact of change in the soul’s perceptions from moment to moment, together with the premise that ‘everything remains in the state in which it is, unless there is something which changes it’, leads to the conclusion that changes in the soul’s perceptions must be produced by something other than the soul itself (ibid.). There must be an external cause for the successive variety in our thoughts. Of course, it is possible, as Descartes himself surmised, that God produces all the varied successive content of our thoughts. But Leibniz believed that, in addition to God, there must be ‘subordinate causes of this variety’ and, moreover, that the causes of these subordinate causes are ‘particular beings’ (ibid.). He concluded, ‘we have established particular beings or substances to whom we ascribe some action, that is, from whose change we think that some change follows in us’. ‘So,’ he went on, ‘we make great strides towards fabricating what we call matter and body’ (ibid.). Leibniz’s conclusion that changes to a substance are brought about by external causes is not entirely consistent with his later views on the nature of substances as spontaneous beings who bring forth their thoughts and perceptions from themselves, bringing to light what before was hidden in the soul’s depths. This extreme form of innatism arose from Leibniz’s enquiries during the early 1680s into the nature of truth and of individual substances and stands in sharp contrast to Descartes’s admission of 26

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DESCARTES AND LEIBNIZ 364/L 390), for it involves the primitive notions of plurality, continuity and co-existence (to De Volder, 24 March/ 3 April 1699: GP II, 169/L 516). Moreover, this abstract concept of extension must be distinguished from its concrete realization. In Descartes’s definition of body as res extensa, even extended space is body, but Leibniz claimed that space in itself is not body: for there to be bodies, there has to be something more – an extended thing by which ‘place is not merely constituted but filled’ (Critical Thoughts, I.52: GP IV, 365/L 390). Actual extended bodies satisfy Leibniz’s definition of extension insofar as they are continuous pluralities of co-existing (corporeal) substances (Phemister, 2005, ch. 3), but these, again in sharp contrast to Descartes, are not substances. Descartes had insisted only on the criterion that substances must be capable of existing independently of anything else other than God (Principles of Philosophy, I.51: AT IXB, 24/CSM I, 210). However, Leibniz demanded that substances be indivisible unities – a criterion that bodies, as mere aggregates of substances, do not satisfy. The substances that constitute actual bodies in Leibniz’s view are living, animal-like creatures. He conferred on them the status of corporeal substances whenever they possess a unity conferred upon them by their having a unifying dominant monad. Each monad – each unity of primitive active and passive force or of entelechy and primary matter – is dominant over an aggregate of substances that is its own organic body and with which it forms a corporeal substance (to De Volder, 20 June 1703: GP II, 252/L 530–1). The organic bodies of these corporeal substances are aggregates of smaller corporeal substances, whose organic bodies in turn are aggregates of even smaller corporeal

Although there is general agreement between Descartes and Leibniz regarding the existence of bodies, the non-existence of a vacuum, the rejection of atomism, and the importance of seeking purely mechanistic explanations of particular physical phenomena, there is little agreement on other matters. The main areas of contention concern extension and the status of body as substance. Descartes conceived the principal attribute of body as extendedness in length, breadth and depth (Principles of Philosophy, I.53: AT VIIIA, 25/CSM I, 210–11). Other attributes such as shape and motion presuppose extension (ibid.). Extension is known clearly and distinctly by the intellect and is one of the ‘simple’ or ‘primitive’ notions. As such, it is unanalysable. It ‘cannot be divided by the mind into others which are more distinctly known’ (Rules for the Direction of the Mind: AT X, 418/CSM I, 44) and ‘can be understood only through itself’ (to Princess Elizabeth, 21 May 1643: AT X, 666/CSMK 218). Extension, like the soul, is known purely intellectually, although imagination can prove a useful aid (to Princess Elizabeth, 28 June 1643: AT III, 691/CSMK 227). Descartes had reached the same conclusion in the Second Meditation. Examining a piece of wax, melting by the heat of the fire, images of the wax’s changing qualities – as it is transformed from solid and opaque to liquid and transparent – are formed in his imagination, but the persisting and unchanging nature of the wax – as an extended body – is “not perceived by the mind alone’ (AT VII, 31/CSM II, 21). The contrast between Leibniz’s understanding of extended matter and Descartes’s could hardly be more striking. Extension, for Leibniz, is not, as Descartes supposed, a primitive notion that admits of no further analysis (e.g. Critical Thoughts, I.52: GP IV, 27

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DESCARTES AND LEIBNIZ AT IXB, 61/CSM I, 240) and although the laws of motion apply consistently and universally, they arise not from reason, but from the arbitrary will of God. Leibniz, however, found fault with Descartes’s position on both counts: from the definition of body as res extensa we can deduce neither the motion of bodies nor the laws of nature (Critical Thoughts, I.52: GP IV, 364/L 390). For Leibniz, motion and resistance signal the presence of forces in bodies themselves. Accordingly, his dynamics posits derivative active and passive forces, grounded metaphysically in the monadic primitive forces, as the immediate physical sources of bodies’ motion, inertia and impenetrability. That all substances act spontaneously from their own force is a keystone for Leibniz’s hypothesis of pre-established harmony (discussed below) and spontaneity in rational beings is a central element of their freedom. Understanding bodies as aggregates of substances each acting spontaneously through the primitive force of its dominating monad and the derivative force of its organic body, defined as that ‘force by which bodies actually act and are acted upon by each other’ (Specimen Dynamicum: GM VI, 237/L 437), Leibniz rejected Descartes’s sharp distinction between motion and rest. Descartes had treated motion and rest as opposites, an error that in Leibniz’s opinion blighted Descartes’s formulation of the laws of nature (Letter of Mr L. on a General Principle Useful in Explaining the Laws of Nature through Consideration of the Divine Wisdom: GP III, 53/L 352). For Leibniz, on the other hand, no body is ever completely at rest. All are in motion to some degree. Rest is only a limiting case of motion, an ‘infinitely small velocity or an infinite slowness (GP III, 52–3/L 352). Motion and rest are not opposites. Rather, the opposite of motion is simply

substances, to infinity. ‘[E]ach living body has a dominant entelechy, which in the animal is the soul; but the limbs of this living body are full of other living beings, plants, animals, each of which also has its entelechy, or its dominant soul’ (Mon. 70: GP VI, 619/ AG 222). In this way, Leibniz conceives an infinity of primitive forces, of souls and entelechies with primary matter, scattered throughout the material realm, so that ‘there is a world of creatures, of living beings, of animals, of entelechies, of souls in the least part of matter’ (Mon. 66: GP VI, 618/AG 222). At least two points are worthy of note in this context. First, by determining the boundaries of creature’s organic bodies, just as points delimit lines, Leibniz’s primitive entelechies, in being present throughout matter, ensure that bodies are not only, as Descartes proposed, divisible to infinity, but actually divided to infinity into the substances from which they result. To repeat an earlier remark, Leibniz’s conception of matter does not take on all possible forms (not all possible divisions are actual) and so does not entail an absolute determinism. Second, in assigning primitive active forces, substantial forms or entelechies a role as the principle of motion in the bodies to which they are attached, Leibniz was able to locate the cause of motion in bodies themselves. Descartes’s res extensa has length, breadth and depth, but nothing in this geometrical understanding of body serves to explain bodies’ resistance or motion. Knowing that a body is essentially extended in length, breadth and depth provides no clue as to whether it is in motion or at rest. Nor does Descartes expect that it should. For him, the true cause of a body’s motion lies not in the body itself, but in God, ‘the primary cause of motion’ (Principles of Philosophy, II.36: 28

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DESCARTES AND LEIBNIZ Quantity of force and quantity of motion are not equivalent. The calculation of force requires consideration not only of the quantity of motion in a body, but also of the direction of motion (ibid.). Descartes’s failure to recognize this led him to the belief that motion is conserved when in fact it is the quantity of force that is conserved, while the quantity of motion is not (Critical Thoughts, II.36. See also Garber, 2009, pp. 144–55). As we shall see in the final section, Leibniz believed that Descartes’s error in this regard prevented him from discovering Leibniz’s trademark hypothesis of pre-established harmony.

motion in the opposite direction (CriticalThoughts, II.54, 55: GP IV, 385/L 404). Leibniz was no less critical with respect to the specifics of the laws of motion and collision rules set down by Descartes in Part Two of the Principles of Philosophy (II.37–52: AT VIIIA, 62–70/CSM I, 240–5). Even though Leibniz accepted Descartes’s first two laws of motion, he credited others with their discovery, notably Galileo and Gassendi in the case of the first law and Kepler with respect to the second (Critical Thoughts, II.37–9: GP IV, 372–3/L 395). He charged Descartes’s formulation of the third law with neglecting to take into account either the elasticity of bodies or the continuity of motion (Critical Thoughts, II.40–4: GP IV, 375/L 397), a criticism he applied generally to Descartes’s seven collision rules, holding that all bar the first rule are either in conflict with the principle of continuity, inconsistent with the first, or both (Critical Thoughts, II.46–53: GP IV, 376– 81/L 398–402). Besides, Descartes’s rules govern collisions between perfectly hard bodies in ideal conditions, free from the influence of any other bodies, and Leibniz rightly pointed out that they therefore tell us nothing about bodies as we experience them (Critical Thoughts, II.53: GP IV, 381/L 402). Arguably Leibniz’s most damning criticism of Descartes’s physics, however, is his charge that Descartes failed to distinguish quantity of motion and quantity of force (Letter of Mr. Leibniz on a General Principle: GP III, 53/L 352). Although in the operation of everyday machines such as pulleys and levers, force and motion appear to coincide in such a way that it may seem that the amount of force in a body might be calculated from its motion, in fact, so Leibniz argued, such coincidences are ‘merely accidental’ (Brief Demonstration of a Notable Error of Descartes: GM VI, 119/L 298).

MIND-BODY UNION Descartes and his followers were well aware of the tension at the heart of dualism in the conception of minds and bodies as distinct, separable, independent and radically different substances that nonetheless co-exist in a substantial interactive union. Princess Elizabeth was one who asked Descartes to clarify his position as she confided that she herself found it easier to conceive that the soul is extended and material than to understand how a thinking non-extended mind can interact causally with extended, unthinking body (Elizabeth to Descartes, 20 June 1643: AT III, 684–5). Descartes’s follower Nicolas Malebranche later proposed the doctrine of occasional causation as an alternative to direct interaction. This avoids postulating any transfer of force between minds and bodies by proposing instead that God moves bodies directly on the occasion of appropriate volitions in the soul and correspondingly provides souls with sensations to match motions in bodies. Even so, whether minds and bodies are directly affected by each other or are indirectly affected by each other 29

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DESCARTES AND LEIBNIZ Descartes should then have been able to see clearly that minds cannot directly interact with bodies and would have been led inevitably to Leibniz’s own hypothesis of preestablished harmony (Considerations on Vital Principles: GP VI, 540/L 587; Theodicy, Part 1, §61: GP VI, 136/H 156; to Rémond, 10 January 1714: GP III, 607/L 655; Mon. 80: GP II, 620/AG 223). But why, we may ask, would Descartes have been led to pre-established harmony rather than, as were his followers, to versions of occasionalism, such as those advanced by Géraud de Cordemoy, Louis de la Forge and Nicolas Malebranche? In fact, Descartes himself is sometimes read as an occasionalist (Nadler, 1994; cf. Gaukroger, 1995, p. 390). Leibniz, however, found occasionalism objectionable, not least because it invokes the miraculous activity of God to explain what should be explicable by natural means (to Masham, 30 June 1704: GP III, 354–5/WF 212–13). The objection, in Leibniz’s opinion, applies equally well to interactionism (ibid.), as do others of his criticisms. For instance, Leibniz charged that both theories make the mind-body relation arbitrary since although in both the correspondence between sensations and motions is regular, neither offered any reason why certain types of sensations are regularly associated with certain types of physical states and motions (New Essays, Preface: A VI, vi, 55/RB 55). Besides, all Cartesians violate what Leibniz regards as the most basic law of physics, namely, that ‘a body never receives a change in motion except through another body in motion which pushes it’ (Considerations on Vital Principles: GP VI, 541/L 587), for insofar as they admit that the direction of bodies can be changed directly either by God or by individual souls, they allow non-physical interventions within the physical realm.

through the mediation of God, the theories advanced by Descartes and Malebranche seem to allow that the purely mechanical operations of bodies can be interrupted by volitions in the non-mechanical soul. The problem is particularly acute for Descartes. He held that the total amount of motion in the universe is conserved at all times, but if souls as well as bodies can influence the motion of bodies, it would seem that the soul might introduce new motion into the universe and thereby upset the overall balance. There is some evidence that Descartes, aware of the problem, ingeniously restricted the soul’s influence by denying that it can impart new motion into the system and allowing only that the soul can change the direction of bodies’ motion. It is this view that Leibniz attributed to Descartes (Considerations on Vital Principles and Plastic Notions: GP VI, 540/L 587). However, this ‘solution’ works only because Descartes erroneously excluded directionality from the calculation of conserved motion, basing this solely on bodies’ size and speed (Garber, 2009, p. 146). Leibniz, on the other hand, held that force is conserved and that the calculation of force must take into account not only the quantity of motion but also its direction. Moreover, greater force must be applied in order to change the direction of a body in a collision than is needed if the body is merely brought to rest or its advance slowed (Critical Thoughts, Part Two, on articles 40–4: GP IV, 374/L 397). Had Descartes realized that force is conserved rather than motion per se, he would also, Leibniz claimed, have realized that the mind is incapable not only of imparting motion to a body, but is also unable to change the direction in which a body moves without increasing or decreasing the total amount of force in the universe. 30

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DESCARTES AND LEIBNIZ than piety. (Critical Thoughts, II.64: GP IV, 391–2/L 409–10).

In contrast, Leibniz believed his theory of pre-established harmony offered an intelligible account of psycho-physical correspondences whereby changes in the soul and changes in the body are each a ‘natural result of its preceding state’ (to Arnauld, 9 October 1687: GP II, 113/L 340). Despite there being no actual interaction between minds and bodies, their regular and exact correspondence is effected without divine intervention and without violence respectively to the laws that govern the sequence of perceptions and appetitions in the soul or to the laws that govern the sequence of motions and resistances in bodies. So it was that Leibniz could declare:

The final sentence here reminds us of Leibniz’s early remark to Christian Philipp that ‘[t]he true philosophy . . . must give us an entirely different concept of God’s perfection, one that will be of use in both physics and ethics’ (January 1680: GP IV, 284/L 273). The Cartesian philosophy falls short on both counts: in physics, by not recognizing its reliance on God’s wisdom and his appeal to final causation in the determination of the laws of efficient causation; in ethics, by proposing a divine voluntarism that fails to appreciate God’s wisdom and benevolence in creating the best possible world in accordance with principles of perfection, order and beauty that are true independently of God’s will, and by failing to recognize that the created world includes a kingdom of grace comprising rational individuals who follow the same principles as they act freely and spontaneously by their own essence and force.

Nature has, as it were, an empire within an empire, a double kingdom, so to speak, of reason and necessity, or of forms and the particles of matter . . . These kingdoms are governed, each by its own law . . . By thus combining both types of interpretation, we shall serve, in the consideration of the individual phenomena of nature, both our welfare in life and our perfection of mind, and wisdom no less

Pauline Phemister

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3 LEIBNIZ AND HOBBES

philosophy alongside Descartes and Galileo. In England, by contrast, Hobbes had long been vilified on account of the political theory espoused in Leviathan. Particularly his views on the relations between church and state had gained him many enemies after his return to England from French exile in 1652. By the early 1660s there were rumours afoot that certain bishops were planning to prosecute Hobbes for heresy, but things became even worse for the so-called ‘Beast of Malmesbury’ after the Great Fire of London, when influential political and religious figures declared the tragedy to be divine retribution for the spread of atheism in the country (Martinich, 1999, pp. 319–20). In October 1666, a bill was introduced in the House of Commons which explicitly named Hobbes and the Roman Catholic philosopher Thomas White as authors who were to be investigated ‘for atheism, blasphemy, or profaneness’. Seen against the backdrop of a supposed spread of libertinism after the Restoration, Hobbes was effectively made responsible for the licentiousness of the age (Collins, 2005, pp. 272–3; Mintz, 1970, pp. 135–47). Nor was this opposition to Hobbes confined only to political and religious quarters, where it was perhaps most to be expected. His enemies were also to be found in the universities of Oxford and Cambridge, which

INTRODUCTION When Leibniz at the height of his philosophical creativity in the mid 1680s came to consider the intellectual legacy of his great English counterpart Thomas Hobbes, he found nothing worthy of praise. Identifying Hobbes in his draft essay entitled Elementa rationis with a series of ‘harmful doctrines’, he echoed the scorn which had been poured on the author of Leviathan (1651) and De corpore (1655) since these works had first left the printing press in mid-century. In effect, Leibniz reduced the whole compass of Hobbes’s political and philosophical thought to three central propositions which, taken together, could in his view only serve to undermine the principles of religion and human reason and indeed the very foundations of the state: • That there are no incorporeal substances. • That all truth is arbitrary and depends on posited names. • That the principle of law and society is the fear of fear. (A VI, iv, 724) Such an assessment was unusual at the time in continental Europe, where Hobbes continued to be revered as one of the great figureheads of the modern rationalist approach to 32

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LEIBNIZ AND HOBBES doctrines he espoused – with the weakness of his mathematics and his willingness to call into question even the most basic accepted mathematical truths. Almost graciously, Leibniz concludes his assessment of Hobbes in Elementa rationis with the remark that he chooses to remain silent on Hobbes’s ‘scarcely to be believed geometrical errors’ (A. VI, iv, 724; cf. GP III, 422 and Knobloch, 1976, p. 76/77).

he had attacked in Leviathan as being the ideological sources of civil war. At the same time he claimed to the ire of many scholars that the universities had failed to accommodate modern mathematical science, and that they preferred instead what he regarded as the pernicious doctrines of Aristotle (Jesseph, 1999, pp. 57–62). But this is not to say that the Royal Society, which defined itself in contradistinction to the universities and which embraced the new scientific and technological learning wholeheartedly, welcomed him either. Although Hobbes had a small number of good friends among the fellows of the Royal Society, including John Aubrey, Sir Jonas Moore and Robert Hooke, none of his numerous attempts at gaining acceptance himself were successful. His reputation as an atheist was clearly one of the grounds for his exclusion, although this was perhaps no more than a pretext. Of far greater significance were his mathematical endeavours, including his attempts at solving the three classical problems of mathematics, namely, the duplication of the cube, the trisection of the angle, and the quadrature of the circle. Rejecting modern arithmetical and algebraic methods, and steadfastly proposing his own geometrical solutions against better judgement, he soon came into conflict with the Savilian professor for geometry at Oxford, John Wallis, who himself enjoyed considerable power within the Royal Society. In the ensuing intellectual war, which witnessed personal attacks in numerous publications on both sides, Wallis gladly paraded the many mistakes in Hobbes’s mathematical reasoning in front of a contemporary audience (see Jesseph, 1999; Probst, 1997; Beeley, 2008, pp. 31–3). Leibniz was among those who found it hard to reconcile Hobbes’s undoubted intellectual prowess – despite all the misgivings relating to the philosophical

THE YOUNG LEIBNIZ AND HOBBES Looking at Leibniz’s assessment of Hobbes in Elementa rationis, one could be forgiven for thinking that the two philosophers have nothing or at most very little in common. But this could not be further from the truth. In his youth, when much of the groundwork for the later philosophy of monads was laid, the writings of Hobbes represented for Leibniz a profound source of inspiration. Already in the Dissertatio de arte combinatoria (1666) we find that Leibniz’s interest in Hobbes’s logic leads him to draw remarkable conclusions on the nature of thought in broad agreement with the English philosopher. Leibniz’s first philosophical system, the Hypothesis physica nova (1671), to which he appended his Theoria motus abstracti, abounds with references to Hobbes, and indeed the theory of abstract motion developed by Leibniz can be seen to emerge directly from his intensive reading of De corpore. Nonetheless, the relation of the young German philosopher to Hobbes is complex (cf. Violette, 1984, p. 107). On the one side Hobbes’s doctrine of body, together with the geometry of Euclid, served as a model for his own methodological approach to dealing with the mind (A II, i (2006), 182; cf. A II, i 33

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LEIBNIZ AND HOBBES de arte combinatoria, Leibniz was struck by passages in Hobbes’s work which seemed to confirm his own conception of the applicability of combinatorics to human reasoning and to our understanding of the general composition of things within a mechanistic perspective. Crucially, Hobbes identifies reasoning with computation and thus with the single mental operation of adding or subtracting names, or propositions consisting of names:

(2006), 279; A II, i (2006), 361; Hannequin, 1908, p. 154; Kabitz, 1909, p. 83), while on the other side Leibniz rejected fundamental aspects of the materialism inherent in Hobbes’s position. But the significance of Hobbes for Leibniz does not end with his progression to the mature philosophy of monads. Leibniz’s later writings on ethics and natural law display a remarkable consistency with those of earlier years and contain much which for all of Leibniz’s claims to the contrary is in agreement with the English philosopher. From the evidence provided by Leibniz’s early philosophical letters and papers we know that he became acquainted with Hobbes’s De cive and De corpore while still a student in Leipzig in the early 1660s. His youthful rebellion against modern Aristotelianism, which he couched in terms of a rejection of substantial forms as explanatory principles, was consciously described by him as a decision for the mechanistic philosophy represented by Descartes, Gassendi and above all by Hobbes. As he tells a number of correspondents in the early 1670s, he found the elegance of Hobbes’s style of writing and the force of his argumentation especially appealing. By the time of his arrival in Mainz, Leibniz was not only defending the Hobbesian basis of natural law against criticisms levelled by Aristotelians, but was also stating quite explicitly that he held Hobbes’s new logic in equally high if not higher esteem than the logic of Aristotle (A II, i (2006), 153; cf. Goldenbaum 2009, p. 193). Leibniz’s early reverence for Hobbes is nowhere better explained than through the inspiration which the English philosopher’s De corpore provided for his own deliberations on the nature of mind and body. Already by the time of writing the Dissertatio

By reasoning I mean computation. Now, to compute, is either to collect the sum of many things that are added together or to know the remainder when one thing is taken away from another. Reasoning is therefore the same as adding and subtracting. I do not mind if someone adds multiplying and dividing, since multiplication is the same as the addition of equals, and division is the same as the subtraction of equals as many times as is possible. So that all reasoning is comprehended in these two operations of the mind, addition and subtraction. (Hobbes, 1655, p. 2; OL I, 3) Instead of there being different kinds of reasoning – traditionally a distinction would be made between that employed in mathematics and that employed in logic – all was now to be reduced, according to Hobbes, to a single form (Ross, 2007, p. 21; Yakira, 1990, p.130). Leibniz’s reaction to what he found in De corpore could scarcely have been more enthusiastic. Not only does he refer explicitly in De arte combinatoria to Hobbes’s definition of reasoning, but he also subscribes to it himself unreservedly: ‘Thomas Hobbes, that most famous investigator of the principles of all things, rightly laid down that every operation of our mind is 34

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LEIBNIZ AND HOBBES computation, and by this is to be understood either adding a sum or subtracting a difference. Elem. de Corp. p. I. c. I. art. 2.’ (A VI, i, 194; see also A VI, i, 557) Nor was this approbation of Hobbes confined to the moment of completing the Dissertatio de arte combinatoria. Leibniz remained deeply indebted to Hobbes’s conception of human reasoning for the rest of his life. The identification of reasoning with calculation was the ultimate principle on which all of his extensive work on universal character was based. And it led also to his conviction that through the development of this ‘most suitable instrument of the human mind’ (A VI, iii, 170; cf. Beeley, 2009, pp. 42–5) fallacies or false argumentation would be shown to be nothing else but errors of calculation, just as all controversies would turn out to be resolvable through calculation rather than through the kind of harmful disputation which had long plagued philosophical discourse (Ross, 2007, p. 22; cf. Dascal, 2009). This fundamental agreement with Hobbes over the nature of human reasoning finds expression in important assumptions which he and the young Leibniz make when seeking to explain the nature of the mind and its relation to body. In marked contrast to Descartes, both men seek to develop a mechanistic model of the mind complementary to that of the body. This means effectively the removal of any radical distinction between the mental and the corporeal sphere. However, if we compare their positions closely, fundamental differences in Hobbes’s and Leibniz’s conceptions of mind and its relation to body become apparent; differences which allow us to see Leibniz’s position to no small degree as the result of a critical analysis of the ideas of the English philosopher.

THE MECHANIZATION OF MIND IN LEIBNIZ AND HOBBES First of all there is a common path. Leibniz and Hobbes start out from an almost identical point of view in the question of the nature of mind – one which is diametrically opposed to the doctrine we find in Descartes. To be more precise, they share the aim of providing a mechanistic explanation of the mind and emphasize thereby that their respective approaches result from methodological considerations. While Hobbes proceeds from physics to the true philosophy of morals (Hobbes 1655, p. 45, OL I, 64; see also Hobbes, 1655, pp. 53–4, OL I, 77), Leibniz sets out from geometry and arrives at the doctrine of mind via the doctrine of motion or phoronomia (A II, i (2006), 278). Despite proceeding in somewhat different ways, both men effectively develop their theory at the limits of mechanistic physics where they draw on similar conceptual tools in order to explain mental activity. One can consider this as an expression of the nominalist approach shared by both men, but pursued by Hobbes in a much more consequent fashion leading to a restrictive ontology (Hobbes, 1651, pp. 12–17, EW III, 18–29; cf. Hübener, 1977; Mugnai, 1990). However, deeper significance lies in the fact that within mechanistic physics itself the preconditions are created for a causal explanation of the interaction of mind and body. Thus, the approach in itself ensures that mind and body are situated on one and the same ontological level; the fundamental and substantial difference in Descartes between the res existensa and the res cogitans is overcome already at the outset (cf. Schneider, 1993, p. 207). While recognizing the French philosopher’s achievements in respect of the definition of the self (A II, i (2006), 179; see also 35

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LEIBNIZ AND HOBBES need to distinguish his own position from that of the English philosopher is present throughout the writings of the young Leibniz. He counts himself among Hobbes’s supporters against the likes of Wallis and Seth Ward (Goldenbaum, 2009, pp. 194–5) and repeatedly expresses his admiration for Hobbes’s demonstration of the principle that the whole is greater than the part (totum esse maius parte) (A VI, ii, 480; cf. A VI, ii, 482–3). Moreover, he characterizes this principle as the foundation of the science of quantity and thus effectively credits Hobbes with supplying the foundation of mathematics – something most contemporary mathematicians would have found hard to stomach. At the same time Leibniz credits himself with having shown that the principle that nothing is without reason (nihil sine ratione) is the foundation of the science of mind and motion. He evidently feels empowered to make this not inconsiderable claim on the basis of the demonstrative rigour he employed in producing his Theoria motus abstracti, starting out from clear and distinct definitions. Mechanization of the mind signifed for Hobbes and the young Leibniz primarily the mechanization of intellectual activity. This is why their choice of approach is so important. Just as the theory of motion deals with the activity of physical bodies, the theory of mind which they develop, starting out from considerations of corporeal activity, likewise has its roots in phoronomy. The central concept which both Hobbes and the young Leibniz employ in their respective models of mental activity is that of effort or initial motion, for which they used the term ‘conatus’ or ‘endeavour’. As Leibniz makes clear in his writings at the beginning of the 1670s, the concept of conatus represented for him the gate to the

A IV, i, 36 (prop. 39)), Leibniz was not surprised that Descartes failed to come to terms with the mind-body problem (A II, i (2006), 164). In his view precisely because Descartes contemplated mind in itself, that is to say through self-reflection, and did not proceed to the mind through considerations on body he was unable to penetrate its innermost being (A VI, ii, 285). Leibniz sought to overcome this deficit and provide for the first time insight into the true nature of the mind through his planned Elements of Mind (elementa de mente), conceived along the same lines as Euclid’s Elements of Geometry and Hobbes’s Elements of Body (see, for example, A II, i (2006), 361; cf. A II, i (2006), 164; A II, i (2006), 182; A II, i (2006), 279; A II, i (2006), 209; A VI, ii, 285). But Hobbes not only provided a methodological model for Leibniz’s project. The importance of the Elementa de mente can only be gauged against the background of Leibniz’s fundamental concern to reconcile mechanistic philosophy with the principles of Christian religion. In view of the essential materialism of Hobbes’s philosophy, involving as it did the subsumption of mind under body, Leibniz sought to present his own as a theologically palatable alternative, combining the argumentative rigour of De corpore with a philosophically sound basis for the possibility of the immortality of the soul. For Leibniz, Hobbes had mechanized the mind at the price of destroying the mind-body distinction. The task which he therefore set himself was one of developing a theory of mind from clear definitions (A II, i (2006), 181; see also A IV, i, 568), and at the same time of saving the concept of mind philosophically, by distinguishing it precisely from body (A II, i (2006), 104; see also A II, i (2006), 147; A II, i (2006), 236; A VI, ii, 266). This combination of fundamental admiration for Hobbes with recognition of the 36

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LEIBNIZ AND HOBBES beginning of motion, but is also identified by him with the mental beginnings of action. Furthermore, he conceives conatus as accompanying every actual motion of body, insofar as anything in motion must in his view continually strive (or endeavour) to continue its motion (A VI, 2, 265). At first glance this might seem to preclude any use of conatus in explaining how mind and body differ, for conatus is not apparently the preserve either of the mental or the corporeal sphere alone. What in his view distinguishes conatus belonging to the mind from those which pertain to physical motion is their mode of existence: ‘No conatus without motion lasts more than a moment except in the mind’ (A VI, ii, 266; see also A II, i (2006), 174), he writes in the Theoria motus abstracti. Put simply, conatus in the mind are always retained, whereas in the body they have only a momentary or fleeting existence. Hobbes effectively subsumes activity of the mind under activity of the body. For the young Leibniz in contrast, mechanization of mental activity entails that mind is attributed to a specific place in body, namely a physical point. After summarizing the content of his Hypothesis physica nova and Theoria motus abstracti in his letter to Antoine Arnauld of November 1671, Leibniz presents his conclusions on the location of mind as part of a great harvest which he had reaped from fundamental propositions:

understanding of the fundamental difference between mind and body which up to that time no one in his view had succeeded in explaining (A VI, ii, 266; see also A II, i (2006), 147; Hannequin, 1908, pp. 156–7,164). But it was a concept which he had largely gleaned from reading the English philosopher and then developed further. Conceiving conatus as a limiting case of motion (Hobbes, 1655, p. 122, OL I, 177; see also Hobbes 1655, p. 191, OL I, 271, and Hobbes 1678, p. 21, EW VII, 87), Hobbes holds that although a body can only have one actual motion at any one time, it can be subjected to numerous conatus, from which the actual motion results. Moreover, since conatus can be propagated infinitely through the plenum, each body must in his view be subject to an infinite number of such forces. Decisively, from here Hobbes develops the thesis that conatus constitutes not only the infinitesimal element of motion, but also the volitional beginnings of motion. Distinguishing between vital motions such as the circulation of the blood and breathing on the one side and selfinitiated, volitional motions on the other side, Hobbes argues that volition must be considered as an infinitesimal motion which gives rise to an actual motion of the body: ‘These small beginnings of Motion, within the body of Man, before they appear in walking, speaking, striking, and other visible actions, are commonly called Endeavour’ (Hobbes, 1651, p. 23, EW III, 39). Like Hobbes, Leibniz defines the concept as movement through a spatial point in an instant of time (A II, i (2006), 181; see also A VI, ii, 185; A VI, ii, 171; A II, i (2006), 103; A II, i (2006), 93–4; A VI, ii, 265). Indeed, in a letter to Henry Oldenburg he explicitly names Hobbes as the source of this concept (A II, i (2006), 103). But conatus for Leibniz represents not only the

Further, from these propositions I reaped a great harvest, not only in demonstrating the laws of motion, but also in the philosophy of mind. For having demonstrated that the true location of our mind is a sort of point or centre, I deduced from this some surprising consequences about the indissolubility of mind, about 37

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LEIBNIZ AND HOBBES doctrine of the immortality of the soul and thus to reconcile his mechanistic conception of mind with Christian religion. Since this option is not available to Hobbes, Leibniz feels justified in portraying the English philosopher as one who has abandoned religion: ‘The otherwise very acute man, Thomas Hobbes, being far too keen to apply himself to physics, quite abandoned religion, nor did he hesitate to declare in his book on body that our souls are corporeal and through their nature mortal.’ (A VI, i, 84; see also A VI, i, 178)

the impossibility of refraining from thinking, about the impossibility of forgetting, and about the true and hitherto unknown difference between motion and thought – that thought consists in conatus, just as body consists in motion. (A II, i (2006), 279; see also A II, i (2006), 174; A II, i (2006), 181) It is for this reason that in the position which Leibniz presents in letters and writings in 1671 the mechanization of mental activity is complemented by a geometrical model of mind itself (see Beeley, 1996a, pp. 351–63). At that time Leibniz not only saw in the concept of conatus the constitutive element of motion which as such could provide an explanation of the relation of thought to corporeal motion, but also conceived points to be the ultimate elements from which the geometrical continuum is composed. In reflection of this he emphasizes that insight into the composition of the continuum is essential in order to comprehend the innermost nature of the mind (A II, i (2006), 179; see also A VI, ii, 274). By assigning mind to a point in body, Leibniz was able to construct a model of mental-bodily commerce in his first philosophy in which essentially geometrical elements are contained. We can speak here of a mechanistic-geometrical explanation and thus distinguish it from the explanatory model of Hobbes in which the mechanism was fundamentally physiological in nature. In the English philosopher as in one of the most important trends in modern theory of consciousness, functions of the mind are essentially reduced to the physiology of the brain. Leibniz on the other hand conceives the nature of mind to be essentially distinct from the nature of body. Moreover, by situating the mind in a point, he believes that he is able to provide an ontological foundation for

POINTS, LINES AND MINDS It is not by accident that Leibniz stresses that geometry was the starting point of his investigations. In the question of geometrical principles the young German philosopher stands (see, for example, A VI, ii, 266; see also A II, i (2006), 146–7; A II, i (2006), 278), like Hobbes (see, for example, Hobbes, 1655, p. 122, OL I, 177), in the nominalistic tradition of which traces are also to be found in contemporary mathematicians such as Isaac Barrow (see, for example, Barrow, 1674, p. 6; cf. Mahoney, 1990, pp. 193 and 205–6). In this nominalist spirit the young Leibniz conceives point to be a line which is smaller than any line that can be given. As such, points are not distinct entities and require no ontologically distinct foundation apart from lines. However, aside from this fundamental agreement with Hobbes there are important differences in their views, as Leibniz makes clear in his Theoria motus abstracti. These differences have their roots partly in mathematical, partly in theological and philosophical considerations and reflect the diverse goals of the two authors. In respect of 38

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LEIBNIZ AND HOBBES the theory of mind one of the essential differences is expressed in the ontology of the continuum: whereas for Hobbes points like everything else in nature can be divided (Hobbes, 1655, p. 122, OL I, 177), Leibniz holds the view that points, lines, and the continuum in general are not just divisible, but actually divided (A II, i (2006), 103; see also A II, i (2006), 146; A II, i (2006), 278). Moreover, Leibniz effects a greater conceptual distinction between line and point than is the case in Hobbes. More precisely, the young German philosopher conceives points to be unextended and defines their parts as having no distance between them and defines his concept in contradistinction to Hobbes’s definition of point as having inconsiderable magnitude:

model he sets out in the Theoria motus abstracti the mind is contained in a point (see, for example, A II, i (2006), 174; see also A II, i (2006), 265; A II, i (2006), 279; A VI, i, 494 (zu Z. 19)). The structure of the mind and its relation to the body is thus comparable to the rays emanating from the sun. Indeed, he claims that the workings of the stars confirm his model (A VI, ii, 285). Admittedly, minds in this sense are not integrated into Leibniz’s philosophical system of the time, as this is presented in the Hypothesis physica nova, for this work essentially sets out to provide a plausible explanation of natural phenomena. But the theoretical basis of mind and its place in body is nonetheless developed to a high degree in the Theoria motus abstracti. Thus he writes in a contemporaneous letter to Duke Johann Friedrich that the lines which coincide in the point correspond to the nerves which from every part of the body convey movement to the mind: ‘Just as in the central point all lines converge, so, too, do all impressions converge in the mind’ (A II, i (2006), 265; see also A II, i (2006), 174). And in many ways this is an idea which has lasting significance in his philosophy. It is from here, namely, that Leibniz deduces his metaphysical principle of the mind as being a microcosm of the universe, since conceived in this way any mind is evidently capable of receiving impressions of all natural events. Indeed, Leibniz describes the mind at this time as being ‘a small world contained in a point’ (A II, i (2006), 265; see also A II, i (2006), 174; A IV, i, 532; A VI, i, 513). For Hobbes, in contrast, there is no need to localize the mind. Quite the opposite, he seeks to show that mind and thought in the final call are nothing other than movements in certain parts of the body. As he writes in Humane Nature, ‘conceptions and apparations are nothing really, but motion in some

Point is not that, whose part is nothing, nor that, whose part is not considered, but whose extension is nothing or whose parts are not distant, whose magnitude is inconsiderable, inassignable, smaller than any relation, except that which can be expressed in any infinite to some other sensible, smaller than any relation which can be given. And this is the foundation of the method of Cavalieri. (A VI, ii, 265; see also A II, i (2006), 147) Leibniz employs the term ‘partes indistantes’ in order to distinguish the parts of point from the discrete parts or ‘partes extra partes’ of extension, implying that these parts in some way superimpose one another. This conception is of central importance to the way in which Leibniz understands the nature of mind. Then mind is for him not only structured analogous to a point in which innumerable lines can be imagined to meet, but is actually conceived to be this way ontologically. As already mentioned, according to the 39

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LEIBNIZ AND HOBBES 1655, p. 224, OL I, 316–17). Whether it is a case of past or present things, he writes in De corpore, ‘when we carefully consider what we do when we think and draw conclusions we will discover that we always just observe and compare our own phantasmata’ (Hobbes, 1655, p. 56, OL I, 82; see also Hobbes, 1655, p. 229, OL I, 325). In the same manner, he notes in Leviathan that the movement of reaction which persists even after the object which causes it is removed, is that which ‘we call imagination and memory’ (Hobbes, 1651, p. 352; EW III, 637), these two terms being in his understanding one and the same thing, as emerges elsewhere in that work (Hobbes, 1651, p. 5, EW III, 6). Leibniz quotes Hobbes’s concept of phantasma in a conjecture on Anaxagoras which he produced for his former teacher, Jakob Thomasius, in February 1666, and does this as a means to explain why colours are impressions produced in our sensory apparatus rather than being qualities in things themselves (A II, i (2006), 7). There can be little doubt that Leibniz found the reduction of sensation and imagination to motion both plausible and appealing, because this meant that their explanation could be achieved in terms of his concept of conatus. Everything depended thereby on the notion of ‘enduring reaction’ (reactio permanens), since it alone afforded the explanation of something more than momentary on the basis of sensual impressions. A few years later, Leibniz could signal broad agreement between his own concepts of space and time as imaginary things abstracted from their subject with Hobbes’s concept of place as the phantasma of existence and time as the phantasma of motion (see A VI, iii, 279). But he and the English philosopher were fundamentally at odds over the question of the

internal substance of the head’ (Hobbes, 1650, p. 7, EW IV, 31; Hobbes, 1651, p. 8, EW III, 11–12). The mechanism of bodily sensation and of sense perception, just as emotions like pleasure and aversion are explained in his view by means of a model of arteries and veins, of blood and vital spirits and indeed to a high degree of sophistication (See Hobbes, 1655, p. 226, OL I, 319–20; see also Hobbes, 1655, p. 224, OL I, 317 and Hobbes, 1658, p. 67, OL II, 104). Such are the differences to Leibniz, that it is not possible to make a genuine comparison of the two models. However, things are somewhat different when it comes to the concept of phantasma with which Hobbes attempts to explain how sensations are perceived by the knowing subject. Leibniz opposes this for him untenable concept with his own views on the nature of conatus in the mental sphere.

LEIBNIZ’S CRITIQUE OF HOBBES’S CONCEPT OF PHANTASMA According to the well-known definition of sensation in Hobbes, a phantasma is caused in our sense organs by an outwardly directed conatus, which comes about in reaction to an inwardly directed conatus, and continues as long as this reaction lasts (Hobbes, 1655, p. 225, OL I, 319; cf. Hobbes, 1650, p. 25, EW IV, 11–12). The decisive concept here is that of ‘reactio permanens’, since it is through this that everything which we perceive as phantasmata, and all the ideas based on them, are consigned to memory in such a way that at any instant – brought about for example by the introduction of a new conatus (see Hobbes, 1655, p. 226, OL I, 320) – they can be retrieved in thought (see Hobbes, 40

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LEIBNIZ AND HOBBES explaining the true nature of thought (A II, i (2006), 181; see also A II, i (2006), 164; A II, i (2006), 174; A II, i (2006), 209; A II, i (2006), 279), as mental activity in his view – and he agrees here with Digby (A II, i (2006), 180) – could not be explained by means of the orthodox mechanistic concepts of figure and motion. Precisely for this reason, Leibniz was in no doubt whatsoever that mind could not be resolved into body in the way that Hobbes had sought to show. Furthermore, he saw as a decisive characteristic for distinguishing mental and corporeal activity the fact that in mind traces of all previous conatus can be retained (see A VI, ii, 285). For even if all corporeal motion, according to the position he sets out in Theoria motus abstracti, is composed of conatus, only those elements which are effective in the immediately preceding moments can actually determine the present motion of body (see A VI, ii, 266; cf. A II, i (2006), 279). Conatus in body has thus for him only momentary character, while in the mind they carry the mark of continuity: ‘In this the actions of the body differ from mind, that in body only the last conatus are considered, and in the mind all conatus backwards’ (A VI, ii, 285). By means of the concept of conatus Leibniz explains the capacity of the mind in the process of thought to compare different things. He defines thought itself as being ‘nothing more than the sense of comparison’ (A VI, ii, 282). Likewise, he is able to use the concept of conatus to provide an explanation for the corporeal impressions of objects of perception and for the ability of the mind to be affected by feelings such as pleasure and pain. The mind, which for Leibniz as for Descartes is never at rest, distinguishes itself from body precisely through these abilities. In dramatic contrast to Hobbes, Leibniz views body as being that which is sensed, not

conservation of conatus, which the concept of reactio permanens requires. In Leibniz’s view the conservation of conatus could not be effected in the body, but only in the mind which precisely in this way is distinguished from it (A II, i (2006), 93–4; cf. A VI, i, 495). Thus, Leibniz sets out the framework of his own theory in which he seeks to give the idea of the conservation of conatus more depth and indeed an ontological foundation. In so doing he denies that animals are capable of true perception, since in his view they do not have minds (see, for example, A II, i (2006), 94; see also A II, i (2006), 179). This is a further clear contrast to Hobbes (see, for example, Hobbes, 1655, p. 229, OL I, 325). As already indicated, in the young Leibniz’s theory of mind there are alongside theoretical considerations on perception also theological and moral elements which Hobbes by comparison ascribes to the nonphilosophical domain of religious doctrines and conventions – a domain for which philosophical explanations neither exist nor are required.

CONATUS AND MEMORY One of the most intractable problems of seventeenth-century mechanistic philosophy was to explain how impressions in the mind or in the brain could be retained. Already Kenelm Digby (Digby, 1644, p. 284), reflecting on Descartes, had stressed the importance of this question and Leibniz sought to solve it by developing further the concept of conatus he had found in the writings of Hobbes. In effect, the conceptual tools of conatus and actually divided points represent for the young German philosopher the key to 41

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LEIBNIZ AND HOBBES which in his view distinguishes intellectual activity from the mechanistic activity of body, where everything is determined by the addition and subtraction of conatus and that is to say in a purely mathematical manner (see A VI, ii, 315; see also A VI, ii, 282). Just as division in the corporeal sphere leads to variety and distinction, so, too, is the actual division of points indispensable for understanding our ability to make distinctions when conducting intellectual activity. The comparison and careful examination of different things finds its expression in Leibniz’s early model of mind, where the concept of variety is realized in structural unity. The same applies to reflexion, which is founded structurally in the immediacy of intellectual activity. It is in the concept of the conservation of conatus in the mind that Leibniz finds the origin of memory. He argues cogently that the ability to remember always has a relation to the present in the sense that recollection involves the production of a present harmony from earlier ones (A VI, ii, 285; A II, I (2006), 279; see also Hannequin, 1908, p. 174; Beeley, 1996a, pp. 352–4). Hobbes, in contrast, conceives memory as a kind of self-perception, in which one senses what one has already sensed before (Hobbes, 1655, p. 224, OL I, 317). Memory, while being reduced materially to reactio permanens takes place subjectively by means of a constant and actual impression of the senses (see Hobbes, 1655, p. 226, OL I, 320). Similarly, consciousness is for Hobbes not something which supervenes on a mental event, but is rather resolved nominalistically. The young Leibniz, too, despite all his differences from Hobbes in respect of the theory of mind, follows this path by reducing consciousness to thought. As he writes to Jean Gallois shortly after the beginning of his sojourn in Paris, ‘in sensation it is certain that I am aware of myself sensing. Therefore, I am

that which senses (A VI, ii, 283). On the Leibnizian model body can therefore on the one side be characterized as a means of perception and as an object of sensation, and on the other side as an object and means of voluntary and involuntary actions. Whereas for the young Leibniz sensation consists simply in the impression of motion, thought is conducted through harmonies composed of conatus. Just as various ideas and memories which go into our thoughts can lead us in different directions, so, too, the conatus which the young German philosopher conceives as constituting these very ideas and memories. Only when a kind of equilibrium or unity is achieved can thought have a clear intention. This is evidently how Leibniz understands the thought process. In order to describe the nature of the harmonies which this process involves he employs an expression which in many ways is characteristic of his philosophy as a whole, namely as variety balanced in identity (varietas identitate compensata) (see A II, i (2006), 279; A VI, i, 479; A VI, ii, 283; A VI, iii, 116: Piro, 1990; Leinkauf, 1996, 1997). Pleasure and pain, too, are conceived in these terms, namely in the sensation of harmony itself or of the disturbance and destruction of harmony (see A II, i (2006), 164; A II, i (2006), 279–80; A IV, i, 247, 249; A VI, i, 444, 484; A VI, ii, 282; A VI, iii, 116). But it is the process of thought that merits most attention, for Leibniz succeeds here in introducing unmistakably moral aspects into his theoretical model. In the comparison of different moments of thought, of compositions of ideas and memories or of various schemes of action, Leibniz holds that ideally the most harmonious is chosen (A VI, ii, 282). That which is most harmonious is most conducive to the general good and thus clearly represents a moral imperative. It is precisely this 42

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LEIBNIZ AND HOBBES characterization of points as being actually divided he establishes an intimate relation to body which is likewise characterized through actual division. It is from this commonality that according to his model both knowledge and extra-mental activity are rendered possible. If nerves, like lines, meet in a point, then, as Leibniz recognizes, the angles which these lines form will be in the point itself: the doctrine of angles, he tells us, ‘is none other than the doctrine of the quantity of point’ (see A II, i (2006), 103; see also A II, i (2006), 265; A II, i (2006), 279). But this is not to say that we should speak here of intensive infinity; such an interpretation would make the compositional role of points with respect to the continuum incomprehensible. One of the consequences of this model is that the mind, for the young Leibniz, is situated in the place of concourse (locus concursus) of all the motions arising from objects which impress upon our senses (see A II, i (2006), 174; VI, ii, 285). If the mind were larger than a point, he argues, it would be truly a body, as in the position set out by Hobbes, and this would mean at the same time that it could not be intimately present in body. Intimacy is the decisive concept. The concentration of point which, by reason of its division makes the inclusion of diversity in its unity understandable, explains also the possibility of the reflexion of the mind ‘on all its parts and all its actions’. Indeed, as Leibniz emphasizes in a letter to Duke Johann Friedrich of Hannover, it is in this that the essence of the mind consists:

aware of myself directly when sensing, there being no medium between me and myself, for in the mind there is no medium’ (A II, i (2006), 350).

THE RELATION OF MIND AND BODY This immediacy of intellectual activity is exactly what the young philosopher Leibniz explains by means of his geometrical model. The mind is in a point, otherwise it would occupy extended space in body and therefore not be fundamentally distinguishable from it (see A II, i (2006), 174; cf. A VI, i, 509; A VI, i, 535; Mercer and Sleigh, 1995, p. 81). Evidently it is for this reason that Leibniz adopts the view in contrast to Hobbes that points are not extended. Extension and therefore the existence of actual and discrete parts (partes extra partes) is that which characterizes body. Admittedly, shortly after Leibniz published the Theoria motus abstracti the concept of motion began to take on more significance in relation to the definition of corporeal nature. Thus, in his letter to Arnauld, dated the beginning of November 1671, he describes movement and not extension as being the essence of body (A II, 1 (2006), 281; cf. A VI, iii, 56). However, one should not underestimate the importance of this apparent switch for explaining the possibility of the mysteries of the Eucharist (Cf. Fouke, 1992, p. 153–4). Nonetheless, points do not thereafter cease to have their metaphysical significance, as, for example, the Système nouveau of 1695 makes clear (see Beeley, 1996b). By situating minds in points, the young Leibniz sets them sufficiently far apart from body ontologically in order to avoid materialism. At the same time, through the

If we give the soul a larger place than a point it will already be a body and have parts beyond each other; it will then not be intimately present in itself and will not be able to reflect on all its pieces and actions, whereas the essence of the soul consists precisely in this. (A II, i (2006), 174) 43

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LEIBNIZ AND HOBBES 1978, p. 138). The actio in se ipsum of the mind on the one side is opposed to the motus localis of the body, conveyed to it by the pressure or collision of other bodies, on the other side (see A II, i (2006), 166; cf. A IV, i, 179; A II, i (2006), 279). In addition, the mind cannot cease to act and to propagate itself without new creation, while the body according to the laws of motion which Leibniz sets out in the Theoria motus abstracti would inevitably in the course of time arrive at a state of rest (see A VI, ii, 280; see also A II, i (2006), 104; A II, i (2006), 265; A VI, ii, 298; cf. A VI, iii, 57, 65; A VI, iii, 100).

Hobbes solves the problem of the mind and its relation to body in a much more radical way than Leibniz – corresponding to his more radical nominalism – and in a way which, as we have already mentioned, is much closer to modern approaches to solving the problem of consciousness. In so doing, the English philosopher pushes materialism to its logical consequence: his theory aims at eliminating the mind or spirit at least in so far as it is understood to be an incorporeal substance, since he finds this concept to be philosophically contradictory and over and above this superfluous (see, for example, Hobbes, 1655, p. 231, OL I, 327–8; Hobbes, 1655, p. 304, OL I, 431; Hobbes, 1651, pp. 207–8, EW III, 381–2; Hobbes, 1651, pp. 373–4, EW III, 676; Hobbes, 1650, p. 138, EW IV, 61–2). In his view, nothing exists apart from body with its uncreatable accident of extension and its creatable accident of motion. The concept of pressure and reaction, on which amongst other things perception is based, is not attributed to a mind or spirit detached from body, but uniquely to certain organs of the body itself. Leibniz counters Hobbes by asserting that the reactio permanens he employs in order to explain sense perception and thought cannot be present in body except apparently or ad sensum (A II, i (2006), 93–4; Kabitz, 1909, pp. 90–1). According to his own concept it is impossible for contradictory conatus, such as a reaction of this kind presupposes, to occur simultaneously in body. If this were possible, he argues, each body would be truly a mind (A II, i (2006), 147). Here, as elsewhere, Leibniz’s theory emphasizes the difference between corporeal and mental activity. Thus he emphasizes, too, that the mind on account of the conservation of conatus and the potential for activity which results from this is able to act by itself (A II, i (2006), 265; See Poser,

MATERIAL MINDS AND MENTAL BODIES The young Leibniz fundamentally believes he is able to prove not only that there must be minds or spirits in the world, but also that these are incorporeal. As such the mind can according to his mechanistic model only be situated in an unextended point. At the same time, the conception of point as unextended but actually divided, together with the proposed mode of existence of conatus, permits the German philosopher to explain all activity of the mind, including reflection. In contrast, the concept of body, which plays centre stage in Hobbes, is scarcely developed by Leibniz in his first philosophy. This accentuation is characteristic. The body has for Leibniz a two-sided function. On the one side it is the means by which the outside world is perceived and on the other side it is the means of expression of all activity issuing from the mind. The body has no memory, no past, and no identity other than that which it receives from the mind. Its movement is determined from moment to moment by the effective 44

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LEIBNIZ AND HOBBES momentanea makes their fundamental differences evidently clear. Like Hobbes, Leibniz seeks to mechanize the mind, but in the opinion of the author of Theoria motus abstracti this must not be done at the price of destroying that which is specific to mind itself, namely thought and consciousness. By defining body as a momentary mind, Leibniz emphasizes that body necessarily lacks those characteristics which for him are essentially connected to mental activity. To read more into the definition of body as mens momentanea than this means going beyond any evidence which available texts are able to supply (cf. Garber, 1982, pp. 171–2; Bassler, 2002, p. 224; Moll, 1996, pp. 198–200; Mercer and Sleigh 1995, p. 83). Although the need to conceptualize the distinction between his own position and Hobbes’s materialism was greatest in his youth, Leibniz was consistent in his opposition to the English philosopher in this respect. Time and again he speaks of Hobbes in one breath with ancient atomists such as Leucippus and Epicure and attacks him for rejecting immaterial minds as sources of action. While he hails Hobbes for having upheld the very same mechanical principle which he himself holds dear (see A II, i (2006), 272), namely that a body never changes its motion except when impelled by another body, he rebuts him for having taken its consequences too far. As Leibniz contends in his Considérations sur les principes de vie, Hobbes effectively attested irrationality to those thinkers who, like the German philosopher himself, continued to uphold immaterial principles in their metaphysics: ‘The followers of Democritus, Hobbes, and some other thorough-going materialists, who have rejected all immaterial substance, having alone up to this time preserved this law have believed that they found therein ground

conatus, for the conatus in body have only a momentary existence (cf. A VI, ii, 282; see also A VI, ii, 299; A VI, ii, 333; A VI, iii, 95; A VI, iii, 393), whereas the mind conserves all its conatus. In consequence, Leibniz is able to define body starting out from the mind, thereby reversing the relation found in Hobbes who defines mind in terms of body. The young German philosopher’s definitive answer to the English philosopher’s materialism is not only to negate any claim to permanence on the part of the body, but also to define it in terms of mind. Put simply, body is for him nothing else than a momentary mind or mens momentanea. Almost euphorically, Leibniz introduces this concept in his Theoria motus abstracti: No conatus which does not result in motion lasts more than an instant, except in minds. For what happens at an instant is conatus, whereas what happens over time is the motion of a body. This opens the door to arriving at the true distinction between body and mind, which no one has hitherto discovered. For every body is a momentary mind, or a mind that lacks memory, because it does not retain its own conatus together with the contrary conatus of another body beyond an instant. But two things are required for there to be sensation, namely action and reaction, or in other words comparison, and hence harmony – and also pleasure or pain, without which there is no sensation. So a body lacks memory; it lacks any sensation of its actions and passions, and it lacks thought. (A VI, ii, 266; see also A II, i (2006), 147; A II, i (2006), 166; A II, i (2006), 279) Even if in some ways the positions of Hobbes and Leibniz are remarkably similar, particularly in respect of the theoretical function of conatus, the definition of body as a mens 45

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LEIBNIZ AND HOBBES Both von Boineburg and Leibniz seem to have been blissfully unaware that Hobbes had long become a figure held widely in contempt in intellectual circles in England and that most members of the Royal Society wanted nothing to do with him. Oldenburg in his reply to von Boineburg’s enquiry politely avoids any direct reference to Hobbes’s unpopularity, choosing instead to present him as one who now sought a quieter life: ‘Our Hobbes has published nothing since the recent collection of his works printed in Amsterdam, unless I am mistaken. He is already more than eighty years old and seeks quiet and repose; and refuses to be drawn by the lively sallies of younger protagonists’ (Hall and Hall, 1970, p. 107/108). In his reply to Leibniz, which he enclosed in that to Boineburg, Oldenburg mentioned the letter to Hobbes only in a postscript, claiming that he had already forwarded it to the philosopher in his residence out in the country. He also added the none too promising remark: ‘If he makes any answer I will send it on to you without delay’(A II, i (2006), 100). Oldenburg was undoubtedly not being candid, but he was at the same time concerned not to rebuff Leibniz on account of his interest in Hobbes. On Oldenburg’s death in 1677 Leibniz’s letter to Hobbes could still be found among his papers and indeed all the evidence suggests that the secretary of the Royal Society consciously ignored Leibniz’s request for it to be forwarded. He would have had good reason for this, since he was keen to promote his promising fellow-countryman in the influential circles of the then most illustrious scientific institution in Europe. One of the fellows he particularly had in view in this regard was no other than Hobbes’s arch enemy John Wallis. Oldenburg would have been well aware that influential men such as Wallis and Robert Boyle would

for insulting other philosophers, as if they thus maintained a very irrational opinion.’ (GP VI, 541; see also GP VI, 519)

LEIBNIZ’S LETTERS TO HOBBES In view of the substantial agreement in philosophical principles – looking aside from the question of materialism – it is perhaps not surprising that the young Leibniz in the summer of 1670 sought to enter into correspondence with the aging philosopher he so much admired. It is probable that his patron, Johann Christian von Boineburg, who had introduced him into the service of the Elector of Mainz in 1667, encouraged this contact, just as he encouraged, and indeed brought about, the correspondence between Leibniz and Henry Oldenburg at the same time (see Beeley, 2004). The political and philosophical thought of Hobbes was very much an interest which the two men shared: von Boineburg had a susbstantial collection of Hobbes’s publications in his library and Leibniz clearly used every opportunity he could find to read these publications avidly. From von Boineburg’s letter to Oldenburg of 26 July 1670, which enclosed that of Leibniz, we see that the councillor and diplomat enquired about the current work and recent publications of Hobbes (Schuhmann, 2005, p. 148; Hall and Hall, 1986, p.422/3). Leibniz also had Hobbes on this mind. Admittedly, in his introductory letter to the secretary of the Royal Society Leibniz presented himself as one whose interests went to the heart of the scientific concerns of that institution. But he used the opportunity of this letter to enclose one for Hobbes, asking Oldenburg to forward it to the philosopher for him. 46

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LEIBNIZ AND HOBBES Claiming that he had always understood Hobbes’s theories, Leibniz continues by outlining the projects he was currently undertaking, such as the construction of a system of rational jurisprudence, his work on the abstract theory of motion, and his model of cohesion. Like von Boineburg, he expresses his interest in Hobbes’s latest works, supposing these to reflect recent developments in English science in general, and he concludes by combining a request for a more precise explanation of the nature of the mind with a denial of the possibility of the very concept of permanent reaction on which that explanation rests. Effectively Leibniz politely hides his rejection of Hobbes’s materialism behind the demand for an account of how human beings can experience true sensation – something which in contrast to Hobbes he explicitly denies of brute animals (A II, i (2006), 93–4). It would appear that Leibniz at some stage, possibly during his first visit to London in 1673, discovered the fate of his introductory letter to Hobbes. For, sometime after that visit, while he was still living in Paris, he took the opportunity of an acquaintance planning to visit Hobbes to draft, though probably not send, another letter to the English philosopher. This was altogether a different introduction, not full of the gushing admiration and innumerable references to points of intellectual agreement which had marked the 1670 letter. He talks at length of Hobbes’s De cive, confronting the author’s deliberations on the right of the individual to undertake anything to the end of preserving his own life with his concept of the transfer of rights to the state. Even within the state, Leibniz argues, individuals have the inalienable right when subjected to oppression by a tyrant, to join together in resistance. More controversially, Leibniz questions whether

have kept their distance from Leibniz had they discovered that he was in correspondence with the author of Leviathan. Despite Leibniz’s failure to establish correspondence with Hobbes, his letter of 1670 is instructive; it reveals not only a precocious young man trying to impress one he admired, but also displays his engagement with key areas of Hobbes’s thought, reflecting almost the full breadth of his publications. Indeed, right at the outset Leibniz claims to have read most of Hobbes’s works, partly in separate volumes, partly in the edition of his Opera philosophica which had been published in Amsterdam in 1668. He then proceeds with almost unrestricted praise, even extending to the mechanical principle which he was later to accuse Hobbes himself of having misused: I freely confess that I have profited from few other works of our age as much as I have from yours. I am not in the habit of flattering, but everyone who has been able to understand your writings on political theory agrees with me that nothing can possibly be added to the clarity of their arguments, which are so admirable when they are expressed so concisely. Nothing could be more well turned or more consistent with ordinary usage than your definitions. As for the theorems which are deduced from them, some people hold fast to them and others misuse them for bad purposes; I think the latter has happened in many cases through ignorance of how they should be applied. Take, for example, the general principles of motion: ‘nothing can begin to move, unless it is moved by another thing’; ‘a body at rest, however large, can be made to move by the slightest motion of another body, however small.’ (A II, i (2006), 91) 47

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LEIBNIZ AND HOBBES thing whose happiness is pleasing to us’ (A VI, i, 457). There were other points of enduring agreement, too. As we have seen, Leibniz subscribed to Hobbes’s concept of thought as calculation and employed this as the basis for much of his work on universal character. He also agreed with Hobbes that all necessary truths, such as the truths of mathematics, could be demonstrated from definitions – this of course extends to Hobbes’s demonstration of the axiom totum esse maius parte. However, he stopped short of agreeing with the English philosopher that definitions are always nominal and arbitrary and that all truth is therefore arbitrary as well. Thus he points out to Jean Gallois in October 1682 that Hobbes should have considered ‘that it does not depend on us to form the definitions, since it is necessary to employ notions, which are possible and compatible’ (A II, i (2006), 833–4; see also GP IV, 158; GP III, 443; A III, ii, 929, 938; Yakira, 1990, p. 133). Rejecting Hobbes’s extreme nominalism, Leibniz asserts consistently that every real definition must in this sense contain the possibility of its subject or mode of its construction.

the concept of personal well-being, as the aim implied in self-preservation, can be adequately understood without reference to divine justice. Nor was this a new insight. Already in June 1671 Leibniz suggested to Lambert van Velthuysen that the principles of De cive could in his view be held equally by atheists (A II, i (2006), 197). But his rejection of Hobbes is never absolute. Despite criticizing central features of Hobbes’s political philosophy, Leibniz was already in his youth fundamentally in agreement with Hobbes that human beings do not do anything except insofar as they are for their own personal use or advantage. Writing to Hermann Conring in 1670, he makes clear that any account of natural law which did not ultimately rest on selfinterested motives was highly implausible, if not to say foolish. This was a position to which Leibniz always remained loyal throughout his life. I suppose with Carneades (and Hobbes is of the same opinion) that to be just without any gain for oneself (current gain or future gain) would be the height of foolishness. The Stoics and Saducees are far away from human nature when they arrogantly boast that virtue is desirable in itself. So every just thing must be a privately beneficial thing. (A II, i (2006), 47; see Goldenbaum, 2009, p. 199)

CONCLUSION The different conceptions of Hobbes and Leibniz of the nature of mind reflect fundamental differences in their understanding of the systematic importance of religion in respect of philosophy. As recent investigations have shown (see Mercer, 2001; Goldenbaum, 1999), theological considerations play a decisive role in the development of Leibniz’s first philosophy, whereas

Remarkably, when Leibniz brings the concept of love (amor) into his discussion of natural law, he does so in terms which make love appear fundamentally and privately useful to the individual. A completely disinterested love would in his view be as far removed from human nature as the Stoic concept of virtue as desirable in itself. As he wrote already in Elementa juris naturalis ‘we love a

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LEIBNIZ AND HOBBES refers to them at the same time. The mind or the spirit is incorporeal, since it is located in an unextended point which although being divided is not divisible in the same way as the discrete parts of extended bodies are. After all, bodies are always in flux for Leibniz and effectively at death their parts are scattered in all directions. Not so with souls. Their point nature is sufficient in order to ensure their integrity beyond death (A II, i (2006), 181). The proof of the possibility of immortality belongs to the most important demands which Leibniz makes of his first philosophy. He refers time and again to the need to prove the truth of religion and at the same time to fight atheism (see, for example, A II, i (2006), 175; A II, i (2006), 265–6). The claim of atheism was one of the biggest weapons in the arsenal employed against early modern representatives of mechanism, and therefore religious considerations always played a central role in Leibniz’s thought. Moreover, already in his early writings, immortality provided a decisive connection between natural philosophy and ethics. For it guaranteed not only the continued existence of substance, but also, through this continued existence, personal identity through time and over and above this the possibility of divine justice, with accompanying punishment and reward, transcending earthly life (A VI, i, 268). Personal identity has its foundation ultimately in the conservation of the history of the individual by means of the conservation of conatus. This is precisely what the concept of body in Hobbes is not able to achieve: ‘it is the mind and memory of experiences and deeds which make us one and the same, not flesh and bones,’ Leibniz writes (A II, i (2006), 184; cf. A VI, iii, 588).

Hobbes rejects any attempt to provide a philosophical or scientific explanation for matters of belief such as the mysteries of the Eucharist or the immortality of the soul (Hobbes, 1651, p. 195, EW III, 360; Hobbes, 1650, p. 139, EW IV, 63; see also Hobbes, 1655, p. 6, OL I, 9; Schilling, 1947, p. 285). Moreover, Hobbes’s theory removes the philosophical basis to immortality. Thus when he seeks in Leviathan to reconcile his philosophy with stories recounted in the Bible he declares that nothing prevents us from conceiving the spirits which are mentioned there as being entities with very fine bodies (Hobbes, 1651, p. 211, EW III, 388; see also Hobbes, 1651, p. 371, EW III, 672; Hobbes, 1650, pp. 135–8, EW IV, 60–2). Not surprisingly, Leibniz deplores that Hobbes through his efforts in the field of physics practically destroys religion. For, as Leibniz explains in one of his early writings on the philosophy of law, Hobbes in De corpore ‘did not hesitate to admit that our soul is corporeal and therefore of its very nature mortal’(A VI, i, 84; see also A VI, i, 178). Leibniz’s own theory is intended as a reply to Hobbes. Not least for theological reasons the young German philosopher presents his first philosophy as a reformed philosophy in which every body is ascribed an intimate incorporeal principle (principium intimum incorporeum) (A II, i (2006), 266). He overcomes Hobbes’s materialism by rehabilitating those incorporeal substances which the English philosopher destroyed at the same time as he destroyed true indivisibles (A VI, ii, 275; cf. A VI, iv, 724–5). These two concepts, indivisibles and incorporeal substances, are indeed closely related and it is therefore no accident that Leibniz in Theoria motus abstracti

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LEIBNIZ AND HOBBES mechanize mental activity in a similar fashion he was convinced that through his geometrical approach, in contrast to the physiological approach adopted by Hobbes, he would be able to save most if not all of what Hobbes had ultimately sacrificed.

Our investigation has shown that Leibniz took his reading of Hobbes’s De corpore and Leviathan as a pretext for occupying himself with central theses of the English philosopher on the question of the nature of the mind and its relation to body. On fundamental points he adopted a position clearly in opposition to Hobbes. While he sought to

Philip Beeley

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4 LEIBNIZ’S FASCINATION WITH SPINOZA

God’s attributes, thought and extension, as he wants God to be purely mind. But above all, he could not accept Spinoza’s strict determinism with his denial of free will. But all these ideas belong to the heart of Spinoza’s philosophy. Thus the two philosophers clearly are the strictest opponents in metaphysics and Leibniz must have understood this since he first read the Tractatus theologico-politicus (Spinoza, 1670), on 3/13 October 1670. Whoever reads its fourth and sixth chapters ‘On Divine Law’ and ‘On Miracles’ cannot but grasp the thoroughgoing determinism of Spinoza and his identification of God and Nature (compare Leibniz’s later comment on the TTP in A VI, iii, 269–70). But although it is so absolutely obvious that Leibniz disagreed with Spinoza about their essential metaphysical ideas and thus could never even consider becoming a Spinozist, discussions about their close intellectual relationship have emerged again and again during the reception of Leibniz’s ideas, starting during his lifetime. To be sure, such authors did not take Leibniz to be a Spinozist. Nevertheless, while discussing Leibniz’s philosophy they easily slipped into a discussion of Spinoza or vice versa. Brandon Look has discussed this in an illuminating way

It is well known that on different occasions Leibniz gave very different and even contradictory judgements about Spinoza and his ideas. You can find both very high regard for the Dutch philosopher on the one hand and clearly dismissive, even nasty comments on the other. What seems clear, however, from the very beginning is that Leibniz could never agree with the main ideas of Spinoza’s philosophical project, i.e. he could never have intended to become a Spinozist. Thus, all the ‘proofs’ of the last hundred years that Leibniz was not a Spinozist were rather superfluous (see Goldenbaum, 2007). No one but Leibniz’s declared contemporary opponents had ever tried to make such a claim, and they did so in order to denounce him more effectively (Andala, 1712; Lange, 1727; cf. Bamberger, 2003). Although it has been and is still often argued that Ludwig Stein had made this claim (Friedmann, 1962, pp. 21–2, 345–7), Stein rather explicitly rejected such a view (Stein, 1890, pp. 26, 109–10). Leibniz could certainly not accept Spinoza’s nonpersonal God – a God who does not will anything and knows neither good nor bad because everything is just as perfect as it is real. Likewise, Leibniz could not agree with Spinoza’s understanding of the identity of 51

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LEIBNIZ AND SPINOZA thoughts were not only beautiful but in the greatest agreement with his own (A II, i2, 592). To be sure, he adds immediately that Spinoza also holds quite paradoxical ideas (the ones mentioned above), which would destroy providence and immortality. Leibniz made a very similar statement to Vincent Placcius on the very same day (A II, i2, 593). Both letters were written precisely in the days when Leibniz was studying and annotating Spinoza’s Opera posthuma (Spinoza, 1677) thoroughly. Well, does this mean an influence? Not necessarily. Does this mean partial agreement? He says so. These two letters are especially interesting as they include both of Leibniz’s positions, i.e. strict disagreement and agreement with Spinoza. Thus it cannot be the question whether Leibniz was either a Spinozist or an opponent of Spinoza. Neither of these interpretations is actually of interest. The first is obviously wrong and the second is right. But so what? The latter does not answer the question. The problem is rather how Leibniz could hold both opinions at the very same time. Thus how can these two statements in both of the letters be compatible (assuming Leibniz was not schizophrenic)? This question was raised by Ludwig Stein and his book provides an interesting explanation – though he lacked much of the material we have now available. Stein wrote the first ‘Entwicklungsgeschichte’ of Leibniz’s thinking, trying to explain the intellectual genesis of his mature philosophical system. Having studied the then-known Leibniz material, he argued that the most intense interest of Leibniz in Spinoza can be found in the period between 1676 and 1680 (Stein, 1890, pp. 17–30 and 109–10). He acknowledged, however, that Leibniz was never inclined to embrace Spinoza’s philosophy. Nevertheless he believed that Leibniz was interested in Spinoza’s ideas and – in

with reference to the more recent example of Goedel’s efforts to prove the existence of God. Taking his starting point from Leibniz’s approach, Goedel felt immediately the threat of slipping into Spinoza’s position (Look, 2006, pp. 510–17). A rather classical example is Lessing’s famous talk with Jacobi on Spinoza and Leibniz, published by Jacobi in 1785 (Jacobi, 1985), thereby initiating the Pantheismusstreit. It had a huge impact on the development of subsequent German philosophy, theology and literature. It stirred up Goethe and Herder, Schelling, Hegel and Hölderlin, the romantics including Schleiermacher, and finally Kant (it seems he did not read Spinoza prior to this). It still impressed Kierkegaard. In this famous conversation, Lessing, being extremely familiar with the work of Leibniz and Spinoza, asked Jacobi at some point whether Leibniz had not been a Spinozist in his heart – only then to admit immediately that he had said too much (Spinoza Conversations, 1988, pp. 90–1). These examples nicely illustrate the conundrum of Leibniz’s relation to Spinoza, foreshadowing the many discussions to come. Obviously, the relation of Leibniz to Spinoza is not a simple question of influence and reception as it is usually discussed, i.e. picking up an idea from another philosopher and integrating it into one’s own system. Even more puzzling are some of Leibniz’s own statements about the closeness of his ideas with those of Spinoza, as he simultaneously expressed his opposition to other ideas of Spinoza. We learned about these puzzling statements only at the end of the nineteenth century when Ludwig Stein published two letters of Leibniz together with other unedited Leibniz material from the Leibniz archive in Hanover (Stein, 1890, pp. 307–8). On 4/14 February 1678, Leibniz wrote to Henri Justel that many of Spinoza’s 52

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LEIBNIZ AND SPINOZA the controversy against Stein. The first book that fully developed this thesis is the (still highly regarded) famous monograph of Willy Kabitz about the young Leibniz (Kabitz, 1909). Unfortunately, this thesis has been confirmed again and again since that time (Friedmann, 1962, pp. 85–6; Moll, 1996, iii, p. 233; Mercer, 2001, p. 132), most recently by Antognazza (Antognazza, 2009, throughout, see, for example, the title of chap. 3). But this thesis has hindered an adequate understanding of the obvious essential changes, new approaches and breakthroughs in Leibniz’s philosophical development to his mature philosophical system. It even dismisses the obvious fact that Leibniz in Leipzig did not even intend to become a philosopher but energetically pursued the career of a lawyer, clearly indicated by his move to the University of Altdorf for his Ph.D. in law. In addition, he had not dreamed of mathematics when he arrived at Mainz. Neither his intense engagement with mathematics in Mainz and Paris 1669–76, nor his fascination with Hobbes in Leipzig and Mainz 1666–71 and with Spinoza, first in Mainz in 1670–1 and then in Paris and Hanover from autumn 1675 until spring 1678, can be explained in terms of continuity, i.e. as due to his Aristotelian education at Leipzig. Of course, he knew Aristotle, Plato (and Duns Scotus) and used their concepts as did Descartes, Hobbes and other moderns as well. But in order to become Leibniz he certainly had to deviate from the old authorities, and it is well known that he began to do so in the Rosenthal at the age of 15. It is not surprising at all that he tried to reconcile mechanical philosophy with Aristotle and Plato as has been done by many partisans of mechanical philosophy who wanted to reconcile both philosophies, such as Jean Raey, Kenelm Digby, Thomas White and others.

that period – absolutely keen to read every single line of Spinoza. Thus Stein raised the right question – what fuelled Leibniz’s interest in a philosopher with whom he disagreed from the very beginning about the core ideas? He then tried to identify the problems Leibniz was struggling with during this particular period in order to explain how Leibniz could have learned something from Spinoza to solve these problems. He did not claim, however, that any of Leibniz’s solutions were owed to Spinoza but rather that reading Spinoza helped him to make up his mind. Stein’s heuristic approach and his resulting thesis stirred up a nasty campaign against him by some of the leading Leibniz scholars in Germany, France and Austria. The result was the completely unnecessary proof – that Leibniz was no Spinozist. Therefore Stein was supposed to be completely wrong. The dismissive judgement about Stein as a poor scholar is still lingering around and has to be corrected given his solid research principles as well as his impressive findings in spite of some shortcomings due to his limited availability of textual resources (Goldenbaum, 2007). Unfortunately for Leibniz research, this controversy produced another more important bad result – the problematic thesis about the thoroughgoing continuity of Leibniz’s intellectual development from his earliest youth in Leipzig until the end of his life. This thesis served very well to prove that Leibniz could not have been influenced by Spinoza ever because he had finished the main features of his own philosophical system well before he could have read Spinoza’s Ethics. This thesis was first stated by Guhrauer (Guhrauer, 1842) and Trendelenburg (Trendelenburg, 1847) against Erdmann (Leibniz, 1840) and then by Gerhardt (Gerhardt, 1889) and others (Zimmermann, 1890) in 53

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LEIBNIZ AND SPINOZA Leibniz’s interest diminished during his mathematical rapture in Paris but it flared up immediately when he met Tschirnhaus, a personal acquaintance of Spinoza, who came from the Netherlands, where he had recently seen Spinoza. Tschirnhaus not only fuelled Leibniz’s curiosity about Spinoza’s personality, he also provided quite exhaustive information about the main positions of Spinoza’s metaphysics. We know this from a short but dense resumé of their talks about Spinoza (A VI, iii, 384–5; LOC, pp. 40–3). Leibniz’s interest is confirmed by Tschirnhaus’s request (via Schuller) for Spinoza’s permission to offer the Ethics in manuscript to Leibniz (Spinoza, 1995, p. 327). In addition, we have an excerpt of the TTP indicating a second thoroughgoing study of this book (A, VI, iii, 248–74), comments on Schuller’s excerpts from Spinoza’s letters to the Spinoza circle, especially his letter on the infinite (A VI, iii, 275–282; LOC, 101–17), quite some evidence for Leibniz’s insight into Tschirnhaus’s correspondence with Spinoza and moreover for the possibility that some of Tschirnhaus’s questions to Spinoza in 1676 resulted from discussions Leibniz had with Tschirnhaus (Stein, 1890, pp. 40–6; Goldenbaum, 1994, pp. 266–75; Kulstad, 1999a, pp. 69–85, and 1999b, pp. 245–62; Laerke, 2008, pp. 392– 437). Given the strength of his interest and the rereading of the TTP, it is more than likely that Leibniz finally read Spinoza’s demonstration of Descartes’s Principles (Spinoza, 1663; CWS, pp. 224–346). But the most impressive indicator of Leibniz’s enormous interest in Spinoza was certainly the route that Leibniz chose for his trip back to Germany. One can tell that he did not choose the shortest way in order to take up his service at the court of Hanover, where he had been expected with increasing urgency since spring 1676 (Antognazza, 2009, p. 176). On

But emphasizing the significance of his early Aristotelian teachers at Leipzig does not have the power to explain Leibniz’s innovations, or the development of his own position which was in no way eclectic as is often claimed (Mercer, 2001, pp. 23–59; Laerke, 2008, pp. 33, 74, 853) but aimed for thoroughgoing coherence. It is true, he was always conciliatory and open to negotiations, but he was adamant in his striving for a coherent, overarching philosophical system including mathematics, mechanics and sciences as well as law and morals. Whatever one may think about Leibniz’s possible debt to Spinoza’s philosophy, one thing can no longer be denied – that he was deeply interested in Spinoza’s ideas, from his first reading of the Tractatus theologico-politicus until the end of his studies of the Opera posthuma, that is, between 3 October 1670 and spring 1678, with interruptions, however. But even after this time of special interest in the infamous philosopher, Spinoza remains on Leibniz’s mind and Leibniz is always ready to recall a passage of Spinoza’s writings by heart as is clear from his encounters with Toland (Dragon, 2009; Dutens, 1768/1989, pp. 142–9) or his Animadversiones ad Wachterum (Leibniz, 1999; Schröder, 1987, pp. 59–123; Otto, 1994, pp. 95–101). The result of his first intense critical engagement with Spinoza was Leibniz’s Commentatiuncula de judice controversiarum, therefore to be dated more precisely at 1670–1. One of its remaining philosophical results is Leibniz’s specific notion of the idea clara et confusa. His interest is still present in his ‘early theodicy’, the Confessio philosophi (A VI, iii, 115–49), dated as 1672 or 1673, producing the conception of God’s intellect as including the necessary things and of God’s will as creating contingent things (Laerke, 2008, pp. 361–92). 54

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LEIBNIZ AND SPINOZA Europe-wide as the most infamous atheist, this is more than a remarkable interest – it really looks as if Leibniz had urgent questions for Spinoza and held high expectations. Thus, the simple (although correct) statement of the disagreement of these two philosophers or even the blunt denial that Leibniz struggled with Spinoza in this early period of his life is not helpful, as it does not address the question of the cause of his eager interest in Spinoza. Those who reject any impact of Spinoza on Leibniz (Mercer, 1999, pp. 273– 300; Mercer, 2001, pp. 19, 458) bear the burden of explaining the eager and at times risky interest of Leibniz in Spinoza. Leibniz had been a courtier and knew how to adapt to the rules, but he in no way resembled the caricature of the cautious, cowardly courtier that has been drawn of him recently (Stewart, 2006). In the following I want to focus on two rather specific theoretical pieces which were developed by Leibniz as a result of his struggling with his own problems as well as with Spinoza, without claiming these to be the only theoretical encounters of Leibniz with Spinoza. The first piece is interesting as it clearly indicates Leibniz’s acquaintance with Spinoza’s ideas as early as October 1670, that is, before he even published his theories of motion. The second piece is of still greater interest as it shows the intense presence of Spinoza’s ideas in Leibniz’s mind precisely during the period when he first developed the central concept of his mature philosophy, the notion of potentia agendi et patiendi together with the new measure of force mv2 in January and February 1678 (Fichant, 1990; Fichant, 1994). This breakthrough is clearly prepared during the years of 1675–7, that is, exactly during the years of Leibniz’s deepest interest in Spinoza. Thus these two pieces may challenge the traditional thesis of

his way, during his visit to London in October 1676, Leibniz copied and commented on three of Spinoza’s letters to Oldenburg (A VI, iii, 364–71). Thus he obviously talked with Oldenburg about Spinoza as well. That Oldenburg allowed Leibniz to see and even to copy these letters signifies an extraordinary trust between the two Germans. Moreover, that Oldenburg asked Leibniz to deliver his letter to Spinoza shows that they even talked about Leibniz’s planned visit to Spinoza. The odd fact that Leibniz would not deliver this letter when in fact visiting Spinoza – whatever the reason was – is obviously due to the enormous stress entailed in contacting the infamous atheist Spinoza (Malcolm, 2003). When Leibniz visited Spinoza, well prepared with writings formulated for the discussion, they met several times and discussed for hours (A III, ii, 327) particularly about various demonstrations of God. But according to one report, quoted by Foucher de Careil and since then lost (Garber, 2009b, p. 105; Laerke, 2008, pp. 368–9), their discussion also touched on Descartes’s rules of collision (FC, LXIV). Leibniz convinced Spinoza in spite of the latter’s hesitancy that they were all wrong – by his principle of aequipollence. That means Spinoza explicitly accepted this principle. Finally, we have Leibniz’s correspondence with Spinoza’s friend Schuller, starting right after Leibniz’s arrival in Hanover. After the death of Spinoza in February 1677, Leibniz tried to obtain Spinoza’s manuscripts and, when it had been decided to publish them, on the Opera posthuma (A II, i2, 474–7 and 574–5). Last but not least, we have Leibniz’s long letter to Duke Johann Friedrich from February 1677, where he also discusses Spinoza at length (A II, i2, 466–74). Given the danger for the soon-to-be courtier of meeting with a man known 55

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LEIBNIZ AND SPINOZA for 13 October 1670 (A, I, ii, 452; Laerke, 2008, p. 97) and Rüdiger Otto draws our attention to the interesting coincidence of Boineburg’s letter to Spizel and Leibniz’s letter to Thomasius written on one day, 3/13 October 1670 (A II, i, 105; Otto, 1992, p. 19). Otto takes this coincidence as an expression of their excitement about the book, although their attitude greatly differed. Whereas Boineburg did not express anything but indignation, Leibniz, as Otto sees it, immediately entered into a discussion about Spinoza’s argument. In fact, it is the content of Leibniz’s letter to Thomasius from this day which clearly shows that he had already – i.e. almost immediately – read the book. Otherwise, he could not have objected to Thomasius’s claim (Thomasius, 1693) (which he read at the same book fair) that Spinoza owed his argument about religion to Herbert of Cherbury (whereas his political theory followed the contours of Hobbes’s theory). Leibniz sees Spinoza in full agreement with Hobbes in both areas. Thus he did not take the seven dogmas in chapter 14 of the TTP as minimal dogmas of a natural religion as Herbert intended his five dogmas to be (and Laerke thinks Spinoza does too – Laerke, 2008, pp. 134–44). And Leibniz is right because Spinoza’s dogmas serve only as the condition which all positive denominations should include in their dogmatic doctrine in order to be tolerated. They are not religion in themselves. Leibniz’s position on the TTP is very ambivalent, however. It is quite clear that he shared Boineburg’s shock about and rejection of this book. This can be seen from his letter to Thomasius where he calls the book intolerable and impudent (A II, i2, 106). But from a letter of Tschirnhaus to Spinoza (via Schuller) in May 1676 (Spinoza, 1995, p. 327) we also know that Leibniz had held this book in high regard

the thoroughgoing continuity of Leibniz’s philosophical development while at the same time revealing how much Spinoza was on Leibniz’s mind when he worked with the greatest energy on a solution to his metaphysical problems – to overcome Spinoza.

LEIBNIZ’S FIRST ENCOUNTER WITH SPINOZA AND THE IDEA CLARA ET CONFUSA AS ITS REMAINING EPISTEMOLOGICAL RESULT Although Leibniz mentions Spinoza in a letter to Thomasius on 20/30 April 1669 (A II, i2, 24/L 94), there is general agreement that he did not yet know Spinoza’s demonstration of Descartes’s Principia philosophiae well, if at all (Spinoza, 1663; CWS, pp. 221–346). He rather counts Spinoza among a group of Cartesians. Thus Leibniz’s first intense study of Spinoza was that of the Tractatus theologico-politicus. His thoroughgoing acquaintance with the TTP has been doubted until recently (Parkinson, 1978, pp. 74–5), in spite of Leibniz’s many assertions that he did read the book (A I, i, 148 and 193; A II, i2, 277 and 320). However, this unjustified doubt vanished completely when I found Leibniz’s marginalia in a copy of the TTP which had been owned by Leibniz’s mentor the Baron of Boineburg since 1670 and to which Leibniz had access until March 1672 when he left Mainz for Paris (Goldenbaum, 1999a, pp. 93–5; Goldenbaum, 2008b). Thus it became absolutely clear that Leibniz had read this infamous book with a pen in his hand as soon as he obtained it in October 1670. After the general doubt has been removed we can trust the dates provided by contemporary statements. Mogens Laerke nicely points to the neglected bookseller’s bill 56

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LEIBNIZ AND SPINOZA Eucharist and the Trinity (A VI, i, 501–32), as well as in his letter to Johann Friedrich and its attachment (A II, i2, 169–85; Dascal, 1987, pp. 93–124; Fouke, 1992, pp. 145–59; Antognazza, 1994; Goldenbaum, 2002b; Antognazza, 2007). On the one hand, Leibniz had offered the ‘negative method’ against specific attacks on the mysteries as often put forward by Socinians. This method could only be applied, however, if they made particular claims which could then be refuted. He continued to use this method in his Theodicy against Bayle (GP VI, 49–101/H 73–122), showing that no single critique of the mysteries could ever succeed since the mysteries were vague and incomprehensible by definition and any objection could be disputed. On the other hand, he had come up with his new understanding of body and motion, minds and conatus, which provided him with the tools to show the possibility of transubstantiation or real presence of Jesus Christ in the Eucharist as well as of other mysteries. In the winter of 1670/1 he was just about to publish the Hypothesis physica nova and the Theoria motus abstracti which were supposed to provide the foundation of his argument (A VI, i, 219–76/L 139–42). When Leibniz came to read Spinoza’s TTP in October 1670, having (as he believed) just solved the entire problem of the mysteries, his fresh confidence was again threatened. Neither of his two methods of defending the mysteries would work against Spinoza’s critique of the mysteries. Spinoza neither attacked the mysteries by any formal claim which could be disputed nor did he question their possibility at all. He simply asked to be silent about those things we do not understand. Otherwise, we would speak like parrots or automata (Spinoza, 1670, chap. 13). It is impossible that Leibniz was not deeply concerned about Spinoza’s arguments. He had to work out a

and had written about this to Spinoza (Goldenbaum, 1999a, pp. 67–8). Spinoza in his answer remembers having received such a letter. Does this need to be a contradiction? Must Leibniz have been dishonest when he says he held the book in high regard? I think he could well have appreciated the objective argument of Spinoza and his great erudition on the one hand and still be alarmed on the other hand – no, he had to be even more alarmed because of his admiration for the learned man. The stronger Spinoza’s argument, the more dangerous it was. That this was indeed the position of Leibniz at the time of his first reading is supported by his great efforts, together with Boineburg, to initiate a campaign of learned Hebrew scholars to refute the linguistic arguments of the TTP instead of offering mere theological rejections or slandering of the author. I have presented the whole campaign elsewhere (Goldenbaum, 2004) but it can be said that the urgent pleas of Leibniz and Boineburg for learned refutations show how much Leibniz was concerned about problems concerning the comprehensibility of the Hebrew sources of the Bible as they had been raised by Spinoza. Obviously, Leibniz did not have sufficient Hebrew to deal with Spinoza’s arguments in the chapter 13 of the TTP about the equivocations of Hebrew, the lack of a Hebrew grammar and the loss of texts. Thus it was hard for Leibniz to judge whether Spinoza was right with his statement that some original Hebrew texts of the Bible will never be understood due to these problems (Spinoza, 1670, chap. 13). In order to understand fully the impact on Leibniz of Spinoza’s critique of the mysteries we need to remember that our philosopher had worked on a defence of Christian mysteries since 1668, as he tells Arnauld in November 1671 (A II, i2, 277). Traces of his struggle with the mysteries can be found in his works about transubstantiation, the 57

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LEIBNIZ AND SPINOZA 2. Leibniz discusses critically Spinoza’s argument that in speaking of the mysteries we would be speaking like parrots or automata, not understanding what we say, simply repeating words. Leibniz spends thirteen paragraphs (ibid., pp. 550–2, §§20–32) on the refutation of this argument – one-third of the first and longer part of the Commentatiuncula. Later Leibniz coins the term psittacisme for Spinoza’s argument (NE, ii, ch. 21, §13; A, VI, vi, 186).

new third strategy to rescue the Christian mysteries (Goldenbaum, 2002b). This time, Leibniz had to show that we can know the mysteries to the extent that when we say ‘This is my body’ we do not speak like parrots. At the same time he had to make sure that we do not fully understand what is going on in the mysteries as they would then cease to be mysteries. Thus he had to walk between Scylla and Charybdis. He took up this challenge in his Commentatiuncula de judice controversiarum (A I, i, n. 22) and thus I see this text as his first critical discussion of Spinoza. I have presented my argument at length in the article in which I first published Leibniz’s marginalia in Spinoza’s TTP (Goldenbaum, 1999a, pp. 76–93). It is not just the parrot in Leibniz’s Commentatiuncula which reminded me of Spinoza’s statement in the TTP as Laerke seems to assume (Laerke, 2008, p. 161). This speaking bird has of course been referred to quite often when meaningless speech was under discussion. It is the two chains of arguments together which made me think of the Commentatiuncula de judice as Leibniz’s first intense discussion of Spinoza’s TTP.

It is obvious that both questions were of the greatest importance for Leibniz as his intense efforts to defend the Christian mysteries were due to his newly won conviction that they were the specific difference of Christian religion. Any of the rationally understandable contents of this religion – as, for example, the command to love your neighbour – could be shared by nonChristians as well, Spinoza being an example. In paragraph 13 of the Commentatiuncula Leibniz goes in media res, suggesting that we consider only those Hebrew passages as essential for faith which agree in all versions, following the procedure of negotiations between Catholics and Protestants about their differing versions of the Bible. He argues that there are no disagreements in articles of faith of great significance in the original Greek text. Obviously, however, Leibniz is not so sure about the Hebrew. He simply states there should be agreement too even if the texts were more obscure. But the abovementioned campaign with Boineburg clearly shows that Leibniz feels the need of Hebrew scholarship to find a better argument against Spinoza’s dismissal of Christian mysteries. Concerning the epistemological parrot argument Leibniz is much more confident, although it is closely connected with that of the Hebrew equivocations. He states that belief is given to meaning and not to words.

1. Leibniz defends the unequivocal meaning of all propositions of the Hebrew texts of the Bible which are essential for Christian faith, in spite of all equivocal expressions in the original text. The problem of ambiguity in the Hebrew wording is extensively discussed by Spinoza. These equivocations, together with our lack of a full Hebrew vocabulary and (even more) a grammar, along with the incompleteness of the remaining manuscripts, guarantee that we will never understand all the texts of the Bible which have come down to us. Leibniz’s argument (A VI, i, 549, §§13–15) has to be seen in close relation with his above-mentioned effort to recruit Hebrew scholars. 58

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LEIBNIZ AND SPINOZA of the words. It is sufficient that we understand something and, although doubting it, or even inclining to another understanding, do not altogether reject it. Sometimes, Leibniz says, it is even enough to believe that any arbitrary meaning of the given words is true, especially in the mysteries, where the practice does not change whatever the meaning eventually will be (§22). Nevertheless, the intellect must not choose arbitrary words like a parrot but always needs to keep in mind some general, confused, and somehow disjunctive meaning, as is commonly held by peasants or any other common man about almost all theoretical things. This is the result: a confused cognition of the mysteries is sufficient for faith in mysteries as well as for distinguishing the believer from a parrot. Marcelo Dascal has pointed to the epistemological problem of empty words which still remains (Dascal, 1987, pp. 93–124). That Leibniz was aware of this becomes clear by his repeated warnings of empty words – sine mente soni (T, Prel. Disc. §66; GP VI, 88). That Leibniz was aware of his epistemological achievement by providing the new idea clara et confusa becomes clear simply from his later comments on Spinoza’s letters to Tschirnhaus (via Schuller) in April 1676. There Leibniz sensitively notices that Spinoza had distinguished between clear ideas simpliciter and clear and distinct ideas (A VI, iii, 276; LOC, 100–3).

Therefore it is not sufficient that we believe him who said ‘this is my body’ if we do not know what he said. We do not know what he said, however, if we only keep the words without their force. And as in his introduction to Nizolius (A VI, i, 398–476/L 121–30), Leibniz then argues that faith means to believe. Believing, however, means to take something as true (verum putare). There is no truth of words, however, but of things. Because, if somebody thinks that something is true, he feels that the thing is as the words indicate. Nobody can think if he does not know what these words mean. At least he has to think of their meaning. In paragraph 22, Leibniz calls this a not modest difficulty and in the following paragraph even a durissimus nodus. That Leibniz has in mind the passage fromChapter 13 of Spinoza’s TTP is clear from his own later formulation of Spinoza’s argument within the excerpt of the TTP produced during his stay in Paris. There he presents Spinoza’s opinion correctly but in wording that clearly resembles his former refutation in the Commentatiuncula: ‘Dei attributa credere tantum non scire nihil est. Nam ut credas intelligi opus est, at ista non aliis oculis quam demonstrationis intelliguntur.’ (‘To believe God’s attributes only, not to know them, is nothing. For in order for you to believe there must be understanding, but those attributes are not understood by other eyes than the eyes of demonstration’) (A VI, iii, 268 – my emphasis). In the following paragraphs of the Commentatiuncula, Leibniz develops an extended solution for the problem which is of the greatest significance for his epistemology. He answers Spinoza by his notion of an idea clara et confusa. He did not use this term in public, however, until his famous essay in 1684, the Meditationes de ideis, de veritate, et de cognitione (A VI, iv, 585–92). According to Leibniz, it is not always necessary for faith that we know the true meaning

LEIBNIZ’S SEARCH FOR A MENTAL PRINCIPLE ENABLING THE BODY TO REMAIN THROUGH MOTION AND HIS APPROPRIATION OF SPINOZA’S TERM POTENTIA AGENDI ET PATIENDI When Ludwig Stein claimed in 1890 that Leibniz was particularly interested in Spinoza during the late 1670s, his opponents answered 59

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LEIBNIZ AND SPINOZA January and February 1678. Thus it is written precisely within those weeks in which Leibniz intensely studied the Opera posthuma of Spinoza, which had just arrived from Amsterdam in January. In addition, Fichant emphasized that Leibniz had worked on the problems solved in De concursu corporum since his last two years in Paris and throughout 1677 (Fichant, 1974), i.e. again just in the period of Leibniz’s strongest interest in Spinoza according to Stein and recent research (for literature after 1985 see fn 14 in Goldenbaum, 2007). Richard Arthur in his instructive introduction to his edition of writings on the continuum (Arthur, 2001, pp. li–lxxiii) and most recently Daniel Garber in his enlightening monograph about Leibniz’s concept of body (Garber 2009b, 106–25), both emphasize Leibniz’s intense work on mechanical problems during the years 1675–8, i.e. during the period of his greatest interest in Spinoza. Does this coincidence of Leibniz’s interest in Spinoza and his breakthrough in January and February 1678 necessarily mean that De concursu corporum is due to Leibniz’s Spinoza studies? Not at all! Does this close chronological coincidence of two crucial intellectual activities of Leibniz in the period of 1675–8 – with a climax in both during the months January and February of 1678 – justify reopening the case of Leibniz and Spinoza due to new evidence? I certainly think so. Of course this cannot be the task of this short survey. I will rather point to the interesting and striking appropriation of one central concept of Spinoza by Leibniz, an appropriation, however, which is at the same time an adaptation, very similar to Leibniz’s appropriation of Hobbes’s conatus. I would like to recall the fact that Leibniz’s appropriation of Hobbes’s conatus, so widely accepted today, had been strongly rejected by Louis Couturat

this apparent challenge with one simple argument: Leibniz could not have been influenced by Spinoza because he had already developed the main structure of his mature philosophical system before he first obtained Spinoza’s Ethics, which happened only in January 1678. This answer did not really address Stein’s argument as he had already pointed to earlier sources from which Leibniz could have learned about Spinoza’s ideas. Today, however, with the full publication of Leibniz’s philosophical writings and letters from this period (AVI, iii and iv; A, II, i2; A III, i-iii; DSR and LOC), this argument no longer holds water at all. It is especially one group of texts of this period that clearly seems to display Leibniz’s fascination with the ideas of Spinoza (Kulstad, 1994; Arthur/Loptson, 2006; Laerke, 2008, pp. 439–556; Laerke, 2009) confirming Stein’s claim. I am speaking of those manuscripts that were named De summa rerum by their first editor Ivan Jagodinsky (Leibniz, 1913), after a headline used by Leibniz. These texts together with some other texts of the same period are now widely available under the same title in the Akademieausgabe, (VI, iii, 461–588). But the most important achievement for our understanding of Leibniz’s thinking within this period was the admirable edition of De concursu corporum by Michel Fichant in 1994. On the basis of this edition Fichant could show how this work was Leibniz’s decisive breakthrough to his new and mature metaphysical approach. It is in this manuscript that Leibniz came up with his new and crucial concept of force, mathematically backed by the new suggested measure of power as mv2. Thus it became clear that Leibniz did not yet have the main structure of his mature philosophy any time before February 1678. Most important, the crucial text De concursu corporum is well dated – at 60

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LEIBNIZ AND SPINOZA 1995, p. 325) as well as by Oldenburg (Oldenburg, xi, pp. 434–5). We know that the two young Germans had a great time together, discussing mathematics, exploring the mathematical Nachlass of Pascal and Descartes, and discussing metaphysics. But we also know that Tschirnhaus was a strong admirer of Spinoza and that Leibniz very often argued with him about the challenging philosopher. This becomes clear from a later remark of Leibniz to Tschirnhaus (A, III, ii, 425–6). Thus it is of no surprise that many texts from Leibniz’s brief year with Tschirnhaus in Paris show relatively sound knowledge of some major ideas of Spinoza. The obvious object of Leibniz’s renewed philosophical work of these years is again his critical discussion of Descartes’s rules of motion and the ongoing controversy of alternative rules stirred up since 1669 by Wallis, Wren and Huygens. Leibniz had already participated in this critical discussion in 1670/1 when he published his Hypothesis physica nova and the Theoria motus abstracti (A VI, ii, n. 40 and 41). These publications had signalled an earlier breakthrough, at the same time, in Leibniz’s struggle with Hobbes’s mechanical philosophy. His surprising solution had been the adoption or rather adaptation of Hobbes’s notion of conatus. He had developed a metaphysics built on mechanics considering bodies as constituted by motion, understanding motion as being caused by the conatus of the mind. When he now turned again to Descartes’s rules of collision in 1675/6, he had achieved a quite different level of competency. While he was a mere beginner in mathematics and mechanics in Mainz in 1670, he had now become one of the leading mathematicians in Europe and had just come up with the calculus. But why did he turn again to Descartes’s rules of motion at all? He knew quite well that they were long considered

(Couturat, 1901, pp. 457–72) when Ferdinand Tönnies first pointed to it in 1887 (Tönnies, 1887, pp. 557–73). Given the mathematical character of De concursu corporum, it seems very unlikely that Leibniz could have learned his dynamics from Spinoza. Although it is acknowledged today that Spinoza had good skills in mathematics and performed experiments related to mechanics and chemistry, he did not want to write either a book on mechanics or even on metaphysics but rather on ethics. And there is no doubt that it was Leibniz’s critical discussion of Huygens, Mariotte and Galileo as well as of Descartes that shaped his mathematical discussion of the rules of motion (Fichant, 1974, pp. 198–204; Fichant, 1990). Nevertheless, Leibniz’s new and very close friend Ehrenfried Walter von Tschirnhaus was convinced that Spinoza’s ideas on mechanics could provide solutions for physical problems left unsolved by Descartes. That he thought so is clear from a letter he wrote to Spinoza from London in January 1675 when he asked Spinoza to come up with his general physics (Generalia in physicis) pointing to the lemmata in Spinoza’s Ethics, part 2, after prop. 13. Tschirnhaus is especially interested in the definition of motion and wants to know how diverse things and different shapes can originate from an indivisible, unchangeable extension (Spinoza, 1995, p. 287). Note that this is just the problem Leibniz is also interested in at that time. But Spinoza put off his answer to Tschirnhaus. In September 1675, Tschirnhaus arrived in Paris and soon met Leibniz, at the latest on 1 October 1675, as we have a dated note about a talk he had with Tschirnhaus (A VI, iii, 380–1). The contact could easily have been mediated by Huygens to whom Tschirnhaus was recommended by Spinoza (Spinoza, 61

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LEIBNIZ AND SPINOZA providing hardly anything new in De concursu corporum. He pointed especially to the new principle of equipollence between cause and effect which emerged as early as August 1676 in Leibniz’s writings (Hess, 1978, pp. 190–1). Exaggerated as this was (the published version is of course much more moderate – Garber 2009a), Garber’s illuminating survey about Leibniz’s philosophical work in the years 1675–7 gives important evidence of how much Leibniz’s mathematical-mechanical breakthrough of 1678 did indeed grow out of his metaphysical considerations in the years before. Thus, in fact, Fichant, Breger, Stammel, Arthur and Garber all agree that Leibniz discussed the mechanical problems from the new beginning in 1675 in the light of metaphysical questions, using since summer 1676 his principle of equipollence between cause and effect and searching for a solution for the world system. But given the interest of Leibniz in a metaphysical conception of bodies in collision, what exactly fuelled his interest in these years? Already in 1670, while struggling with Hobbes, Leibniz wanted to find a way to show how bodies in motion could not be a self-sufficient foundation of an understanding of the world. In 1670, he tried a solution by dividing his approach into (1) a theory of abstract motion, providing merely geometrical rules of collision being in obvious disagreement to experience, and (2) a theory of concrete motion, adding the ether which would mediate the abstract rules of collision with those motions of bodies we can observe, thus bridging theory with experience and Descartes with his critics. Most important, however, he succeeded in implementing the mind as the active principle in his theory of abstract motion, concluding that the body is nothing but motion, clearly rejecting Descartes’s understanding of

to be wrong by Wallis, Wren, Huygens and more recently by Mariotte. With respect to his new breakthrough in De concursu corporum it is important to note that when he worked on these problems Leibniz was not interested in mechanics as such, but in the metaphysical problems related to mechanics. This has been emphasized already by Gueroult (Gueroult, 1934, pp. 1–9), then by Michel Fichant since 1972, by Hans Stammel (Stammel, 1982, p. 6), Herbert Breger (Breger, 1984, p. 120), Richard Arthur (Arthur, 2001) and Daniel Garber (Garber, 2009a; Garber, 2009b, pp. 99–125). According to Michel Fichant Leibniz was ‘looking for a global explanation and a universal understanding’. He underlines the difference of Leibniz’s approach from that of scientists: [Leibniz] did not search as did Huygens and Wallis for a means to specify the exchange of motion of different bodies as exactly as possible; he rather wanted to lay the grounding for the comprehensibility of the ‘world system’, a term used in De concursu corporum. It was on this level that the substitution had to take place which would allow for the use of mv2 as a real definition of force in single phenomena as well as in the unity of the whole. Thus the reform from which the Dynamics originated consists in the identification of the same formula for the calculation of particular effects of collision as for the discovery of the global constitution of the universe. (Fichant, 1990, p. 67 – my translation) Moreover, Daniel Garber, at a conference on The Young Leibniz in 2003 at Rice University, challenged the significance of De concursu corporum when he provocatively argued that Leibniz had developed all the necessary pieces already in the years 1675–7, 62

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LEIBNIZ AND SPINOZA De concursu corporum in 1678. Thus it will be the force which enables the bodies to remain the same despite being divisible to infinity, it will be the force which will be preserved in the ‘world system’, and it will be the force which will be the bridge between the world of bodies and that of morals, law and religion. Since the potentia agendi is considered a mental power, it does not come as a surprise that this new solution can serve to revive the doctrine of substantial forms (Arthur, 2001, p. lxxxii) and to support his theological project as Fichant points out (Fichant, 1994, p. 59). But how could Leibniz’s intense work on this solution in January and February 1678 relate to Spinoza? His reading of Spinoza’s Ethics in January/February 1678 seems to have been quite exciting as well. He clearly read it with a pen in hand, not only underlining but producing one of the more extended excerpts, which has come down to us (A VI, iv, 1705–64). However, his above-mentioned letter to Justel from these days seems to express some degree of frustration as well, as if he had expected something more. At the hint of Tschirnhaus regarding a ‘general physics’ in Spinoza’s Ethics, Leibniz might well have been looking for a more specific or even mathematical physical theory. Nevertheless, the Ethics did provide some interesting metaphysical ideas about the identity of bodies and about their power to resist motion, which could very well be of interest to Leibniz in his search for a conception of bodies and motion during these years. Moreover, it offered a metaphysical concept of power that was related to bodies as well as to minds. First of all, Spinoza offers an interesting concept of the individual body which is often neglected because he is considered the philosopher of the one substance whereas Leibniz

bodies defined as extension and Hobbes’s conatus, understood only as the smallest motion of bodies but embracing it as an active mental principle. When Leibniz came to Paris, he realized that he had to come up with a mathematical theory for motion as it is experienced instead of adding the mediation to experienced motion afterwards, if he wanted to convince such Cartesian scientists as Huygens or Mariotte. Moreover, his notion of a body as constituted by motion made it quite difficult (if not impossible) for him to understand how the resting body in case of a collision with a moving body would not vanish but remain the very same body. Richard Arthur emphasizes the contradiction between two positions Leibniz held at that time which he needed to fix. On the one hand, Leibniz accepted that bodies are actually infinite as they can always be infinitely divided into smaller bodies, finding still smaller bodies within bodies. I should note that Leibniz learned in March 1676 from a letter of Schuller to Tschirnhaus that Leeuwenhook in Delft had improved a microscope to such a degree that he could observe the daily growing of plants and particles of air (A IV, iii, 390). Leeuwenhook was to be one stop during Leibniz’s trip through the Netherlands in November 1676. Arthur argues convincingly, however, that Leibniz’s view of bodies as divisible into smaller bodies to infinity does not fit well with the other line of Leibniz’s thinking around 1676, that is, his critique of purely material wholes. Leibniz is convinced that only minds can be wholes due to his metaphysical project. But now Leibniz had to explain how bodies could ‘remain something’ instead of falling apart while being exposed to collision (Arthur, 2001, p. lxiii). Arthur sees Leibniz’s solution in his new concept of force or power as it has been worked out in 63

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LEIBNIZ AND SPINOZA certainly lacks any mathematical backing. Moreover, given the intention of Leibniz, Spinoza’s concept of the individual body provides obviously the wrong answer. Spinoza’s individual bodies can retain their identity without any need of a mind. But there is another concept in Spinoza’s Ethics which seems to have drawn Leibniz’s attention as we can see from his underlining and commenting (A VI, iv, 1722–3). I would like to point to the interesting but seldom recognized fact that the well-known Leibnizian term – potentia agendi et patiendi – is used by Spinoza for the central concept of his philosophy. Of course, although potentia agendi is not just a mental power for Spinoza as it will be for Leibniz, it is clearly a mental power as well. For Spinoza everything is in God, because God has infinite potentia agendi, while all its modifications, seen under the attribute of extension, i.e. as bodies, or seen under the attribute of thought, i.e. as minds/ideas, share this potentia agendi. However, since they are finite things, they limit each other, they both act and are acted upon, therefore they are constituted by potentia agendi et patiendi, in order to act as well as to endure or to remain. Thus Spinoza’s concept of potentia agendi et patiendi nicely connects not only God’s power with that of single modes, which all exist in God, but the power of the minds with that of bodies without a causal relation between them. As is well known, it is the concept of force or power that will become the central concept not only of Leibniz’s dynamics but also of his metaphysics and epistemology, his philosophy of morals, as well as his philosophy of law. What makes a body a unity, what makes it remain the same through time will be its mind, both together being a potentia agendi et patiendi. It is important to keep both aspects together, when speaking about

posited individual substances. Spinoza developed his concept of the individual body and its interaction with others in the lemmata after proposition 13 in part 2 of the Ethics and in the following scholium. It was these lemmata, to which Tschirnhaus had referred as a general physics and about which Leibniz must have heard from his friend. Given the intense discussion of Spinoza between the two young philosophers, I find it more than likely that Leibniz also knew Spinoza’s letters to Tschirnhaus and that they discussed them together and even wrote responses together (Goldenbaum, 1994; Kulstad, 1999a; Kulstad, 1999b; Laerke, 2009). Thus I consider Tschirnhaus’s repeated question to Spinoza about the origin of diverse bodies and their different shapes from homogenous extension (in May 1676) to be the result of his talks with Leibniz. However, Spinoza did not answer the question this time either. As a matter of fact, Leibniz did study the passages of the lemmata after proposition 13 in part 2 of the Ethics with particular interest, especially proposition 13, its scholium, the following lemmata 5–7, and the then following scholium – on memory (!) (A VI, iv, 1714–15) when he obtained the Opera posthuma in January 1678. According to Spinoza, a bodily individual can remain the same while exchanging parts with other individuals in its environment, it can grow and shrink, and it can move, without losing its identity as one and the same bodily individual. The identity of such an individual is preserved according to Spinoza as long as it keeps a certain ratio of motion and rest. With his notion of an individual, Spinoza offers an answer to exactly the question Leibniz was struggling with – how bodies can ‘remain something’ throughout time in spite of their divisibility and exposure to change. But it is of course a very general explanation and 64

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LEIBNIZ AND SPINOZA individual potentiae agendi et patiendi will become the individual moving minds (the substantial forms, acting forces) with their bodies (the enduring forces). I see it as a confirmation of his critical appropriation of Spinoza’s concept of the potentia agendi et patiendi that Leibniz embraces at this same time the idea that all things are animated – as did Spinoza (see Wilson, 1989, p. 104). Of course, the notion of potentia agendi et patiendi can be considered as simply an appropriation of Aristotelian scholastics or Protestant metaphysics of the time where Spinoza might have picked it up and changed it into his own concept. Moreover, Leibniz used similar expressions a few times before 1677, although always in writings on moral activity of humans, speaking of vis agendi or voluntas agendi. According to the information of Heinrich Schepers in 1994, the exact term potentia agendi et patiendi appears for the first time in Leibniz’s Confessio philosophi. However, it is quite obvious that it is only from the time of De concursu corporum that Leibniz will use the concept of potentia agendi et patiendi in a precise sense and in a thoroughgoing way, and it will become the pinnacle not only of Leibniz dynamics and metaphysics but also of his philosophy of law and of morals. The striking similarity of Leibniz’s understanding of actions and passions of substances to Spinoza’s approach, the actions consisting in growing power, the passions expressing decreasing power, has been recognized already by Catherine Wilson in her comprehensive and enlightening monograph about the emerging of Leibniz’s metaphysics (Wilson, 1989, p. 111). There she also provides an interesting explanation for Leibniz’s reason to adopt this position. His critical appropriation of Spinoza’s parallelism of body and mind has been recently suggested

Leibniz’s notion of force. It was particularly the potentia patiendi or resistendi which caught the interest of Leibniz and which would constitute the body as relatively stable over time as can be seen by many manuscripts from this period, especially in De concursu corporum. What I would like to emphasize here, however, is the fact that it is the notion of potentia which becomes the starting point in quite a few of the earliest manuscripts of De concursu corporum from January 1678, for it is now the potentia, necessarily equal in cause and effect, that are the basis of Leibniz’s account of the equation system (Leibniz, 1994, p. 145). Of course, Leibniz could not like the symmetry of Spinoza’s approach and he explicitly criticized it in his comments. But a parallel can be drawn here to Leibniz’s approach to Hobbes’s idea of conatus. I have argued elsewhere that Leibniz did not embrace this concept until he found out about the crucial role of the conatus in sensation in De homine – because it happens in a point (Goldenbaum, 2008a). I would suggest that Leibniz could adopt – or rather adapt as he did in the case of Hobbes’s conatus – Spinoza’s concept of potentia agendi et patiendi as soon as he learned how Spinoza’s whole theory of bodies and minds, affects and cognition, freedom and morals, law and politics, is built on the growing and shrinking potentia agendi et patiendi of human beings (and all natural beings or individuals). Thus this concept provides a foundation for a theory of morals, as well as a mechanical foundation for the ‘world system’. What Leibniz needed to change in order to appropriate Spinoza’s concept of potentia agendi et patiendi in his own way was just to cancel the symmetry between the two attributes of the one substance. Leibniz’s potentia agendi of God becomes mere mind. But even the 65

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LEIBNIZ AND SPINOZA In 1686 Leibniz finished his Institutiones generales, the Discourse on Metaphysics and the Systema Theologicum. He tested a first cautious draft of the main theses of his metaphysics on the leader of the Jansenists, using the Catholic convert Ernst of HessenRheinfels to urge the unwilling Antoine Arnauld to enter the discussion. He is well aware of the half-public character of this correspondence which is fuelled by the unpublished Discourse on Metaphysics. All he asked for was the acknowledgement of the influential Catholic cleric that his metaphysics was tolerable by the standards of his church. He seems to have settled upon opening the battle with Cartesianism and Spinozism when he leaves for Italy in 1687. There he is surprised by the publication of Newton’s Mathematical Principles, which open a new and very different line of arguments and force Leibniz to publish his dynamics as an alternative foundation of physics rather soon (Meli, 1993, pp. 95–110). When he returns to Hanover, it will be Newton and the English philosophy he has to struggle with. In contrast, Descartes, Hobbes and Spinoza had been overcome, so it seems. The first time that Leibniz was challenged by Spinoza was in October 1670 and he had to work out a solution to solve the epistemological problem raised by Spinoza. He did so in his Commentatiuncula de judice controversiarum by providing his new concept of a clear and confused idea, a remaining result for his own epistemology and for his defence of Christian mysteries. Leibniz then struggled with Spinoza’s metaphysical foundation during the years 1675–8, resulting in his adaptive appropriation of the potentia agendi et patiendi. He overcame Spinoza in spring 1678, in the same way he had overcome Hobbes in 1669/70, by adopting a central concept of the opponent, adapting it to his

in two different ways by a challenging but highly interesting article by Richard Arthur and Peter Loptson (Arthur/Loptson, 2006). But indeed, such a surprising (critical) appropriation and adaptation of Spinoza’s parallelism of attributes by Leibniz has been recognized earlier, as early as in 1755, by the Jewish philosopher Moses Mendelssohn (Mendelssohn, 1972, i, pp. 13–19). The Leibnizian Mendelssohn emphasized however, correctly, that Leibniz improved Spinoza’s solution by taking away the symmetry of extension and thought in God.

CONCLUSION It should be clear today that Leibniz developed his mature philosophy only after his breakthrough in 1678. Thus he certainly had sufficient time to study Spinoza in advance and he obviously did so. From this breakthrough in 1678 Leibniz steadily works out his mature philosophy, although without publishing it before his departure to Italy in 1687. However, he did begin to publish some on philosophy in 1682 (after a break since 1671). But instead of exposing his new metaphysical system to the public, he preferred to put little bombs in the cracks in the huge rock of Cartesianism. The first such bomb is certainly his critique of the Cartesian denial of final causes, backed by his admirable mathematical demonstration of the law of refraction (1682). The second published article was the Meditations on Cognition, Truth, and Ideas (1684), criticizing the Cartesians and offering his epistemological approach, including the clear but confused idea. The third is his famous Short Demonstration of a Remarkable Error of Descartes (1686), where he proudly offers his new measure of force. 66

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LEIBNIZ AND SPINOZA an opponent of Spinoza into his partisan. But Leibniz did not feel challenged by their arguments anymore as he knew them all and felt content with the way he had solved the problems. Rather he was annoyed by their insolence and enthusiasm. His late public mentions of Spinoza, however, show Leibniz rather relaxed and wise as if he had never been struggling so hard with Spinoza’s arguments. In the Nouveaux Essais (responding to Locke) he praised Spinoza for his emphasis on a priori knowledge against Boyle’s empirical approach, and in the Theodicy he openly tells how he met him – once upon a time. Note that it is this writing which he intended to publish as his credo and for which he took the greatest care to obtain a smooth reception! However, even with all the rather hostile remarks in the time between 1680 and 1705, Leibniz never denied the great stature of Spinoza and his ideas, although many of them were paradoxical. As he says in the Nouveaux Essais (NE455), he was not afraid even to quote Spinoza when he said something right and important. We should be aware what an uncommonly courageous public statement this was for his day.

own needs and using it to provide an alternative and improved theoretical solution of the problem – or so it seemed to him. Having overcome his opponent, he believed himself to have found an alternative solution to the problem at hand. As soon as he had found a solution, his interest in Spinoza decreased. However, the intense critical discussion of this amazing, although highly dangerous philosopher would have carved his arguments into Leibniz’s long-term memory. Whenever he was confronted again with Spinoza he could quote him by heart, as is obvious from the slight deviations of the original texts. His reaction to the mention of Spinoza varies during his life and very much depends on how sure he felt about his overcoming of Spinoza at that time. But even more it depended on how much he felt himself under attack for being a Spinozist (Bartuschat, 1981). Meanwhile, Spinoza served him well to be shown as a consequence of Cartesian metaphysics (Laerke, 2008, pp. 851–921). He could become still more excited if he was confronted with Spinoza’s impact on his contemporaries, such as the English deist John Toland, who wanted to discuss Spinoza with him or the German Spinozist and Prussian courtier Johann Georg Wachter, who had turned from

Ursula Goldenbaum

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5 MALEBRANCHE AND LEIBNIZ

differences between them. In what follows, I therefore seek both to present Malebranche’s metaphysical doctrines and to give the reader a sense for the way in which he deploys those doctrines in the service of his own overarching philosophical aims. (Given space limitations, in what follows I refer only to those works on which I have drawn directly in writing this piece. Readers interested in alternative, introductory presentations of Malebranche’s philosophy may consult Moreau, 2004; Pyle, 2003; the estimable and still unsurpassed Rodis-Lewis, 1963; or Schmaltz, 2009.) After giving an overview of Malebranche’s life and works, I present his main metaphysical doctrines; I conclude by considering Leibniz’s criticisms of some of Malebranche’s metaphysical doctrines, and address the systematic significance of the two philosophers’ differing metaphysical views.

Pierre Bayle judged Nicolas Malebranche to be ‘one of the greatest philosophers of this century’ (Bayle 1695–7, ‘Epicurus’ Note T). Leibniz gave due attention to the works of ‘the excellent author of the Search After Truth’ (T §204/GP VI 238), engaging with them throughout his philosophical career. The two philosophers met in 1675, towards the end of Leibniz’s time in Paris, and remained in epistolary contact until Malebranche’s death in 1715. Leibniz read and annotated many of Malebranche’s published works and engaged Malebranche’s doctrines in works of his own, including the ‘Discourse on Metaphysics’, the correspondence with Arnauld – a substantial portion of which, treated at length in Sleigh, 1990a, was dedicated to distinguishing Leibniz’s pre-established harmony from occasionalism – the ‘Conversation between Ariste and Philalethe’, and the Theodicy. (Most of Leibniz’s writings on Malebranche may be found in Robinet, 1955.) There has been considerable scholarly attention to the relation between certain of the metaphysical doctrines of Leibniz and Malebranche. Although much less attention has been given to the relation between these philosophers’ overarching systematic aims, I believe that the divergences in Leibniz’s and Malebranche’s approaches to particular topics in metaphysics reflect systematic

LIFE AND WORKS Malebranche’s lifetime overlapped with that of Louis XIV: Malebranche was born on 5 August 1638 and died on 13 October 1715. (It is tempting to think that his metaphysics, with its emphasis on the thoroughgoing 68

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MALEBRANCHE AND LEIBNIZ 1661, he was deemed to have a ‘mediocre mind’ – but he was nevertheless ordained in September 1664. The year 1664 was perhaps the most significant of Malebranche’s life: several months before his ordination, an encounter with Descartes’s newly published Treatise on Man occasioned the transformation of an indifferent student into a philosopher. ‘This study,’ Father Lelong writes, ‘gave him such a taste for philosophy founded on clear ideas that he renounced all other study in order to apply himself to it.’ Following ten years of study, in 1674 Malebranche published the first volume of Of the Search After Truth: Wherein Is Treated the Nature of the Mind of Man and of the Use that Must Be Made of It in order to Avoid Error in the Sciences (henceforth referred to as ‘Search’). Although most commentators tell the story of Malebranche’s encounter with the Treatise on Man, only one commentator, Henri Gouhier, even addresses the question of how a work on physiology could have occasioned Malebranche’s conversion to philosophy. Gouhier concludes his searching discussion: ‘Cartesian mechanism has two faces: it liberates matter and mind . . . it restores to the mind its own function of thinking and not of being the form of the body . . . Thus projected into a Christian mind . . . Cartesian mechanism evokes Christian echoes’ (Gouhier, 1926, p. 62). Gouhier’s remarks are suggestive, but he does not say just what Christian echoes are evoked by Cartesian mechanism. The following passage from Paul’s Letter to the Romans 7, to which Malebranche alludes at various points in his writings (see, inter alia, OM I, 15/LO xxxvii; OM IV, 88), is especially pertinent in this context: ‘For I delight in the law of God . . . But I see another law in my members, warring against the law

dependence of all aspects of the created world on God, may reflect the reality of life in the age of Louis XIV, the Sun King, who dominated all aspects of French life and society. This social context for Malebranche’s philosophy, hitherto neglected by commentators, merits attention.) Malebranche’s own life remains understudied, and it merits sustained treatment: an updating of André, 1886, a biography begun shortly after Malebranche’s death but not published until the nineteenth century – decried by Malebranche’s friend, Father Lelong, as burdened by ‘useless declamations’ and by ‘the author’s inventions’ (Gouhier, 1926, p. 4) – is long overdue. Relatively little is known about Malebranche’s youth, although sources testify that he was a sickly child who remained at home until the age of sixteen, when he entered the Collège de La Marche, where he studied philosophy for two years, from 1654 to 1656; from 1656 to 1659, he studied theology at the Sorbonne. He did not distinguish himself at either school. ‘Although he learned Latin and Greek well enough,’ Father Lelong reports, ‘he did not apply himself in the same way to philosophy and theology because he did not find them to his taste.’ In 1660, on the advice of his uncle, a canon of Notre-Dame of Paris, he took orders and entered the Oratory, which had been founded in 1611 by Cardinal de Bérulle. (Malebranche’s Oratorian background, and the relation between his thought and Oratorian spiritual life and teaching in particular and broader currents of French spiritual life in the seventeenth century, remains little studied, but it deserves in-depth attention if his philosophy is to be situated properly in context.) Malebranche was no more impressive at the Oratory than he had been at the Sorbonne or the Collège de La Marche – after his first-year examinations, in 69

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MALEBRANCHE AND LEIBNIZ Malebranche examines how the cognitive and conative faculties of the mind dispose Fallen human beings to error. Each of the first five books of the Search is devoted to a different faculty of the mind: the first three books treat the cognitive faculties – the senses, the imagination and the pure intellect – and the fourth and fifth books treat the conative faculties – the natural inclinations (including the will, the desire for the good in general, the principal natural inclination), and the passions. Malebranche focuses in these books of the Search on explaining the different ways in which the faculties can malfunction, but in identifying the malfunctions to which the mind is prone, Malebranche thereby also shows how these faculties ought to function so that these errors might be avoided. It is only once this background is in place, that Malebranche can turn, in the final book of the Search, ‘On Method’, to explaining how the mind should be used in order to seek the truth. Malebranche’s treatment of method leads to the unmasking of the ‘most dangerous error of the philosophy of the ancients’, the attribution of causal power to created beings, and the presentation of the antidote to that error, occasionalism, the doctrine that God is the only true cause. Occasionalism is one of the two doctrines – along with the ‘Vision in God’, his account of intellectual cognition – for which Malebranche is best known, and it serves as the starting point for the systematic investigation of divine providence in the Treatise on Nature and on Grace (1680) – henceforth referred to as ‘Treatise’ – which clarifies the nature of God’s causal activity in the realms of nature and of grace. The Dialogues on Metaphysics and on Religion (1688) – henceforth referred to as ‘Dialogues’ – widely considered to be Malebranche’s masterpiece, unites the

of my mind, and bringing me into captivity to the law of sin which is in my members.’ In light of Malebranche’s evident interest in this passage, combined with his references to the opposition between the interests of the body and the mind (see inter alia, OM II, 161–2/ LO 359–60; OM IV, 88–95), I hypothesize that one thing that the treatment, in the Treatise on Man, of the functions of the human body independent of the soul suggested to Malebranche was how to explain the war between the mind and the body, a war not only known to Paul but also central to the thought of Malebranche’s other philosophical mentor, Augustine. The war between the ‘law of the mind’ and the ‘law of the body’ is a manifestation of the effects of original sin: since the Fall, human beings are in bondage to the body and govern themselves in accordance with its ‘law’ – the needs and demands of the body. This is a grave error. As Malebranche writes in the Preface of the Search, ‘the relation that minds have to God is natural, necessary, and absolutely indispensable; but the relation of our mind to our body, although natural to our mind, is neither absolutely necessary, nor indispensable’ (OM I, 10/LO xxxiv). Malebranche admits that in order to show ‘that it is more of the nature of the mind to be united to God, than to be united to the body . . . it would be necessary to ruin the principal foundations of pagan philosophy, to explain the disorders of sin, to combat what is falsely called experience, and to reason against the prejudices and illusions of the senses’ (OM I, 10–11/LO xxxiv). Pagan philosophy, the disorders of sin, a false conception of experience, and the prejudices and illusions of the senses are all interrelated manifestations of the misconception that it is the mind’s nature to be united to the body. In order to combat this error, in the first five Books of the Search, 70

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MALEBRANCHE AND LEIBNIZ Over the course of his philosophical career, Malebranche was drawn into several polemical exchanges: the most famous was the lengthy and often acrimonious ‘quarrel’ with Antoine Arnauld, which began with Arnauld’s attack on Malebranche’s account of cognition in Of True and False Ideas (1683), and after several volumes of exchanges on that and related issues, extended to the topics of occasionalism, the nature of God’s operation in the realms of nature and of grace, and the nature of pleasure. Malebranche’s Treatise on the Love of God (1697), an intervention in the ‘quarrel of pure love’ between Fénelon and Bossuet, was prompted by attacks on Malebranche’s views, as was his final work, the Reflections on Physical Premotion (1715), a response to criticisms of his views on grace and freedom advanced by a certain Father Boursier. Leibniz, like Malebranche’s other contemporaries and most recent commentators, devotes the most attention to Malebranche’s most distinctive metaphysical and epistemological doctrines: occasionalism; his account of cognition; the Vision in God; and his accounts of God’s ordinary and special concurrence with the created world, that is, his accounts of nature and of grace. I begin my presentation of Malebranche’s metaphysical doctrines, however, by considering his philosophical starting point, the Fall, in order to show how his metaphysics reflects a distinctively Malebranchean philosophical vision.

projects of the Search and the Treatise: Dialogues 1–6 focus on the cognitive faculties, covering similar ground to Books 1–3 and the relevant Elucidations of the Search; Dialogues 7–13 explicate God’s nature and ways, mostly treating material first elaborated in the Treatise and further developed in exchanges with Arnauld following publication of the Treatise. The Search, the Treatise and the Dialogues have received the most sustained attention from commentators, and justly so, for they are Malebranche’s central systematic works. Malebranche did, however, write several other systematic works: the Christian Conversations (1677), a more popular presentation of his main philosophical ideas, written in dialogue form and emphasizing the moral and practical implications of the philosophical views elaborated more systematically and theoretically in the Search and the Treatise; the Christian and Metaphysical Meditations (1683) – henceforth referred to as ‘Meditations’ – sadly neglected by English-language commentators, which takes the form of a dialogue between the Word (Reason or Christ) and an unnamed philosophical interlocutor; the Treatise on Morality (1684) in which Malebranche articulates his account of ethics by appeal to the Order of perfections that human beings can cognize by means of the pure intellect; and the Dialogue Between a Christian and Chinese Philosopher (1712), which manifests Malebranche’s awareness of missionaries’ reports from China, and has even been called ‘the single best short exposition of his system’ (Lennon, 2007, p. 275). In a sense, Malebranche never finished presenting his system, for he substantially revised the text of the Search throughout his life – it went through six editions, all of which were marked by substantial additions – and published the final edition of it in 1712, only three years before his death.

THE FALL AND THE TWO UNIONS From Malebranche’s perspective, the Fall is one of the most significant events in the history of the world. (The only event that Malebranche takes to be more significant than the 71

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MALEBRANCHE AND LEIBNIZ us’. ‘The soul, ‘the chief part of [the human] being’ (OM I, 13/LO xxxv), is essentially united only to God, not to the body. Thus the relation between minds and God, is natural, necessary, and absolutely indispensable,’ Malebranche writes in the Preface to the Search, ‘but the relationship between our mind and our body, although natural to our mind, is neither absolutely necessary, nor indispensable’ (OM I, 10/LO xxxiv). Malebranche admits, as I noted above, that it is no easy task to demonstrate ‘that it is more of the nature of the mind to be united to God, than to be united to the body,’ since in order to achieve this end, ‘it would be necessary to ruin the principal foundations of pagan philosophy, to explain the disorders of sin, to combat what is falsely called experience, and to reason against the prejudices and illusions of the senses’ (OM I, 10–11/LO xxxiv). Counteracting the effects of the Fall should therefore be seen as at least one of the aims of the Search as a whole, and it is not altogether hyperbolic to see this as at least one of Malebranche’s overarching philosophical aims. One reason that it is so difficult to overcome the effects of the Fall is because, as punishment for the Fall and for turning away from God, the true good, to the good of the body, Adam’s mind was subordinated to his body (OM I, 76/LO 22). The Fall disordered the relation between mind and body, transforming the union or alliance of mind and body (OM I, 215/LO 102) into a dependence of the mind on the body, which leads human beings to take themselves to be their bodies (OM X, 104). Since human beings now take themselves to be their bodies, God is no longer the natural good of the human being – Malebranche says that God is now only the good of the human being by grace, not by nature (OM II, 163/LO 360) – and human

Fall is the Incarnation, which I treat below.) What is most significant about the Fall, for my purposes, is that it resulted in the subordination of the human mind to the body (OM I, 11–12/LO xxxiv–xxxv). It is the disorder of the Fall that occasions a false conception of experience, disposes human beings to be taken in by the prejudices and errors of the senses, and even disposes them to errors about the good. Although scholars have given relatively little attention to the Fall, attention to Malebranche’s conception of it is essential if one is to understand his philosophical aims. The philosophical starting point of Malebranche’s account of the Fall is his conception of the human being as composed of the really distinct substances of mind and body, each of which has its own proper good (OM I, 12/LO xxxiv–xxxv). According to Malebranche, bodies are only the good of bodies; the good of the mind is God, the true good and the proper object of human love (OM II, 79–80/LO 307–9), and Malebranche even says that if the mind loves bodies, it ‘debases and corrupts itself’ (OM IV, 38; see OM I, 9/LO xxxiii). The difference between the goods of the body and the good of the mind reflects the different relation between the human mind and the body, and the human mind and God, which emerges in the following passage from the Search: Our body is not us, it is a thing that belongs to us, but without which, absolutely speaking, we can subsist. The good of our body is therefore not our good. Bodies can only be the good of bodies . . . Our soul also has its good, namely that good which alone is above it, which alone conserves it [i. e., God] . . . (OM II, 161–2/LO 359) The good of the body is not the good of the human being, because the human body ‘is not 72

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MALEBRANCHE AND LEIBNIZ It is only by the attention of the mind that all truths are to be discovered, and that all the sciences are known; because in effect the attention of the mind is only its return and conversion to God, who is our only Master, and who alone instructs us of all truth, by the manifestation of his substance . . . and without the intermediary of any creature (OM I, 17–18/LO xxxviii).

beings no longer cognize God as their good by means of sensible pleasure, the natural mark of good (OM I, 72/LO 21).’ The good of the body having remained the only good that is now felt,’ Malebranche writes, ‘it necessarily acts on man with more force’ (OM II, 163/LO 363). This is problematic. Because post-lapsarian human beings feel pleasure only on the occasion of their experience of sensible things, they are inclined to take those things to be their true goods, thereby further strengthening their union with the body and weakening their union with God. Since it is sensations that give human beings information about the relation between things in the world and the body (see, inter alia, OM I, 153–4/LO 65–6; OM XII–XIII, 100/JS 62), post-lapsarian human beings attend chiefly to sensations and neglect pure cognitions, which alone reveal the truth about the nature of things. Malebranche’s best-known philosophical doctrines, the Vision in God and occasionalism, which I treat in the following two sections of this paper, may therefore be seen as intended, at least in part, to counterbalance these effects of the Fall, by bringing the reader to understand the nature of cognition and of the true good and thus to occasion his or her reorientation to God.

In the first chapter of the Search, Malebranche draws a distinction between two kinds of perceptions that is central to this project of redirecting his readers’ attention: ‘The first, that are called pure perceptions, are, as it were, superficial to the soul: they do not penetrate it and do not modify it sensibly. The second that are called sensible, penetrate it in a more or less lively manner. Such are pleasure and pain, light and colour, tastes, odours, etc.’ (OM I, 42/LO 2; cf. OM I, 408/LO 213). This phenomenological difference has cognitive significance, ‘for the mind applies itself to what touches it greatly, and it neglects to apply itself to things that do not touch it’ (OM I, 141/LO 59). Malebranche maintains that it is beneficial that the embodied mind should ‘apply itself’ to sensations. ‘It is necessary that [the mind] should have sensations of heat, cold, colour, light, sounds, odours, tastes . . . in order that it might remain united to the body. All these sensations apply it to the conservation of its machine’ (OM I, 385/LO 200). (Simmons, 2008 treats the biological significance of sensations according to Malebranche in particular and the Cartesians in general.) Yet the fact that the mind so applies itself has deleterious cognitive consequences. According to Malebranche:

COGNITION: PERCEPTIONS, IDEAS, AND THE VISION IN GOD By occasioning readers to recognize that knowledge is only acquired in attending to ideas in God, Malebranche seeks to bring his readers to withdraw their minds from the senses and thereby to turn their attention away from the body and towards God. Malebranche writes in the Preface of the Search:

generally, all the cognitions [connaissances] that the mind receives from the body, or are caused by certain movements of the body, 73

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MALEBRANCHE AND LEIBNIZ relation between the purported objects of knowledge: since one not only does not know the relation between the modifications of one’s mind, but one cannot even know, simply by considering the modifications of one’s mind, whether those modifications are modifications of one’s mind or of the body, Malebranche maintains that modifications of mind are entirely ‘obscure and confused’. Ideas, by contrast, present relations of extension and perfection that do admit of comparison, and so Malebranche thinks that ideas are not themselves perceptions, or modifications of the human mind. The epistemological distinction between knowing (connaître) and feeling (sentir) thus reflects an ontological distinction: the epistemology and ontology of cognition seem to be intertwined for Malebranche. According to him, perceptions are private mental states that cannot provide the basis for intersubjective knowledge claims. Since, according to him, knowledge concerns what is necessarily the case, and perceptions are not eternal states of the mind, perceptions cannot themselves be the objects of knowledge. Finally, since the human mind is not eternal, and knowledge claims regard what is eternal, the objects of human knowledge cannot themselves be modifications of the human mind, but must instead be modifications of an eternal mind. Malebranche concludes that the objects of knowledge, ideas, must be located in God.

are entirely false and confused, with respect to the objects that they represent, although they are very useful to the conservation of the body, and of goods that are related to the body (OM I, 19/LO xxxix). Although there is a phenomenological distinction between pure and sensible perceptions, there is no ontological difference between them: all perceptions are modifications of mind (OM I, 415/LO 218; OM XII– XIII, 45/JS 16). Perceptions must therefore be sharply distinguished from ideas, which are not modifications of mind. ‘It is true to say,’ Malebranche writes in the Dialogues, ‘that the soul is not a light unto itself, that its modalities are only darkness, and that it discovers exact truths only in ideas contained in Reason’ (OM XII–XIII, 116/JS 77). Consideration of Malebranche’s reasons for claiming that the modalities of the mind are obscure, and that truth may therefore only be achieved by consideration of ideas, illuminates both the Vision in God and its systematic significance in Malebranche’s philosophy. Malebranche insists on the epistemic insignificance of perceptions. It can be said that one has a clear idea of a being and that one knows its nature, when one can compare it with the others, of which one also has a clear idea, or at least one can compare the modifications of which the being is capable . . . one cannot compare one’s mind with other minds, in order clearly to recognize some relation among them; one cannot even compare the modes of one’s mind, its own perceptions, among themselves. (OM III, 167–8/LO 636; italics added)

The [intellectual] perception that I have of . . . extension . . . belongs to me, it is a modification of my mind. It is I who am aware of [qui aperçois] this extension. But this extension of which I am aware [que je aperçois]is not a modification of my mind. For I do very well sense that I do not see myself, when I think of infinite spaces, of a circle, of a square, of a cube, when I look at this room, when I turn my eyes towards

According to Malebranche, one may be said to have knowledge only when one knows the 74

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MALEBRANCHE AND LEIBNIZ the sky. The perception of extension is of me [is a modification of me, that is, of the human mind] . . . The perception that I have of extension cannot exist without me. It is therefore a modification of my mind. But the extension that I see subsists without me. For you can contemplate it without my thinking of it (OM XII–XIII, 45/JS 16; italics added)

error may only be rooted out through concerted attention to ideas. His doctrine of occasionalism, to which I now turn, is therefore tightly bound up with his conception of cognition.

OCCASIONALISM: CAUSALITY AND DIVINITY

All perceptions – including pure perceptions, or perceptions of ideas – are modifications of the mind; ideas, on account of their epistemic status, cannot be modifications of the human mind and must instead be located in God. (The metaphysical status of these ideas is a vexed question: Cook, 1998 forcefully argues that ideas are not modifications of God, but are the substance of God, seen from different perspectives as it is representative of created beings.) Although, according to Malebranche, the human mind is necessarily united to God, and therefore must always have ideas as the intentional object, or target, of its perceptions (OM XII–XIII, 46/JS 17), he nevertheless maintains that only pure perceptions enable the mind to gain access to ideas. Sensible perceptions, composed of a pure idea and an image, a modification of the mind, do not enable the mind to gain access to ideas, because the sensation distracts the attention of the mind from the idea and focuses it on the sensation itself. Consequently, Malebranche maintains that in order to discover the truth, agents must consult only ideas, not perceptions, and must seek insofar as it is possible to withdraw their minds from the senses. This methodological point is of special significance for him, for he thinks that the idea that finite beings are genuine causes reflects the prejudices of the senses, and that this

Malebranche introduces occasionalism in Book 6, Part 2, Chapter 3 of the Search, in a chapter entitled ‘the most dangerous error of the philosophy of the ancients’. While it might seem surprising that Malebranche would not advertise one of his most famous contributions to metaphysics in the title of the chapter in which he first presents that doctrine, this reflects the fact that the aim of the examination of the faculties of the mind undertaken in the Search – as manifest in the subtitle of the work – is to root out error in order that readers may thereby set out on the search after truth, freed of their erroneous epistemological preconceptions. In the Preface of the Search, as I noted above, Malebranche traces the general source of error to the reliance on the senses to which human beings are predisposed by original sin, a reliance enshrined in the Aristotelian commitment to the idea that ‘there is nothing in the intellect that is not first in the senses’. Malebranche even says of the Aristotelians that ‘if the heart is Christian, the mind is basically pagan’ (OM II, 310/LO 446). The error of attributing genuine causal power to bodies also derives from the senses (OM III, 207/LO 660). ‘When I see one ball hit another, my eyes tell me, or seem to tell me, that the one ball is the cause of the movement that it impresses 75

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MALEBRANCHE AND LEIBNIZ I think that the reason may be rooted in his own education. In 1678, according to Ashworth, 1986, p. 152, the Oratorians, purportedly coerced by the Jesuits, officially subscribed to substantial forms, real accidents and the Thomistic soul, thereby repudiating Cartesian positions. This would account not only for the virulence of Malebranche’s attack on Aristotelianism, it would also explain why he discovered Descartes only late in his studies and almost by chance. More work, of course, needs to be done in order to substantiate this hypothesis.) Malebranche seeks to prove that natural causes ‘are not true causes [i. e. are not genuinely causally efficacious] but only occasional causes’ by attending to ideas. According to Malebranche, human beings have ideas of only two kinds of finite things, bodies and minds. Consideration of the idea of body, which Malebranche, following Descartes, takes merely to be extension, reveals that bodies have no power to move themselves (OM II, 313/LO 448); when one considers the idea of finite minds, according to Malebranche, ‘one does not see a necessary connection between their will and the movement of any body whatsoever’ (OM II, 313/ LO 448).

in the other ball, for the true cause that moves bodies does not appear to my eyes’ (OM III, 208/LO 660). What is dangerous about this error, according to Malebranche, is that it predisposes those who fall into it to idolatry. Malebranche explains why this is the case by attending to the idea of cause. If one comes next to consider attentively the idea that one has of a cause or power to act, it cannot be doubted that this idea signifies something divine. For the idea of a sovereign power is the idea of the sovereign divinity, and the idea of a subordinate power is the idea of an inferior divinity, but of a true divinity, at least . . . if it is assumed that it is the idea of a power or a real cause. (OM II, 309/LO 446) If one takes created beings to be real causes, then, since ‘we should only fear and love what can be the true cause of good and evil . . . reason seems in a certain way to justify a religion similar to that of the pagans, and to approve the universal disorder of morals’ (OM II, 311/LO 446), and even to warrant the ‘adoration of leeks and onions’ (OM II, 311/LO 447). Malebranche writes: In order that the falsehood of this miserable philosophy can no longer be doubted, it is necessary to establish clearly the truths that are opposed to the errors of the ancient philosophers, and to prove in few words that there is only one true cause, because there is only one true God . . . that all natural causes are not true causes but only occasional causes . . . (OM III, 312/LO 448)

By contrast, when one considers the will of God, that is to say of an infinitely perfect and consequently omnipotent being, one knows that there is such a connection between His will and the movement of all bodies, that it is impossible to conceive that He should will that a body be moved, and that it not be moved. We ought therefore to say that there is only His will that can move bodies, if we wish to say things as we understand them, and not as we feel them. (OM II, 313/LO 448)

(Malebranche’s references to the Aristotelians in this context prompt a question: why does he devote so much attention, especially in the Search, to combating Aristotelianism? 76

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MALEBRANCHE AND LEIBNIZ since it is necessary that at every moment God create bodies either at motion or at rest, God is causally responsible at every moment for the existence of bodies. Consequently, according to Malebranche,

Created beings are not true causes, but merely serve as the occasion for God’s power to bring about some effect (OM II, 315/LO 449). Malebranche concludes: ‘There is therefore only one true God and only one true cause that is really a cause: and one must not imagine that what precedes an effect might be the true cause. God cannot even communicate His power to creatures . . . He cannot make them true causes, He cannot make them gods’ (OM II, 318/LO 451). The principle that underwrites Malebranche’s argument for occasionalism in the Search is his conception of cause: ‘a true cause is one between which and its effect the mind perceives a necessary connection’ (OM II, 316/LO 450). This definition of cause reflects the fact that Malebranche believes that metaphysical truths may be cognized only by the pure intellect, operating independently of the senses. The implication of this definition, of course, is that only God is a true cause, since the mind can perceive a necessary connection only between some effect and the will of an omnipotent being (OM II, 313–18/LO 448–51). In later writings, such as the Meditations and the Dialogues, Malebranche gives what appears to be a very different sort of argument for occasionalism. This argument starts from the distinction between a substance and its modifications, a distinction that he takes to be exhaustive (OM XII–XIII, 33–4/JS 7). Every body, according to Malebranche, must be created either at motion or at rest, for ‘there is a contradiction that a body might neither be at motion nor at rest’ (OM XII– XIII, 155/JS 111). Since it is God’s will that creates bodies, that same will must create bodies either at motion or at rest. According to Malebranche, God’s will is necessary both to create the world and all the creatures in it and to sustain it in existence – conservation is just continued creation – and

there is a contradiction that one body might move another . . . there is a contradiction that you might even move your chair . . . there is a contradiction that all the angels and demons joined together might even move a wisp of straw . . . For no power, however great one imagines it, can overcome, or even equal, that of God. (OM XII–XIII, 160/JS 155–6; see OM X, 50) Although this argument is only presented in terms of bodies – naturally, since it is bodies that are the objects of the senses, and since it is the attribution of causal powers to bodies that is ‘the most dangerous error of the philosophy of the ancients’ – insofar as the distinction between substance and modification applies to minds as well as bodies (OM XII–XIII, 33–4/JS 7), the argument could be applied, mutatis mutandis, to created minds as well as to bodies, simply by starting from the fact that it is a contradiction that one mind might move a body or bring about a change in itself or some other mind, although to my knowledge, Malebranche does not give such an argument anywhere in his writings. The role of the doctrine of continuous creation in Malebranche’s later arguments for occasionalism has received considerable attention, especially from English-language commentators, such as Nadler, 2000 and Sleigh, 1990b. It is taken to be a much stronger, because more general, argument for occasionalism than that offered in the body of the Search, since, unlike the argument given in the Search, it does not turn on Malebranche’s 77

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MALEBRANCHE AND LEIBNIZ exclaims in the Dialogues: ‘Nothing is more sacred than power. Nothing is more divine’ (OM XII–XIII, 167/JS 122; cf. OM XI, 166). The doctrine of occasionalism reflects the sanctity of the notion of power by establishing that God is the only true cause, but Malebranche somewhat surprisingly maintains that human beings do not understand the nature of causal power itself. ‘I do not give to human beings any distinct idea that answers to the words “power” and “efficacy” ’, the Word (i.e. reason), says in the Meditations, ‘because God has given no genuine power to creatures, and I ought only to give ideas in order to make known God’s works and the wisdom of His conduct’ (OM X, 96). Although, according to Malebranche, human beings are unable to understand the causal power by which God brings about effects in the world, they can understand the ways in which God brings about those effects, because ‘God only acts according to . . . reason: He depends on it in a sense: he must consult and follow it’ (OM III, 131/LO 614), and human beings also may consult that very same reason.

definition of cause, and instead starts from the doctrine of continuous creation, commonly accepted by most orthodox Christians. I am not convinced that Malebranche himself would have taken his arguments for occasionalism to be so very different: both turn crucially on the concept of divine omnipotence, although it is, of course, deployed very differently in the two arguments. Admittedly, in later works he does not emphasize his definition of causality to the extent that he does in the Search, but I am inclined to think that this merely reflects differences in the kinds of works in which he offers arguments for occasionalism. The aim of the Search is to train readers to use their minds properly in order to grasp the truth, and because the errors to which agents are disposed by the faculties of the mind have been unmasked in the preceding parts of the work, it can culminate in an appeal to the proper use of the pure intellect in order to grasp the truth of occasionalism. By contrast, neither the Meditations nor the Dialogues systematically investigates the faculties of the mind, and thus in those works Malebranche cannot appeal to the deliverances of the pure intellect but must instead argue from premises that could be accepted by non-Malebranchean philosophers.

If I were not convinced that all men are only reasonable because they are illuminated by eternal wisdom, I would doubtless be quite temerarious to speak of God’s ends, and to wish to discover certain of his ways in the production of His work. But since it is certain that the eternal Word is the universal Reason of minds, and that by means of the light that it spreads in us ceaselessly we can all have some interaction with God, it should not be objected that I consult that same reason . . . (OM V, 24–5)

OCCASIONALISM, THE DIVINE NATURE AND THEODICY In advancing the doctrine of occasionalism, as noted in the preceding section, and in accordance with Malebranche’s concerns for the deleterious effects of the Fall on the human cognitive condition, he seeks to bring his readers to recognize the dependence of all created beings on God’s causal power. This recognition glorifies God, for, as Aristes

The driving idea behind Malebranche’s attempt to justify the ways of God to man – the project that Leibniz later dubbed 78

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MALEBRANCHE AND LEIBNIZ has no limits, can even make a plan to produce anything external. But if you join Jesus Christ to his Church, and the Church to the rest of the world . . . you will raise to the glory of God a temple so august and holy that you will maybe be surprised that He set its foundations so late. (OM V, 15/R 112–13)

‘theodicy’ – is that human beings have access to the very same ideas – they both consult Reason – as God. Malebranche’s theodicy thus depends on his conception of cognition, and so, as Kremer, 1997 argues, Arnauld quite astutely begins his attack on the doctrines elaborated in the Treatise by trying to undermine Malebranche’s account of cognition. According to Malebranche, attention to ideas enables human beings to understand the nature and basis of God’s actions. Reason, Malebranche says, dictates that God can have no other end than his own glory, which he can only find in himself (OM V, 12/R 112), because the proper object of God’s will, the desire for the good in general, is nothing other than God himself. Malebranche explains in the Dialogues what it is for God to act for his glory:

‘If I put [Jesus Christ] at the head of all things; if I make him the chief end of God,’ Malebranche writes in the Treatise, ‘it is because I believe in this way to justify even the thought, or the desire, that God had to go beyond Himself by communicating Himself to creatures’ (OM V, 18). Although the Incarnation takes place after the Fall in the order of causes, it precedes the Fall in the order of reasons, since the Incarnation justifies the creation of the finite world in which the Fall occurred, thereby making necessary the Incarnation of Christ as redeemer. ‘It was therefore necessary that God create the universe for the Church, the Church for Jesus Christ, and Jesus Christ to find in him a victim and a sovereign priest worthy of the divine majesty’ (OM V, 20/R 114). Since God’s will is identical to his love for himself, and God cannot act except by his will, Malebranche believes that we can understand that

It is certain that God loves Himself and all His qualities necessarily. Now it is obvious that He can only act according to what He is. Therefore His work bearing the character of His attributes, of which He glorifies Himself, He gives honor to Himself. Because God invincibly esteems and loves Himself, He finds His glory, He takes satisfaction in a work, that expresses in some way His excellent qualities. Here therefore is one of the senses in which God acts for His glory. And as you see, this glory is not foreign to Him, for it is only founded on the esteem and love that He has for His own qualities. (OM XII–XIII, 203/JS 153)

God always acts in accordance with His own nature, always in a way that bears the character of His attributes . . . In a word, God does not have and cannot have any foreign law, any other Law, any other motive than the immutable order of His attributes or of His divine perfections. (OM VIII–IX, 1084)

The created world, therefore, is not the proper object of God’s love, since God is infinite, and the created world is finite. Thus, separate Jesus Christ from the rest of the creatures, and see if He who can only act for His glory, and whose wisdom

God can act only in accordance with Order, which demands that God acts in the simplest 79

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MALEBRANCHE AND LEIBNIZ simple ways, by means of an action that is always uniform, constant, and perfectly worthy of an infinite wisdom, and of a universal cause. (OM V, 148/R 196)

ways (OM V, 28/R 116); it is only insofar as both God’s work – the realization of the providential order – and the ways in which he brings about that work manifest the character of his attributes that creation can honour him. ‘It suffices for my end, that God acts by simple and general ways, because these ways are more worthy of Him than those that are particular, and that, among those simple and general ways, He chooses those that are most worthy of His wisdom, in relation to His work’ (OM V, 28). This principle underlies Malebranche’s account of God’s general and special concurrence with the created world – his account of the orders of nature and of grace – according to which God’s power is exercised in accordance with laws, and underlies Malebranche’s belief that occasionalism provides the only account of God’s general and special concurrence that reflects the divine attributes. Because God’s incomprehensible causal power is manifested in accordance with his wisdom, and is therefore governed by laws, human beings are able to understand the orders of nature and of grace, which I consider in turn.

The simplicity and universality of God’s ways, manifest in the fact that he acts in accordance with general laws, reflect his wisdom; the fact that God is the only real cause reflect his power. The fact that the order of nature must reflect both the power and the wisdom of God, however, in a certain sense constrains God’s action in the order of nature. God could have doubtless created a world more perfect than that in which we live. He could have, for example, made it in such a way that the rain, which serves to render the earth fecund, fell more regularly on the earth that had been worked, than in the sea, where it is not as necessary. But to make this more perfect world, it would have to have been the case that God change the simplicity of His laws, and that He multiply the laws of the communication of motion, through which [par lesquels] our world subsists; and thus there would no longer have been the proportion between the action of God and this so perfect world, as there is between the laws of nature and the world in which we live. (OM V, 29/R 116–17)

THE ORDER OF NATURE Malebranche thinks that occasionalism underwrites the only conception of nature befitting the Christian God.

Two aspects of Malebranche’s claim that God could have created a better world merit special note in this context. First, Malebranche is sanguine about the fact that there are limits on God’s action in the created world: ‘His wisdom makes Him as it were impotent [impuissant] . . . it obliges Him to act in the most simple ways’ (OM V, 47). Second, as Moreau, 1999 argues, this position reflects

I maintain . . . that it is God who does everything in all things; that the nature of the pagan philosophers is a chimera; and that, properly speaking, what is called nature is nothing other than the general laws that God has established to construct or to conserve his work by very 80

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MALEBRANCHE AND LEIBNIZ Malebranche here implicitly distinguishes between acting as a general cause, that is, acting in accordance with general laws, and acting as a particular cause, that is, acting in accordance with particular volitions. (The question of what it is for God to act by general laws is a controversial topic: for an entry into it, see the different interpretations offered in Nadler, 1993 and Sleigh, 1990a, pp. 152–5.) Only those effects that result from particular volitions are directly willed by an agent, and so it is only for those effects that the agent is responsible. Since natural events are determined in accordance with general laws, that is, in accordance with general volitions, determined by particular occasional causes, God himself does not directly will that particular natural events take place. Consequently, God is no more responsible for natural disasters, such as destructive earthquakes, than he is for the fact that rain falls and allows crops to grow.

the limits of Malebranche’s Augustinianism: in maintaining that natural evils are genuine evils, and not merely the privation or absence of goodness, Malebranche faces up to the reality of genuine suffering in the world, and does not explain it away as a mere privation. It can be said in a very true sense that God wishes that all His creatures should be perfect; that He does not will [qu’il ne veut pas] that children should perish in their mothers’ belly; that He does not love monsters; that He did not create the laws of nature in order to give birth to them; and that if He could, by ways that were just as simple, have made and conserved a more perfect world, He would not have established the laws, of which such a large number of monsters are the necessary consequence; but it would have been unworthy of His wisdom to multiply His volitions, to prevent certain particular disorders. (OM V, 35/R 119–20) Given that God is the only real cause, one might, however, wonder – as Arnauld did – how Malebranche is able to avoid the conclusion that God is the author of natural evil. Malebranche responds to this worry in an addition to the Treatise prompted by his exchanges with Arnauld.

THE ORDER OF GRACE The fact that Malebranche frequently uses rain as an example of a natural event paves the way for his extension of occasionalism from the order of nature to the order of grace, since grace is often compared to rain by the Church Fathers. In the Treatise, Malebranche maintains that the order of grace, no less than the order of nature, is law-governed. (I limit my discussion of grace to the grace of feeling, the grace of the Redeemer, the counterbalance to original sin, which Malebranche distinguishes from the grace of light, the grace of the Creator.)

If God made the earth for man, why are there so many sterile lands, why are there more oceans than habitable lands? It is because all this is a consequence of the simplicity of His ways. It is not because God wills by particular volitions that such a land lacks water, for this would be a formal disobedience [désobéissance formelle], this would be to find something to gainsay in God’s conduct, and to insult His wisdom (OM V, 36)

Thus, since God is a general cause, Whose wisdom has no limits, it is necessary, for the reasons that I gave before, that in the 81

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MALEBRANCHE AND LEIBNIZ about that grace was always distributed only to those who would accept it, and only to the extent that it was needed efficaciously to bring about its effects (OM V, 50/R 158; OM V, 55/R 162). This conduct would not be worthy of God, however – it would be unworthy of him to correct the unfortunate consequences of general laws by means of particular volitions – so he does not act in this way; human beings nevertheless have no right to complain about the distribution of grace, for its distribution in accordance with general laws reflects the power and wisdom of God. What inequities there are in the distribution of grace must be attributed to the occasional cause of grace, just as defects in the order of nature reflect the occasional causes of the laws of the communication of movements. The reason that there must be an occasional cause of the distribution of grace is because simply to appeal to God as a general cause is not to explain anything, since God is of course the cause of all things: causal explanation comes to an end with the determination of the occasional cause of some effect (OM V, 66–7). Malebranche maintains that Christ must be the occasional cause of grace, because it is only on account of Christ’s intercession with God that human beings even merit grace, and since it is in order to incarnate Christ that God created the world and, hence, permitted original sin, ‘it was appropriate [il était à propos] that He established him [Christ] as the occasional . . . cause of grace’ (OM V, 70/R 141). Since Christ’s desires regarding particular individuals are the occasional causes of the distribution of grace to those individuals, and since those desires reflect Christ’s human, rather than his divine nature, Christ sometimes errs with respect to which human beings ought to be given grace, which accounts for those defects that arise in the order of grace (OM V, 76).

order of grace, just as much as in the order of nature, He acts as a general cause; and insofar as He has as His end His glory in the construction of His church, He establishes the most simple and most general laws (OM V, 45/R 154) Malebranche believes that there must be general laws of grace because such general laws reflect the divine attributes better than particular volitions. The appeal to general laws of grace enables Malebranche to solve a theodicean problem regarding the distribution of grace akin to the problem of natural evil. In 1 Timothy, it is written that God wills that all men be saved; manifestly, however, not all men are saved, so there is a question how these apparently contradictory data may be reconciled. Malebranche deftly disposes of this apparent tension. God being obliged always to act in a manner worthy of Him, by simple, general, constant and uniform ways . . . He had to establish certain laws in the order of grace, as I proved that He had done in that of nature. But these laws, on account of their simplicity, necessarily have unfortunate [fâcheuses] consequences with respect to us: but these consequences do not merit that God change these laws . . . It is true that God could remedy these unfortunate consequences by an infinite number of particular volitions: but His wisdom, which He loves more than His work, His wisdom, the immutable and necessary Order, which is the rule of His volitions, does not permit it (OM V, 49–50/R 157) If God distributed grace by means of particular volitions, then he could of course bring it 82

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MALEBRANCHE AND LEIBNIZ Union of Soul and Body’: characteristically, the passage begins with an expression of apparent agreement with Malebranche’s view that finite substances have no genuine causal powers of their own.

LEIBNIZ ON MALEBRANCHE Given Leibniz’s irenic tendencies, it should be unsurprising that he often downplays the differences between his metaphysical views and those of Malebranche. The metaphysical views of Leibniz and Malebranche do, however, sharply diverge. I briefly present Leibniz’s main criticisms of Malebranche’s accounts of causation, intellectual cognition, and theodicy, and then address the systematic significance of the differences in their metaphysical views. Leibniz criticizes both of Malebranche’s arguments for occasionalism, that stemming from the definition of true cause (see Sleigh, 1990b, p. 171), and the argument from the doctrine that conservation is continued creation (see Sleigh, 1990b, pp. 172 ff.). The criticism of the latter argument turns on the attribution of genuine causal power to created substances, and its success depends on Leibniz’s ability to sustain a distinction between God’s causal power and that of created substances, a distinction that Malebranche thought could not be drawn (OM VIII–IX, 700–4). Since the pioneering work of Sleigh, 1990b, commentators have sought to make sense of Leibniz’s conception of divine concurrence, but the notion remains elusive, perhaps because, as Malebranche says, ‘this general and confused word “concurrence” . . . does not awaken any distinct idea in an attentive mind’ (OM I, 440/LO 231). Leibniz’s attempts to establish the doctrine of divine concurrence turn on his conception of substance, and in this respect, they intersect with his most famous and oft-repeated criticism of occasionalism as introducing a perpetual miracle into nature. A representative formulation of this criticism is to be found in ‘A New System of the Nature and Communication of Substances, and of the

It is quite true that, speaking with metaphysical rigour, there is no real influence of one created substance on another . . . . But in solving problems it is not sufficient to make use of the general cause and to invoke what is called a Deus ex machina. For when one does that without giving any other explanation derived from the order of secondary causes, it is, properly speaking, having recourse to a miracle. (GP IV, 483/AG 143) Leibniz’s objection is that occasionalism’s appeal to God as the one true cause – the ‘use of the general cause’ – explains all phenomena in terms of God’s causal power and thereby renders secondary causes explanatorily otiose. Leibniz’s criticism might seem to miss the mark. Malebranche maintains that natural phenomena such as apparent changes brought about in the mind by the body are to be explained by appeal to particular, natural causes, not by appeal to God, the general cause (OM III, 212–13/LO 662). Nevertheless, Leibniz would maintain that since Malebranchean secondary causes do not have true causal power, genuine explanations must invoke God, and so on Malebranche’s account, the explanation of all natural phenomena must ultimately be resolved into God’s causal power and, hence, would be miracles. From Malebranche’s perspective, this criticism is also misplaced: he explains natural phenomena, such as the apparent interaction between mind and body, by appeal to general laws, and he claims that God only works a miracle when he acts through a particular 83

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MALEBRANCHE AND LEIBNIZ Although Leibniz calls Malebranche’s views on cognition ‘fine thoughts’ (GP VI, 593/AG 268), he appeals to his own conception of substance in order to justify his rejection of the Vision in God (Jolley, 1988). ‘It appears to me,’ Leibniz writes in the ‘Discourse on Metaphysics’, that the doctrine of the Vision in God ‘arises from the fact that [philosophers] have not yet considered sufficiently . . . the full extent and independence of our soul . . . it must already have in itself . . . an active power’ (DM 29). Leibniz’s objection to the Vision in God thus seems to manifest similar considerations that underwrite his criticisms of occasionalism, namely the demand that all phenomena be explained in terms of the nature of the substance in question. Since, according to the Vision in God, the objects of intellectual cognition must be located in God, the mind’s capacity for intellectual cognition cannot be explained in terms of its own nature. Leibniz also rejects Malebranche’s theodicy. Near the beginning of the ‘Discourse on Metaphysics’, Leibniz implicitly criticizes the view that Malebranche seems to endorse, that God could have done better than he did, ‘because it seems . . . that the consequences of this view are entirely contrary to the glory of God’ (DM 3). According to Leibniz, if God could have created a better world, then it follows that this world is imperfect, and to hold this position is even ‘to find fault with his work’ (DM 3). What separates Leibniz and Malebranche here, as Rutherford, 1993 emphasizes, is a disagreement over the nature of God’s aims in creation: Leibniz’s God seeks to maximize perfection in the universe, but Malebranche’s God acts only for his own glory, in accordance with his own nature, and so cannot maximize absolutely the greatest amount of perfection in the universe, since he must be honoured both by his work

volition (OM V, 34). Leibniz has an altogether different conception of miracles from Malebranche: ‘strictly speaking,’ Leibniz writes in a letter to Arnauld, ‘God performs a miracle when He does something that surpasses the forces he has given to creatures and conserves in them’ (GP II, 93/AG 83). Malebranche, of course, does not believe that forces may be attributed to created beings (the attribution of forces to created beings would conflict with occasionalism): consequently, from Leibniz’s perspective, Malebranche obliterates the distinction between nature and miracles. The disagreement between Leibniz and Malebranche on this score is not merely limited to the correct characterization of the metaphysics of miracles: Rutherford, 1993 explains that implicit in Leibniz’s charge that occasionalism has ‘recourse to a miracle’ is the view that natural phenomena must be explained in terms of the nature of substances, in terms of the order of secondary causes. Underlying this criticism is the question of what constitutes nature: Leibniz’s criticism of occasionalism thus marks a rejection of Malebranche’s conception of nature itself. Leibniz’s emphasis on substances as fundamental to philosophizing motivates a further, related criticism of occasionalism. In ‘On Nature Itself’, Leibniz charges that occasionalism threatens to reduce individual substances into mere modifications of God: ‘since that which does not act, which lacks active force, which is robbed of discriminability, robbed finally of all reason and basis for existing, can in no way be a substance’ (GP IV, 515/AG 165–6). The basis for this charge, like Leibniz’s objection that occcasionalism constitutes a perpetual miracle, reflects Leibniz’s assumption that natural phenomena must be explained in terms of the nature of substances.

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MALEBRANCHE AND LEIBNIZ placed in them, and it can be said that everything else is made only for them, these very revolutions being adapted to the happiness of the good and the punishment of the wicked. (GP IV 479– 80/AG 140)

and the ways that he employs to bring about that work, and, consequently, may not be able to create absolutely the best possible world. Leibniz does not explicitly recognize the extent of the difference between these two positions: The ways of God are the most simple and the most uniform; that is, He chooses the rules that limit each other the least. They are also the most fruitful in relation to the simplicity of the ways . . . One can even reduce these two conditions, simplicity and fruitfulness to one advantage alone, which is to produce the greatest possible perfection, and, in this way, the system of the Reverend Father Malebranche in this matter is reduced to mine. (T §208/GP VI 241)

Leibniz’s concern for what Jolley, 2004 calls the ‘excellence of minds’ is manifest in his conception of human beings as substances with causal and cognitive powers of their own, in virtue of which they can imitate God and are thereby capable of forming a community with God (Mon. 85; cf. GP IV 479–80/ AG 140). Although Malebranche, no less than Leibniz, believes that human beings are created in the image of God (OM XI, 186–92), he denies that any created beings even approach the divine, and he believes that the only reason that human beings can come to form a community with God is because of the intercession of Jesus Christ. Indeed, from Malebranche’s perspective, Leibniz’s conception of the excellence of minds even verges on idolatry, because it implies that finite beings, as genuine sources of causal power, are worthy of love and esteem. Underlying the deep metaphysical divergences between Leibniz and Malebranche to which commentators have devoted the most attention is, I venture, a fundamental ethical disagreement about the nature of the relationship between God and human beings. The metaphysical differences between Leibniz and Malebranche thus reflect a gulf between their moral and religious outlooks.

Given the nature of Malebranche’s God, however, He cannot seek ‘to produce the greatest possible perfection’, and thus Malebranche’s and Leibniz’s theodicies are irreducibly opposed. We have seen that Leibniz’s criticisms of occasionalism and the Vision in God reflect his conception of substance: one reason that he is as concerned as he is with the notion of substance is because of the importance of one particular type of substance, minds or rational souls, which, he writes in ‘The New System of Nature’, are like little Gods made in the image of God, having within them some ray of the divine light. . . . minds have special laws which place them above the revolutions of matter by the very order that God

Sean Greenberg

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PART II: LEIBNIZ’S PHILOSOPHY

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6 LEIBNIZ’S METAPHYSICS: THE PATH TO THE MONADOLOGY

true and whether we have a right to make knowledge claims about certain of his fundamental principles is another matter and will not be addressed here. Understanding Leibniz’s thought, especially his metaphysics, is made difficult because he did not leave the philosophical world with a magnum opus like Descartes’s Meditations, Spinoza’s Ethics, Locke’s Essay or Hume’s Treatise; the one philosophical book published in his lifetime, the Theodicy (1710), is a straightforwardly popular piece that, while containing much of this thought, does not give the details and have the depth that one might wish. Rather the primary texts for students and scholars are his letters, his published and unpublished essays, and the myriad scraps of writing that he kept squirrelled away in his rooms. Moreover, Leibniz appears to go through constant revisions and refinements of his thought – possibly never arriving at a ‘system’ that completely satisfies him. And he expresses himself differently in different contexts, depending upon his audience and the particular nature of the debate. Thus, the student of his thought does not have an easy task. Nevertheless, there are sufficient clues in Leibniz’s writing for the process of

‘I consider the notion of substance to be one of the keys to the true philosophy.’ (Leibniz to Thomas Burnett, 30 January 1699: GP III, 245/AG 286)

INTRODUCTION Leibniz’s metaphysics is strange – or so it appears at first. Bertrand Russell summed up the feeling of many when he said that, upon first encountering Leibniz’s monadology, he believed it to be a ‘fantastic fairy tale’ (Russell, 1937, p. xvii). And it is still the case that when students first encounter Leibniz’s philosophy, they adopt an incredulous stare. This essay presents the basic outlines of Leibniz’s metaphysics: from his theory of truth and the great principles of all human reasoning, to his account of substance, idealism and phenomenalism. (Leibniz’s theory of causation will be treated separately.) When seen in their proper context, Leibniz’s philosophical views on truth, substance, matter and mind represent an important and fascinating theory of the way the world is. Further, his deep reflections on metaphysics reveal him to be truly a philosopher’s philosopher. Whether his philosophy is 89

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LEIBNIZ’S METAPHYSICS (Mercer, 2001). This view, however, is very much in the minority and will largely be ignored here. Rather, the story told here will begin in Hanover, when Leibniz first claims to have restored the substantial forms of scholastic philosophy. Even here there is substantial disagreement among Leibniz scholars: it has been argued that (b) Leibniz endorsed a ‘quasiAristotelian’ ontology, in which the fundamental beings are ‘corporeal substances’ or hylomorphic compounds of form and matter, from the late 1670s to at least the 1690s, when he finally endorsed an idealistic metaphysic of monads (Garber, 1985 and 2009); it has been argued that (c) Leibniz was committed to an ontology of simple, mind-like substances in these ‘middle years’ (Sleigh, 1990; Adams, 1994; Rutherford, 1995); and it has been argued that (d) he was committed to the reality of corporeal substance throughout his career (Phemister, 2005; Hartz, 2008; Smith, 2011). It has also been argued that (e) he is committed simultaneously to conflicting metaphysical theses, a subset of which can entail the reality of corporeal substance, another subset of which can entail a commitment to monads (Wilson, 1989). This essay seeks to develop view (c) and to show that Leibniz’s metaphysics had as its fundamental or primary beings souls, forms or minds from the 1680s on. In his groundbreaking study, Russell claimed that he was able to overcome his impression that Leibniz’s metaphysics was a fantastical tale once he grasped its logical foundations, and he went on to claim that all of his metaphysics is reducible to five basic premises (Russell, 1937, p. 4). There are reasons to be critical of Russell’s interpretation, especially with its emphasis on the logical dimension of Leibniz’s thought, but it is certainly helpful to understand Leibniz’s metaphysics of substance as arising in part from his conception of truth. Indeed,

philosophical interpretation and rational reconstruction of Leibnizian arguments to succeed. Indeed, the first clue is contained in his autobiographical account to Nicolas Rémond (also mentioned in the introductory chapter). There he claims that as a youth he turned from the scholasticism of his schooling to the modern, mechanical philosophy. But, according to Leibniz, when I looked for the ultimate reasons for mechanism, and even for the laws of motion, I was greatly surprised to see that they could not be found in mathematics but that I should have to return to metaphysics. This led me back to entelechies, and from the material to the formal, and at last brought me to understand, after many corrections and forward steps in my thinking, that monads or simple substances are the only true substances and that material things are only phenomena, though well founded and well connected. (GP III, 606/L 655) In other words, Leibniz’s mature metaphysics is one that starts with the rehabilitation of substantial forms and ends with his metaphysics of simple substances or monads. The first question to be addressed in this essay is when and why he rejected a strictly mechanistic picture of the world and was led from the material to the formal. The second question is how he arrived at his idealistic metaphysics of monads. The first question can be answered relatively easily and straightforwardly, the second question less so. In fact, in Leibniz scholarship a number of competing interpretations have arisen that purport to explain when Leibniz adopted his idealistic theory of simple substances or monads. For example, it has been argued recently that (a) his philosophy was largely in place by the time he left for Paris 90

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LEIBNIZ’S METAPHYSICS will deal with his account of modality and his account of causation.)

one may safely say that one pillar of his metaphysics is his logic and his conception of truth. A second pillar or ground of his metaphysics relates to his rejection of the Cartesian account of body or corporeal substance. This physical, or natural philosophical, element of his thought is constant in his mature thought and ultimately explains his emphasis on the essential unity and activity of substances. Finally, along with the logical and physical pillars of Leibniz’s metaphysical thought, there is a third part of the foundation of his metaphysics: a theological one, which represents the Christian Platonist (or neo-Platonist) strand in his thought. Separate essays have treated the philosophies of Descartes, Spinoza and Hobbes, against whose metaphysics Leibniz rebelled most forcefully. But, very briefly, Leibniz’s main points of contention are three. First, according to the Cartesian account of corporeal substance, the essence of body is extension and, therefore, body or matter is infinitely divisible. Second, according to Hobbes and Spinoza (and most of the moderns, from Leibniz’s point of view), the world unfolds with strict necessity and could not have been other than it is. Third, Descartes, Spinoza and Hobbes and all the moderns reject final causes and seek to explain the world solely in terms of efficient causation. For Leibniz, the Cartesian account of body cannot explain the essential unity and activity of substance; a science without teleology lacks explanatory power and completeness; and a necessitarian world destroys human and divine freedom. These three criticisms lead Leibniz to substantial forms and a kind of teleology in the world, and they also parallel the three modes of his philosophy mentioned above. (This essay will mainly be concerned with Leibniz’s metaphysics of substance and will, therefore, focus principally on the first issue. Separate essays

THE REHABILITATION OF SUBSTANTIAL FORMS In late 1678 or early 1679, Leibniz began to conceive of a new project, the Elementa Physicae (Elements of Physics), which he would never complete. He did, however, compose a Conspectus for this work, where he makes explicit criticisms of the modern, mechanical philosophy that he claimed to adopt while a youth. In his view, souls or forms are necessary because, without them, bodies would be infinitely divisible and have no being, and he appeals explicitly to the neo-Platonic notion of the causal relation between souls and the divine intellect. Certain things take place in a body which cannot be explained from the necessity of matter alone. Such are the laws of motion, which depend upon the metaphysical principle of the equality of cause and effect. Therefore we must deal here with the soul and show that all things are animated. Without soul or form of some kind, body would have no being, because no part of it can be designated which does not in turn consist of more parts. Thus nothing could be designated in a body which could be called ‘this thing’, or a unity. On the nature of the soul or form; that there is a kind of perception and appetite which are the passions and actions of the soul. And why; because souls result from God’s knowledge of things, or they are imitations of the ideas. (A VI, iv, 1988–9/L 278–9) Later, in a draft preface to the work, Leibniz also reveals his underlying conception of 91

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LEIBNIZ’S METAPHYSICS ascribe a substantial form and perception, or a soul, to man alone is as ridiculous as to believe that everything has been made for man alone and the earth is the centre of the universe. (A VI, iv, 2008–9/L 288–9)

metaphysics and natural philosophy and deepens his critique of contemporary mechanistic views of the world. Ultimately, there must be a reconciliation of scholastic and mechanistic philosophy. But what form will this reconciliation take? According to Leibniz, philosophers need final causes as well as efficient causes in a full explanation of things, for the world can only be understood when one recognizes that it is a product of a divine mind; metaphysics must be combined with mathematics (and mechanism) because metaphysics furnishes the philosopher with the concepts of being, causation and mental activity. Thus, Leibniz writes:

In the last line, however, Leibniz reveals (again) his somewhat surprising advocacy of a neo-Platonic idea: that there is a kind of animation at every level and in everything in the world. What is very Leibnizian, as will be shown more clearly below, is that sensation (perception) and appetition will be in all things. By the fall of 1679, Leibniz is confident enough of his newly found synthesis of scholasticism and mechanism that he announces his ‘restoration of substantial forms’ to his Hanoverian patron, Duke Johann Friedrich. Explaining his earlier project of the Catholic Demonstrations (begun in Mainz under the Elector Johann Philip), Leibniz writes the following:

[T]hose who are wise know that every effect has a final as well as an efficient cause – final because everything that happens is done by a perceiving being, efficient because everything that happens naturally in a body takes place through the corporeal organ and according to the laws of bodies. If those who oppose mechanical laws had known that these laws themselves are finally resolved into metaphysical reasons and that these metaphysical reasons arise from the divine will or wisdom they would not have so strongly opposed mechanistic explanations. . . . Here it will be well, however, to explain a little more distinctly how a middle way can be found, in my opinion, between the scholastic and mechanistic basis for philosophy; or better, in what sense there is truth on both sides. . . . Mathematical science provides magnitude, figure, situation and their variations, but metaphysics provides existence, duration, action and passion, force of acting, and end of action, or the perception of the agent. Hence I believe that there is in every body a kind of sense and appetite, or a soul, and furthermore, that to

There is another important thing in my philosophy which will give it access to the Jesuits and other theologians. This is my restoration of substantial forms, which the atomists and Cartesians claim to have exterminated. It is certain that without these forms and the distinction that exists between them and real accidents, it is impossible to explain our mysteries. For if the nature of body consists in extension, as Descartes claims, it involves a contradiction, beyond all doubt, to maintain that a body may exist in many places at once. (A II, i2, 754/L 261) The restoration of substantial forms takes on an important theological role, of course; it is that which will help to explain the mysteries of the Christian faith, principally 92

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LEIBNIZ’S METAPHYSICS Let us call this the ‘predicate-in-notion principle’ (PIN). The PIN principle is closely connected with ‘the two first principles of all reasoning’: the principle of contradiction (PC) and the principle of sufficient reason (PSR). As Leibniz puts it in another writing of the same period, his Specimen Inventorum de Admirandis Naturae Generalis Arcanis (Specimen of Discoveries About Marvelous Secrets of a General Nature), there are two first principles of all reasonings:

transubstantiation. Since Leibniz was a Lutheran and therefore not obliged to hold the doctrine of the real presence of Christ in the Eucharist, it is uncertain that this should count as a real reason for his appeal to substantial forms. Yet, it is clear that he believes that he has found a use for substantial forms in other realms, most notably in his physics and metaphysics as mentioned above.

a principle of contradiction, to the effect that every identical proposition is true and its contradictory is false; and a principle of the need for giving a reason, to the effect that every true proposition which is not known per se has an a priori proof, or, that a reason can be given for every truth, or as is commonly said, that nothing happens without a cause. (A VI, iv, 1616/MP 75)

SUBSTANCE IN THE 1680S: THE COMPLETE INDIVIDUAL CONCEPT AND ITS CONSEQUENCES Among the many projects that he turned to in his first decade in Hanover, Leibniz spent considerable time working on an improved logic. While his logical thought is treated separately in this book, it is important that one aspect of his views be considered here, for this has a strong bearing on his metaphysics. In these logical works of the 1680s and in the works that straddle the boundary between metaphysics and logic, Leibniz reveals a deep commitment to a certain conception of truth, according to which a proposition is true if and only if the concept of the predicate is contained in the concept of the subject. In a short piece from late 1685 to mid-1686, Leibniz expresses his view in the following way:

While Leibniz presents these three logicometaphysical principles as if they were innocuous and obviously unproblematic, they underlie much of Leibniz’s metaphysics of substance; indeed, he draws very strong consequences from them. In the Discourse on Metaphysics, written in the same period as the above-mentioned logico-metaphysical works, Leibniz gives one of his most famous accounts of the nature of individual substance. Noting that the Aristotelian idea that a substance is that which is the subject of predication and which cannot be predicated of something else is insufficient for a true analysis of the nature of substance, he then invokes the PIN and PC. Since it is the case that in every true predication the concept of the predicate is contained in the concept of the subject, he writes in §8, ‘we can say that the nature of an individual substance or of a complete being is to have a notion so complete that it is

An affirmative truth is one whose predicate is in the subject; and so in every true affirmative proposition, necessary or contingent, universal or particular, the notion of the predicate is in some way contained in the notion of the subject, in such a way that if anyone were to understand perfectly each of the two notions just as God understands it, he would by that very fact perceive that the predicate is in the subject. (A VI, iv, 1515/MP 96) 93

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LEIBNIZ’S METAPHYSICS when we consider carefully the connection of things, we can say that from all time in Alexander’s soul there are vestiges of everything that has happened to him and marks of everything that will happen to him and even traces of everything that happens in the universe, even though God alone could recognize them all. (A VI, iv, 1541/AG 41)

sufficient to contain and to allow us to deduce from it all the predicates of the subject to which this notion is attributed.’ (A VI, iv, 1540/AG 41) In other words, Leibniz proposes the following definition of substance: (1) x is a substance if and only if x has a complete individual concept (CIC). The hallmark of the complete individual concept is that it contains within it all predicates past, present and future of the substance. According to Leibniz, this entails that the CIC individuates substances; it picks out its bearer from an infinity of other finite created substances. To use Leibniz’s example, consider Alexander the Great. The concept of Alexander contains the predicates being a king, being the student of Aristotle, conquering Darius and Porus, dying in India, and so on. Indeed, according to Leibniz, ‘God, seeing Alexander’s individual notion or haecceity, sees in at the same time the basis and reason for all the predicates which can be said truly of him’ (A VI, iv, 1540–1/AG 41). Thus, the complete individual concept is just a metaphysical extension of Leibniz’s predicate-in-notion principle of truth and his commitment to the principle of sufficient reason for contingent truths. But Leibniz’s appeal to the Scotist notion of a haecceity is interesting and important, for he is thereby indicating that Alexander’s thisness is determined by the complete set of his qualitative properties. The further metaphysical aspect of this logical conception of substance is that the complete individual concept of a substance is the notion or essence of the substance as it is known by God. There is another important corollary to this conception of substance that Leibniz immediately emphasizes in this section: the doctrine of marks and traces. According to Leibniz,

The doctrine of marks and traces, therefore, claims that, because the CIC contains all predicates true of a substance past, present and future, the entire history of the universe can be read (if only by God) in the essence of any individual substance. In the following section (§9) of the Discourse on Metaphysics, Leibniz points to the ‘notable paradoxes’ that follow from this conception of substance, and these paradoxes include some of the central tenets of his metaphysics. Unfortunately, Leibniz’s reasons for drawing these consequences are not in all cases obvious. His list is the following: (a) No two substances can resemble each other completely and be distinct. (b) A substance can only begin in creation and end in annihilation. (c) A substance is not divisible. (d) One substance cannot be constructed from two. (e) The number of substances does not naturally increase and decrease. (f) Every substance is like a complete world and like a mirror of God or of the whole universe, which each expresses in its own way. The first paradoxical consequence of his account of substance is his famous principle of the identity of indiscernibles (PII). How does the PII follow from the logical account of substance? In the other short and classic 94

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LEIBNIZ’S METAPHYSICS guarantee that the substance begins with creation and ends in annihilation. But if to the complete individual concept thesis is added its corollary that each substance is a mirror of the entire universe, then it does follow, for each substance contains truths about its relation to the rest of creation. It is also not obvious at first glance why Leibniz’s third and fourth consequences should follow. In fact, Leibniz nowhere gives an argument for these claims, but it must run approximately thus. Let substance x have within its complete individual concept predicates g, h, i . . . which are true of its past, present and future. Imagine x were to be divided into xα and xβ. Yet, it cannot be the case that the two new substances would have all of x’s pre-division predicated in common and unique predicates thereafter, for Leibniz’s thesis in the CIC is such that all predicates past, present and future are deducible from it. In other words, the pre-division predicates cannot entail different sets of post-division predicates. In other words, if g, h, i, . . . imply lα, mα, nα, they cannot also imply lβ, mβ, nβ. A similar argument works against the possibility of the fusion of two substances. Moreover, if PII is already in Leibniz’s metaphysical arsenal, then it should be clear that the substance having within its CIC predicates g, h, i, . . . lα, mα, nα, and the substance having within its CIC predicates g, h, i, . . . lβ, mβ, nβ are numerically distinct substances and not simply one substance in its pre-division phase that has multiplied. As for Leibniz’s fifth consequence, it should now be clear that since substances can only naturally arise during God’s creation of the world and cannot undergo fusion or fission, the number of substances must remain constant. Finally, if it is the case that it is of the nature of a substance to have a notion so complete that one can deduce from it all its predicates past, present and future and if substances exist

exposition of his philosophy from this period, the Primary Truths, Leibniz derives PII from PIN, PC and PSR and uses PII to argue that each substance has a CIC (see A VI, iv, 1644–6/AG 30–2). In other words, the argumentative structure of that piece is different – and probably superior. Nevertheless, one can reconstruct Leibniz’s argument in the following way. Since in every true affirmative proposition, the predicate is contained in the subject, if two things differ, ‘it certainly must be possible to explain why they are different [from PSR], and that explanation must derive from some difference they contain [from PIN]’ (A VI, iv, 1645/AG 32). The important corollary of the principle of the identity of indiscernibles is the denial that spatiotemporal location suffices to differentiate and individuate substances. In Leibniz’s view, if two things, a and b, were qualitatively identical and differed solely in their spatiotemporal location, then God would have no reason to create a in its place and b in its place. That is, there must always be a reason, found within the complete individual concept of substances and issuing from the free decree of God, that a is discernible from b. This fact points to another important feature of Leibniz’s CIC account of substance: it is not only the case that each substance has a complete individual concept – the essence of the substance as it exists in the divine mind – but for every essence or complete individual concept there is one and only one substance in a world. Further, perfect similarity, Leibniz believes, is only found in incomplete concepts of substances. Leibniz’s second notable paradoxical consequence is that substances can only arise naturally in creation and end in annihilation. Why should this be so? If the CIC of an individual substance contains within it all predicates past, present and future, it would seem that there is no 95

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LEIBNIZ’S METAPHYSICS The denial of the causal interaction of substances forms an essential premise of Leibniz’s argument for the pre-established harmony of mind and body. Thus, Leibniz continues in Primary Truths to explain his ‘hypothesis of concomitance’:

from the creation of the world, then it is natural to conclude that each substance contains within it a kind of story of the entire universe from its own particular perspective. While more will be said below and in a separate essay in this collection, what Leibniz is suggesting here is a set of doctrines that he will develop in greater detail: the worlds apart doctrine (i.e., the denial of causal interaction between finite substances), the mirroring (or expression) thesis, and the doctrine of universal harmony. In the Discourse on Metaphysics §14, Leibniz explains the meaning of the worlds apart doctrine: ‘each substance is like a world apart, independent of all other things, except for God; thus all our phenomena, that is, all the things that can ever happen to us, are only consequences of our being.’ (A VI, iv, 1550/AG 47) This is even clearer in the Primary Truths, where (again) a very similar argument concerning the nature of substance is given. Not only is it the case, Leibniz claims, that genuine physical influx – the transfer of some property within one substance to a second property – is inexplicable, but more important the logical conception of substance shows us that the reasons for any property that a substance may have are already contained within its CIC. In other words, every state of a substance is explained, grounded or caused by its own notion or CIC. (Of course, the ground or reason for the existence or actuality of any particular substance is to be found in God and his free choice of worlds.)

Also, assuming the distinction between soul and body, from this we can explain their union without the common hypothesis of an influx, which is unintelligible, and without the hypothesis of an occasional cause, which appeals to a Deus ex machina. For God from the beginning constituted both the soul and the body with such wisdom and such workmanship that, from the first constitution or notion of a thing, everything that happens through itself [per se] in the one corresponds perfectly to everything that happens in the other, just as if something passed from one to the other. This is what I call the hypothesis of concomitance. This hypothesis is true in all substances in the whole universe but cannot be sensed in all of them, unlike the case of the soul and the body. (A VI, iv, 1647/AG 33) Thus, from Leibniz’s perspective, if one accepts this logical account of substance, according to which a being is a substance just in case it has a complete individual concept, then one is committed to a set of deep and perplexing metaphysical theses.

Strictly speaking, one can say that no created substance exerts a metaphysical action or influx on any other thing. For, not to mention the fact that one cannot explain how something can pass from one thing into the substance of another, we have already shown that from the notion of each and every thing follows all of its future states. (A VI, iv, 1647/AG 33)

UNITY AND REALITY IN LEIBNIZ’S METAPHYSICS If a finite substance is to have a CIC, it must, in Leibniz’s view, exhibit another characteristic of true substancehood: unity. While it is 96

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LEIBNIZ’S METAPHYSICS Physicae, discussed above). Briefly, the argument is the following: if the essence of body is extension alone, then any body is infinitely divisible; if it is infinitely divisible, then it lacks a principle of unity; and if it lacks a principle of unity, then it cannot be an individual substance (cf. Sleigh, 1990, p. 119). On the other hand, if something does have a principle of unity, then it is a substance. What can that principle be, if not material? Leibniz’s answer, as has been indicated, is that the principle of unity is formal. Thus, in a letter from 8 December [NS] 1686 to Arnauld, Leibniz claims that we should accept substantial forms or souls. In giving the anti-Cartesian argument, however, Leibniz also combines it with his complete individual concept view of substance. That which has a notion that includes everything that has happened to it and will happen to it must be indivisible and indestructible; it cannot be material.

the nature of an individual substance to have a CIC, only a genuine unity can be a substance. In fact, as he will put it later in his correspondence with Des Bosses, Leibniz holds the Aristotelian thesis of the reciprocity of being and unity, which is one of the core ideas of his metaphysics. To Arnauld he expresses his position in a very clear and forceful manner: To put it briefly, I hold this identical proposition, differentiated only by the emphasis, to be an axiom, namely, that what is not truly one being is not truly one being either. It has always been thought that one and being are reciprocal things. Being is one thing and beings are another; but the plural presupposes the singular, and where there is no being still less will there be several beings. (A II, ii, 186/AG 86; translation altered)

A substantial unity requires a thoroughly indivisible and naturally indestructible being, since its notion includes everything that will happen to it, something which can be found neither in shape nor in motion . . . , but which can be found in a soul or substantial form, on the model of what is called me. These are the only thoroughly real beings, as was recognized by the ancients, and above all, by Plato, who clearly showed that matter alone is not sufficient to form a substance. Now the aforementioned I, or that which corresponds to it in each individual substance, can neither be made nor destroyed by the bringing together or separation of parts, which is a thing entirely external to what constitutes a substance. I cannot say precisely whether there are true corporeal substances other than those that are animated, but souls at least serve to

In other words, paralleling the definition of substance given above, one could say now that Leibniz is also committed to the following thesis: (2) x is a substance if and only if x is a true unity. Now, in the 1680s, as has been shown, Leibniz claimed to have restored substantial forms to philosophy. While in later years this scholastic notion seems to drop out of his philosophical vocabulary to some degree, the fundamental idea remains: there must be something that guarantees or makes possible the unity of a substance, and this is the substantial form or soul. This metaphysical view is part of Leibniz’s rejection of the Cartesian account of matter and goes back to the works from the late 1670s (as seen in the Conspectus to the Elementa 97

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LEIBNIZ’S METAPHYSICS (absent a single substantial form) fail to have an intrinsic unity, they are nevertheless represented as being single and unified objects, much as a rainbow is represented as one thing when it is in fact merely the result of the refraction of light through innumerable water droplets. Yet, just as a rainbow results from the existence of these real unities (the water droplets), so do the bodies of the natural world result from the existence of the genuine individual substances. Put somewhat differently, the reality of these aggregates is derived from the reality of the unities. ‘I believe that where there are only beings by aggregation, there aren’t any real beings. For every being by aggregation presupposes beings endowed with real unity, because every being derives its reality only from the reality of those beings of which it is composed’ (A II, ii, 184/AG 85). This relation between the phenomena and the underlying simple substances is what Leibniz means when he talks about ‘well-founded phenomena’. Unfortunately, during the 1680s and into the 1690s, Leibniz is not entirely clear and consistent about what counts as a paradigmatic individual substance or a true unity. Often he suggests that a man or an animal is a paradigm of substancehood (see, e.g., DM 34). Insofar as an animal is to be considered an organism, or an animated body, Leibniz could be seen as being committed to ‘corporeal substances’ as fundamental to his ontology. Even here, however, it is the soul or substantial form that serves as the principle of unity of the corporeal substance and that is, therefore, primary. Yet, Leibniz just as often if not more often suggests that the paradigmatic individual substance is the self or the ‘I’. This view is on clear display in Leibniz’s December 1686 letter to Arnauld (quoted above) and is a constant in his

give us some knowledge of others by analogy. (A II, ii, 121/AG 79) In other words, Leibniz moves from the complete individual concept thesis (which he sees as following from the Aristotelian predicate-in-notion principle) and the Aristotelian thesis of the reciprocity of unity and being and arrives at the Platonic conclusion that only a soul or substantial form is thoroughly real. Moreover, substances are to be understood on the model of souls or selves. Leibniz’s commitment to the reciprocity of unity and being has important consequences. It is not simply that his ontology has, as its ground-floor constituents, beings endowed with a unity; he explicitly states that nothing else at all is real in the same way. As he writes to Arnauld, ‘I hold that philosophy cannot be better re-established and reduced to something precise, than by recognizing only substances or complete beings endowed with a true unity, together with the different states that succeed one another; everything else is only phenomena, abstractions, or relations’ (A II, ii, 191/AG 89). In other words, the logical and metaphysical commitments to the CIC view of substance and substantial forms or souls lead Leibniz to the following sharp ontological distinction: there are true unities or substances, on the one hand, and phenomena, abstractions or relations, on the other hand. Those beings that possess true unity or are ‘unities per se’ are real. Other things, which one would normally consider ‘inanimate’ objects, such as bicycles, books and beer bottles, can at best be said to possess ‘unity by aggregation’; they are, as Leibniz will put it, ‘mere aggregates’ and are relegated to the realm of the phenomenal. Leibniz’s favourite comparison in the case of phenomenal unities is to a rainbow. While bodies 98

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LEIBNIZ’S METAPHYSICS the CICs exist in the divine intellect prior to the creation of the actual world and, therefore, the CICs or forms or souls are prior to and fundamental to the created world of concrete individual substances.

thought. Twenty years later, employing the language of monads (to be explored in greater detail presently), Leibniz writes, ‘It is contrary to experience that we are not substances, since we really have no concept of substance except from the intimate experience of ourselves when we perceive the “I”, and by this example we attribute the name “substance” to God himself and other monads’ (Grua II, 558). While Leibniz is critical of the Cartesian account of matter or corporeal substance, he is at the same time part of the Augustinian tradition that culminates in the metaphysics of Descartes and that holds the ‘I’ to be essentially immaterial, a mind or a soul. As Leibniz writes in Primary Truths, ‘Something lacking extension is required for the substance of bodies, otherwise there would be no source [principium] for the reality of phenomena or for true unity . . . But since atoms are excluded, what remains is something lacking extension, analogous to the soul, which they once called form or species’ (A VI, iv, 1648/AG 34). Even if it cannot be determined whether the paradigmatic simple substances are akin to animals or selves, it should be clear that, for Leibniz, the soul or some immaterial analogue to the soul is fundamental in his metaphysics. The soul-analogue is primary in his metaphysics, serving to ground all other beings. Further, as has been shown, it is the nature of a substance to have a complete individual concept; this CIC is the essence of the substance and is associated with the indivisible and incorruptible form or soul of the individual. Now, in Leibniz’s account of the creation of the world, God surveys all possible worlds, selects the world richest in phenomena and simplest in laws, and instantiates that world. But what is a possible world? It is a set of ‘compossible’ essences or complete individual concepts of substances. Therefore,

ACTIVITY One other important way in which Leibniz’s commitment to the CIC view becomes ramified in his thought is through the thesis that substances are essentially active. Since each substance has a complete individual concept which contains within it everything that was or will be true of the substance and its consequence, ‘every substance has a perfect spontaneity . . . [and] everything that happens to it is a consequence of its idea or of its being’ (DM 32: A VI, iv, 15581/AG 64). Indeed, Leibniz rejected the Cartesian doctrine of corporeal substance not only because Cartesian matter lacked unity but also because it lacked a ground of the activity central to substances. In other words, in Leibniz’s view, substances are fundamentally active unities, or as he says in the opening line of the Principles of Nature and Grace (1714): ‘A Substance is a being capable of action’ (GP VI, 598/AG 207). To echo the formulae already given, one could say the following: (3) x is a substance if and only if x is capable of acting (or has the grounds of its actions within it). Cartesian corporeal substance, however, insofar as its essence is extension, cannot be itself a source of activity (GP IV, 510/AG 161). There are at least two strands to Leibniz’s argument on this point. First, he 99

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LEIBNIZ’S METAPHYSICS adheres to the classical and scholastic idea that actions pertain to supposita; that is, only something that can be the subject of predication can be active, and only true unities can be genuine subjects of predication (and not mere phenomena). Put differently, Cartesian corporeal substance cannot, insofar as it is infinitely divisible, constitute a suppositum, or subject of predication, and therefore cannot constitute a substance per se. Second, Leibniz believes that something is active if and only if the source of its activity can arise from within itself, that is, if and only if its activity arises spontaneously. This is another reason, then, that individual substances will be understood as analogous to minds or souls, for Leibniz believes that only minds or mind-like things can originate and alter their modifications. Leibniz’s claim that substances are essentially active has an important dynamical component, for, in Leibniz’s view, substances are essentially endowed with forces; or better, substances essentially are centres of force. In his De Ipsa Natura (1698), for example, one sees this quite clearly; he writes that ‘the very substance of things consists in a force for acting and being acted upon’ (GP IV, 508/ AG 159). The full (anti-Cartesian) argument is on even better display in the opening of the Specimen Dynamicum (1695).

stood by reason to be everywhere in matter, even where it is not obvious to sense . . . [This nisus] constitute[s] the innermost nature of bodies, since to act is the mark of substances, and extension means nothing but the continuity or diffusion of an already presupposed striving and reacting (that is, resisting) substance. So far is extension from being able to constitute a substance itself. (GM VI, 235/AG 118)

In the previous section it was shown that the form or soul-analogue grounds the material, and one sees the same kind of claim here: that a force of nature is prior to extension; that force is what grounds bodies. As Leibniz will go on to explain, each simple substance is endowed with what he calls primitive active and passive powers. The idea here again sounds Aristotelian: a substance has a certain essentially active component, the soul or substantial form or first entelechy, and a passive component, primary matter. In A New System of Nature (1695), his first major philosophical publication best known for his introduction of the theory of pre-established harmony, Leibniz combines unity and activity in arguing for vital atoms of substance. He writes,

[I]n corporeal things there is something over and above extension, in fact, something prior to extension, namely, that force of nature implanted everywhere by the Creator. This force does not consist in a simple faculty, with which the schools seem to have been content, but is further endowed with conatus [striving] or nisus [effort], attaining its full effect unless it is impeded by a contrary conatus. This nisus frequently presents itself to the senses and, in my judgement, is under-

There are only atoms of substance, that is, real unities absolutely destitute of parts, which are the source of actions, the first absolute principles of the composition of things, and, as it were, the final elements in the analysis of substantial things. We could call them metaphysical points: they have something vital, a kind of perception . . . Only metaphysical points or points of substance (constituted by forms or souls) are exact and real, and without them there would be nothing real, since without true unities there would be no multitude. (GP IV, 482–3/AG 142)

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LEIBNIZ’S METAPHYSICS This passage is important for a number of reasons. First, it makes the explicit claim that there are only atoms of substances. On the one hand, this is exactly what one might suspect given his commitment to the reciprocity of unity and being. On the other hand, it does show that Leibniz is moving away from an ontology of ‘individual substance’ and towards an ontology of ‘simple substance’. Second, the passage continues the theme of the relation between composites and true unities on display in the correspondence with Arnauld. Not only can one say that the reality of composites is derived from the reality of the unities, one can also say that the atoms of substance are the ‘first absolute principles’ of composites and the ‘final elements in the analysis of things’. Third, Leibniz is explicit that these elementary or simple substances are in fact forms or souls. Therefore, even if the jury was out about the ultimate existents in the texts that were considered above, here there can be little doubt. Fourth, and perhaps most important for the moment, the vitality and activity of these metaphysical points is described as perceptual. For Leibniz, then, the fundamental activity of substances is representational and proceeds according to a certain law inherent in each substance. That is, the primitive active force is the law of unfolding or the law of the series of the simple substance. As he puts it in a letter to De Volder, ‘I recognize a primitive entelechy in the active force exercising itself in various ways through motion and, in a word, something analogous to the soul, whose nature consists in a certain eternal law of the same series of changes, a series which it traverses unhindered’ (GP II, 171/AG 173). And in a later letter to De Volder the perceptual or representational character of this law of the series is explained:

I think that it is obvious that primitive forces can be nothing but the internal strivings [tendentia] of simple substances, strivings by means of which they pass from perception to perception in accordance with a certain law of their nature, and at the same time harmonize with one another, representing the same phenomena of the universe in different ways, something that must necessarily arise from a common cause.’ (GP II, 275/ AG 181) Since simple substances are minds, their modifications are representations or perceptions, and the activity of the simple substance will relate to the change or succession of its perceptions. One way to think of this is that each substance has a unique series of perceptions programmed by God to play in harmony with all other substances, and the internal tendency of a substance to move from perception to perception is its active force, or what Leibniz also calls appetite or appetition. Leibniz’s commitment to the essential activity and spontaneity of substances is what grounds one of his most notorious philosophical doctrines: pre-established harmony. While pre-established harmony is treated in detail in the separate chapter on Leibniz’s views on causation, it is important to say a few words about it here. According to Leibniz, as has been shown, each substance acts spontaneously; that is, the grounds for the actions of a substance are contained within it. The actions of simple, mind-like substances are the transitions from perception to perception within the substances; but God has created each (and the world in its entirety) so that they are in perfect harmony with each other. Thus, when substance a perceives itself as acting upon substance b, the

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LEIBNIZ’S METAPHYSICS latter perceives itself as being acted upon by the former. Most famously, of course, Leibniz applies this thesis of pre-established harmony to the problem of the relation between mind and body and argues that the mind and body act spontaneously, independently and harmoniously: ‘It is this mutual relation, regulated in advance in each substance of the universe, which produces what we call their communication, and which alone brings about the union of soul and body’ (GP IV, 484–5/AG 143).

Leibniz writes to his friend, Nicolas Rémond, at the end of his career, ‘absolute reality rests only in the monads and their perceptions’ (GP III, 636/L 659). In a strict sense, the bodies of the natural world are ‘mere’ phenomena – even if ‘well-founded’. Thus, for example, Leibniz says to De Volder, [C]onsidering the matter carefully, we must say that there is nothing in things but simple substances, and in them, perception and appetition. Moreover, matter and motion are not substances or things as much as they are the phenomena of perceivers, the reality of which is situated in the harmony of the perceivers with themselves (at different times) and with other perceivers. (GP II, 270/AG 181)

LEIBNIZ’S MONADOLOGICAL METAPHYSICS ‘The key to my doctrine on this subject consists in this consideration of what is properly a real unity, a monad.’ (Leibniz to l’Hospital, 22 July 1695: A III, vi, 451/ GM II, 295) With the theses of the reciprocity of unity and being and the fundamentality of force and representational activity in place, it should now be relatively easy to understand what for many appears so fantastical: Leibniz’s metaphysical system of monads. Only something that is a true unity can be a genuine being or a genuine substance; the only things that can be genuine unities are mind-like beings; the activity of these beings is perceptual or representational; thus, they are discernible by their representations alone. Yet, Leibniz’s monadological metaphysics is an even stronger view. As in his account of individual substances in the 1680s, Leibniz holds that only the simple substances are real (‘in metaphysical rigour’) and that all other beings derive their reality or being from the reality or being of the simple substances. As

And similarly: ‘I don’t really eliminate body, but reduce [revoco] it to what it is. For I show that corporeal mass [massa], which is thought to have something over and above simple substances, is not a substance, but a phenomenon resulting from simple substances, which alone have unity and absolute reality’ (GP II, 275/AG 181). It seems clear what Leibniz intends here: simple substances, monads or minds, are the ultimately real things; everything else is ontologically dependent upon them. If ‘idealism’ is the thesis that the fundamental beings of the world are minds and their ideas, then, in an important sense, Leibniz is an idealist. Of course, Leibniz will also recognize that ‘there are’ other things as well – bodies, animals and so on – but they all derive their being or reality from the monads. While Leibniz presents relatively forceful reasons for holding an idealistic metaphysics in earlier writings – reasons related to the essential unity and activity of substance – it is instructive to consider his later, popular

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LEIBNIZ’S METAPHYSICS essays. In his well-known Monadology (1714), for example, Leibniz presents an argument that is slightly different from what has been considered thus far. He writes the following: §1 The monad, which we shall discuss here, is nothing but a simple substance that enters into composites – simple, that is, without parts. §2. And there must be simple substances, since there are composites; for the composite is nothing more than a collection, or aggregate, of simples. §3. But where there are no parts, neither extension, nor shape, nor divisibility is possible. These monads are the true atoms of nature and, in brief, the elements of things. (GP VI, 607/AG 213) The argument, such as it is, can be recast in the following way: (i) if there are composites, there must be simples; (ii) there are composites; therefore, (iii) there are simples. Premise (i) states a seemingly innocuous conditional proposition, by which, with premise (ii) and modus ponens, the monadological conclusion is arrived. The crucial premise is, then, (ii). Leibniz can affirm (ii), however, for simple metaphysical and phenomenological reasons: the observed world presents to us as various bodies in space; those bodies, insofar as they are extended, must be composed of parts. Strictly speaking, however, this justification for premise (ii) is surely not entirely satisfactory. As has been shown, the claim that matter is extended only entails that it is infinitely divisible; it does not entail that it is composite. The difference is that infinite divisibility is merely a claim about what is in potentia, not what is in actu. Indeed, it might seem that, far from being a simple but sound little argument, the Monadology opens with

a petitio principii. At the very least, it should be clear that Leibniz makes explicit appeal here neither to the reciprocity of unity and being nor to the idea that substances are essentially active. The situation is slightly better in Leibniz’s other late, great, popular essay, the Principles of Nature and Grace (1714). He begins with the definition of a substance as a ‘being capable of action’ (considered in the previous section) and goes on to assert baldly that there are simple substances (‘lives, souls and minds’) and composite substances. His argument for the existence of monads or simple substances, however, is as deep as that contained in the opening of the Monadology. But in §2 Leibniz does provide the reader with more enlightenment: Since the monads have no parts, they can neither be formed nor destroyed. They can neither begin nor end naturally, and consequently they last as long as the universe, which will be changed but not destroyed. They cannot have shapes, otherwise they would have parts. As a result, a monad, in itself and at a moment, can be distinguished from another only by its internal qualities and actions, which can be nothing but its perceptions (that is, the representation of the composite, or what is external, in the simple) and its appetitions (that is, its tendencies to go from one perception to another) which are the principles of change. For the simplicity of substance does not prevent a multiplicity of modifications, which must be found together in this same simple substance, and which must consist in the variety of its relations to external things . . . (GP VI, 598/AG 207) Thus, while one does not find a convincing argument for the existence of monads or simple substances, one does find an important

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LEIBNIZ’S METAPHYSICS account of the nature of the simple substances. Indeed, in both the Monadology and the Principles of Nature and Grace, Leibniz presents a relatively clear metaphysical picture: the simple substances are the elements of everything in the world; they are lives, souls or minds; they are individuated solely by their internal (that is, representative) states. Moreover, while monads are not (indeed, cannot be) extended or have shape, they nevertheless represent the world from a unique point of view. Most important, all things are ontologically dependent upon the simple substances. While everything depends upon simple substances, the nature of this dependence must still be explained. On the one hand, Leibniz often suggests that the bodies or secondary matter of the natural world or the body associated with a particular monad are intentional objects. The strong conclusion to draw from this claim is that bodies are merely phenomena. This is what Leibniz means in the passage from the letter to De Volder considered above: ‘[C]onsidering the matter carefully, we must say that there is nothing in things but simple substances, and in them, perception and appetition. Moreover, matter and motion are not substances or things as much as they are the phenomena of perceivers . . . ’ (GP II, 270/AG 181). On the other hand, Leibniz suggests elsewhere that bodies are, in fact, aggregates of substances. For example, in a subsequent letter to De Volder, he writes, ‘in the mass of extension, or rather, of extended things, or, as I prefer, in the multitude of things, I say that there is no unity, but rather innumerable unities’ (GP II, 276/AG 182). While there is some debate in the literature regarding the proper interpretation of Leibniz’s view of bodies – represented by these two views (cf. Adams, 1983 and 1994; Rutherford, 1990a, 1990b,

1993, 1995a) – they ought to be seen as complementary: bodies are ‘well-founded’ phenomena (phenomena bene fundata) precisely because they result from innumerable monads. A crucial feature of monads is, however, that they are always joined to a body. What Leibniz means by this is complicated but also important. Consider first his explanation in §3 of the Principles of Nature and Grace: [E]ach distinct simple substance or monad, which makes up the centre of a composite substance (an animal, for example) and is the principle of its unity, is surrounded by a mass composed of an infinity of other monads, which constitute the body belonging to this central monad, through whose affections the monad represents the things outside it, similarly to the way a centre does. And this body is organic when it forms a kind of automaton or natural machine . . . (GP VI, 598–9/AG 207) The claim that every monad is surrounded by a mass composed of other monads which constitute the body of the central monad is ultimately related to a parorganicist strain in Leibniz’s thought. Indeed, it is closely connected to his view that ‘all of nature is full of life’ (PNG 1: GP VI, 598/AG 207). There must, however, be a certain kind of hierarchy among monads. In a letter to De Volder ten years earlier, Leibniz gives a slightly different picture of his basic ontology, but one that is nevertheless helpful for the issue at hand. He writes, I distinguish: (1) the primitive entelechy or soul; (2) the matter, namely, the primary matter or primitive passive power; (3) the monad made up of these two things; (4) the mass [massa] or secondary

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LEIBNIZ’S METAPHYSICS matter, or the organic machine in which innumerable subordinate monads come together; and (5) the animal, that is, the corporeal substance, which the dominating monad makes into one machine. (GP II, 252/AG 177) One of the points Leibniz is making here is that in an animal there is a dominant monad that bears a special relation to all the monads subordinate to it that make the ‘organic machine’ of that animal. But, ultimately, the picture is even more complex than this, for each of the subordinate monads can be considered as having an organic machine attached to it, and this relation continues on to the infinitely small. Thus, for example, Leibniz writes in the Monadology §70, ‘Thus we see that each living body has a dominant entelechy, which in the animal is the soul; but the limbs of this living body are full of other living beings, plants, animals, each of which also has its entelechy, or its dominant soul’ (GP VI, 619/AG 222). Similarly, in a letter to Bierling, he writes, Any mass contains innumerable monads, for although any one organic body in nature has its corresponding [dominant] monad, it nevertheless contains in its parts other monads endowed in the same way with organic bodies subservient to the primary one; and the whole of nature is nothing else, for it is necessary that every aggregate result from simple substances as if from elements. (GP VII, 502)

infinity of monads and their organic bodies, which are nothing more than more monads and their organic bodies. Leibniz’s version of idealism tends to produce confusion precisely because of the two strands of his philosophy considered in the preceding paragraphs: the commitment to the ‘embodiment’ of monads along with the rejection of the reality of bodies; the view that monads are not spatial but have a point of view. Leibniz’s point, however, is that, while monads are not extended, they do have a situation insofar as they bear an ordered relation to other bodies through the body in which they are present or through the body to which they represent themselves as being attached (GP II, 253/AG 178). In other words, in the Leibnizian monadology, simple substances are mind-like entities that do not, strictly speaking, exist in space but that represent the universe from a unique perspective. Leibniz’s conception of such a perspectival universe has, however, a distinctively neoPlatonist origin. Again, each mind-like simple substance represents itself as having a body and a position relative to other bodies, but in doing so each simple substance offers a perspective on the world for the Divine mind. This idea comes out very clearly in the Discourse on Metaphysics §14, where Leibniz writes the following:

In other words, each monad will have an organic body which is in turn composed of other monads, each of which likewise has an organic body. Similarly, any seemingly inanimate chunk of matter will be the result of an

Now, first of all, it is very evident that created substances depend upon God, who preserves them and who even produces them continually by a kind of emanation, just as we produce our thoughts. For God, so to speak, turns on all sides and in all ways the general system of phenomena which he finds it good to produce in order to manifest his glory, and he views all the faces of the world in all ways possible, since there is no relation that escapes his

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LEIBNIZ’S METAPHYSICS A related neo-Platonic thought can be seen in the Monadology:

omniscience. The result of each view of the universe, as seen from a certain position, is a substance which expresses the universe in conformity with this view, should God see fit to render his thought actual and to produce this substance. (A VI.4.1549–50/AG 46–47) This is a striking passage. Leibniz is telling us that each finite substance is the result of a different perspective that God can take of the universe and that each created substance is an emanation of God. The argument here can be expressed in several different ways. First, since God could occupy any and all points of view of the universe, there must be a simple substance to represent the world from that perspective. (And since the simple substance must have representations of its unique perspective, it must be a mind-like substance, a monad, capable of having perceptions.) Second, and stronger, God’s omniscience entails knowledge of the world from every perspective simultaneously, and the infinite perspectives of the world originating from God’s nature simply are monads. As he writes in a 1714 letter to Pierre Dangicourt, The true substances are only simple substances, or what I call Monads. And I believe that there are only monads in nature, everything else being only the phenomena that result from them. Each monad is a mirror of the universe according to its point of view, accompanied by a multitude of other monads which compose its organic body of which it is the dominant monad. . . . The monad therefore envelops in advance and in itself its past and future states, in such a way that an omniscient being could read them, and the monads are in agreement among themselves, being mirrors of the same universe but differently represented. (D III, 499–500)

God alone is the primitive unity or the first [originaire] simple substance; all created or derivative monads are products, and are generated, so to speak, by continual fulgurations of the divinity from moment to moment, limited by the receptivity of the creature, to which it is essential to be limited. (GP VI, 614/AG 219) The created monads of the world are, as it were, effects of the emanation of the divine nature. Not only do they represent the universe from their unique points of view but they are also so many little sparks of the original divine mind.

SOME PROBLEMS FOR THE MONADOLOGY What are the fundamental beings of Leibniz’s metaphysics? By now, the answer should be clear: simple substances or monads. But even in his last decades of philosophical activity, Leibniz speaks often of ‘composite substances’, ‘corporeal substances’ and ‘animals’. What is their ontological status? Can there really be corporeal substances in Leibniz’s monadological metaphysics? What is at issue here is whether or not some group of monads can effectively be united in such a way that this composite can be said to constitute a genuine unity. Yet, given the conceptual resources of his monadology, it is not at all clear that Leibniz’s metaphysics can provide a satisfactory answer. Indeed, in a very revealing moment, he wrote and then deleted the following from a letter to Des Bosses: ‘The union I find some difficulty explaining is that which

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LEIBNIZ’S METAPHYSICS joins the different simple substances or monads existing in our body with us, such that it makes one thing from them’ (LDB 22–3). If the basic beings of Leibniz’s ontology are mind-like simple substances, or monads, then the differences between them must be explicable in terms of mental features. Further, as it was stated above, a central feature of Leibniz’s account of substance is the claim that substances are endowed with primitive active and passive forces. In the Monadology, the active and passive forces of a substance will be expressed in terms of the relative clarity of perceptions. Thus, for example, in §49 of the Monadology, Leibniz writes that, ‘we attribute action to a monad insofar as it has distinct perceptions, and passion, insofar as it has confused passions’ (GP VI 615/AG 219). But, as we learn later in the same work, ‘Monads all go confusedly to infinity, to the whole; but they are limited and differentiated by the degrees of their distinct perceptions’ (GP VI 617/AG 221). The fundamental idea here is two-fold: first, activity and passivity are features of the relative clarity and distinctness of the representations of the monad, and, second, insofar as the organic bodies of a particular monad are themselves constituted by monads, they – the monads of the organic body – will have confused perceptions. This chain goes down to the infinitely small, with monads having only very confused and inexact perceptions of the world. Since there is a hierarchy of monads within any animal, from the soul of a person to the barest of monads, the relation of domination and subordination among monads is a crucial feature of both Leibniz’s idealism and panorganicism. But this hierarchy is not simply a relation of containment, in which one monad has an organic body which is the result of other monads, each of which has another organic body. The relation of domination and

subordination in an animal is supposed to explain both the unity of the composite substance and the control of the ‘machine of nature’. What is it then that explains the relation of dominant and subordinate monads? In a letter to Des Bosses, Leibniz claims that ‘considered in terms of the monads themselves, domination and subordination consist only in degrees of perception’ (LDB 256–7). Since monads are to be differentiated in terms of their perceptions, one natural reading would simply be that suggested in the paragraph above: monad a is dominant over monad b when a has clearer perceptions than b. But, if we follow the description of the appearance of causal interaction that we find in the Monadology (§§49–51), we can get a slightly more sophisticated picture. Monad a is dominant over monad b when a contains within it reasons for the actions of b. This is why the mind of an animal can be said to direct the actions of its body, and why, for example, there will be a hierarchy of functionality within any one animal. Thus, one’s mind has clearer perceptions than those contained in the monads of its organic body, but it contains the reasons for everything that happens in one’s body; one’s liver contains the reasons for what happens in its cells; a cell contains the reasons for what happens in its mitochondria; and, according to Leibniz, this relation continues infinitely on down. (See Look, 2002, for a more detailed analysis.) But this account is not entirely satisfactory. It is not enough to say that a is dominant over b if and only if a has clearer perceptions than does b. For example, Leibniz had clearer perceptions than did the monads underlying his desk, but he did not become one with his desk. In other words, Leibniz might be able to explain the hierarchy of monads and even their control, but he still has not explained how the disparate monads can be unified.

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LEIBNIZ’S METAPHYSICS In his correspondence with Des Bosses, Leibniz recognizes this problem and experiments with a new idea: the vinculum substantiale (or ‘substantial bond’). While the idea of the substantial bond arose in the context of a discussion of transubstantiation, it ultimately relates to some deep issues in Leibniz’s metaphysics. Des Bosses, a Jesuit philosopher and theologian, asked Leibniz how he could explain the Catholic doctrine of transubstantiation in his theory of monads. After all, according to Catholic dogma, the bread and wine of the sacrament truly become the body and blood of Christ; there must be a real change of substance. If the phenomena of the bread and wine remain the same, Des Bosses wonders, how can the monads, the substantial ground of those phenomena, change? Leibniz’s tentative answer – after saying that, as a Lutheran, he does not endorse the doctrine of transubstantiation – is that there would have to be a substantial bond over and above the monads of the bread and wine that is destroyed in the service of the Eucharist and replaced with a substantial bond, a substance, that is the body and blood of Christ. Now, it is easy to be sceptical of this doctrine. Indeed, according to Russell, it is ‘rather the concession of a diplomatist than the creed of a philosopher’ (Russell, 1937, p. 152). But there is something important going on here. According to Leibniz, for example, the substantial bond (or something!) is required to make phenomena real; that is, if a corporeal substance is to have true unity and hence reality, there must be something over and above the monads. Thus, as Leibniz says to Des Bosses, ‘if faith drives us to corporeal substances, this substance consists in that unifying reality, which adds something absolute (and therefore substantial) . . . to the things to be unified’ (LDB 226–7) and

‘the unity of corporeal substance in a horse does not arise from any refraction of monads but from a superadded substantial bond, through which nothing at all is changed in the monads in themselves’ (LDB 256–7). Leibniz certainly did not endorse the doctrine of the substantial bond. Doing so would have contradicted too many other deeply held tenets of his philosophy: a substantial bond would be a substance without representational activity, and it would have been a substance that exercised real causal power over other substances. Nevertheless, Leibniz’s consideration of it does reveal that he saw a difficulty in accepting the full consequences of his monadology while also affirming the existence of corporeal substances. (For more on the substantial bond, see Look, 1999, 2004, and the introduction to LDB.)

CONCLUSION Leibniz’s idealism, his monadological metaphysics, thus follows from a group of more basic philosophical commitments. Leibniz held that the nature of truth entailed the thesis that every individual substance must have a notion so complete that it contains all truths past, present and future. This complete individual concept in turn must be associated with something indivisible and ingenerable, hence, to a substantial form or soul. More generally, that which is not a true unity is not a true being; hence, there are true unities, on the one hand, and the phenomena that result from them, on the other hand. Since each substance contains within it the grounds for its activity, it is causally isolated from all other beings; at the same time, however, all substances stand

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LEIBNIZ’S METAPHYSICS in a perfect harmony pre-established by God. Since the only substances are true unities, and the only true unities are mind-like beings, their activity is mental or representational activity. And, thus, as Leibniz says, ‘there is nothing in things but simple substances, and in them, perception and appetite’ (GP II, 270/AG 181). The corporeal

substance of Cartesianism is thoroughly rejected, and the corporeal substance of Aristotle (of hylomorphic compounds), while at times seemingly endorsed in word, is ultimately also rejected. Brandon C. Look

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7 LOGICAL THEORY IN LEIBNIZ

INTRODUCTION: ELEMENTS OF LOGICAL THEORY IN LEIBNIZ’S PHILOSOPHY After Aristotle, Leibniz’s advances in logic surpass those of any writer before the nineteenth century and rival those of anyone up to Frege. Yet like so much of his pioneering intellectual work, Leibniz’s ideas in logic were not published and remained mostly unknown until the twentieth century. As a logician he is notable now for his prescience rather than for his influence, and while he can fairly be said to have discovered symbolic and mathematical logic, the actual lineage of contemporary logic goes back not to Leibniz’s work but to the later, independent discoveries of Boole, Schröder, Venn, Frege, Peano and others. Still, readers of Leibniz’s philosophy will have come hard against the shoals of his logic in a few places even without exposure to his logical works. His intensional theory of truth and his doctrine of complete individuals concepts, for example, have enjoyed philosophical acclaim, and notoriety, although both are in fact just consequences of more basic principles of his logic. In a characteristic and celebrated passage Leibniz writes to Arnauld on 14 July 1686 about truth: ‘[I]n every true affirmative proposition, necessary or

contingent, universal or particular, the concept of the predicate is in a sense included in the concept of the subject. Praedicatum inest subjecto, or else I do not know what truth is’ (GP II, 56/M 63). Take the universal statement ‘Every human is mortal’. It is true if and only if the concept expressed by the predicate term ‘mortal’ is included in the concept expressed by the subject term ‘human’. As Leibniz indicates, the account extends also to particular propositions (e.g. ‘Some human is mortal’) and to singulars (‘Socrates is mortal’), and generally to all propositions of the basic subject-copulapredicate form ‘A is F’. This ultimately includes negative propositions as well, despite his restriction to ‘affirmative’ ones in the letter to Arnauld, a qualification he had crossed out in another, though earlier, formulation of the same claim (cf. A VI, iv, 223/AG 11). Further, it appears to be part of Leibniz’s larger view of language that all statements can be expressed or captured in this form, including relational statements, conditionals etc.; as he writes in a paper on language dated to 1687–8: ‘Everything in discourse can be analysed into the noun substantive, Ens or Res, the copula or substantive verb est, adjectives and formal particles’ (A VI, iv, 886/LLP 16). So the reach of this analysis purports to be extremely wide. But even setting this aside,

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LOGICAL THEORY IN LEIBNIZ already just as an initial claim about the analysis of truth it is surprising to philosophers in two ways. First, it has questionable consequences for the content of concepts in many instances. Perhaps mortality is included in the concept human, but creating a race of robot philosophers does not seem to belong to that concept even if it is true that humans should achieve such a breakthrough. Singular statements such as ‘Aristotle wore a beard’ likewise yield counterintuitive results about the concepts of subject terms. And only a little reflection is required to see that, once an unrestricted principle of bivalence is adopted, the concept associated with a singular term, i.e. the concept of the individual denoted by that term, will include the concept of every predicate ever true of that individual. This doctrine of complete individual concepts is the one that so shocked Arnauld and triggered an avalanche of subsequent criticism and scholarship concerning Leibniz’s view of individuals, freedom, necessity and essentialism. Second, the analysis of truth inverts what we would (now) typically take to be the natural interpretation of truth conditions for statements, on which the truth of a statement is a matter of the relations among the extensions of its terms and not of their concepts or intensions. ‘Every human is mortal’ is true because the individuals to which the term ‘human’ applies belong to the class of individuals to which the term ‘mortal’ applies. Also, it is not hard to see that this inversion is precisely what generates the counterintuitive results about concepts. While it is astonishing to think that an individual’s concept might contain the concept of every predicate ever true of him or her, it is wholly unremarkable to suppose that an individual might belong to every class of individuals that

makes up an extension of a predicate true of him or her. Aristotle is among the humans, the beard wearers, the philosophers, the political advisers, etc., by virtue of the facts, known or unknown – even if, as we might think, his concept does not include each and every one of the corresponding concepts. The embrace of an intensional theory of truth instead of an extensional one is not an accident on Leibniz’s part. He was well aware of the options and can be found spelling out the extensional analysis of truth in various texts and explicitly deploying an extensional approach to logic from time to time as well, as we shall see below. Indeed, it was Leibniz himself who coined the term ‘intension’ to contrast with ‘extension’ (cf. A VI, vi, 486), and he understood it as having the same meaning that ‘comprehension’ or ‘connotation’ had in such logic treatises of the day as the Port-Royal Logic (cf. Arnauld and Nicole 1996, p. 39). On this use, the intension of a term is the concept it expresses, while its extension consists in the (class of) individuals to which it applies. Concepts were taken to be composed of those sub-concepts they included and, if the account is pressed all the way to the limit, ultimately to be made up of simple conceptual ‘notes’ – primitive concepts – as basic elements of thought. In contrast, extensions were understood as composed of the individuals (or classes of individuals) included in them, and the individuals themselves are the basic elements in this scheme. Thus the intensional theory of truth has a relation of concept containment at its centre, while the extensional theory gives priority to a relation of class inclusion. Leibniz’s preference for an intensional theory of truth is part of his more general intensional approach to logic as a whole, one he sees as natural and for certain reasons superior to an extensional approach,

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LOGICAL THEORY IN LEIBNIZ all animals, and all animals in all corporeal substances; therefore all men are contained in all corporeal substances. On the other hand, the concept corporeal substance is in the concept animal and the concept animal is in the concept man; for being a man contains being an animal. (A VI, iv, 838–9/LLP 136)

although he also considers the two to be formally equivalent, mere inverses of one another. As he writes in Elements of a Calculus (1679), in noting his own favour for an intensional approach as against the extensional approach of the scholastics: The Scholastics speak differently; for they consider not concepts but instances which are brought under universal concepts. So they say that metal is wider than gold, since it contains more species than gold, and if we wish to enumerate the individuals made of gold on the one hand and those made of metal on the other, the latter will be more than the former, which will therefore be contained in the latter as the part in the whole. By the use of this observation, and with suitable symbols, we could prove all the rules of logic by a calculus somewhat different from the present one – that is, simply by a kind of inversion of it (A VI, iv, 199/LLP 20)

In fact Leibniz takes the intensional and extensional interpretations of logic and of the relation expressed by the copula itself to be reciprocals: the concept expressed by a term A contains the concept expressed by a term B if and only if the class of Bs includes the class of As. Using the symbols ‘≥’ for concept containment and ‘⊆’ for class inclusion (cf. Swoyer, 1995a; Mugnai, 2006), we may abbreviate this reciprocity principle with the formula: (PR)

Leibniz articulates the same thought that the two approaches are ‘inverses’ of one another even more clearly in a paper written nearly a decade later (A Study in the Calculus of Coincidents and Inexistents, 1686–7?): Being quadrilateral is in parallelogram, and being a parallelogram is in rectangle (i.e. a figure every angle of which is a right angle). Therefore being quadrilateral is in rectangle. These can be inverted, if instead of concepts considered in themselves we consider the individuals [singularia] comprehended under a concept. . . . For all rectangles are comprehended in the number of parallelograms, and all parallelograms are comprehended in the number of quadrilaterals; therefore, all rectangles are contained in quadrilaterals. In the same way, all men are contained in

(A ≥ B) iff (A ⊆ B).

This is an important claim, and we shall consider it with more attention when we turn to the formal details of the logic. Also, we shall sometimes need a neutral term for the relation expressed by the copula in Leibniz’s account, and for this I shall use the label ‘inherence’ for Leibniz’s est, though in contexts in which there is no risk of unclearness I shall sometimes just use the more natural ‘inclusion’ as the generic term for which concept containment or class inclusion are specific interpretations. For now let us focus a little longer on the intensional and extensional interpretations and some broader philosophical issues linked with the choice between the two (cf. Adams, 1994, pp. 57–63). Leibniz, like his predecessors, orders much of his work in logic around the traditional categorical propositions from the theory of syllogism, the first four of which make up the ‘square of opposition’, given here with examples:

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LOGICAL THEORY IN LEIBNIZ universal affirmative: universal negative: No A is B Every A is B. No man is a Every man is a soldier. soldier. particular affirmative: particular negative: Some A is not B Some A is B Some man is not Some man is a a soldier. soldier. The contrast between intensional and extensional interpretations is plainest in the case of the universal affirmative, as is Leibniz’s claim that the two are inverses of one another. On the intensional account, the predicate is included in the subject: the concept soldier is contained in the concept man. On the extensional account the subject is included in the predicate: the class of soldiers contains the class of men. The idea of inherence or inclusion as simple containment runs short after this case, however, and a more subtle treatment is required. For the particular affirmative, ‘Some man is a soldier’, the extensional interpretation is still quite straightforward: the class of soldiers intersects the class of men (and the intersection is non-empty), though it may not contain the whole of the class of men. On the intensional interpretation, it is less evident what to say, as the analogy with intersection is harder to make out in the case of concepts. Leibniz’s proposal, as he puts it forward in Elements of a Calculus, is that the particular affirmative will be true when something can be consistently added to the concept of the subject to include the predicate concept (A VI, iv, 198/LLP 19). So ‘Some man is a soldier’ is true if the concept soldier, or one including it, can be consistently added to the concept man. ‘A soldier-man is a soldier’ is clearly true using this device, and, therefore, so is ‘Some man is a soldier’. An immediate objection to this ‘consistent addition’ proposal is that it counts too many

particular affirmatives as true. Although consistency may rule out some cases, it seems too lax a constraint. ‘Some philosopher is a ruler’ is true by Leibniz’s account, since ‘philosopher-ruler’ marks a consistent addition to ‘ruler’ and ‘A philosopher-ruler is a ruler’ will clearly come out as true on the intensional approach. But it may yet be that there are no philosopher-rulers, and counting the statement as true seems therefore to fly in the face of the facts. How can the particular affirmative be true without the existence of a subject satisfying the predicate? The objection assumes the standpoint of the extensional interpretation: the truth of the proposition should be a matter of the individuals to which the terms refer, not (only) the relations among the concepts. To that extent a defender of an intensional approach need not be distressed by the objection. Still, if Leibniz’s principle of reciprocity (PR) between extensional and intensional interpretations is correct, there should not be disagreement in the truth values the two interpretations assign to the same sentence. We shall want to ask whether Leibniz can answer the objection, a matter to which we shall return below. Negative categorical propositions, universal or particular, present a puzzle to both interpretations. The natural extensional reading of ‘No man is a soldier’ would be that the class of men and the class of soldiers do not intersect. Likewise, on the intensional interpretation, if we carry over Leibniz’s device of ‘consistent addition’, the result would be that on no consistent addition does the concept man include the concept soldier. In both cases this is to treat the relevant relation between subject and predicate not as a form of inclusion but as exclusion: class exclusion or concept exclusion. Leibniz is aware of this, and his preferred treatment is to read the negation as qualifying the predicate

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LOGICAL THEORY IN LEIBNIZ rather than the copula. ‘No A is B’ then is understood as ‘Every A is not-B’; and ‘Some A is not B’ likewise is understood as ‘Some A is not-B’. Thus we have ‘Every man is a nonsoldier’ and ‘Some man is a non-soldier’. We shall want to ask whether this is a satisfactory resolution to the problem, and again we shall return to it later. In addition to the four categorical forms in the traditional square of opposition are the singular affirmative and singular negative, proposition types that include individual terms, here written as ‘X’: singular affirmative: singular negative: X is B. X is not B. Peter is a soldier. Peter is not a soldier. Singular propositions present a case of special interest and are illuminating for Leibniz’s philosophy of logic. We shall consider two issues, one raised by each interpretation. Extensionally interpreted, the expected analysis is that ‘Peter is a soldier’ is true just in case Peter is included in the class of soldiers. In this case it can be asked whether ‘inclusion’ is containment or merely intersection. Either answer seems to suffice, for the singular can effectively be treated equally as universal and as particular. As Leibniz notes, ‘Every Apostle Peter’ and ‘Some Apostle Peter’ coincide, since there is but a single individual (cf. GP VII, 211). So a class contains the class of (every) Peter if and only if it intersects the class of (every) Peter, thus yielding the desired equivalence. There is a second fine point arising here concerning the inclusion relation. Are we to say that it is the class whose sole member is Peter which is included in the class of soldiers, or Peter himself? This forces us to confront two distinct notions of inclusion: (1) the relation of an element to a class, i.e. class

membership, and (2) the relation of a subclass to a class. In modern terms we distinguish these relations as x ∈ y and x ⊆ y. Standard set-theoretic treatments of quantification would assign the unit class or singleton rather than the individual that is its single member as the object included in the extension of the predicate. As scholars have noted, the relevant concepts are still embryonic in Leibniz’s work and, moreover, they are intertwined with the part-whole relation (cf. Mugnai, 2006, p. 217), and the distinction between a singleton and its single member is not observed in Leibniz. So his extensional interpretation of logic slightly resists a direct translation into the usual contemporary settheoretic framework. It is possible with only small accommodations to let (extensional) inclusion be interpreted as the subclass relation, building in an epicycle to handle the case of singular propositions (cf. Swoyer, 1995a, pp. 97f.). The mechanics matter little. What is of interest is that Leibniz’s own statements of the extensional interpretation are typically framed not with the device of classes at all but with plural terms, and this suggests a relation of inclusion that forgoes sets or classes entirely. ‘Every man is a soldier’ is true just in case all the men are included among the soldiers. ‘Some man is a soldier’ and ‘Peter is a soldier’ will be true just in case at least one man is among the soldiers or Peter himself is among the soldiers, respectively. This is no accident on Leibniz’s part. He consistently opts for plural phrasing rather than set-theoretic ones in his analyses of expressions for infinitely large classes precisely in order to avoid commitment to infinite sets (cf. A, VI, iii, 503; A VI, vi, 157). And in his most advanced work involving quantified statements, the plural forms are explicit as well (cf. GP VII, 215f., C 193f.). It would seem that the most natural

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LOGICAL THEORY IN LEIBNIZ logical development of this phrasing is not by means of set-theoretic devices with an epicycle for singletons but with the logic of plurals, an area of study that has come into its own only recently (cf. Boolos, 1984; McKay, 2006; Nickel, 2012; see section 7 below). When the logic of plurals becomes more widespread and standard, replacing the usual artifice of set-theoretic analyses of natural language expressions for many purposes, as is my guess, Leibniz may again be regarded as having been ahead of his time and many of his successors. On the intensional interpretation, singular propositions raise a similar question, and Leibniz’s answer produces one of his signature metaphysical doctrines (cf. Kauppi, 1960, 213; Adams, 1994, pp. 62–3). The singular affirmative ‘Peter is soldier’ is true, intensionally understood, just in case the individual concept Peter includes the concept soldier. But must the predicate concept be directly included in the subject or may it be included only by means of a consistent addition? That is, as in the extensional case, ought the singular to be treated as universal or as particular? Again the answer is both: ‘the singular is equivalent to a universal and a particular’ (GP VII, 211/LLP 115). Such an equivalence requires that the concept Peter includes the concept soldier if and only if a consistent addition to the concept Peter will include the concept soldier. It is clear enough that if the concept Peter includes the concept soldier, then so will a consistent addition to the concept Peter, for the concept soldier is already included in it. But what underpins the opposite implication that if the concept soldier is a consistent addition to the concept Peter, then the concept Peter includes it? This will be true only if every concept that can be consistently added to the concept Peter is already included in it: that is, the concept

Peter must be complete. This holds equally for affirmative and negative singular propositions, and Leibniz explicitly holds that for any opposed pair of singular propositions, one must be true and the other false: ‘If two propositions of precisely the singular subject are presented, one of which predicates one of a pair of contradictory terms and the other predicates the other, then necessarily one proposition is true and the other is false.’ (C 67) Therefore the concept of any singular term must likewise be ‘logically complete’ or ‘negation complete’ in the strict sense: for any individual term X, for every predicate P, either the concept of P or the concept of ~P is included in the concept of X. Leibniz’s preference for the intensional approach over the extensional one is defended on grounds of naturalness (to Leibniz, anyway) and the wish to have the rules of logic free from a commitment to the existence of individuals. In Elements of a Universal Calculus, after noting the scholastics’ way of reading logic in terms of individuals that are instances of universal concepts, he writes: ‘I have preferred to consider universal concepts, i.e. ideas and their combinations, as they do not depend for their existence on individuals’ (A VI, iv, 199–200/P 20). The idea, presumably, is that the validity of the rules of logical inference should be prior to any contingent facts about what individuals there are, or whether there are any at all; so logic is best studied without the presupposition of the existence of individuals. Another point in favour of an intensional approach is a familiar oddity involved in the extensional approach. The extensional approach faces a sort of dilemma about universal propositions. If ‘Every A is B’ requires that there exist some As to constitute the relevant extension of ‘A’, then it seems universal claims carry ontological commitment to

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LOGICAL THEORY IN LEIBNIZ individuals. But sometimes we should like to allow some universal claims to be true even if they lack instances: for example, ‘Glass spheres are fragile’ is true even if there happen not to be any (though note the shift here to the generic rather than the universal proper). If, on the other hand, the extension of ‘A’ does not require the existence of any As but can stand empty as the null class, it seems to follow that in the case in which there are no As, both ‘Every A is B’ and ‘Every A is not B’ will be true, since the null class is automatically included as a subclass in any class. So, for example, it will be true that all philosopher-rulers are wise and that all philosopher-rulers are not wise. These are not strictly contradictory claims (we have been taught to accept), but it remains an uncomfortable result. And so too does the usual bromide that universal statements with no instances are always true but ‘only vacuously so’. The intensional approach avoids those difficulties. But as we have noted along the way, it has problems of its own. First, it seems to put too many sub-concepts into subject concepts, most spectacularly in the case of singular propositions. Second, the ‘consistent addition’ analysis seems to count particular propositions as true so long as the predicate is consistent with the subject even without instances of the subject having the predicate. (This is in effect the inverse of the problem that the extensional interpretation faces with universal propositions.) It is counterintuitive in itself and also apparently at odds with Leibniz’s claim that the intensional and extensional interpretations are equivalent, since, for instance, ‘Some philosopher-rulers are wise’ will be true intensionally interpreted but not extensionally interpreted. A third worry not yet mentioned concerns the identity of intensions. Suppose ‘Every A is B’ and ‘Every B is A’ are both true. In that case the intensions of ‘A’

and ‘B’ include each other. This implies that they contain all and only the same sub-concepts. If intensions are exhausted by their component concepts, then it seems that the concept of A and the concept of B are identical. (As we shall see below, Leibniz explicitly formulates this principle that co-inclusion implies identity.) Even if the concepts should somehow contain further (non-concept) ingredients to distinguish them, they will nonetheless be at least equivalent and thus guaranteed to apply to exactly the same things. Either way this seems too strong, for even when coextensive the concept of A and the concept of B may seem distinct and to contain distinct sub-concepts; and it may be only by chance that every A is B, or that every B is A. Even if all and only senators are corrupt, it seems at least possible for the concepts senator and corrupt to involve different sub-concepts and to pick out distinct classes of individuals (overlapping or not). Yet on the intensional approach those possibilities seem ruled out. Again, that seems counterintuitive, and it seems at odds with the idea of the equivalence of the intensional and extensional interpretations, since it seems extensions can coincide without necessarily coinciding, whereas intensions cannot. The problems for the claimed equivalence between the intensional and extensional interpretations are mitigated once we see that Leibniz intends the domain of individuals for the extensional interpretation of logic to include not just actual individuals but all possible individuals. This ensures the equivalence of the intensional and extensional readings of ‘Some As are Bs’, for there will be a consistent addition of the concept of B to the concept of A if and only if it is possible for an individual to be an A and a B. Likewise, ‘Every A is B’ and ‘Every B is A’ will both be true, extensionally interpreted, only if the terms ‘A’ and ‘B’ are necessarily coextensive, and it is not

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LOGICAL THEORY IN LEIBNIZ entirely implausible to treat necessarily coextensive terms as conceptually equivalent. (Leibniz was aware of ‘hyperintensional’ differences between necessarily coextensive terms; cf. Mugnai, 2006, p. 218.) Still, the difficulty remains for the intensional interpretation that it puts too much into subject concepts in its requirements of concept inclusion. It may help to recall that even in his logical works Leibniz inclines towards a divine view of intensions and the possibilities of things (cf. A VI, 4, 762), and perhaps God’s concepts of things really do include the whole truth about them. Also, if individuals are taken to be ‘world-bound’, it becomes easier to suppose that the concept of, say, this Peter (as opposed to any other possible individual) includes the concepts of everything that is ever true of him. If it did not, how would it be the concept of Peter himself rather than the concept of some other counterpart possible individual similar to Peter? Nonetheless, this spills over into a vast metaphysical debate about which it can fairly be doubted whether it belongs in the foundations of logic. Although Leibniz was fond of the ambitious claim that his metaphysics and logic were essentially two sides of the same system – as he wrote to Sophie, ‘the true Metaphysics is hardly different from the true Logic’ (GP IV, 292) – the right reply for Leibniz at this point may instead be an instrumentalist one: ‘It’s only a model, and it’s enough that it correctly identifies the valid inferences.’ In any case, we shall move on now to consider some details of the logical systems devised by Leibniz.

LEIBNIZ’S LOGICAL CALCULI Leibniz’s writings on logic are scattered across many texts and topics. For our

purposes we can simplify the landscape by focusing on the formal logical calculi presented in four concentrated studies. The first dates from 1679 and is presented concisely in the Specimen of a Universal Calculus and the Addenda to the Specimen (A VI, iv, N. 69 and 70). The second is worked out during the first half of the 1680s and culminates in Leibniz’s great 1686 work General Inquiries About the Analysis of Concepts and Truths (A VI, iv, N.165). It incorporates the results of the earlier Specimen and expands on them significantly, yielding Leibniz’s most extensive logical system, a fullblown ‘algebra of concepts’ if one that remains only quite roughly drafted. The third study of logical calculi comes in a series of papers written directly after the General Inquiries and is commonly referred to as the ‘studies in the calculus of real addition’, although this is slightly misleading as the key papers include both a calculus of real addition and a more comprehensive calculus of real addition and subtraction, the ‘plus-minus calculus’. The most notable documents here are A Study in the Calculus of Real Addition (1686/7, A VI, iv, N 177), and A not inelegant specimen of abstract proof, also known as A Study in the Plus-Minus Calculus (1687, A VI, iv, N. 178). These are more polished works than the General Inquiries, although narrower in focus and encompassing ‘weaker’ logical systems in that they do not have the resources to define all the key technical concepts of the General Inquiries. The fourth logical system is on display in On the Mathematical Determination of Syllogistic Forms (C 410–16) and A Mathematics of Reason (C 193–206), dating from about 1705. It provides the clearest notice of Leibniz’s full analysis of categorical logic and the theory of syllogism as well as his most intriguing insights into the theory of quantification.

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LOGICAL THEORY IN LEIBNIZ Only a very limited report on any of these logical calculi can be offered here. I shall sketch the 1679 calculus most briefly and save the majority of the comments for the General Inquiries and the studies in real addition. We shall end with a short consideration of Leibniz’s efforts to capture syllogistic logic, his insights into quantification, and a fairly deep problem his preferred intensional approach faces concerning the concept of negation.

THE 1679 CALCULUS OF THE SPECIMEN

‘if’, ‘then’, ‘not’, ‘and’ and ‘iff’ in their usual meanings. Here then is a sample of the propositions of this calculus, grouped roughly by the logical concepts they highlight and not observing Leibniz’s order or numbering from the Specimen (cf. Rescher, 1954). Predication: est, and negation: non-a (i) (ii) (iii) (iv) (v) (vi) (vii)

a est a a est b iff non-b est non-a if a est b and b est c, then a est c if a est b and b est a iff a = b a non est b iff not a est b a non est non-a if a est non-b, then a non est b

Conjunction- juxtaposition: ab

Leibniz’s system in the Specimen of a Universal Calculus and the related papers arises out of his earlier attempts to give an arithmetical treatment of logic. In the calculus of the Specimen, Leibniz uses lower-case Roman letters for terms (a, b, c, etc.), a unary operation of term negation (expressed by the Latin non), a binary conjunction-like operation (by juxtaposition: ab), and a binary predication relation between terms (by the Latin copula est) and its negation (non est), and relations of identity (eadem sunt) and distinctness (diversa sunt). Leibniz reached no stable decision about which propositions were to be axioms and which were to be derived theorems, changing his mind about the membership of the axiom base across different expositions. This is characteristic of his logical studies, and we shall mostly ignore the distinction in considering the propositions of his calculi here and elsewhere below. In presenting elements of the 1679 calculus, we adopt the usual convention of using the symbols ‘=’ and ‘≠’ for Leibniz’s Latin phrases for identity and distinctness, and we use the metalinguistic terms

(viii) (ix) (x) (xi) (xii) (xiii)

ab est a ab est b a est bc iff a est b and a est c if a est b and b est c, then a est c if b est a and c est a, then bc est a if a est b and c est d, then ac est bd

Identity (xiv) (xv) (xvi) (xvii) (xviii)

aa = a ab = ba If a = b and b = c, then a = c a ≠ b iff not a = b if a = b, then b = a

Leibniz expressly states the principle of substitutivity salva veritate for identicals: ‘Those terms are the same of which one can be substituted in place of the other salva veritate.’ (A VI, iv, 282/LLP 34) He also makes it clear that he construes this calculus intensionally: ‘By term I understand, not a name, but a concept, i.e. that which is signified by a name; you could call it a notion, an idea.’ (A VI, iv, 288/LLP 39) It is in the Addenda that Leibniz states outright his idea that the est relation should be interpreted as that of container to content, whereas in the Specimen itself est is

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LOGICAL THEORY IN LEIBNIZ left unspecified but obviously is read as the ‘is’ of predication, without forcing a deeper analysis of the structure of that relation. Interestingly, Leibniz also makes clear that his calculus allows a systematic interpretation that reverses the content-container relation: ‘All this is easily proved from the one assumption that the subject is as it were a container and the predicate a simultaneous or conjunctive content; or, conversely, that the subject is as it were a content, and the predicate an alternative or disjunctive container.’ (A VI, iv, 291/LLP 42) When ‘a est b’ holds by virtue of the fact that a contains b, we find that b is a conjunct of a, so that, in effect, a = by for some y (though y need not be distinct from b: for example, if a = b, since ‘a est a’ is always true as well). If, however, ‘a est b’ means that a is contained in b, then b turns out to be a ‘disjunctive container’. The point is clearer if we consider an extensional interpretation on which ‘a est b’ is true just in case the extension of a is contained in the extension of b. The term b now serves as a container of ‘alternatives’ or ‘disjuncts’ in the familiar way: its extension consists in a class of individuals, say, x, y, z, etc., and ‘a est b’ will be true just in case a is (identical with) either x or y or z, etc. Still, the fact that the link between the predication relation and the operation of conjunction is not yet made explicit as a principle is a notable difference between the Specimen and Leibniz’s later calculi. The 1679 calculus provides resources for rendering the traditional categorical forms for propositions, although in the Specimen and Addenda Leibniz says he is only going to address the universal affirmative, and he says he always assumes the subject letters to be prefixed with the ‘sign of universality’ (A VI, iv, 280). This time noting the traditional

letter names for the categorical types, the translations are:

A: universal affirmative E: universal negative Every A is B No A is B a est b a est non-b I: particular affirmative O: particular negative Some A is B Some A is not B a non est non-b a non est b With est indicating a container-content relation, the categorical propositions come out true in much the way described earlier. Intensionally construed: (A) ‘a est b’ is true just in case the concept a contains the concept b; (E) ‘a est non-b’ is true just in case the concept a contains the concept not-b; (I) ‘a non est non-b’ is true just in case the concept a does not contain the concept not-b; (O) ‘a non est b’ is true just in case the concept a does not include the concept b. As noted earlier, it is not directly clear why we should accept this account of the particular affirmative and negative, I and O, and although Leibniz’s explanation, in terms of the ‘consistent addition’ account is in place in the same year in Elements of a Calculus, an explicit statement of the theory of complete individual concepts that this will require is still years away. As Rescher (1954, p. 4) points out, this calculus will have to incorporate conditions of propriety for its terms requiring that they not be self-contradictory. In later developments Leibniz expressly demands that a term is an Ens or a possible being, and says this is always ‘tacitly assumed’ (GP VII, 214; cf. A VI, iv, 783: ‘A non-A non est res’). This is not observed in the Specimen or the Addenda, however, and exposes the system to inconsistency if we allow ‘b non-b’, for example, to

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LOGICAL THEORY IN LEIBNIZ count as a term permitted for any principle of the calculus. Suppose, from (vi), that b non est non-b. Then by (viii), b non-b est non-b; by (vii) b non-b est b; by (ii) non-b est non-(b non-b); and thus (b non-b) est non-(b non-b), apparently refuting (vi). Problems will also arise for the traditional inference rules of opposition and subalternation in the absence of a requirement of consistency of terms. The difficulties are precluded if it is required that for any ‘proper’ term a, there is no b such that a est b non-b.

THE CALCULUS OF THE GENERAL INQUIRIES The General Inquiries provides a remarkable construction of an ‘algebra of concepts’ articulated in 200 numbered entries. Leibniz evidently thought well of his results, and noted on the text: Hic egregie progressus sum (‘Here I have made great progress’, A VI, iv, 793n). Again, we shall select only a few items to consider and not follow Leibniz’s order or numbering. Leibniz uses capital letters as terms for concepts or propositions. He then sets out a relation of inclusion expressed by the copula (sometimes continet but mainly est is used so that ‘A est B’ means ‘in A is B’ or ‘A includes B’); a conjunction-like operation expressed again by the juxtaposition of letters (e.g. AB); an operation of negation expressed by affixing the Latin non to any combination of letters; and the principle of substitutivity salva veritate. Again using the expedient of rendering Leibniz’s work here in semi-formal terms, updating some of his notation (e.g. using ‘=’ for Leibniz’s ‘∞’), and enriching the formalism to note the more evolved state of the system of the General Inquiries, we may set out the elements of this calculus as follows (cf. Lenzen, 2004; Mugnai, 2006).

Capital letters A, B, C and so on will stand for non-logical terms. For logical symbols, we use the following: A=B

identity: A is identical (coincides) with B AB conjunction-juxtaposition: AB (for example: ‘philosopher ruler’) ~A negation: non-A A ≥ B inclusion: A includes B (Leibniz’s ‘A est B’) We shall help ourselves also to parentheses and the following metalinguistic symbols with their usual meanings: ‘&’, ‘→’ and ‘iff’. In the General Inquiries Leibniz considers but does not settle on a set of axioms from which to derive his many results. The principles he states, and often proves, are interesting independently of their status as theorems or assumptions of his calculus. The selection of principles below, all of which he expressly states, gathers together a sample to help describe formal properties of his logical terms. We also note relevant article numbers in the General Inquiries where the principles may be found. INCLUSION (1) (2) (3) (4)

A≥A [§37] ((A ≥ B) & (B ≥ C)) → (A ≥ C) [§19] (A ≥ B) iff (AB = A) [§83] ((A ≥ B) & (B ≥ A)) iff (A = B) [§§30, 110, 119] (5) ((A ≥ B) & A) → B [§55] (6) (A ≥ BC) iff ((A ≥ B) & (A ≥ C)) [§35] CONJUNCTION (7) (8) (9) (10)

AA = A AB ≥ A AB ≥ B AB → BA

[§§18, 24, 26, 171] [§38] [§38] [§6]

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LOGICAL THEORY IN LEIBNIZ IDENTITY (11) A = A [§§10, 156, 171] (12) ((A=B) & (B = C)) → (A = C) [§8] (13) (A = B) → (AC = BC) [§102]

which Leibniz regards as explaining the nature of intensional conjunction. Given his principle of reciprocity between extensional and intensional interpretations of inclusion, (PR)

NEGATION (14) (15) (16) (17) (18) (19)

~A = ~A A ≠ ~A ~~A = A (A ≥ B) iff (~B ≥ ~ A) (A = B) → (~A = ~B) ((A ≥ ~B) & (A ≥ ~C)) → (A ≥ ~B~C)

[§15] [§11] [§96] [§77] [§§2, 9, 171] [§103]

It is a striking collection, even as a small sample, and to the eye of readers familiar with the celebrated nineteenth-century developments in algebraic logic, several of Leibniz’s principles will jump out. Principles (1), (2) and (4) show that Leibniz’s inclusion relation ≥ is reflexive, transitive and anti-symmetric, respectively. This means that ≥ amounts to a partial ordering. But even more notable among his principles are (7) and (3), and, together with those two, (10). He regards principle (7), AA = A, as the characteristic law of his calculus, and it is precisely what would later become known as ‘Boole’s Law’. AA = A expresses the property of idempotence, and it is by Boole’s own account his main innovation in logic. Although the earlier 1679 calculus likewise included aa = a, this takes on greater significance for the system of the General Inquiries in the light of Leibniz principle (3), (A ≥ B) iff (AB = A),

(A ≥ B) iff (A ⊆ B),

from (7) the following principle concerning extensional conjunction is an immediate consequence: (*)

(A ⊆ B) iff (AB = A).

This tells us that extensional conjunction is, in effect, intersection, or the Boolean ‘meet’, an impression that is further confirmed in the obvious extensional interpretations of (5) and (6). Principle (10) expresses the commutativity of conjunction. Leibniz also assumes, though he does not state, the associativity of conjunction (i.e. A(BC) = (AB)C). With conjunction then defined as associative, commutative and idempotent, now adjoined to principle (*), plus the basic principles of negation, Leibniz’s formal algebra, interpreted extensionally, precisely describes a system equivalent to the structure of a meet semilattice with complement. In fact, as Lenzen has observed, principles (1), (2), (5), (6), (16), and Leibniz’s principle (stated at §200 of the General Inquiries and more perspicuously at C 407–8) A~B is impossible iff A ≥ B, taken together provide a complete axiomatization for an algebra of concepts that is isomorphic to Boolean algebra: i.e. the algebra resulting from those axioms can be proved to be deductively equivalent to Boole’s (cf. Lenzen, 1984, p. 200). This last principle just mentioned, concerning impossibility of a term, opens up a

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LOGICAL THEORY IN LEIBNIZ further layer of the logic of the General Inquiries. It is a modal system as well. Tied to Leibniz’s discussions of negation is the idea of the possibility or consistency of concepts or terms. In various places in the text Leibniz notes that a term A is taken to be possible (possibile) or a being (Ens). As he writes in a marginal note on §2: ‘A non-A is a contradictory term [contradictorium]. Possible is that which does not contain a contradictory term, i.e. A non-A. Possible is what is not: Y non-Y.’ (A VI, iv, 749n8) Although he considers the idea of allowing terms to be contradictory and to correspond to no being (cf. §154), it is clearly regarded as a theoretical option outside his preferred framework. An interesting expression of the use of the concept of possibility for terms is on display in §55. Principle (5) above is stated there, and it looks at first glance simply to be the correlate for modus ponens for terms or propositions: ‘If A contains B and A is true, B also is true.’ (A VI, iv, 757) A modal component comes to light, however, as Leibniz then further explains: ‘By a false letter I understand either a false term (i.e. one which is impossible, i.e. is a non-being [non-Ens]) or a false proposition. In the same way, by true can be understood a possible term, or a true proposition.’ (Ibid.) Thus ‘true’ and ‘false’ applied to terms are indicators of possibility and impossibility. Construed as denoting concepts, terms are true if the expressed concepts are consistent and false if they are contradictory. Construed as a denoting term for individuals, a term is true if it corresponds to a possible individual (or a class of them) and false if it does not. (Leibniz makes no affordance for ‘impossible individuals’ to instantiate false ideas.) This fits smoothly with his view that the extensions of terms include all possible individuals and not merely actual ones.

The modal aspect of the account plays more than an incidental role in the logic of the General Inquiries. It serves to underpin a theory of propriety for terms – which seemed missing from the calculus of the Specimen – and, arguably, it shows that Leibniz’s propositional calculus, in its treatment of conditional statements, includes an account of strict implication. Like Boole, Leibniz sees that his algebra of concepts can be used to construct a logical calculus for propositions. He is quite clear that his formal letters are meant to be interpretable either as terms (concepts) or as propositions. Even before the General Inquiries he had already noted that the containment relation can be taken as a relation of implication between propositions, and he treats the relation of antecedent to consequent in a conditional as one of containment (cf. A VI, 4, 551). In the General Inquiries, Leibniz says that from the proposition A contains B can abstracted a single term, A’s being B, which itself can serve as a term to stand in a relation of inclusion (cf. §138). So, for example, the hypothetical proposition ‘If A is B, then C is D’, linking two categorical propositions, can then be represented as the containment of the consequent in the antecedent, so that A’s being B contains C’s being D. At §75 Leibniz writes: ‘If, as I hope, I can conceive all propositions as terms, and hypotheticals as categoricals, and if I can treat all propositions in a very general way, this promises a wonderful ease in my symbolism and analysis of concepts, and will be a discovery of the greatest importance.’ (A VI, iv, 764/LLP 66) The simple principle that is the key to the account comes at §189: ‘Whatever is said of a term that contains a term can also be said of a proposition from which another proposition follows.’ (A VI, iv, 785/LLP 85) The plan for a logic of propositions is then to

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LOGICAL THEORY IN LEIBNIZ treat categorical propositions as terms and to treat the relation of implication for conditionals by the same rules he uses to analyse categorical propositions in the theory of term-containment. He can thereby show that ‘absolute and hypothetical truths have one and the same laws and are contained in the same general theorems’ (A VI, iv, 777). The outline of the account is straightforward. Using the familiar notions from propositional logic, the rules for terms can be translated into rules for propositions by replacing ‘A ≥ B’ with ‘P → Q’, replacing ‘~A’ with ‘¬P’, and replacing ‘AB’ with ‘A & B’. This yields a rich set of principles in propositional logic, but Leibniz provides little more than the key schematic suggestions and does not develop propositional logic in detail here or elsewhere, although in passages across many texts he can be observed correctly formulating various of the related rules. For all his interest in logic, he did not concern himself much with the propositional calculus. Still, the link between the modal theory of propriety for terms and the analysis of implication as containment holds his attention long enough for Leibniz to put his finger on the idea that the relevant notion of implication is that of entailment:

corresponds not to ‘¬(P & ¬Q)’ of the material conditional but rather to ‘¬ Possibly ¬(P & ¬Q)’ of the strict conditional. It is a delicate matter to parse the meaning of the conditional occurring in an author’s logical texts prior to the full clarification of the difference between the material and strict conditionals in the twentieth century. Leibniz does not discuss the distinction himself, and his formulations can be more ambiguous than the one just given. For example at A VI, 4, 656, he writes: ‘If L is true follows from M is true, this means that it cannot at the same time be supposed [non simul supponi potest] that L is true and M is false.’ Here the intended force of ‘cannot’ is not simply put beyond doubt. Given the careful deployment of the concept of possibility in the General Inquiries, the case for regarding Leibniz’s logic for propositions as including strict implication is quite plausible. Still, as Mugnai (2005, p. 178) observes, it would have been rather more revolutionary if Leibniz had given pre-eminence to the material conditional, as later authors of logical calculi did.

A contains B is a true proposition if A non-B entails a contradiction. This applies both to categorical and to hypothetical propositions, e.g. If A contains B, C contains D can be formulated as follows: ‘A contains B’ contains ‘C contains D’; and thus, A containing B and at the same time C not containing D entails a contradiction. (C 407).

Leibniz refines his work in logical calculus in essays written soon after the General Inquiries in which he elaborates his calculus of ‘real addition’ and the fuller ‘plus-minus calculus’. These are perhaps his most polished writings in logic, although they are by no means comprehensive of his views and are less ambitious than the General Inquiries. In these papers Leibniz introduces a binary operation of conjunction denoted by the symbol ‘⊕’, taken to be analogous to but distinct from arithmetical addition, and a binary operation analogous to subtraction denoted by a long bar ‘–’

This accords precisely with his view that ‘A≥B’ is equivalent not only to the falsity of ‘A~B’ but to its impossibility. Translated into propositional terms, this means that ‘P → Q’

THE CALCULUS OF REAL ADDITION

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LOGICAL THEORY IN LEIBNIZ infixed between terms. Leibniz also includes symbols for identity (or ‘coincidence’) and distinctness, along with the principle of substitutivity salva veritate. He does not offer a study of negation. (The novel and difficult treatment of the idea of ‘real subtraction’ will have to be set aside here; for a development, see Lenzen, 2004, pp. 20–34.) Again, a few extracts may help to give the flavour of the account, this time taking directly from the language of the texts, in this case from the paper A Study in the Plus-Minus Calculus. In this paper Leibniz uses the plain symbol ‘+’ with the same technical meaning as he does elsewhere with ‘⊕’; and even in other places he often uses ‘+’ for convenience once the new symbol ‘⊕’ is introduced. To highlight the intended meaning of the operation, I use ‘⊕’ throughout. Here, then, is a sample from the Plus-Minus Calculus: Definition 1. Those terms are the same of which one can be substituted for the other salva veritate. Definition 2. Those terms are different which are not the same, i.e. in which a substitution sometimes does not hold good. Symbol 1. A = B means that A and B are the same, or coincident Symbol 2. A ≠ B, or B ≠ A, means that A and B are different. Definition 3. If several terms taken together coincide with one , any one of those several is said to be in or to be contained in that one term, and the one term is said to be the container. Conversely, if some term is in another, it will be among several others which together coincide with that other term [ . . . and this term] is called an inexistent or content. . . . It can happen that container and content coincide, e.g. if one should have A ⊕ B = L, and A and L coincide; for then B

will contain nothing other than A, but if it does not signify A, it will signify Nothing. Symbol 3. A ⊕ B = L means that A is in L, or is contained in it. Definition 5. If A is in L, and some other term, N, should be produced, in which there remains everything which is in L except what is also in A (of which nothing must remain in N), A will be said to be subtracted or removed from L, and N will be called the remainder. Symbol 4. If we have L – A = N, what is meant is that L is a container, of which the remainder is N if you subtract A from it. Axiom 1. If the same term is taken with itself, nothing new is constituted; i.e. A ⊕ A = A. Axiom 2. If the same term is added and subtracted, then whatever is constituted in another as a result of this coincides with Nothing. That is, A – A = Nothing. Postulate 1. Several terms, whatever they may be, can be taken together to constitute one ; thus, if they are A and B there can be formed from these A ⊕ B, which can be called L. (With omissions, from A VI, 4, 846–8/LLP 123–4) Leibniz goes on to prove a little over a dozen theorems, including (Thm. I) if A = B and B = C, then A = C; (Thm. III) if A = B, then A ⊕ C = B ⊕ C; and (Thm. VII) if B is in A, then A ⊕ B = A, and its converse (call it ‘Thm. (VII*)’) if A ⊕ B = A, then B is in A. Those last two, (VII) and (VII*), together yield the principle that A contains B if and only if A ⊕ B = A, or again using ‘≥’ for containment: (#) A ≥ B iff A ⊕ B = A. This is of course familiar from the General Inquiries already, having been noted as (3) in

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LOGICAL THEORY IN LEIBNIZ our discussion above, and it illuminates an important property of the conjunction operation ⊕. In this later essay, the remark in Leibniz’s Definition 3 shows a nice property of ⊕. Leibniz considers the case in which A ⊕ B = L and A = L, and says that B either coincides with A or signifies Nothing. (As Mugnai [2006, p. 224] observes, Leibniz overlooks here the possibility that B is itself contained in A without coinciding with A.) Pursuing the latter alternative yields the result that A ⊕ Nothing = L, and then since A = L, it follows that A ⊕Nothing = A. In his paper A Study in the Calculus of Real Addition, of the same year or perhaps the year before, we find very much the same treatment of the key concepts, though Leibniz stresses certain features of the ⊕ operation in a way that throws further light on the subject. For instance, the commutativity of ⊕ is given explicitly as an axiom, B ⊕ N = N ⊕ B, alongside the axiom expressing the characteristic law of idempotence A ⊕ A = A. In a scholium to those two axioms, the properties of ⊕ and aspects of Leibniz’s view of his logical calculus in general are made even clearer: As general algebra is merely the representation and treatment of combinations by signs, and as various laws of combination can be discovered, the result of this is that various methods of computation arise. Here, however, no account is taken of the variation which consists in a change of order alone, and AB is the same for us as BA. Next, no account is taken here of repetition; i.e. AA is the same for us as A. Consequently, whenever these laws are observed, the present calculus can be applied. It is evident that this is observed in the composition of absolute concepts when no account is taken of order or repetition. Thus, it is the same to say ‘hot

and bright’ as to say ‘bright and hot’, and to speak of ‘hot fire’ or ‘white milk’, with the poets, is a pleonasm; ‘white milk’ is simply ‘milk’, and ‘rational man’ – i.e. ‘rational animal which is rational’ – is simply ‘rational animal’. It is the same when certain determinate things are said to exist in things: real addition of the same thing is vain repetition. When two and two are said to be four, the latter two must be different from the former. If they were the same, nothing new would result; it would be just as if, for a joke, I wanted to make six eggs out of three by first counting three eggs, then taking away one and counting the remaining two, and finally taking away one again and counting the remaining one. But in the calculus of numbers and magnitudes, A, B or other signs do not stand for a certain thing, but for any thing of the same number or congruent parts. (A VI, iv, 834/ LLP 142–3) We now have the elements for a nice complement to the results concerning logical conjunction from the General Inquiries in which Leibniz’s calculus (extensionally interpreted) yielded a meet-semilattice with conjunction equalling set-theoretic intersection. In the later papers, the principles of commutativity and idempotence are again expressly formulated for ⊕, and again associativity (i.e. A ⊕ (B ⊕ C) = (A ⊕ B) ⊕ C) is assumed by Leibniz in his proofs but not stated. Adding now (#) A ≥ B iff A ⊕ B = A, and the principle that A ⊕Nothing = A, the resulting system describes a structure equivalent to a join-semilattice in which ‘⊕’ denotes an operation that behaves formally like set-theoretic union (cf. Swoyer, 1995a and Mugnai, 2006). Still, care must be taken in considering these results about the formal behaviour of Leibniz’s symbol ‘⊕’. To ‘read’ Leibniz’s

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LOGICAL THEORY IN LEIBNIZ algebraic logic extensionally – i.e. to interpret its symbols as implicitly defined by its laws and then consider a model of it in terms of sets of individuals – is one thing. To consider his theory of the extensions of terms in his preferred semantics is another. Thus, if we read inherence extensionally, so that ‘A est B’ means ‘the extension of A contains the extension of B’, we find that ‘⊕’ denotes union and the formal structure is a join-semilattice. If we read inherence intensionally, so that ‘A est B’ means ‘the concept of A contains the concept of B’, ‘⊕’ denotes Leibniz’s relation of ‘real addition’. Yet certainly for Leibniz those two interpretations are not themselves equivalent; rather they are reciprocal. When Leibniz asserts (#) A ≥ B iff A ⊕ B = A, his meaning for the copula est (here ‘≥’) is indexed to the notion of concept containment. What ‘⊕’ denotes, for him, is ‘real addition’ for concepts. His principle of reciprocity (PR) then tells us that the equivalent truth about extensions is A ⊆ B iff A ⊕ B = A. Under those conditions, of course, ‘⊕’ denotes intersection and the relevant structure is a meetsemilattice, as noted above in connection with the General Inquiries. (See Swoyer, 1995a, pp. 105ff. for further analysis.) When the semantics comes apart from the abstract formal systems in this way, we encounter one of the deep, defining facts about logic: the same formal system of rules allows a plurality of different interpretations, yielding theories that may have in common only their abstract structure. This is a very ‘modern’ idea about logical systems, and one that Leibniz appears to have seen as well. As he points out, his inherence relation – ‘to be in’ or inesse – can be interpreted to stand for any number of different relations: We say that concept of the genus is in the concept of the species, the individuals of

the species in the individuals of the genus, a part in the whole, and in the indivisible in the continuum. . . . In general this consideration extends very widely. We also say that inexistents are contained in those terms in which they are. Nor does it matter here, with regard to this general concept, how those terms which are in something are related to each other or to the container. So our proofs hold even of those terms which compose something distributively, as all species together compose a genus. (A VI, iv, 832–3/LLP 141) Leibniz was aware as well that his operator ‘⊕’ which he understood to express real addition, a relation of conjunction, would express instead a relation of disjunction if inherence is interpreted extensionally. This is what we noted earlier in connection with the Addenda to a Specimen of a Universal Calculus where Leibniz observed that ‘a est b’ could be read as ‘a contains b’ or ‘a is contained by b’, requiring only a switch from interpreting the content as a conjunct of the container to a disjunct or alternative within it (cf. A VI, iv, 291) – a choice of stances that naturally invokes either the intensional or extensional interpretation, respectively. So in many respects Leibniz shows an attitude towards the study of logic far ahead of his time. O’Briant (1968, p. 25) suggests that Leibniz never published his works in logic in part because they lacked a suitable audience: ‘Who would have been his readers?’ This outpouring of ideas in the algebra of logic comes 150 years or more before the same ideas would be discovered with fanfare by the nineteenth-century algebraists. It is those sorts of results above all – though not only those results – that readers of the history of logic have had in mind when retrospectively giving Leibniz a position in the top

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LOGICAL THEORY IN LEIBNIZ rank of writers in logic. George Boole’s widow, Mary Everest Boole, reports that Boole himself felt ‘as if Leibniz had come and shaken hands with him across the centuries’ when he learned of Leibniz’s anticipations of his own work in algebraic logic (quoted in Latia 1976, p. 243; cf. Peckhaus, 2009). Boole was not alone in the sentiment. The mathematical logicians at the end of the nineteenth century, although their discoveries were independent of Leibniz’s, immediately recognized the importance of his results when they finally became known and accepted his priority. There is much more in the details of the General Inquiries and the studies in real addition and subtraction than can properly be examined here. For the moment let us consider what the algebraic results already reviewed mean about Leibniz’s place in the canon of logic. As we noted above, principles can be extracted from Leibniz’s writings on logical calculus that together constitute a set of axioms and rules of inference sufficient to capture all of Boolean algebra. Still, it is not clear how far Leibniz’s anticipations amount to a first discovery of Boole’s logic. We should want more than just the fact that key principles stated by Leibniz would amount to a complete axiomatization. The grasp of the relations between the propositions and the logical system itself, at least as reflected in the proof practices, should be central here as well. On this score there are certainly gaps evident between Leibniz’s work and standard formulations of Boolean algebra, probably the most striking of which is his relative silence about the operation of disjunction that is the logical dual of conjunction. Although conjunction and complement are together sufficient to define disjunction, and although in A Mathematics of Reason

(c. 1705) Leibniz reserves the letter ‘v’ (short for the Latin vel) as a symbol for inclusive disjunction (cf. GM VII, 57), Leibniz shows no interest in or evident awareness of the duality of conjunction and disjunction, whereas in modern logic this duality is central to the basic algebraic practice of logic. The passage from A VI, iv, 291, quoted above, noting how ‘⊕’ can be interpreted either as conjunction or as disjunction, is one of the very few mentions in the texts, and the idea is not further developed. It is worth observing as well that the familiar equivalences between statements involving the two operations are normally effected by means of De Morgan’s rules, which themselves are quite neglected by Leibniz, even in the few places where he notes or employs them in passing (cf. Mugnai, 2005, pp. 22f.). So although Leibniz’s principles can readily be codified in a way that yields a system equivalent to Boole’s, and Leibniz himself gives primacy to many of the key elements, it also seems clear that Leibniz did not share the grasp of a number of analytical relations among the terms of the calculus that would seem integral to the characteristic understanding of modern algebraic logic. Commentators through most of the twentieth century tended to underestimate the depth and breadth of Leibniz’s advances in logic, and often quite greatly. But it is not hard to exaggerate his accomplishment either, especially in algebraic logic where his papers are so rich with premonitory insights.

THE JUSTIFICATION OF SYLLOGISTIC LOGIC As is widely recognized, one of Leibniz’s central aims in logic across his career was to develop a formal system that would justify

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LOGICAL THEORY IN LEIBNIZ the traditional theory of syllogism. It has often been suggested that his efforts fell short on exactly this point and, even, that he ‘never succeeded in producing a calculus which covered even the whole theory of the syllogism’ (Kneale and Kneale, 1962, p. 337). This negative verdict seems to be incorrect. Moreover, the logical papers in which Leibniz offers his most comprehensive treatment of the theory of syllogism are also where his most advanced work on a theory of ‘indefinite terms’ and other forays into the nature of quantification can be found. The theory of syllogism concerns the traditional syllogistic inference forms involving the four types of categorical propositions, A, E, I and O, as well as the laws of ‘immediate’ inference: opposition, subalternation and conversion. Each syllogism is a three-part argument, with a major premise, a minor premise and a conclusion, where the premises share a common middle term that is eliminated in the inference to the conclusion. So, for example, we may have: A Every C is D A Every B is C A Every B is D This syllogism can be generically coded AAA for its constituent propositions; its traditional mnemonic name is Barbara. In a shorthand sometimes favoured by Leibniz, categorical propositions can be more precisely coded by category letter, subject term and predicate term, so that ‘Every C is D’ becomes ACD, and a whole syllogism can be then expressed as a sequence of three proposition codes. For Barbara this yields the sequence: ACD ABC ABD. There are 256 possible types of syllogisms, ignoring the order of major and minor premises, of which 24 are traditionally identified as valid

forms. The valid forms are further classified into four ‘figures’ with six ‘moods’ each. The moods of the first figure are Barbara, Celarent, Darii and Ferio, Barbari and Celaro, named after their constituent categorical forms: AAA, EAE, AII, AEO, AAI and EAO. A logical theory that justifies the traditional theory of syllogism would need to prove the validity of the 24 valid forms and of the 8 immediate inferences: Opposition:

¬ABC iff OBC, ¬EBC iff IBC Subalternation: ABC → IBC, EBC → OBC Conversion: EBC iff ECB, EBC → OCB, ABC → ICB, IBC iff ICB Leibniz discovers that the project of justifying traditional syllogistic theory can be reduced to proving the validity of Barbara, Celarent, Darii and Ferio, and the two rules of opposition. As he shows in the paper Of the Mathematical Determination of Syllogistic Forms (C 410–16), all the rest of the figures and moods can be derived from those six pieces plus a basic logical inference form he calls ‘regress’. In Leibniz’s approach there are five major elements. Barbari and Celaro follow from the first four moods plus the rules of subalternation. The rules of subalternation follow from Darii and Ferio. The moods of the second and third figures can be reduced to those of the first by ‘regress’. The rules of conversion can be derived from the second and third figures. Leibniz says also that the moods of the fourth figure follow from the others by the rules of conversion, but he leaves only the words ‘Figura Quarta’ at the bottom of the manuscript as a reminder for the promised analysis without carrying it out. In A Mathematics of Reason, however, Leibniz produces that proof as well, and the reduction is complete (cf. Lenzen, 1988 and 2004). In the Syllogistic Forms, Leibniz argues from first principles concerning containment

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LOGICAL THEORY IN LEIBNIZ relations for the validity of the four ‘primitive’ moods of the first figure (C 410f./LLP 105–6). In doing so he appeals to the mereological concepts of part and whole in spelling out the ideas of containment, and having completed his justification he remarks: ‘These statements have no less geometrical certainty than if it were said that that which contains a whole contains a part of the whole, or that that from which a whole is removed has a part of that whole removed from it.’ (C 411/ LLP 106) The general scheme of part and whole can be applied equally to intensional and extensional interpretations of the logic. For Leibniz, subconcepts are parts of concepts and subclasses are parts of classes, and in both cases the constituents can be resolved down to elements, whether primitive simple concepts or individuals. But as it is clear from the actual ‘direction’ of the containment relations described in Syllogistic Forms, Leibniz is working here with an extensional interpretation: in the universal affirmative, for example, the individuals named by the subject term are contained in those named by the predicate.

QUANTIFICATION AND PLURALS Leibniz’s handling of ‘indefinite’ terms in various texts on logic is often reminiscent of contemporary uses of variables and quantifiers, and it shows that he was at least feeling his way towards a theory of quantification. Already by 1679 Leibniz had, in the context of a mathematical model of the syllogisms, worked out a formulation of the universal affirmative ‘a est b’ as ‘a = by’, where the intended reading of the identity is that a is the product of b together with some y (cf. C 57). The idea of expressing the categorical

propositions as algebraic equations is a lasting thread of his formalism, and so too is the use of indefinite letters to indicate the idea of quantity. Across many later texts Leibniz uses capital letters, mostly from the end of the alphabet, as privileged symbols for quantity in his expressions of the categorical propositions and typically with an eye towards formalizing syllogistic inferences. In the General Inquiries, the use of a letter for an indefinite terms seems closer still to the existential quantifier when Leibniz explains his expression ‘A = BY’ this way: [B]y the sign Y I mean something undetermined so that BY is the same as some B . . . , so A est B is the same as A coincides with some B, or, A = BY. (A VI, iv, 751/LLP 56) Since ‘B’ itself is a definite term, the sign ‘Y’ appears to act as a quantified variable so that ‘some B’ means ‘something Y that is B’. Lenzen (2004, pp. 48–9) explicitly writes ‘∃Y(A = BY)’ for this, and with some justice. There are various passages in the fragments on logic in which Leibniz’s own words strike directly the canonical contemporary phrasing ‘there is a Y such that . . . . Y . . . . ’ (for example, at C 235/LLP 90: Si A = AB, assumi potestY tale ut sit A = YB; or C 261: dicere A non est B, idem esse ac dicere: datur Q tale ut QA sit non B). Leibniz can also be found appearing to formulate and apply instances of the rule for existential introduction in the General Inquiries at §§23, 24, 49 and 117. Yet Leibniz often does not have elementary aspects of the quantifiers sorted out in his use of indefinite terms, and in particular he does not see with clarity the quantifier negation rules ¬∀XP iff ∃X¬P and ¬∃XP iff ∀X¬P. This puts into doubt the degree to which his treatment of indefinite terms

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LOGICAL THEORY IN LEIBNIZ effectively distinguishes between the existential and universal quantifiers. Still, there are moments at least where he is strikingly trying to mark the difference, as for example in §112 of the General Inquiries where, struggling to sort the two out, he reserves a distinct notation ‘Ῡ’ expressly to mean ‘any Y’ in contrast to the plain sign ‘Y’ for ‘some Y’. And in a similar passage at C 271, he – writes: ‘Let us see how X and X differ, certainly as some and any, but this occurs by accident and I want it to be X simpliciter.’ This might have been the start of a close study of the quantifiers and their rules, but he does not pursue the subject (cf. Lenzen, 2004, p. 53). There are other provocative insights as well. As has been widely noted, in the later paper A Mathematics of Reason, Leibniz offers an interpretation of the categorical propositions that involves quantifying the predicate. The laws of syllogism, says Leibniz, can be proved by an analysis given in terms of ‘same’ (euisdem) and ‘distinct’ (diversum), and he renders the categorical forms as follows (quotations excerpted from C 193/LLP 95): A Every A is B: ‘Any one of those which are called A is the same as some one of those which are called B.’ E Some A is B: ‘Some one of those which are called A is the same as some one of those which are called B.’ I No A is B: ‘Any one of those which are called A is distinct from any one of those which are called B’. O Some ‘Some one of those which are A is not B: called A is distinct from any one of those which are called B’

Leibniz remarks, ‘Hence, by virtue of logical form, the predicate is particular in affirmative propositions and universal in negative propositions’ (ibid.). Commentators have typically followed Couturat’s surprising claim that Leibniz puts this analysis forward in order to reject it (C 194 fn. 1). I agree here with Lenzen (2004, p. 65) that this opinion is ‘somewhat incomprehensible’, as it is plainly Leibniz’s preferred apparatus in the paper, and he puts it to use in the crucial derivation of the moods of the fourth figure. Nevertheless, quantification of the predicate admits of different interpretations, and it remains to consider how best to understand Leibniz’s treatment. One way would be to use the familiar modern set-theoretic framework employed in interpreting second-order logic, so that, for example, the universal affirmative ‘Every A is B’ is taken to mean that for every member x of the set A, there is a member y of the set B such that y = x. With ‘∈‘ indicating set membership and capital letters denoting sets, we put this into symbols as: (∀x)(x∈ A → (∃y)(x∈ B &y = x)) (cf. Lenzen, 2004, pp. 63f.). Thus Leibniz’s statements of the categorical propositions turn out to be ‘set theory in sheep’s clothing’. But the set-theoretic device seems to be an unnecessary add-on to Leibniz’s own formulations, which read very naturally instead as quantification with plural terms. Just what are ‘those which are called A’ and ‘those which are called B’? The As and the Bs themselves. We do not need sets to express this or the corresponding categorical statements. The relation of sameness Leibniz isolates with the phrase ‘one of those which are called A’ can be stated more simply as ‘x is one of the As’. We then have: (∀x)(x is one of the As → (∃y) (y is one of the Bs &x = y)).

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LOGICAL THEORY IN LEIBNIZ This agrees quite closely with Leibniz’s own words, in Parkinson’s translation: ‘Any one of those [quemlibet eorem] which are called [qui dicuntur] A is the same as [eundeum esse cum] some one of those [aliquo eorum] which are called B.’ Leibniz’s Latin terms quemlibet and aliquo mark the number of the quantifiers as singular, but the underlying logical ideas can be presented in number-neutral terms that allow a plural reading of the variables as well. A few easy pieces of formalism will help to draw this out. First, we use ‘variably polyadic’ variables that admit of singular or plural readings (written here with a surface plural form): ‘xs’, ‘ys’, etc., and their corresponding quantifiers ‘(∀xs)’ and ‘(∃ys)’. Second, we interpret the sign ‘=‘ for identity as not marked for number so that it can be taken as ‘is’ or ‘are’ as needed. Last, we introduce a variably polyadic relation of inclusion in a plurality denoted by ‘