Leibniz’s naturalized philosophy of mind [First edition.] 9780198714583, 0198714580

Table of contents :
IntroductionPart I: Leibniz's Naturalizing Project1: Nature and Natures2: Naturalizing Constraints: Equipollence and Continuity3: The Intelligibility of NaturePart II: The Metaphysical Basis of Minds4: Substance and Force5: Living Mirrors: Expression and Perception6: Perceptual Distinctness and Mental ActivityPart III: Mind in the Natural Order7: Perception, Consciousness, and Continuity8: Looking Back: Memory and Consciousness9: Looking Forward: Appetite and DesirePart IV: The Prerogative of Minds10: Rational Beings and Animal Souls11: Moral Identity and the Appearance of the Self12: Self-Reflection, Perception, and Conceptual ThoughtConclusion

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Leibniz’s Naturalized Philosophy of Mind

OUP CORRECTED PROOF – FINAL, 11/2/2019, SPi

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Leibniz’s Naturalized Philosophy of Mind Larry M. Jorgensen

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Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Larry M. Jorgensen 2019 The moral rights of the author have been asserted First Edition published in 2019 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2018965179 ISBN 978–0–19–871458–3 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.

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For Lillian and Evan

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Contents Acknowledgments List of Abbreviations

ix xi

Introduction

1

Part I. Leibniz’s Naturalizing Project 1. Nature and Natures

11

2. Naturalizing Constraints: Equipollence and Continuity

32

3. The Intelligibility of Nature

56

Part II. The Metaphysical Basis of Minds 4. Substance and Force

89

5. Living Mirrors: Expression and Perception

101

6. Perceptual Distinctness and Mental Activity

120

Part III. Mind in the Natural Order 7. Perception, Consciousness, and Continuity

145

8. Looking Back: Memory and Consciousness

172

9. Looking Forward: Appetite and Desire

201

Part IV. The Prerogative of Minds 10. Rational Beings and Animal Souls

225

11. Moral Identity and the Appearance of the Self

244

12. Self-Reflection, Perception, and Conceptual Thought

259

Conclusion—Nature and Grace: Striking a Leibnizian Harmony

283

Bibliography Index

291 301

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Acknowledgments Karl Barth’s commentary on the book of Romans opens with an acknowledgement that the book was written against the background of the echoing of guns and entrenched warfare.¹ This historical moment gave Barth’s work a spirit of urgency, a sense that theologians needed to read carefully once again and with fresh eyes one of the foundational works of their discipline. As he said in the preface to the first edition, “The understanding of history is an uninterrupted conversation between the wisdom of yesterday and the wisdom of tomorrow.”² I would have liked to produce a similar sort of book. The sounds of war have been ricocheting in the background of this book as well—starting when my second year of graduate studies was interrupted by the 9/11 attacks and ending now with two consecutive summers in the United States where a sanctuary was violated by mass murder (the Emmanuel AME Church in Charleston, South Carolina, on June 17, 2015, and the Pulse nightclub in Orlando, Florida, almost exactly one year later on June 12, 2016), and in mediating years between 2001 and today, there has been continuous conflict around the world and, more recently, a major refugee crisis. This book is an academic book on Leibniz’s philosophy of mind, not directly connected with the tragic scene I have just mentioned. And yet, I do think that we often need to look back before we are prepared to move forward. Leibniz was writing in the midst of a religiously and politically fractured Europe. And his philosophy of mind is a piece of a much larger vision of the life of a mind oriented towards justice. While Leibniz’s optimism has met with caricature and derision, he sought to give it a deep metaphysical grounding, some of which will come out in the course of this book. Leibniz’s double vision—of a regular and intelligible natural order, which would allow for scientific and technological progress, and of a value-rich natural order, which would allow for actions motivated by justice and love here and now—grounded a hope for reconciliation and peace in Europe. And while I have no fantasies that an academic book in the history of philosophy will do the same for our fractured world, it is animated by a similar vision for serious work motivated by the genuine interest, thoughtfulness, and respect that is a pre-requisite for any real change. In this, I have been deeply shaped by my relationships with colleagues and advisors. Michael Della Rocca, Robert Merrihew Adams, and Alison Simmons made opportunities for long conversations that deepened my thinking on Leibniz in innumerable ways. Samuel Newlands, Mark Kulstad, Martha Bolton, Julia Jorati, Jeffrey MacDonough, Andrew Chignell, Donald Rutherford, Daniel Garber, Christian Barth, Gregory Brown, Paul Lodge, Maria Rosa Antognazza, Marleen Rozemond, and Markku Roinila have all enriched my work. Peter Momtchiloff at Oxford University Press deserves particular thanks for his help in getting this project to completion. ¹ Karl Barth, The Epistle to the Romans, trans. Edwyn C. Hoskyns (London: Oxford University Press, 1933), v. The first edition was printed in 1918. ² Ibid., 1.

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I emphasize to my students the need for a strong community of philosophers, and this is my community. But my community extends much wider than this. I presented portions of this work at the X Leibniz Congress in Hannover, Germany; the Second Arctic Circle Seminar in Early Modern Philosophy in Finland; the “Force Forschung: Modern Philosophical Conceptions of Force” at Cornell University; the Second and Sixth Biennial Margaret Dauler Wilson Conferences at UCSD and Dartmouth; the Scottish Seminar in Early Modern Philosophy in Aberdeen, Scotland; “Early Modern Conceptions of Consciousness” at Humboldt University, Berlin; the Midwest Seminar in Early Modern Philosophy at Marquette University; the First Annual Leibniz Society Conference at Rice University; the Houston Early Modern Group; and the Central Canada Seminar for the Study of Early Modern Philosophy at the University of Guelph. I am grateful for the many conversations I had with participants at each of these conferences. I would like to acknowledge the Department of Philosophy and the administration of Skidmore College and an NEH Summer Grant for support of this project. The writing groups at Skidmore College were an invaluable source of encouragement. Colleagues and students at Skidmore College and Valparaiso University and friends in Saratoga Springs have been endlessly supportive of my work, and I find it a real boon to work and live amongst these amazing and wonderful people. At a more fundamental level, this book took shape around a rich and complicated life with my family. For Lillian, this book has taken shape around cooperative fulltime childcare, a brief life in London, and concerts ranging from chamber ensembles to Imagine Dragons. From the beginning of this project—naming a neighborhood cat “Light Miss” (after Leibniz)—until today, Lily has become a fellow traveler out of The Cave, full of insight and a passion for justice. For Evan, this book took shape around trampolines and ADK fire towers. He is the only kid I know who is enticed into drinking his milk by Zeno’s paradox. Through his unending curiosity and questioning, Evan has shown the polymath drive that Leibniz himself had: science, philosophy, math, history, theology, and literature all have a space in Evan’s head (and often in unexpected ways!). And, finally, Caitlin’s encouragement and grace infuse this book with meaning. She has been my full partner in exploring with wonder the life of the mind, and we are together building something that we merely glimpsed twenty years ago. She is our local superhero (seriously!), and she persists. * * * Portions of this book have been published previously, although most of the work has been revised and reworked for this volume. A part of chapter 2 overlaps with “By Leaps and Bounds: Leibniz on Transcreation, Motion, and the Generation of Minds,” The Leibniz Review 23 (2013): 73–98. Chapters 3 and 7 make use of material from “The Principle of Continuity and Leibniz’s Theory of Consciousness,” Journal of the History of Philosophy 47 (2009): 223–48. Chapters 5 and 6 make use of material from “Leibniz on Perceptual Distinctness, Activity, and Sensation,” Journal of the History of Philosophy 53 (2015): 49–77. Chapters 8 and 9 revisit material from “Leibniz on Memory and Consciousness,” British Journal for the History of Philosophy 19 (2011): 887–916 and “Mind the Gap: Reflection and Consciousness in Leibniz,” Studia Leibnitiana 43 (2011): 179–95. The conclusion draws in part from “Consciousness in Western Philosophy” in The Routledge Handbook of Consciousness, ed. Rocco Gennaro (New York: Routledge, 2018), 24–37.

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List of Abbreviations Abbreviations for Editions of Leibniz’s Works: A AG Arthur

C Child

CP

DM DSR Dutens G GM Grua L LA LC

Langley Lodge

Sämtliche Schriften und Briefe (Darmstadt and Berlin: Berlin Academy, 1923–). Philosophical Essays, trans. Roger Ariew and Daniel Garber (Indianapolis, IN: Hackett, 1989). The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672–1686, trans. Richard T.W. Arthur (New Haven, CT: Yale University Press, 2001). Opuscules et Fragments Inédits de Leibniz, ed. Louis Couturat (Hildesheim: Georg Olms, 1966). The Early Mathematical Manuscripts of Leibniz; translated from the Latin texts published by Carl Immanuel Gerhardt with critical and historical notes, trans. J.M. Child (Chicago; London: The Open Court Publishing Company, 1920). Confessio Philosophi: Papers Concerning the Problem of Evil, 1671–1678, ed. and trans. Robert C. Sleigh, Jr. (New Haven, CT: Yale University Press, 2005). Discourse on Metaphysics, A 6.4.1529–88/L 303–30. De Summa Rerum: Metaphysical Papers, 1675–1676, trans. G.H.R. Parkinson (New Haven, CT: Yale University Press, 1992). Opera Omnia, ed. L. Dutens, 6 vols. (Geneva: Fratres de Tournes, 1768). Die Philosophischen Schriften, ed. C.I. Gerhardt, 7 vols. (Leipzig: Lorentz, 1879). Leibnizens Mathematische Schriften, ed. C.I. Gerhardt, 7 vols. (Berlin: A. Asher, 1849–63). Textes Inédits, ed. by Gaston Grua (Paris: Presses Universitaires de France, 1948). Philosophical Papers and Letters, trans. Leroy E. Loemker, 2nd ed. (Dordrecht: D. Reidel, 1970). The Leibniz–Arnauld Correspondence, trans. H.T. Mason (Manchester: Manchester University Press, 1967). The Leibniz–Clarke Correspondence, ed. H.G. Alexander (Manchester: Manchester University Press, 1956), cited by author, letter number, and section number. The correspondence can also be found in G 7.352–420. New Essays Concerning Human Understanding, trans. A.G. Langley, 2nd ed. (New York: Macmillan, 1896). The Leibniz–De Volder Correspondence, trans. Paul Lodge (New Haven, CT: Yale University Press, 2013).

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xii

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LR M MP NE

NS

PG

PNG Riley RML Shorter T Wiener WF

The Leibniz–Des Bosses Correspondence, trans. Brandon C. Look and Donald Rutherford (New Haven, CT: Yale University Press, 2007). Monadology, G 6.607–23/L 643–53. Leibniz: Philosophical Writings, trans. Mary Morris and G.H.R. Parkinson (London: Dent, 1973). New Essays on Human Understanding, trans. Peter Remnant and Jonathan Francis Bennett (Cambridge: Cambridge University Press, 1996). Leibniz’s ‘New System’ and Associated Contemporary Texts, trans. Roger S. Woolhouse and Richard Francks (New York: Oxford University Press, 1997). “Extrait d’une Lettre de M.L. sur un Principe Général, Utile à l’Explication des Loix de la Nature, par loa Consideration de la Sagesse Divine; pour Servir de Réplique à la Réponse du R.P.M.,”Nouvelles de la Republique des Lettres (1687); also included in G 3.51–5/L 351–4. Principles of Nature and Grace, G 6.598–606/L 636–42. Political Writings, trans. and ed. by Patrick Riley (Cambridge: Cambridge University Press, 1988). Malebranche et Leibniz: Relations Personelles, ed. André Robinet (Paris: J. Vrin, 1955). The Shorter Leibniz Texts, trans. Lloyd Strickland (London: Continuum, 2006). Theodicy, trans. E.M. Huggard (LaSalle, IL: Open Court, 1985). Leibniz: Selections, trans. Philip P. Wiener (New York: Charles Scribner’s Sons, 1951). Philosophical Texts, ed. and trans. by R.S. Woolhouse and Richard Francks (Oxford: Oxford University Press, 1998).

Abbreviations for the Works of Other Seventeenth-Century Figures: AT CSM

Search

René Descartes, Oeuvres de Descartes, ed. C. Adam and P. Tannery, 11 vols. (Paris: J. Vrin, 1973). René Descartes, The Philosophical Writings of Descartes, trans. John Cottingham, et al., 3 vols. (Cambridge: Cambridge University Press, 1984). Nicolas Malebranche, The Search after Truth, trans. Thomas M. Lennon and Paul J. Olscamp (Cambridge: Cambridge University Press, 1997).

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Introduction The moderns have cut the Gordian knot with Alexander’s sword, and have introduced miracles into a natural thing, like gods in the theatre at the denouement of an opera.¹ My aim was to explain naturally what they explain by perpetual miracles.²

The celebrated American author Willa Cather (1873–1947) writes in a letter to a close friend: It has been very dry down here, and every one has been talking about rain. Mamma told Elsie that God made the rain. Yesterday Mr. McNitt had his two lawn sprinklers going for the first time this year. Elsie came running in screaming, “O Willie! come quick and see, there are two little Gods out in McNitt’s yard just raining away like everything.”³

Elsie made a mistake that Gottfried Wilhelm Leibniz (1646–1716) thinks is easy to make. In DM §8, Leibniz says that “it is rather difficult to distinguish the actions of God from those of creatures; for some believe that God does everything, while others imagine that he merely conserves the force he has given to creatures.”⁴ And yet, there is something quite right about Elsie’s claim, since, as Leibniz goes on to say, the nature of minds is “so noble that it brings them as near to divinity as it is possible for simple creatures”⁵ and, elsewhere, that “each mind [is] like a little divinity in its own realm.”⁶ The key to understanding Leibniz’s position, and the mistake of Elsie, is to see that the expression of the divine is fully grounded in the natural properties of the mind. Leibniz’s theology generates naturalizing constraints that lead him to a fully natural theory of mind, where individuals are genuine agents in their own right. Leibniz sought to show that the actions of creatures can be distinguished from those of God, carving out a middle ground between Spinoza, for whom all creatures are merely finite modes of God, and Malebranche, for whom God operates as the sole genuine cause. Leibniz argues instead that there are individual, causally efficacious substances,

¹ G 3.346/NS 223. ² G 6.595/NS 250. ³ Letter from Willa Cather to Mariel Gere, June 1, 1893 (Willa Cather, The Selected Letters of Willa Cather (New York: Alfred A. Knopf, 2013), 18). ⁴ DM §8. ⁵ DM §36. ⁶ M §83. For more references to passages in which Leibniz describes minds as little gods, see Gregory Brown, “Leibniz’s Moral Philosophy,” in The Cambridge Companion to Leibniz, ed. Nicholas Jolley (Cambridge: Cambridge University Press, 1995), 427.

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even as these minds provide an image of the divine. As stated in the epigraph, what the others sought to explain by means of an appeal to the divine, Leibniz sought to explain in a natural way. The main argument of this book is easy to state: Leibniz offers a fully natural theory of mind. In today’s philosophical climate, in which much effort has been put into discovering a naturalized theory of mind, Leibniz’s efforts to reach a similar goal 300 years earlier will provide a critical stance from which we can assess our own theories. But while the goals might be similar, the content of Leibniz’s theory significantly diverges from the majority of today’s theories. Many philosophers today are working towards an account of mind in fully physical terms. In contrast, the most fundamental elements of Leibniz’s mature theory of mind are indivisible, unextended substances, which he terms monads to identify them as the true unities of nature. Despite this stark difference in the basic elements of the system, or perhaps because of it, Leibniz provides us with a valuable alternative and a possible way forward amidst otherwise intractable debates. Indeed, it is helpful in at least this sense: it allows us to distinguish a broad naturalizing project from the more narrowly conceived physicalist project. Of course, I recognize that the term “naturalism” is deeply disputed. Leibniz himself used the term “naturalism” in a negative sense, although, at the same time, he described his theory as “more natural” than the competitors. Given that, I think there is something important captured in viewing Leibniz’s theory as a naturalized theory of mind. Although the term “naturalism” is a slippery one even today, it is widely regarded as a desirable goal. But it remains unclear just what the goal is. One way to state the goal of contemporary theorists is this: a naturalized theory will be one that has no irresolvable “mysteries”—mysteries like those presented by phenomenal consciousness (i.e., the qualitative aspect of our experience), which David Chalmers has famously called a “hard problem” because it is fundamentally mysterious and it is unclear how to resolve the mystery.⁷ Thomas Nagel thinks the mysteries will remain until we have retooled our conceptual framework.⁸ But naturalists of many stripes offer theories that purport to explain consciousness, removing the mysteries. As Fred Dretske has put it, a naturalized theory may not “remove all the mysteries [but] it removes enough of them . . . to justify putting one’s money on the nose of this philosophical horse.”⁹ So, one way to recognize a naturalized theory is that it provides plausible or satisfactory explanations of all mental states and events in a way that is intelligible to human beings. Naturalism is about discharging explanatory demands. In this, Leibniz was extraordinarily prescient, defending an account of the mind that provides fully natural explanations for mental states and events and providing an explanatory framework that removes any residual mysteries, or at least “enough of them,” to echo Dretske.

⁷ David J. Chalmers, “Consciousness and its Place in Nature,” in Philosophy of Mind: Classical and Contemporary Readings, ed. David J. Chalmers (Oxford: Oxford University Press, 2002). ⁸ Thomas Nagel, “Conceiving the Impossible and the Mind–Body Problem,” Philosophy 73 (1998). ⁹ Fred Dretske, Naturalizing the Mind (Cambridge, MA: MIT Press, 1997), xiii.

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There is also a way in which the historical context of Leibniz’s theory reflects our own situation. In the seventeenth century, the Scientific Revolution was well underway, and numerous previously arcane aspects of nature were being explained in increasingly mechanical terms. But at the same time there were persistent questions about how far these mechanical explanations could extend. Some, like Descartes, limited mechanical explanations to bodies—minds were excluded from that sort of explanation. Others, like Hobbes, were fully prepared to incorporate minds into the material machine, causing some anxiety among philosophers and theologians that important moral and theological categories would be eliminated. Leibniz’s response to this situation was to carve out a middle ground: minds are fully a part of the natural system, but they are not merely material machines. His naturalism is one that, he plausibly thought, is consistent with central moral and theological positions. While this might be seen as an important historical consequence, it also provides a framework for evaluating for ourselves how naturalized theories might cohere with moral and religious philosophical views. This is an issue that has captured popular attention even today—Leibniz stood at the nexus of many of the important debates then and now. Additionally, liberal societies have long been committed to the natural sciences and to religious pluralism. It is a source of much grief that these two positions are now regarded, by people on both sides, as incompatible. The incompatibility is having bad effects on our ability to live together in community, to talk civilly, and to make progress in both science and theology. And so a Leibnizian harmony between nature and the domain of faith is not merely theoretical. This book is an effort to see how the Leibnizian harmony holds up from the perspective of his philosophy of mind. Granted, many of the details of Leibniz’s philosophy of mind would need to be updated in order to make it a plausible candidate theory of mind in today’s discussions, a task I don’t intend to do in this volume, but the overall metaphysic is one that might cast some light on our own thinking. Indeed, as I have worked through Leibniz’s system, I have seen some ways in which I might depart from what he has presented (not all of which are noted in this volume), but this benefit of vision comes only through the hard work of seeing things through his eyes for a bit. Of course, by identifying a broader motivation for this project in the introduction, I open myself to various charges: of taking Leibniz’s metaphysics out of its historical context, of anachronism, or of pressing Leibniz into my own mold. But, for me, this intersection of currents—those that motivate Leibniz’s thinking and those that motivate our own thinking—animates the project all the more. And I suspect that Leibniz would have welcomed the project. Remember that Leibniz is known for continuously revisiting key conclusions, trying out new avenues of thought and revising his thinking in light of the evidence. And it is clear that Leibniz never did finish his project. And so, even a statement of Leibniz’s views will be of a dynamic position, one that was still responding to the worries of his time and the challenges of his own thinking. This dynamics of thought makes Leibniz difficult to interpret, but it also gives us a picture of a highly intelligent person wrestling with difficult issues, and it invites us to do the same. Narrowing in from this broader set of issues, the more specific argument of this book is that Leibniz’s philosophy of mind meets the standards of what he would

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regard as a fully natural theory. Leibniz’s commitment to naturalism is clear. In the New Essays, Leibniz says that: Whenever we find some quality in a subject, we ought to believe that if we understood the nature of both the subject and the quality we would conceive how the quality could arise from it. So within the order of nature (miracles apart) it is not at God’s arbitrary discretion to attach this or that quality haphazardly to substances. He will never give them any which are not natural to them, that is, which cannot arise from their nature as explicable modifications.¹⁰

This is a broad claim about methodology in natural philosophy. As we will see, and as is evident here, Leibniz’s theological commitments yield a thoroughgoing naturalizing methodology: the properties of an object are explicable in term of the object’s nature. If we cannot conceive how this could be in any given case, then we have not yet arrived at the natural explanation. Of course, Leibniz qualifies this claim, allowing for the possibility of miracles, but as I will argue while Leibniz clearly leaves open this possibility, on my view the possibility is only very rarely realized. And so Leibniz concludes this passage: This distinction between what is natural and explicable and what is miraculous and inexplicable removes all the difficulties. To reject it would be to uphold something worse than occult qualities, and thereby to renounce philosophy and reason, giving refuge to ignorance and laziness by means of an irrational system.¹¹

These are strong words, which reveal the depth to which Leibniz’s naturalizing commitments reach. And I will argue that he pursued his philosophy of mind with this methodology in hand. If we keep this commitment to a naturalizing project in mind, then we will find in Leibniz a rich and interesting philosophy of mind. But there are other aspects of Leibniz’s theory of mind that we will need to emphasize as well. Leibniz was not alone in arguing for what we today might call a naturalized theory of mind. Plausibly, Hobbes, Spinoza, and Hume could be seen as engaged in this sort of a project as well. So, it is not merely that Leibniz’s theory of mind is a natural theory that distinguishes his theory from the others. There are two other important aspects of Leibniz’s theory of mind that will be emphasized in this volume. First, Leibniz’s theory of mind preserves a plurality of genuinely individual substances that are themselves causally active. That is, the activity of individual substances provides the basic component of Leibniz’s theory. Second, Leibniz’s theory of mind is a fully representational theory of mind. Each state of a mental substance provides information on the world around it, from its own point of view. The most basic elements of Leibniz’s mature philosophy are simple substances, which, by their very nature, are representational and active. Thus, we have an early expression of a dynamic and representationalist philosophy of mind. But, as I have said, even though his is a naturalized philosophy of mind, he is not a materialist. The basic elements of nature have these same properties—they are mind-like substances that, at their essence, are representational and active. And so Leibniz’s philosophy of

¹⁰ A 6.6.66/NE 66.

¹¹ Ibid.

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mind actually lays claim to explaining more than merely higher-order mental phenomena. It aims to explain much that goes by in minds entirely unnoticed, and which explains how it could be that the basic elements of nature are non-extended. No one (to my knowledge) has brought forward these three commitments—the commitment to a natural theory and the commitments to substances as essentially active and as representational—in an adequate way. These will be the three pillars upon which the theory rests.

The Argument of the Book Of course, we must be cautious about applying our own trendy positions to historical figures, and the naturalizing claims that I defend in this book might threaten to do just that. As I have mentioned, Leibniz’s own use of the term naturalism is largely negative. When Leibniz uses the term “naturalist” (as opposed to “nature” or “natural”), it is pejorative, typically identifying what we today might call materialists or fatalists.¹² He does not explicitly use the term “naturalist” or “naturalized” in reference to his own theory. Leibniz’s failure to apply the term to his own theory should not be considered evidence that the term does not apply. Although he does not explicitly call his theory a naturalized theory, he does call it a natural theory. The use of terms like “naturalized” or “naturalism” today is different than it was in the seventeenth century. In the seventeenth century, the term “natural” was a more appropriate one to use as a descriptor of one’s theory, without an “-ism” suffix. So, one could talk about a “natural science,” a “natural theology,” and a “natural theory of mind.” What does the suffix do, after all? Typically, when discussing a “naturalized” epistemology today, for example, the suffix suggests that something has been rooted out and discarded. The epistemology has been sufficiently brought down to the level of science and none of the speculative residue is left. Given this, it might be appropriate to describe Leibniz’s project as a “naturalizing” project. Descartes’s and Malebranche’s theories of mind still have too much residue—they have not been brought down to earth, as it were. Leibniz’s theory, by his own account, is more “natural.”¹³ So, I think we can consider Leibniz’s theory a naturalized account when considered in reference to Cartesian theories. Even today, the term “naturalized” is opaque, often making sense only once you know what sort of theory is being picked out as not natural enough. This easily leads to a game of philosophical leap-frog, in which each theory tries to better the last. I am hoping that we can turn this game around a bit and look back at some prior moves, considering one position visited along the way. This historical distance can give us a kind of critical distance on our own views. But, for obvious reasons, we cannot assume that everything that Leibniz said about the mind translates without remainder into the terms of today’s debates. In order to get the right sort of critical distance, we need to appreciate just how far the distance is. And that will require that we

¹² See AG 281.

¹³ To Arnauld, October 9, 1687 (G 2.113/LA 145).

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consider carefully how the use of terms, the historical context, and the systematic connections within the theory itself might be distinctive in the seventeenth century. With that in mind, this book will start by considering what, for Leibniz, it means for a theory to be a natural theory. How does he use the term “nature” and what does the division between natural and non-natural amount to? What are Leibniz’s criteria for a natural theory, and why is it that the Cartesian theories do not pass the test? Once we grasp Leibniz’s own account of a natural theory, Part I of this book, only then can we consider how (or whether) his own theory of mind is itself fully natural. This book is in four parts. The first two parts provide the systematic and historical context for the philosophy of mind that is developed in the second half of the book. Readers who are primarily interested in Leibniz’s philosophy of mind may discover that the second half of the book could stand largely on its own. However, the full defense for the systematic constraints I apply in defense of the interpretation developed in the second half of the book is presented in the first half of the book, and so the full picture emerges only with this background in place. The structure of the book will follow this story line. In Part I, I will outline Leibniz’s naturalism. Chapter 1 investigates Leibniz’s concept of “nature,” which focuses on the demand for explanation. Chapters 2 and 3 outline two principles that Leibniz believes will aid in our discovery of natural explanations: (1) the principle of continuity, and (2) the principle of the best. Both of these principles, according to Leibniz, derive from the nature of God’s activity. Since, according to Leibniz, God does nothing without a reason, this gives us confidence that there is a reason or explanation available for any given phenomenon. But beyond a mere promise of explanation, the principle of continuity and the principle of the best prove to be useful heuristics in discovering natural explanations. Part I shows that Leibniz has a clear conception of the requirements of a fully natural theory and that such a theory does not immediately undermine the sharp species distinctions that he argues for in his theory of mind. Part II presents the basic structures of Leibniz’s theory of mind—the things that minds and simpler substances have in common. In this section, I present a new interpretation of Leibniz’s theories of perception and mental representation, which provide the most basic building blocks for his theory of mind. While very good work has been done on Leibniz’s theory of representation, I argue in Part II that interpreters have not given sufficient attention to two other central concepts for Leibniz’s theory of perception: (a) activity and (b) mediation. Chapters 5 and 6 develop Leibniz’s theory of substance, with attention to activity and representation respectively. Chapter 7 supplements Leibniz’s accounts of representation and activity with an account of the mediation of perceptions via the body. An account of perceptual distinctness requires all three. The benefit of this new interpretation will be to dispel some of the oddities (or possible inconsistencies) in Leibniz’s use of the concept of perceptual distinctness. At the end of Part II, the main underlying structures of the Leibnizian mind will be in place. In Part III, I present an account of Leibniz’s theory of what one might call an animal mind, the aspects of perception, sensation, consciousness, appetite, and desire that humans share in common with other animals. Here I investigate his theories of consciousness, memory, and appetite, focusing on how Leibniz explains each of these

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in fully natural terms. In chapter 7, I argue for a same-order theory of consciousness grounded in perceptual distinctness against other prominent interpretations of Leibniz’s theory of consciousness. In chapter 8, I unpack Leibniz’s rich and complex account of memory, which has important implications for a theory of consciousness as well as Leibniz’s account of reflection and moral identity. And in chapter 9, I discuss Leibniz’s theory of appetite and the underlying mental motivations and resistances that lead to action. In Part IV, I discuss those aspects of mind that Leibniz thinks are unique to rational minds. This is the most problematic section from the perspective of a fully natural theory, since, according to Leibniz, reflection and self-consciousness brings minds into community with God and gives them a moral identity. There is some evidence that Leibniz dispenses with the naturalizing constraints at that point, out of deference to the moral and theological implications. But I argue that even here Leibniz is prepared to defend a naturalized theory. Departing from many scholars, I will provide a way of understanding the evidence in light of his natural theory. In chapter 10, I will dig into some fairly controversial passages (from the perspective of my argument), where Leibniz seems to concede that the generation of rational minds would require divine intervention. I provide a way of understanding these passages in light of Leibniz’s naturalizing commitments that allows him to preserve a natural distinction between non-rational and rational minds, even as he pragmatically allows for divine intervention as a way of speaking to his more theologically sensitive audience. In chapter 11, I discuss what Leibniz describes as the “appearance of the self,” which gives human beings moral agency. I discuss what the intentional content of that appearance might be, arguing that there is a complex structure involving a two-fold representation of the self as both passive and active. Chapter 12 takes up this suggestion and argues that the two-fold representation of the self grounds conceptual thought. Many discussions in philosophy of mind focus on questions of how higher-order phenomena, such as consciousness, relate to more fundamental aspects of the mind and brain. Leibniz was one of the first to theorize about the nature of consciousness in its relation to non-conscious perceptions, and it was consideration of the theoretical constraints of a natural theory that led him to this discovery. And he capitalized on it in ways that have not yet been fully appreciated. Once his thought is set against the broader theoretical background, the unusual nature of the system becomes more intelligible and one can more readily see how it provides a plausible alternative to contemporary theories. I want to conclude this introduction with a couple of notes about the scope of my argument. First, although I have started an argument above that Leibniz’s theory of mind would be an interesting dialogue partner in today’s discussions, I will not make the full argument for that conclusion in this volume. What I intend to do here is to provide a faithful representation of what is going on in Leibniz’s texts, and the further work of updating it in such a way that it is clear how his view measures up against today’s positions can come only once we have a clear sense of what he was up to in his own historical context. I will make a few suggestions in the conclusion about the direction I think this might take, but it will not be a central concern of the body of the volume.

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Second, while there is very good work being done on how Leibniz’s views changed or developed over time, this volume does not take up that question in a central way. There are moments where the development of his views is important, especially with respect to the naturalizing constraints in Part I, and I will address those there. But for the broader metaphysical views that serve as the backdrop for Leibniz’s philosophy of mind, I will present here what I take to be views that Leibniz consistently held (perhaps with minor variations) over the latter half of his career (roughly, from 1686 on), with an emphasis on the metaphysics he was working out from around 1695 (with the publication of the “New System”) through 1716.¹⁴ In those contexts, I will bring in earlier texts or discuss the development of Leibniz’s views only to the extent that I think it clarifies or illuminates his more mature views. My own sense is that while it may be controversial when and to what extent Leibniz was an idealist about bodies, Leibniz’s theory of mind was more stable from the middle period onwards.

¹⁴ Readers who wish to learn more about the controversies about Leibniz’s fundamental metaphysics should consult Robert Merrihew Adams, Leibniz: Determinist, Theist, Idealist (Oxford: Oxford University Press, 1994) and Daniel Garber, Leibniz: Body, Substance, Monad (Oxford: Oxford University Press, 2009).

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PART I

Leibniz’s Naturalizing Project

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1 Nature and Natures This vulgar opinion, according to which we ought in philosophy to avoid, as much as possible, what surpasses the natures of creatures; it is a very reasonable opinion. Otherwise nothing will be easier than to account for anything by bringing in the deity, Deum ex machina, without minding the natures of things.¹

Some things exist by nature and some things exist from other causes. For example, animals, plants, earth, air, fire, and water exist naturally, while beds, houses, and coats exist only because they were caused to exist by something else. Aristotle launches book two of his Physics with this intuitive distinction between nature and artifice. The question, then, is what we mean by “nature” (φύσις) when we make such distinctions. Aristotle argues: [E]ach of [the things that exist by nature] has within itself a principle of motion and of stationariness . . . Nature is a principle or cause of being moved and of being at rest in that to which it belongs primarily, in virtue of itself and not accidentally.²

He goes on to say that “things have a nature which have a principle of this kind. Each of them is a substance: for it is a subject, and nature is always in a subject.”³ Aristotle’s conception of nature focuses on the internal principles of change, which are intrinsic to an object, as opposed to the principles of change that are either accidental or extrinsic to the object.⁴ Aristotle goes on to argue that “form is nature rather than the matter,”⁵ since the nature of a thing derives more from actuality than potentiality. While Aristotelian natural philosophy had hit upon hard times in the late 1600s, Leibniz sought to restore at least this aspect of Aristotelianism. In his familiar attacks ¹ LC Leibniz 5, §107. ² Aristotle, “Physics,” in The Complete Works of Aristotle, ed. Jonathan Barnes (Princeton, NJ: Princeton University Press, 1984), 192b10–20. ³ Ibid. 192b30. ⁴ There is interpretive disagreement over whether Aristotle’s conception of nature is of a self-moved thing or of a thing that is moved by something else, since the Greek verb in use could be read as either in the passive or the middle voice. It seems to me that Aristotle’s appeal to form in his discussion of nature will favor reading this in the middle voice, although I realize that this is not decisive. I will not attempt to address this controversy, since it is more important to my argument to see how Leibniz incorporates this notion of nature into his own system. For Leibniz, individual natures will have principles of motion and rest intrinsic to them. For discussion of this interpretive controversy in Aristotle, see Helen S. Lang, The Order of Nature in Aristotle’s Physics (Cambridge: Cambridge University Press, 1998), 39–54. ⁵ Aristotle, “Physics,” 193b5.

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 ’     on Cartesian natural philosophy, Leibniz was not attempting a mere refinement, correcting the math, so to speak. He had a broader goal in mind: he claimed that Cartesian natural philosophy was not sufficiently natural. Leibniz saw himself as providing a more consistently natural account of physics and of mind than the Cartesians. For example, in a letter to Arnauld, Leibniz says: The ordinary Cartesians confess that they cannot account for [the union of mind and body]; the authors of the hypothesis of occasional causes think that it is a “difficulty worthy of a liberator, for which the intervention of a Deus ex machina is necessary;” for myself, I explain it in a natural manner.⁶

And again, in a response to René-Joseph Tournemine, Leibniz says: My intent [with the pre-established harmony] was to explain naturally what [the Cartesians] explain by perpetual miracles.⁷

Similarly, in his criticisms of Descartes’ theory of motion, Leibniz says that: Nature, whose most wise Author uses the most perfect geometry, observes the same rule [i.e. the principle of continuity]; otherwise it could not follow an orderly progress . . . [B]ut the Cartesian rules of motion present . . . a figure which is absurd [monstrosam] and incoherent.⁸

As a fully natural philosophy, Cartesian philosophy was a failure. In contrast, Leibniz’s early admiration of Hobbes and his flirtation with Spinozism is due to the ways that he thought their views promised a fully systematic explanation, and he considered these philosophies seriously as he attempted to discern the relation of God to world and matter to form. Leibniz ultimately rejected Spinoza’s and Hobbes’s theories due in large part to their theological implications, but he at one point or another considered them seriously, provided they were suitably adjusted. Indeed, in 1670–71, Leibniz made a serious attempt at formulating an Elements of Mind, which attempted to do for the mind what Hobbes had done for the body, constructing a theory of mind from geometrical principles and Hobbes’s concept of conatus.⁹ And this present volume can be read as a way of tracing the Elements of Mind into Leibniz’s mature philosophy. Similarly, Leibniz appears to

⁶ To Arnauld, October 9, 1687 (A 2.2.242/LA 145), last emphasis mine. A similar point was made in Leibniz’s letter to Clarke, LC Leibniz 5, §107, which again emphasizes the need to appeal to the natures of things in our philosophy. ⁷ G 6.595/AG 197, emphasis mine. ⁸ G 4.375–6/L 398. ⁹ It is noteworthy that Leibniz thought his promised Elements of Mind would also provide a defense of certain theological positions in a natural way, such as the immortality of the soul. In a letter to Arnauld (A 2.1.279/L 149), he claims that the Elements would shed light on controversies over the trinity, the incarnation, predestination, and the Eucharist. Leibniz wrote a proposal, which included a reference to the Elements of Mind, to Duke Johann Friedrich of Hannover on May 21, 1671 (A 2.1.182), and his preliminary work on the Elements can be found at A 6.2.276–291. For discussion of the influence of Hobbes on Leibniz, see Garber, Leibniz: Body, Substance, Monad, 14–22 and Howard R. Bernstein, “Conatus, Hobbes, and the Young Leibniz,” Studies in the History and Philosophy of Science 11 (1980).

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have considered a version of monism in 1676, departing from Spinoza in ways that would preserve God’s moral nature.¹⁰ And so Leibniz, from very early in his career, found himself between the two poles: Hobbes and Spinoza, on the one hand, whose theories compromise important moral and religious truths, and Descartes and the Cartesians, on the other hand, whose natural philosophy is full of holes. It is well known that, in response to these concerns, Leibniz eventually came to see that a fully natural account of the laws of motion or of the union of mind and body would require the revival of substantial forms. And so, while Leibniz departed from Aristotle in many ways, Aristotle’s emphasis on individual natures, which have their principles of change internal and intrinsic to them, can be seen as motivating Leibniz’s broader naturalizing project.¹¹ Two aspects of Aristotle’s account are worth emphasizing as we approach Leibniz’s theory of mind. First, Aristotle’s emphasis is on the natures of individual things (plural). This will play out in Leibniz’s system as he attempts to avoid charges of Spinozism—there are individual natures that are substantial and present in the plurality of things. Interestingly, Aristotle himself did not set out to prove this claim. Aristotle says: That nature exists, it would be absurd to try to prove; for it is obvious that there are many things of this kind, and to prove what is obvious by what is not is the mark of a man who is unable to distinguish what is self-evident from what is not.¹²

Leibniz will try to provide a fuller argument than this, but at certain points this is precisely the kind of argument he provides, identifying the clearest example from within ourselves—our experience of our own minds gives us evidence of an individual nature.¹³ The second aspect of Aristotle’s discussion of nature worth highlighting is that the natures themselves provide an account of change. This will also become central to Leibniz’s theory, and it will be an important part of the discussion in this volume as he attempts to avoid the two boundaries: this claim will allow Leibniz to avoid the subsumption of individuals into the whole, and it will allow him to avoid the problems of a view (like Cartesianism, especially in its Occasionalist forms) that places the source of activity outside of the subject. These two boundaries define the

¹⁰ For the argument that Leibniz was briefly tempted by monism, see Adams, Leibniz: Determinist, Theist, Idealist, 123–30 and Mark Kulstad, “Leibniz, Spinoza, Tschirnhaus: Metaphysics à Trois, 1675–1676,” in Spinoza: Metaphysical Themes, ed. Olli I. Koistinen and John I. Biro (Oxford: Oxford University Press, 2002). For a thorough discussion of Leibniz’s relation to Spinoza, see Mogens Laerke, Leibniz Lecteur de Spinoza: La Genèse Opposition Complexe (Paris: Champion, 2008). ¹¹ Commentators have noted this connection with Aristotle (for example, see J.A. Cover and John O’Leary-Hawthorne, Substance and Individuation in Leibniz (Cambridge: Cambridge University Press, 1999), 219), but to my knowledge none have fully developed the naturalizing claim that I will be developing throughout this book. ¹² Aristotle, “Physics,” 193a1. ¹³ For example, in a letter to Lady Masham in May 1704, Leibniz argues that “the principle of uniformity” allows him to infer that what we recognize in substances “within our range” extends to “substances beyond our sight and observation.” Therefore, Leibniz argues, “taking it as now agreed that there is in us a simple being endowed with action and perception . . . this leads me to think that there are such active beings everywhere in matter, and that they differ only in the manner of their perception” (G 3.339/NS 204).

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 ’     territory within which Leibniz develops his theory of substance, and these two aspects of Aristotle’s account of nature, if he can give them a proper development within the new science of the seventeenth century, will give him a way to tread this line. In broad outlines, the project of this book is to see how Leibniz develops a natural theory of the mind. Others have emphasized Leibniz’s natural philosophy, but few have brought this discussion to bear on Leibniz’s theory of mind. In this first part of the book, I will unpack more clearly what it is to be a natural theory, according to Leibniz. In this chapter I will try to formulate Leibniz’s naturalizing claims more precisely. In the following two chapters, I will emphasize the systematic principles that help shape his theory—the principle of continuity, the principle of sufficient reason, and the principle of the best. There are three things that I will emphasize in this chapter: (a) Leibniz’s focus on individual natures, (b) Leibniz’s appeal to “rules of the good and beautiful,” and (c) the representational nature of individual substances, building the “rules of the good and beautiful” into the individual, active natures. This allows for a robust natural theory that is informed by the good, and, hence, final causes will form a part of the overall natural theory. There is a problem, however, in identifying the scope of Leibniz’s natural theory. It is not clear how Leibniz can avoid either (1) extending his natural theory to include God’s actions (hence, natural philosophy extends to theology) or, on the other hand, (2) identifying the boundaries of his natural philosophy in an ad hoc way. I will argue that Leibniz does avoid these two landmines. Regardless, we can focus the question more specifically by considering whether he avoids these problems within his philosophy of mind (even if he didn’t in the broader scope of his philosophy). That is, even if Leibniz cannot find a principled way of limiting his natural theory in a global sense, he might nevertheless be able to avoid such problems in his theory of mind. The working hypothesis of this book is that Leibniz can and does develop such a theory of mind. The path to this conclusion may seem a bit digressive at first, since Leibniz establishes what I will call his naturalizing constraints through considerations of the relation of the universe to God. In what follows, I will suggest that it is because of a certain conception of God that Leibniz thinks that the naturalizing constraints hold. So a bit of patience is cautioned—Part I will be giving something of a theological argument for naturalism, which will seem unusual in today’s context but is necessary if we are to see the strength of these constraints for Leibniz.

1. Sophie’s Naturalism: “everything that happens is natural” 1.1. Naturalism of a sort In the early 1690s, Duchess Sophie wrote to Leibniz, asking his opinion about a woman who claimed to prophesy via a special and direct dictation from Christ.¹⁴ ¹⁴ I am indebted to Robert Adams for bringing this correspondence to our attention. See Adams, Leibniz: Determinist, Theist, Idealist, 91–2. The correspondence can be found at A 1.7.29–46 or A 2.2.452ff. The translation here is Adams’s.

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In his response to Sophie, Leibniz claimed to be “thoroughly persuaded that there is nothing but [what is] natural in all that.”¹⁵ But he went on to claim that “the great Prophets, that is to say, those who can teach us the details of the future, must have supernatural graces,”¹⁶ due to the infinite complexity of causes that must be understood in order to predict future events. Sophie follows-up with what Robert Adams describes as a “blunt and sweepingly naturalistic remark”:¹⁷ I believe that everything that happens is natural, even when we do not know the cause of it.¹⁸

Leibniz responds: That is very solid, provided it is explained correctly. It is very true, then, that everything that is done is always natural to the one that does it, or to the one that aids in doing it. Thus what a human being does with the aid of God, if it is not entirely natural to the human being, will at least be natural to God, inasmuch as he aids in it; and it cannot surpass the divine nature, nor consequently all nature in general. But popularly when Nature is spoken of, that of finite substances is understood, and in this sense it is not impossible for there to be something supernatural, which surpasses the force of every created being. It is when an event cannot be explained by the laws of movement of bodies, or by other similar rules that are noticed in finite substances. And I have shown in an earlier letter that one encounters that every time one finds a succession of true prophecies that go into detail. It is true that they are rare, like all other supernatural things.¹⁹

Leibniz’s analysis of “natural” here is enlightening, since it focuses on the activity of a substance—what it is able to do. The ability of a substance to act derives from its nature, which is consistent with Leibniz’s description of nature in DM §16 and in “A Specimen of Dynamics.”²⁰ (These texts will be discussed more fully in chapter 4.) An action is natural if it is a consequence of the natures of the substances involved. That is, if the action falls within the scope of the things the substance is able to do on its own (without assistance), then it is a fully natural outcome for that substance. But if the action falls outside of the scope of what a particular substance is able to do, but that substance could do it with assistance, then it is a natural outcome of the combined substances participating in the action. Therefore, all events are natural, since even those events that might be regarded as miraculous, as being beyond the power of any combination of finite substances, still include the assistance of God, which is to say the divine nature. So, one way to understand Sophie’s claim is this: (1)

Every event follows either from the natures of finite beings (individually or collectively), from the nature of God, or from the natures of finite beings assisted by the nature of God.

The editors of the Academy edition note that the prophetess in question is Rosamunde Juliane von der Asseburg. For more on Leibniz’s attitude towards modern-day prophets, see Daniel J. Cook, “Leibniz on Enthusiasm,” in Leibniz, Mysticism and Religion, ed. A.P. Coudert, R.H. Popkin, and G.M. Weiner (Dordrecht: Kluwer, 1998). ¹⁵ A 2.2.452/Adams, Leibniz: Determinist, Theist, Idealist, 91. ¹⁶ A 2.2.454/ibid. ¹⁸ A 1.7.44/ibid., 91. ¹⁹ A 1.7.46f; A 2.2.460f/ibid., 91–2, emphasis mine. ²⁰ GM 6.235/AG 118.

¹⁷ Ibid.

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 ’     This is a quick route to naturalism for anyone inclined to join the party. All one needs to do is to count actions that derive from God’s nature as natural events. This maneuver would seem strange to most naturalists, and rightly so. It is a cheater’s naturalism, and Leibniz doesn’t fully endorse it. Under this construal, Descartes’s and Malebranche’s theories could be considered natural theories. Leibniz’s resistance to Cartesian theories of mind and motion is evidence that he did not subscribe to such a broad construal of naturalism. But what makes this broad form of naturalism coherent and intelligible is a theory of individual natures that underlies Leibniz’s substance metaphysics. For Leibniz, the claim that an event is natural involves an implicit reference to the natures of the acting substances that participate in or cause the event—we must rephrase any statement of the form “X is natural” to “X is natural for Y ” (where Y might pick out an individual or a set of individuals).

1.2. Limiting “nature” When Leibniz says that “popularly when Nature is spoken of, that of finite substances is understood,” he is advocating a restriction in the domain of the term. But then he needs to give a principled way of restricting the domain. Restricting the domain to finite substances and applying it to the formulation of Sophie’s naturalism above yields a false claim: (2)

Every event follows from the natures of one or more finite beings.

While (2) might be appealing to some, it cannot be attributed to Leibniz. If true, it entails that no events follow from the nature of an infinite being (or, possibly, that there is no infinite being).²¹ While it is an open question just how much supernatural activity Leibniz allows for (more on this later), Leibniz certainly thinks that there is an infinite being whose acts follow from its nature. It would be false to say that all events follow from the natures of finite beings. If the domain restriction implicit in the popular usage of the term is what ultimately undermines Sophie’s naturalism, then Leibniz has a problem: the domain restriction seems unmotivated. Leibniz is not against the modification of language (or the invention of new terms) to provide greater clarity to the theory, provided the modification is linked properly to popular usage. So, the popular usage of the term cannot dictate the theory unless it is given a systematic grounding in that theory. Leibniz claims that Sophie’s usage of the term can be given good sense. That is, it is translatable into something that would not obscure her meaning.²² But once he does so, it seems he is left with an unmotivated domain restriction. In the quoted passage, Leibniz provides a further criterion for a natural act that may not be as ad hoc as simply ruling out divine activity. He says that a supernatural event occurs when it “cannot be explained by the laws of movement of bodies, or by ²¹ Note that this would be problematic for Spinoza as well—if this is the way we should contrast natural and supernatural events, then Spinoza’s philosophy is not a natural philosophy. ²² For discussion of Leibniz’s views about the link between popular usage and the clarity of one’s theory, see Mogens Laerke, “The Problem of Alloglossia: Leibniz on Spinoza’s Innovative Use of Philosophical Language,” British Journal for the History of Philosophy 17 (2009): §2.

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other similar rules that are noticed in finite substances.”²³ And so, the characterization of a natural event, closer to popular usage, might be as follows: (3)

A natural event is an event that can be fully explained by the laws of the movement of bodies or other laws governing finite substances.

Leibniz is here appealing to the explanatory utility of the laws of nature, which provides us some access to what makes an event a natural event. Leibniz’s appeal to individual natures reveals a commitment to the full intelligibility of nature—natural events are susceptible to a full explanation in terms of finite substances and the laws governing them.²⁴ While (3) retains the domain restriction of (2), it gives us a principled way of identifying the distinction. Supernatural acts are not intelligible in terms of the laws proper to bodily motion (or other such laws). Although the appeal to the intelligibility of nature might provide a greater motivation for the restriction of the domain, it is not decisive against Sophie’s naturalism, formulated in (1), since, if there are supernatural events, then there are events among finite substances that cannot be explained by appealing to “the laws of the movement of bodies or other laws governing finite substances.” Thus, in order for nature to be fully intelligible, we would need to include God’s actions as well—the restriction of the domain in this way does not inevitably yield naturalism. This may give us insight into why the popular usage is relevant here. As will become clear in the next chapter, natural events are intelligible to us. Leibniz’s natural theory is essentially connected to the explanatory force of the theory. While we could stretch the term to include even events that are not intelligible to us (such as a genuine miracle), there is value in preserving the emphasis on explanation. Now Leibniz is in the position of having to identify just how far “nature” extends. For Leibniz, the naturalness of a theory will be closely tied to its intelligibility. But this by itself does not provide the principled way Leibniz needs to identify and define the scope. What sorts of events are intelligible? Why think any events are fully intelligible in this way? And if some events are, why aren’t all events intelligible in this way? Leibniz’s claim that his account of the mind-body relation is “more natural” suggests that he regarded it as able to explain more. But should we read this as suggesting that his theory of mind is fully natural?

2. Leibniz’s Middle Way 2.1. Three sects of naturalists Before trying to answer this last question, I want to look at a text in which Leibniz distinguishes multiple types of “naturalist.” In an early essay, written some time ²³ Ibid. ²⁴ For more on this “principle of intelligibility,” see Donald Rutherford, “Leibniz’s Principle of Intelligibility,” History of Philosophy Quarterly 9, no. 1 (1992). I will have more to say about this principle in subsequent chapters.

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 ’     between 1678 and 1680, Leibniz identified “Two Sects of Naturalists.”²⁵ In this essay, Leibniz discusses the shortfalls of naturalist theories that entail either necessitarianism or materialism. The clear suggestion by the end of the essay is that there is a natural theory that navigates clear of these hazards, and so, as I will argue, Leibniz is not undermining naturalism as such. He is arguing for a third form of naturalism that succeeds in ways the other two do not. The first sort of naturalist that Leibniz describes as “fashionable” (en vogue) is the Epicurean naturalist, who “believes that any substance, including the soul and God himself, is corporeal, that is to say, composed of extended matter or mass.”²⁶ This view Leibniz ascribes to Hobbes, and he claims that it has bad consequences for a clear conception of God—if God is material, then it is impossible for God to be all powerful or all knowing, and therefore this sect of naturalism denies God’s providential activity. The second sort of naturalist is associated with the Stoics in ancient times and with Spinoza and possibly Descartes in the modern period. According to this version of naturalism, although there are incorporeal substances, God is the soul of the world, operating on the basis of a “blind necessity.” “God has neither understanding nor will,” and so everything happens by a “mechanical necessity.”²⁷ The denial of final causes follows from this theory, and, Leibniz argues, there is “no justice or benevolence with respect to God.” So, while these naturalists might grant the existence of providence, it is providence “in name only.” However, Leibniz does not deny naturalism. He goes on to identify a third sect,²⁸ the sect deriving from Socrates and Plato, which, he says, is more suitable to piety. Leibniz ends the essay with a long quotation from Plato’s Phaedo,²⁹ in which Socrates is presented as criticizing Anaxagoras. This criticism, Leibniz says, can be imported into the modern period, showing the weakness of the naturalisms then in vogue. The Socratic criticism is that Anaxagoras posits a governing intelligence (νοῦς) over all things, which, Socrates infers, would lead Anaxagoras to discuss the principle of perfection. Since everything would be disposed in the most perfect manner by an intelligent cause, the full account of nature would allow us to show why things are ordered in this particular way rather than another. But, in fact, Anaxagoras makes no use of the governing intelligence. Instead, while Anaxagoras describes certain material causes in the universe, he never gives an account of why those material causes must be as they are. For example, he describes the actions of the human body in terms of the relation of flesh, bones, muscles, etc., as if this gives the full cause of the actions of a human body. These material components of the human body do help make sense of a particular set of causal relations. But Anaxagoras’s invocation of Nous suggests that the true cause

²⁵ “Two Sects of Naturalists” is the title given to the essay by Daniel Garber and Roger Ariew (AG 281). The Gerhardt edition has no title for the essay (G 7.333). The Academy editors have given the title, “Sentiments de Socrate opposes aux Nouveaux Stoiciens et Epicureens” (A 6.4.1384). As it will become clear, I much prefer the Academy title. ²⁶ A 6.4.1384/AG 281. ²⁷ A 6.4.1385/AG 282. ²⁸ A 6.4.1386/AG 283. ²⁹ See Plato, “Phaedo,” in Plato: Complete Works, ed. John M. Cooper (Indianapolis, IN: Hackett, 1997), 97b–9d.

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would be the intelligent cause that orders the human body in such a way due to its connection with the perfection of things. Socrates concludes, “Those who only say . . . that motions of bodies around the earth keep it here, where it is, forget that divine power disposes everything in the finest way, and do not understand that it is the good and the beautiful that join, form, and maintain the world.”³⁰ The naturalists following Socrates and Plato would recognize that the mechanical causes, even if exhaustively demonstrated by the new physics, do not provide the full cause of things. There is a further, overarching cause that must be considered, and this cause is a final cause—it tends towards something, namely the forms of the good and the beautiful. The natural philosophy that Leibniz is pursuing preserves this moral aspect of nature, recognizing in it a perfection of order and beauty that is due to a cause that is not explicable in merely mechanical terms. In sum, the naturalisms of the Stoics and the Epicureans either (a) fail to provide a fully explanatory account of nature or (b) explain nature in a way that has undesirable entailments. In the first case, there are global features of nature, its particular ordering and arrangement, which are not explained in terms of the particular patterns of causes themselves. And so, as Socrates argued, there must be some other principle that governs the overarching structure, some explanation for why it is structured as it is. Of course, the Stoics and Epicureans may simply reply that it is necessarily so ordered—there is no other possible ordering. But this is to move to the other horn of the dilemma, since, as Leibniz argues, this would have undesirable effects, namely in undermining divine providence and principles of justice. The argument here arguably paves the way to a particular interpretation of the principle of sufficient reason and the principle of the best. The principle of sufficient reason, in one of Leibniz’s later formulations, is the principle that there is no “true or existent fact . . . without there being a sufficient reason for why it is thus and not otherwise.”³¹ Either the naturalists can give no such reason for the causal structure of the world, thus violating the principle of sufficient reason, or the reason that is given is “blind,” a mere necessity. In fact, to turn the screw a little tighter, Leibniz does not think that those who appeal to blind necessity are even providing reasons: For what is necessary is so by its essence, since the opposite implies a contradiction; but a contingent which exists, owes its existence to the principle of what is best, which is a sufficient reason for the existence of things . . . Whereas absolute and metaphysical necessity depends upon the other great principle of our reasonings, viz., that of essences; that is, the principle of identity or contradiction.³²

And so, the reply that the world is necessarily as it is plays a different game—it does not supply a reason, it merely recognizes that other orderings are internally contradictory. Leibniz, on the other hand, sides with Socrates and Plato, who provide an explanation from outside the order of finite things, an explanation that is not “blind” but is intelligent and acts in a way that tends towards the perfection of things.

³⁰ A 6.4.1388/AG 284. ³¹ M §32. ³² LC Leibniz 5, §§9–10. I will return to this quotation in chapter 3.

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 ’     The Socratic natural theory, then, provides a full explanation of the causes of nature, leaving no undesirable gaps. But, once again, this sort of theory makes an appeal to an intelligence that is beyond the realm of finite, dependent things. And so, as before, it seems to stretch the meaning of the term to call this a “natural” theory. The Socratic/Platonic naturalist might be closer to Leibniz’s characterization of Sophie’s full-fledged naturalism: all events are natural, given that even so-called supernatural events derive from the natures of higher beings. Nevertheless, the discussion of the Phaedo brings out a difference in the sorts of explanations that are adequate to an effect. Supposing someone wanted to explain why Socrates is sitting in his cell. The Anaxagorian (and Hobbesian) explanation is given in terms of the bones, muscles, and joints, etc. To put it in the language of the mechanical philosophy of the seventeenth century, Socrates is sitting because of a long mechanical process that resulted in his bones and muscles being positioned in just such a way in that particular place. The full explanation, no doubt, would be long and complex (possibly infinitely long and infinitely complex), but it is provided by the interactions of matter and mechanical motions that give rise to the particulars of Socrates’s body and its present placement. But there is a second order of explanation available, as Socrates points out in the Phaedo. Socrates is an intelligent person; he considers options and decides on a course of action that affects the disposition of his body. Socrates is sitting in his cell because the Athenians decided that it was best to convict him, and he decided that it would be better to stay and face the charges rather than to flee or to request exile. The explanation, again, may be long and complex, but in this case it is provided by the intelligent recognition of the best action. On the broadest scale, it is appropriate to regard Leibniz as a part of this third sect, providing what Socrates was looking for in the pages of Anaxagoras. I think this provides at least three things for Leibniz. First, it provides logical and normative constraints on metaphysics. Leibniz complains that Descartes allows no room for justice, since, for Descartes, God’s volition is the source of the principles of justice. But then, on a fully voluntarist conception of God, there is little room to see why God would deem certain orderings as just rather than others, and there is little room to give God credit for doing so. Leibniz’s theology recognizes constraints on the divine nature—God does not cause or create the principles of justice, but they are grounded in the divine understanding, and God desires to act in accordance with them. And so we have a principled way of explaining even God’s choices (if, per impossible, we could enter into the infinite intuition of the divine intellect and see things as God does), and the credit owed to God is based on God’s acting in accordance with the good and the beautiful. As Leibniz frequently asserts, “God does nothing without a reason.”³³ I will unpack the implications of this more fully in chapter 3—I think the principle of sufficient reason, as employed by Leibniz, will have to carry with it some normative weight, connecting it more closely with the principle of the best than others have recognized.

³³ A 6.4.1388.

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Secondly, this version of naturalism yields a full and systematic account of the causes of things. While physics provides a legitimate account of the motions of bodies, it is nevertheless a limited account. Physics must be grounded in some further explanation. In the Socratic case, the ruling intelligence, which acts on the basis of the principles of perfection, complete the account, thus avoiding the “blind” or “mechanical necessity” of the Stoic naturalists and the materialism of the Epicurean naturalists. These lead to a third benefit. Leibniz argues that the Epicurean and Stoic naturalists end up with an ethic of patience. Since all things are connected by mechanical and blind causes, we must simply be content, since “it is madness to oppose the torrent of things and to be discontented with what is immutable.”³⁴ Leibniz continues, “if they knew that all things are ordered for the general good and for the particular welfare of those who know how to make use of them, they would not identify happiness with simple patience.”³⁵ While I do not intend to pursue these particular ethical claims in this volume, the clear implication is that if we get the metaphysics right we will see our way to an ethic of action rather than of patience or contentedness. The higher ideal, for Leibniz, is justice, which Leibniz defines in a novel way: justice is the “charity of the wise,” or “a habit of loving conformed to wisdom.”³⁶ Leibniz argues that happiness is essentially connected with this notion of justice rather than an ethic of patience, that is, the happy person will seek to “know how to make use of ” things for the general good.³⁷ But to get these benefits, it seems that Leibniz will have to extend his explanatory thesis to include what we would otherwise recognize as non-natural events (like God’s act of creating a well-ordered cosmos). Why, then, should we think this to be a fully natural theory at all? It certainly seems to stretch the common usage of the term. And, if we do grant this sort of naturalism, then it seems that occasionalism will be natural in the same way. In section 2.2, I will explore how Leibniz thinks he can separate himself from occasionalism, and then, in section 2.3, I will show how Leibniz brings this sort of naturalism back down to earth.

2.2. The threat of occasionalism Since even the occasionalists appeal to God’s acting on the basis of the principle of perfection, they seem equally capable of exemplifying a Socratic naturalism. Malebranche, for example, is able to account for regularities in nature by God’s consistent action in nature, never departing from his eternal decree, and so it seems that Malebranche’s theory can underwrite a full physical theory even though he regards ³⁴ A 6.4.1385/AG 282. ³⁵ Ibid. ³⁶ See, for example, “Meditation on the Common Concept of Justice” (Riley 45–64) and “Felicity” (Grua 2.579–84/Riley 82–4). For more on Leibniz’s novel definition of justice, see Patrick Riley, Leibniz’ Universal Jurisprudence: Justice as Charity of the Wise (Cambridge, MA: Harvard University Press, 1996) and Robert J. Mulvaney, “The Early Development of Leibniz’s Concept of Justice,” Journal of the History of Ideas 29 (1968). ³⁷ In the “Dialogue between Polidore and Theophile,” written around the same time as “Two Sects,” Leibniz spells this out more fully. Included in his full ethic are a satisfied contentment (rather than mere patience), the love of God above all things, happiness with our current state, charity towards neighbor, a striving for perfection (“especially the mind”), and a recognition that no good act will be without its reward (A 6.4.2238–9/L 219–20).

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 ’     God as the only true cause. And yet Leibniz is insistent that the occasionalist theory is not a fully natural theory, appealing, as he says, to perpetual miracles.³⁸ For Leibniz, mere regularity and the law-like actions of God are not sufficient for a fully natural theory. The difference ultimately rests in Leibniz’s conception of God; his belief in a fundamental naturalism is grounded in a particular kind of theology. The essential difference between Leibniz and Malebranche, according to Leibniz, is a matter of whether God creates natures that could function as genuine causes in their own right. Arnauld defends Malebranche in his March 4, 1676 letter to Leibniz,³⁹ insisting that Leibniz and Malebranche are saying essentially the same thing. Malebranche does not argue that each action, e.g., my decision to raise my arm and the arm rising, requires a new volition of God. Rather, God exercises a “single act of eternal will, whereby he has wished to do everything which he has foreseen that it would be necessary to do, in order that the universe might be what he deemed it was to be.”⁴⁰ This, Arnauld thinks, is precisely what Leibniz is arguing in his claim that the mind does not cause motions in the body or vice versa, but rather they are arranged in a harmony from the beginning by God. Leibniz rejects this conclusion, and in so doing he clarifies his own thoughts on the nature of God and his interaction with the world. Leibniz argues that the occasionalist position fails to be fully natural because the action of God is not based in the nature of the finite substance. That is, Leibniz argues that the common usage of “miracle” appeals to an intrinsic difference—there must be some appeal to what is within the nature of the substance itself when distinguishing the natural from the supernatural.⁴¹ The preferable position, according to Leibniz, is one in which bodily substance has the force to continue its changes according to the laws that God has placed in its nature and maintains there. And . . . I believe that the actions of minds effect no changes at all in the nature of bodies, nor bodies in that of minds, and even that God changes nothing on their occasion, except when he performs a miracle; and in my opinion things are so prearranged that a mind never effectively desires anything except when the body is prepared to do it by virtue of its own laws and forces.⁴²

Thus, a fully natural theory will be one in which each thing does what is already in its nature to do and the force necessary to carry out the effect is resident in the nature of the thing itself. Anything that exceeds the force of the natures involved in the event will be miraculous. Occasionalism, Leibniz argues, continuously has such exceptions, since the force for any action comes from an outside source, namely, God.

³⁸ See, for example, Leibniz’s claims in his correspondence with Arnauld (A 2.2.81/LA 65, A 2.2.179/LA 116), his Letter to Foucher, August 1686 (A 2.2.90/WF 52), and his response to Tournemine (G 6.595/AG 197). This charge wasn’t limited to occasionalists, Leibniz also charges Christiaan Huygens and Isaac Newton with “perpetual miracles”: A 2.2.514/L 414, A 2.2.582, and G 3.517–18. ³⁹ LA 105f. ⁴⁰ LA 106. ⁴¹ This may not be an entirely fair criticism of Malebranche, given that Malebranche also recognizes the need to appeal to the natures of things (Search 663; see A 6.4.1933 for evidence that Leibniz gave some attention on this passage). But as I will discuss below, Leibniz thinks there is a crucial difference in how the natures of things play into the explanations of natural events. ⁴² LA 115–16.

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But this is not yet an argument for why Leibniz’s position is preferable to the occasionalist view. Leibniz goes on to say that: One cannot disagree that this hypothesis is at least possible and that God is a sufficiently great workman to be able to carry it out; thereafter one will easily conclude that this hypothesis is the most probable since it is the simplest and the most intelligible, and at once demolishes all the problems, to say nothing of the criminal actions in which it seems more reasonable to invoke God’s assistance merely in the preservation of created forces.⁴³

Leibniz here provides six criteria for favoring his hypothesis: (a) it is possible; (b) God is capable of creating nature in this way; (c) it is simplest; (d) it is most intelligible; (e) it solves problems in the natural theory; and (f ) it helps resolve the problem of evil. We can divide these criteria into two groups—Leibniz says that his hypothesis is “infinitely more reasonable and worthy of God.”⁴⁴ Logical constraints: (a), (c), (d), and (e) are matters of reasonableness and theory selection—one should favor the theory that is simplest, intelligible, resolves existing problems, and is in itself possible. The second group reflects normative constraints: (b) and (f ) focus on aspects of God’s nature and moral character. If Leibniz is right that his hypothesis is the more reasonable (simplest, most intelligible, etc.) and that God is capable of creating such a world, then it would be a defect on God’s part to have created a world that does not line up with this hypothesis. Similarly, if God is more closely implicated as the author of sin (which, it seems, he is in the occasionalist system), this again is a mark against God’s nature. But, as Leibniz says in DM §3, “God does nothing for which he does not deserve to be glorified,” and so the occasionalist hypothesis is out.⁴⁵ In order for this argument to be successful, Leibniz will have to show that his own system is in fact more reasonable—that it is possible, simplest, most intelligible, and solves all of the problems. And Leibniz does take up this challenge. But the challenge will be to show that his system appeals ultimately only to the individual natures of finite beings, that is, to show just how natural his theory is.

2.3. “Traces of God”: A representational theory of substance One further problem might arise for the Socratic naturalist. The initial suggestion in this chapter was that Leibniz’s natural theory is broadly Aristotelian, as finding an explanatory basis in individual natures. However, section 2.1 introduced a different sort of natural theory, namely one that provides the explanatory basis of nature in an intelligent cause. On the face of it, this will be in tension with a broadly Aristotelian reading, since the intelligent cause appealed to by Plato and others is not one that is immanent in the individual finite natures. That is, for a full explanation of natural ⁴³ LA 118. ⁴⁴ LA 118. ⁴⁵ There is a different sort of argument that could equally apply here, presented in Leibniz’s second letter to Clarke (LC Leibniz 2, §12): 1. If God must “mend the course of nature,” it must be done naturally or supernaturally. 2. If it is done supernaturally, then we must explain natural things by miracles, which is absurd. 3. If it is done naturally, then God will not be supramundane: he will be the “soul of the world,” which is undesirable. 4. It is necessary to “mend the course of nature,” on Leibniz’s reading of Clarke and Newton. 5. And so, Clarke’s and Newton’s natural philosophy entails something absurd or undesirable.

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 ’     events, one must appeal to something beyond the finite individual natures. And so, it seems, we have two competing naturalizing constraints: one that looks to the individual natures as explanatorily basic and the other that looks to an overarching intelligent (non-blind) cause as explanatorily basic. In this section, I will argue that Leibniz believes that he can embrace both of these positions. Leibniz brings the two theories together by appealing to a fully representational theory of substance. When we turn to a text from Leibniz’s mature years—“On Nature Itself ” (1698)—Leibniz says: [I]f, indeed, the law God laid down [in creating] left some trace of itself on things, if by his command things were formed in such a way that they were rendered appropriate for fulfilling the will of the command then already we must admit that a certain efficacy has been placed in things, a form or a force, something like what we usually call by the name “nature,” something from which the series of phenomena follow in accordance with the prescript of the first command.⁴⁶

This argument is again intended to distinguish Leibniz from Malebranche—he argues that God’s command must have a lasting effect on the substances he creates, and, if that is the case, then it is a short step to enduring, causally active, individual substances. But the means of God’s lasting activity on a substance is by preserving the traces of his command on the finite substances themselves, forming a part of their nature. And so the picture that emerges from Leibniz’s theory of substance is that each substance contains in it everything that is necessary for a full explanation of each of its states. As Leibniz says in the Discourse on Metaphysics, “every substance is like a complete world and like a mirror of God or of the whole universe, which each one expresses in its own way, somewhat as the same city is variously represented depending upon the different positions from which it is viewed.”⁴⁷ The Leibnizian extension of internal representations to all substances, not merely minds, allows for a full explanation of things in terms of the representational states of the substances and each substance’s tendencies to change in response to its representations. All of this supports a naturalizing thesis of the following sort: (4)

An event is natural iff it can be fully explained in terms of the natures of finite substances.

Given that each substance preserves a representation of God’s commands within its own nature, this opens the door to a version of naturalism: each individual nature provides the full and sufficient reason for each subsequent state of the substance. Of course, we will have to look further to see just how many events will count as natural events on this reading of “natural.” One obvious cause for continuing to limit the scope will be Leibniz’s commitment to divine activity in the world. With this in mind, we look at one final argument in which Leibniz argues for a restricted scope to the term “nature.” In Leibniz’s discussion of miracles in DM §16, he says that miracles “are always in conformity with the universal law of the general order, even ⁴⁶ G 4.507/AG 158–9, emphasis mine.

⁴⁷ DM §9.

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though they may be above the subordinate maxims.” He follows this up with another restriction on the term “nature”: “if we include in our nature everything that it expresses, nothing is supernatural to it, for our nature extends everywhere.”⁴⁸ Once again Leibniz gives sense to a full-blown naturalism, quickly followed by a qualification: But what our nature expresses more perfectly belongs to it in a particular way, since it is in this that its power consists. But since it is limited . . . there are many things that surpass the powers of our nature and even surpass the powers of all limited natures.⁴⁹

So we have yet another way of identifying the limit on nature, namely, in terms of the power a particular individual has. But, as above, this remains unmotivated, since Leibniz gives no reason to think that God’s nature (i.e., God’s power) shouldn’t be included in the domain. For a further motivation, we must read further: Thus, to speak more clearly, I say that God’s miracles and extraordinary concourse have the peculiarity that they cannot be foreseen by the reasoning of any created mind, no matter how enlightened, because the distinct comprehension of the general order surpasses all of them. On the other hand, everything that we call natural depends on the less general maxims that creatures can understand.⁵⁰

The domain restriction on the term “nature” corresponds with a restriction in intelligibility by a finite mind. There are certain things that the finite mind will never be able to explain. For Leibniz, the scope of intelligibility will mirror the domain restriction on the use of “nature.” Statement (4) allows for this, and this could be useful to the natural scientist who has theistic commitments—for example, physics will explain all events that are explainable in terms of the laws of physics, but if there are exceptions to those laws (through miracles), these events would in principle not be explainable in the terms of physics. With this sense of “natural,” then, we can raise the further question just how wide of a scope does Leibniz think his naturalism will have? I have suggested here that the scope of naturalism will be coextensive with intelligibility for Leibniz, but just how intelligible does Leibniz regard the universe? This question will be taken up in section 3.

3. A Harmony of Nature and Grace 3.1. Miracles To determine the full scope of Leibniz’s naturalizing commitments, we will need to consider just what sorts of exceptions Leibniz is prepared to allow. In his letter to Sophie, he admits that “a succession of true prophecies that go into detail” would require a genuine miracle, but, he goes on to say “they are rare, like all other supernatural things.”⁵¹ It seems, from this letter and other writings, that Leibniz would allow for genuine miracles. But I think at the same time there is good evidence ⁴⁸ DM §16. ⁴⁹ Ibid. ⁵⁰ Ibid. ⁵¹ A 1.7.46f.; A 2.2.460f./Adams, Leibniz: Determinist, Theist, Idealist, 91–2.

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 ’     that Leibniz did not believe there were any genuine miracles, although he would allow for their possibility. The question of just how numerous or extensive miracles are comes up towards the end of Leibniz’s life in his correspondence with Samuel Clarke. In the correspondence, Clarke has argued that a miraculous event is an event conceived as irregular and not explicable by usual causes.⁵² Leibniz’s response provides one of his most common accounts of miracles: Divines will not grant the author’s position against me; viz. that there is no difference with respect to God between natural and supernatural: and it will be still less approved by most philosophers. There is a vast difference between these two things . . . That which is supernatural, exceeds all the powers of creatures.⁵³

Leibniz gives a clear definition of supernatural as that which “exceeds all the powers of creatures.” In response, Clarke objects that, on Leibniz’s account, (a) events we might think of as miraculous, e.g., walking on water, are not miraculous since they do not require infinite power; and (b) events that we otherwise would not regard as miraculous, e.g., the actions of animals, are miraculous, since they are not explicable by the natural powers of bodies.⁵⁴ Leibniz grants the first and denies the second. Many events that might be thought of as miraculous are not miracles of the “highest sort,”⁵⁵ including most of those reported in the Bible. Walking on water, the sun standing still, the flight of Hezekiah, and the stirring of the waters of the pool of Bethesda all have an explanation in terms of finite natures. And so, at best, these are miracles of an “inferior order.”⁵⁶ Additionally, Leibniz resists the claim that the actions of animals are miraculous, being initially content to state it rhetorically, “Why should it be impossible to explain the motion of animals by natural forces?”⁵⁷ The clear tenor of Leibniz’s mature writings is that genuinely supernatural events, miracles of the “highest sort,” are (at least) uncommon, although the uncommonness of the event is not what makes the event supernatural. The examples of genuine miracles that Leibniz gives in his correspondence with Clarke are (a) creation, (b) annihilation, and (c) action at a distance. The latter two Leibniz thinks to be non-actual. Indeed, it is part of Leibniz’s criticism of the Newtonian system that it appeals to miracles—action at a distance—as a part of its so-called natural philosophy. Action at a distance, he argued, cannot be given an explanation in terms of “the natural powers of creatures,” and so it should be rejected. I do not wish to get too bogged down in the discussion of miracles here, but there is good evidence to think that Leibniz severely restricted the number of genuine miracles. The clearest instances of genuine miracles for Leibniz are creation, the incarnation, and biblical prophecy.⁵⁸ And even for these three, there ⁵² See LC 24 and 29–30. ⁵³ LC 29–30. ⁵⁴ See LC 35. ⁵⁵ LC 91. See also T 249. ⁵⁶ LC 93. ⁵⁷ LC 43. ⁵⁸ Some Christian readers might be surprised not to see the resurrection of Christ in this list. One of the benefits Leibniz thought his theory of mind provided was a natural way to account for the immortality of the soul, which, according to him, is always embodied. Since every mind will survive death naturally, there is no reason to suppose that Christ’s resurrection requires any further supernatural aids. See the passage at A 6.3.365, note 5, quoted in Daniel J. Cook, “Leibniz on ‘Prophets,’ Prophecy, and Revelation,” Religious Studies 45, no. 3 (2009): fn. 44.

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are suggestions in Leibniz’s writings that a natural account could be given for these as well. Leibniz seems to be skeptical about miracles, even if personally witnessed, since the Bible itself says that miracles will be done by the Antichrist that may deceive even the elect.⁵⁹ Daniel J. Cook argues that Leibniz viewed biblical prophecy as susceptible of natural demonstration, namely in its exact fulfillment, thus sidestepping the need to verify the accompanying miracles. Cook says: By relying on fulfilled prophecy as corroborating the truth of Christianity, rather than on miracles (biblical or otherwise), one avoids basing one’s faith on possibly unreliable ancient testimony or breaches of the laws of nature, but rather on the demonstrated march of history.⁶⁰

Robert Adams lists the following as miracles of the “highest rank”: creation, conservation, incarnation, and annihilation. Again, as far as I know Leibniz nowhere claims that annihilation is actualized. Further, creation and conservation change nothing in the natures of the things (see, for example, Leibniz’s discussion of “original imperfection” of creatures who are created on the basis of the ideal nature of the creature as conceived by God),⁶¹ and Leibniz in at least one text suggests that there is no initial state of the universe.⁶² These suggest that God’s involvement here is simply that of ontological dependency of finite substances on the infinite. Further, in a very interesting passage quoted by Adams, Leibniz describes the incarnation in a way that “would not change the natural laws of the first creature [Jesus Christ] . . . This union [of God and man] would therefore change nothing in the phenomena, even though the state of union differs internally from non-union.”⁶³ Thus, it seems that there is good evidence that none of the miracles of the “highest sort” would affect the natural unfolding of finite beings. If this is right, then Leibniz’s naturalism is indeed a full-blown naturalism. If Leibniz is willing to go to great lengths in biblical theology to show that reported miracles are open to explanation in terms of the natures of finite beings, it is good evidence that in other domains, such as in the philosophy of mind, Leibniz would restrict extra-natural explanations severely. Indeed, I think in his philosophy of mind, he restricts them entirely. But even if the rare miracle were to occur, which Leibniz never denies, it would not form a part of the natural philosophy of mind. In his fifth letter to Clarke, Leibniz endorses just such a principle: In good philosophy, and sound theology, we ought to distinguish between what is explicable by the natures and powers of creatures, and what is explicable only by the powers of the infinite substance.⁶⁴

This is a good representation of the naturalizing thread running through Leibniz’s work. And this is the shape of the theory that I will be developing in this book. Leibniz’s naturalism is not a blind, mechanical pushing-and-pulling naturalism. Rather, the internal representations of finite substances cause each subsequent state of the substance. But, Leibniz will argue, this is intelligible only if each substance has ⁵⁹ See A 6.4.2214. ⁶² G 3.581–2/L 664. ⁶⁴ LC 92.

⁶⁰ Cook, “Prophecy and Revelation,” 281. ⁶¹ T §20. ⁶³ RML 413, quoted in Adams, Leibniz: Determinist, Theist, Idealist, 99.

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 ’     internal representations of the things surrounding it so that the relations it has to other substances regulate its internal actions. To summarize the exchange with Clarke, we can now characterize Leibniz’s account of miracles in the following way: (5)

An event is supernatural iff the force required for the event exceeds the force of all finite creatures.

Thus, it seems that as long as the sum total of force is conserved in a change, then there is no need to appeal to supernatural aids. A natural event will be an event that is not supernatural, that is, it is an event in which it is not the case that the force required for the event exceeds the force of all finite creatures. And, as I have suggested above, the exceptions to this sort of conservation will be exceedingly few in kind.⁶⁵ This entails the following claim, for Leibniz: (6)

An event is supernatural iff the event cannot be explained in terms of finite natures alone.

And, again, “natural” can be defined as the converse—a natural event is an event that can be explained in terms of finite natures alone. That is to say, if there are no forces beyond those of finite natures grounding the event, then the full explanation will appeal only to those natures alone, and so intelligibility follows from Leibniz’s naturalizing claims.

3.2. Nature and grace The recognition that even God’s causal activity is explicable in terms of the individual natures of finite substances brings out one further aspect of Leibniz’s natural theory. Leibniz believed that each domain of explanation, discussed above, is compatible with and harmonizes with the others. So, for example, the explanation of why Socrates is sitting in his cell has two parallel forms of explanation: one explanation in terms of the mechanical effects of the interactions of bones, muscles, and joints, with surrounding objects, and another in terms of the intellect pursuing what it sees as the best course of action. Leibniz argues that the explanation for Socrates’s sitting can be given fully in terms of both mechanical causation and final causation,⁶⁶ although he recognized that in many cases the causes are more intelligible in terms of efficient causation.

⁶⁵ Of course, Leibniz might also grant a more limited definition: (5*) An event is supernatural iff the force required for the event exceeds the force of all natures involved in the event. This way of characterizing a supernatural event would not require appeal to a global conservation principle. However, if there is some additional force involved in a local event, above what is contributed by the finite substances involved in the event, there would also be an increase in the overall quantity of force, and so (5) should suffice. ⁶⁶ “Any thing in the whole of nature can be demonstrated by final causes and also efficient causes” (A 6.4.1367 (1667–79?)).

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Similarly, Leibniz thought that God’s operations of grace were fully consistent with a natural explanation of the created order.⁶⁷ In his correspondence with the Roman Catholic Bishop of Meaux, Jacques-Benigne Bossuet, Leibniz makes the following argument, commenting on the mechanics of nature: [T]he laws of nature regarding motive force come from superior reasons and an immaterial cause, which does everything in the most perfect way . . . And all this endless infinite variety is animated in all its parts by an Architectural Wisdom that is more than infinite. One could say that there is a harmony of geometry, of metaphysics, and, so to speak, of morality throughout. And surprisingly, to take things in one sense, each substance acts spontaneously, independent of all the other creatures, although in another sense all the others are obliged to accommodate them. So that one could say that all nature is full of miracles, but miracles of reason, and they become miracles by being reasonable, in a way that astonishes us. For these reasons, there is an infinite progress, where our mind, although it sees as it should, can be followed by an understanding of it. Otherwise, nature is admired without being understood . . . [T]he true temperament for appreciating nature is with knowledge, recognizing that the more we advance, the more we discover the wonder and beauty and grandeur of those same reasons that are more surprising and less comprehensible to us.⁶⁸

The benefit of this view, for Leibniz, is that we need not simply settle into a cold, lifeless naturalism. Leibniz’s view, following Lea Schweitz’s suggestion, may be called a “sacramental naturalism.”⁶⁹ Just as Leibniz was willing to grant to Sophie a sense in which all that happens is natural, he is also willing to grant to Bossuet that all that happens is miraculous. This is the spirit of Leibniz’s natural theory—he does not decide between a world that is intelligible on its own terms on the one hand and an account of divine activity on the other. He sees the two as fully harmonious—the one is an instance of the other. Leibniz is using the method of analogy to provide good sense to his terms when used in a novel way—he says nature is full of miracles, but then he provides the analogy. They are miracles of reason, that is, they astonish us by being reasonable. And so his use of “miracle” here is simply to draw attention to the amazement we might feel in the presence of a fully intelligible and reasonable domain every time we investigate more deeply into the system of nature. Leibniz is articulating a theologically rich naturalism. He is fully committed, at the basic level, to causally active individual substances. He is equally committed to a God who acts in a consistent and simple manner, doing always what coheres with the principles of goodness and beauty. When Leibniz merges these two together, the latter becomes fully expressed in the former—the rules of beauty and goodness are intrinsic to the individual natures, and nature becomes intelligible without explicit reference to the divine source.

⁶⁷ For an excellent discussion of how the aids of grace arise naturally, see Donald Rutherford, “Justice and Circumstances: Theodicy as Universal Religion,” in New Essays on Leibniz’s Theodicy, ed. Larry M. Jorgensen and Samuel Newlands (Oxford: Oxford University Press, 2014), 71–91. ⁶⁸ Leibniz to Jacques-Benigne Bossuet, April 8/18, 1692 (A 2.2.516–17), emphasis mine. ⁶⁹ See Lea F. Schweitz, “On the Continuity of Nature and the Uniqueness of Human Life in G.W. Leibniz,” in The Life Sciences in Early Modern Philosophy, ed. Ohad Nachtomy and Justin E.H. Smith (Oxford: Oxford University Press, 2014), §3, 213–7.

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4. Conclusion The scope of naturalism does not get a lot of attention. For example, today some of us might be committed to the following proposition: (B1)

Anything fully explainable in the terms of biology is a natural event.

But (B1) does not entail the stronger claim: (B2)

All events involving biological organisms are natural events.

Of course something like (B2) likely serves as a methodological assumption of a research biologist, but the question is just how far the metaphysical assumptions should extend. There are epistemic limits on the justification for this claim (for example, there may be a few unobserved exceptions to it), and so it would need to be supported by other metaphysical principles. Leibniz not only shows that there are regularities among events that are intelligible in terms of natural processes and laws alone, but he provides a metaphysical grounding for these regularities in the natures of the individual substances and in the moral character of the governing Mind. As he says in the quotation at the start of this chapter, “nature, whose most wise Author uses the most perfect geometry, observes the same rule [i.e. the principle of continuity]; otherwise it could not follow an orderly progress.”⁷⁰ He is making a naturalizing claim—natural events display a regularity and order according to a law. But he alludes to the grounding for this claim as well: the author of nature reasons according to geometric principles. Since the latter is true, one must expect that natural events observe laws analogous to those that hold in geometry. While this is a common trope in the early modern period, Leibniz argues that the Cartesians and the occasionalists have not seen the full sense of it. In sum, I am arguing that Leibniz provides theological grounding for a fully natural theory of mind. Whatever his global commitments, I will argue that, at least with respect to his theory of mind, Leibniz believed that he had offered a fully natural theory. That, at least, is my interpretive hypothesis. The other true miracles that it seems that Leibniz would allow—creation, the incarnation, and biblical prophecy—do not impinge on Leibniz’s theory of mind. Whether or not there are actual miracles, this would not be a part of his theory. That is, supernatural activity has no place in his fully developed theory of mind, even if he allows for its possibility or even its actuality. This, Leibniz thinks, is unlike Malebranche and other Cartesians, for whom the mind is not intelligible without explicit reference to God’s intervention. This will all make more sense once we have seen how his theory of mind derives from broader naturalizing commitments. Indeed, the naturalizing commitments I have started to outline here all refer to fundamentally mental categories—the governing intellect guiding the divine will, the intelligibility of nature, and the internal representation of God and other things in the natures of substances—and each of these play a role in grounding and guiding Leibniz’s ultimate natural theory.

⁷⁰ G 4.375–6/L 398.

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And so, while it might seem odd to call Leibniz a naturalist, I think that may be due to his appeal to mental properties as foundational rather than (what we may be more accustomed to hearing) physical properties. That is to say, Leibniz’s naturalism is clearly not a version of physicalism, and for that reason it is of interest in its own right as articulating an intriguing alternative among competing naturalized theories.

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2 Naturalizing Constraints Equipollence and Continuity I find these leaps of yours very excruciating —Charinus¹

In the previous chapter, I introduced Leibniz’s naturalizing project. In this chapter, I will introduce what I take to be a methodological approach to naturalism—a way of structuring one’s theory to ensure that the overall naturalizing goal is met. The particular theoretical constraint I have in mind is the principle of continuity. In the following sections, I will explore the genesis of the principle in Leibniz’s early work in physics. Leibniz’s work in 1676 on a theory of motion, we will discover, actually allowed for certain kinds of leaps. But even before his full endorsement of the principle of continuity, Leibniz rejects the kinds of leaps that violate the principle of sufficient reason. As Leibniz’s thinking develops between 1676 and 1686, Leibniz becomes much more confident that “nature never makes leaps,” and he develops what he will later call the principle of continuity. Tracing his thinking in these years will illuminate the grounds and implications of the principle of continuity. While I will be focusing primarily on the principle’s application to physics in this chapter—since that is the context in which Leibniz developed his thinking on continuity—the conclusions will be broadly applicable to any natural theory. The principle of continuity serves as a naturalizing constraint for Leibniz, and a clear understanding of this will give us a test for the various interpretations of Leibniz’s theory of mind later in this book. The discussion of the principle of continuity, however, will not be complete by the end of this chapter. In chapter 3, I will consider the metaphysical basis of the principle of continuity, which will require a digression into two further principles: the principles of sufficient reason and the principle of the best. The principle of continuity is grounded on these more basic principles, resulting in a fully systematic outline for Leibniz’s naturalizing project. The larger thesis I will be arguing for in these two chapters is this: Leibniz’s theory of mind must be continuous if it is to be natural. Continuity is a necessary condition for a natural theory. Of course, one might also wonder whether continuity is also a sufficient condition for a natural theory. On an initial pass, it seems not. One could imagine a theory of ¹ A 6.3.560/Arthur 197.

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mind in which the transitions from one mental state to another are continuous but caused by God. This would be a continuous theory but not a natural theory. As it happens, Leibniz believes that occasionalist theories will necessarily include discontinuities, and seeing why this is so will illuminate Leibniz’s commitment to continuity. Leibniz believed that any non-natural theory would include irreducible gaps. All unnatural theories are discontinuous. Strictly speaking, this is a stronger claim than Leibniz needs. For the purposes of developing Leibniz’s theory of mind, we need only see the heuristic value afforded to him in concluding that all discontinuous theories are unnatural.

1. The Rejection of Occasionalism, Part I Leibniz is well known for his defense of the principle of continuity, which he formulates with the Aristotelian slogan, “nature never makes leaps,”² and he compares transitions in nature to the continuous transitions of geometry. A pressing question for anyone defending the principle of continuity, having its basis in geometrical transitions, is why we should assume that geometry is applicable to physics.³ In a 1676 dialogue called Pacidius to Philalethes, Leibniz has one of the characters express the problem exactly: If I may be allowed to offer an inexpert opinion on such matters, I would declare that the transition from Geometry to Physics is difficult, and that we need a science of motion that would connect matter to forms and speculation to practice.⁴

It is not an empirical matter whether the natural world is continuous, since even if certain aspects of the natural world are discovered to be continuous, there are also many apparent discontinuities in nature. (Think, for example, of sudden changes in the weather.) Why should the instances of continuous transitions be generalized into a law or principle governing all physical changes? In this section, I will outline some of Leibniz’s reasons for arguing in favor of the principle of continuity. Despite an ² For a sampling of the wide variety of contexts in which Leibniz appeals to the principle that nature never acts by a leap, see Specimen Inventorum, 1688? (A 6.3.1638), Letter to Foucher, January 1692 (A 2.2.491), Letter to Huygens, March 10/20, 1693 (A 2.2.683), Letter to Bossuet, April 8/18, 1692 (A 2.2.516), Letter to L’Hospital, January 15, 1696 (A 3.6.624), Letter to Bernoulli, September 20/30, 1698 (A 3.7.912), Letter to De Volder, March 24/April 3,1699 (G 2.168/L 515), Essay de Dynamique, 1698–1700? (GM 6.229), the New Essays on Human Understanding, 1704 (A 6.6.56/NE 56), and “The Metaphysical Foundations of Mathematics,” after 1714 (GM 7.25/L 671). The more mathematical formulations of the principle can be found in PG and Specimen Dynamicum (1695) (GM 6.249–50/L 447–8). The term “principle of continuity” or “law of continuity” is used only from 1692 and after. ³ In the history of mathematics, some have regarded Leibniz’s use of the principle of continuity, applied in such a general way to physical transitions, as a mistake. Continuous transitions in mathematics do not entail similar continuous transitions in nature. Carl B. Boyer says, “Leibniz felt the justification for his calculus lay in the ordinary mathematical considerations already known and used, and that is was ‘not necessary to fall back on metaphysical controversies such as the composition of the continuum.’ Nevertheless, when called upon to explain the transition from finite to infinitesimal magnitudes, he resorted to a quasi-philosophical principle known as the law of continuity” (Carl. B. Boyer, The Concepts of the Calculus: A Critical and Historical Discussion of the Derivative and the Integral (Wakefield, MA: Hafner Publishing, 1949), 217). ⁴ A 6.3.531/Arthur 135.

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 ’     early defense of what he calls “transcreation” (a sort of discontinuity), Leibniz defends the principle of continuity as a heuristic for a natural theory.

1.1. Early discontinuities (1676) In 1676, Leibniz is much exercised about the question of continuity, and the conclusions he (reluctantly) comes to are (a) that the link between geometry and physics must be via mind (whether human or divine), and (b) that in the absence of mind there would be radical discontinuities in nature. But (c) given the intervention of mind into the material world, some (less radical) discontinuities remain. In a series of essays, including “On Motion and Matter” (which the Academy edition dates somewhere between the 1st and 10th of April 1676), “Infinite Numbers” (April 10, 1676), and Pacidius to Philalethes (November 1676), Leibniz defends a certain kind of discontinuity in nature, which he calls by the “new but very beautiful name transcreation.”⁵ Transcreation is supposed to provide an account of the motion of bodies that is discontinuous but uniform. According to the position Leibniz develops in these essays, transcreation involves an infinite, non-uniform division of space. Imagine a continuous line of motion being actually divided into infinitely many intervals. Any interval you choose is itself infinitely divided, all the way down. Leibniz explains: [T]here is no portion of matter that is not actually divided into further parts, so that there is no body so small that there is not a world of infinitary creatures in it. Similarly there is no part of time in which some change or motion does not happen to any part or point of a body . . . This does not mean, however, either that a body or space is divided into points, or time into moments, because indivisibles are not parts, but the extrema of parts. And this is why, even though all things are subdivided, they are still not resolved all the way down into minima.⁶

Thus, we have a series of divisions that converges on the infinite, and there is no final resolution of the continuous magnitude into points. But given this account, Leibniz thinks we can make sense of the movement of the body by transcreation. Each boundary of an interval is directly proximate to the boundary of the next interval, without any distance existing between them. (We might say, colloquially, that they are “touching.”) Transcreation, then, is the movement from the boundary of the interval that is being concluded to the boundary of the interval that is being initiated. Since there is no distance between these boundaries, the leap does not involve a jump over any intermediate magnitudes. But this motion from one boundary to the next is effected by divine annihilation of the object at one terminus and a recreation of the object at the next. The resulting motion can appear continuous since, as Samuel Levey has put it, “the divisions . . . in motion that produce the pairs of immediately neighboring points are always densely ordered

⁵ A 6.3.567/Arthur 213. See also A 6.3.560/Arthur 197. For a full analysis of the arguments from these three essays, see Larry M. Jorgensen, “By Leaps and Bounds: Leibniz on Transcreation, Motion, and the Generation of Minds,” The Leibniz Review 23 (2013): 73–98. ⁶ A 6.3.565–7/Arthur 209–10.

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in the interval, and any two pairs will always be separated by a subinterval of the motion.”⁷ This story is complicated, and perhaps not even plausible. But my interest here is not whether Leibniz provides a plausible theory of motion. Rather, I am interested in Leibniz’s philosophical motivations to allow for leaps.⁸ Why should motion require leaps of any sort, much less transcreation? In the dialogue, Pacidius says that: If one person were simply to say that the thing ceases to be in its earlier state and now begins to be in another one, someone else might say that it was annihilated in the earlier state and resuscitated in the later one. Whichever of the two you accept, no distinction can be observed in the thing itself, but only in the fact that the former way of putting it conceals the cause, and the latter brings it out. But no cause can be conceived for why a thing that has ceased to exist in one state should begin to exist in another (inasmuch as the transition has been eliminated), except a kind of permanent substance that has both destroyed the first state and produced the new one, since the succeeding state does not necessarily follow from the preceding one.⁹

One key conclusion of the arguments in Pacidius is that bodies by themselves cannot provide an adequate explanation of their motions.¹⁰ On the definition of motion provided, there is no state of the body that can explain its change from one place to another. Change is defined as an aggregate of two moments, and there is nothing in the body that can unify the moments. Each subsequent state of a body is discrete and no intrinsic property of the body explains its trajectory, and so motion is fundamentally non-uniform and discontinuous. Thus, the state of change must be explained from the outside, as it were. And we cannot assign the state of change to some other body on pain of regress.

⁷ Samuel Levey, “The Interval of Motion in Leibniz’s Pacidius Philalethi,” Noûs 37 (2003): 390. ⁸ Readers who are interested in the plausibility of Leibniz’s proposal as a theory of motion might consider the objections raised by Michael White and Samuel Levey: Michael White argues that if there were genuinely no distance between the points at which a body is destroyed and recreated, then it is hard to see how a body would move at all. See Michael J. White, “The Foundations of the Calculus and the Conceptual Analysis of Motion: The Case of the Early Leibniz (1670–1676),” Pacific Philosophical Quarterly 73 (1992): 304. Samuel Levey agrees. He speculates that the theory of motion presented at the end of Pacidius represents “a tension in Leibniz’s thought between two concepts of motion,” and that “a resolution of motion into a powder of points (or leaps) seems to be inevitable—for having cut back every finite interval into finer and finer parts without end, what extended intervals could remain?” See Levey, “The Interval of Motion in Leibniz’s Pacidius Philalethi,” 402. François Duchesneau suggests a stronger connection between the theory of motion presented in Pacidius and the ultimate postulation of “real, but strictly individualized, centres of force whose qualitative gradual interaction will generate mechanical exchanges at the phenomenal level.” See François Duchesneau, “Leibniz on the Principle of Continuity,” Revue Internationale de Philosophie 48 (1994): 142–3. ⁹ A 6.3.567/Arthur 213–15, emphasis added. ¹⁰ Richard Arthur also makes this point, although he argues that Leibniz, in Pacidius, may be tacitly arguing for the “non-material principles of unity,” which Leibniz will later call “monads.” See Richard T.W. Arthur, “Russell’s Conundrum: On the Relation of Leibniz’s Monads to the Continuum,” in An Intimate Relation: Studies in the History and Philosophy of Science, ed. James Robert Brown and Jürgen Mittelstrass (Dordrecht: Kluwer Academic Publishing, 1986), 190. I am more inclined to read Leibniz as entertaining an occasionalist line of thought in this text.

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 ’     As it is summarized in the dialogue: [T]here is no moment of change common to each of two states, and thus no state of change either, but only an aggregate of two states, old and new; and so there is no state of action in a body, that is to say, no moment can be assigned at which it acts. For by moving the body would act . . . If you really cut to the quick and inspect every moment, there is no action.¹¹

Since there is no intrinsic property or state of the body that can explain its movement, strictly speaking, bodies do not (and cannot) act. The interlocutors are not inclined to eliminate motion, to explain it away, and so the explanation of motion must be from some other source, a source that can and does act, namely a “permanent substance.” Thus, they conclude, the motion of bodies is due to the continuous creative activity of God, acting in the most perfect manner. The resulting picture from these three early texts is that Leibniz does allow leaps of a kind, although he does not regard them as miraculous.¹² And, while this position contradicts Leibniz’s later claims that “nature never acts by leaps,”¹³ ultimately, the more fundamental argument in Pacidius is for the impossibility of accounting for motion by appealing to the properties of the bodies themselves. Rather, appeal must be made to an intelligence. Here Leibniz provides a much more straightforwardly occasionalist theory of motion. Leibniz’s full commitment to a natural theory of motion and the principle of continuity will emerge only as he comes out from under the occasionalist tent.

1.2. The rejection of occasionalism (1676–86) In the decade following Pacidius, Leibniz revisited his theory of motion, and the Cartesian theory of motion became a significant target of criticism. One result of this revision is that the charge of discontinuity became a primary point against the Cartesian theory of motion. It is a criticism Leibniz returns to often. While the theory of motion remains important to this story, the main goal of this section is to investigate how Leibniz came to believe that mathematical continuities can be applied to the natural order. The story of Leibniz’s rejection of the Cartesian theory of motion and of occasionalism is well known.¹⁴ While Leibniz was outlining his theory of transcreation, he was already developing a physics that involved an essential reference to intrinsic qualities of the body. But this new theory was to displace motion in favor of force. As he says in the Discourse on Metaphysics:

¹¹ A 6.3.566/Arthur 211. ¹² On this point, see Jorgensen, “By Leaps and Bounds,” 84. ¹³ See references in fn 2. ¹⁴ See Paul Mouy, Le Développement de la Physique Cartésienne, 1646–1712 (Paris: J. Vrin, 1934), 231–6, 293–302, and RML 243–7. For more on the nature of the disagreement about occasionalism, see Nicholas Jolley, “Leibniz and Occasionalism,” in Leibniz: Nature and Freedom, ed. Donald Rutherford and J.A. Cover (Oxford: Oxford University Press, 2005) and Donald Rutherford, “Natures, Laws, and Miracles: The Roots of Leibniz’s Critique of Occasionalism,” in Causation in Early Modern Philosophy: Cartesianism, Occasionalism, and Pre-Established Harmony, ed. Steven M. Nadler (University Park, PA: Pennsylvania State University Press, 1993).

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[I]f we consider only what motion contains precisely and formally, that is, change of place, motion is not something entirely real, and when several bodies change position among themselves, it is not possible to determine, merely from a consideration of these changes, to which body we should attribute motion or rest.¹⁵

The definition of motion given here is the same as that offered in Pacidius: motion is a change of place. But, given this definition, motion is relative. If X moves with reference to Y and Z, there is no property in X itself that would allow us to identify X as the body in motion rather than Y and Z. But Leibniz continues: But the force or proximate cause of these changes is something more real, and there is sufficient basis to attribute it to one body more than to another. Also, it is only in this way that we can know to which body the motion belongs.¹⁶

The force of a body is the intrinsic quality that grounds all natural changes. He reiterates this in a letter to Arnauld: “bodily substance has the force to continue its changes according to the laws that God has placed in its nature and maintains there.”¹⁷ Thus, the notion of force took a central place in Leibniz’s philosophy, and his view that each substance has within it the force and law necessary for all of its subsequent states became prominent. The revival of substantial forms comes along with this, since force cannot be explained simply in terms of the size, shape, and relative motion of the bodies involved in the natural change. Leibniz’s Specimen of Dynamics (1695) outlines the physics of force and his New System of the Nature and the Communication of Substances, as well as the Union between Soul and Body (1695) shows how the theory of force can be applied more generally and allows for a new theory of the union of mind and body. The theory is clearly anti-occasionalist, and in the years leading up to his publication of these key texts Leibniz presents his specific objections to the Cartesian theory of motion and occasionalism.¹⁸ The natural laws are now no longer grounded by the laws of God’s own nature but in the laws governing the localized forces in finite substantial forms. Natural changes are explained by reference to the natures of the individual substances involved, and the miraculous will be any change that “surpass[es] the powers of our nature and even the powers of all limited natures.”¹⁹ It is in the context of his movement away from Cartesianism and occasionalism that Leibniz develops the principle of continuity. Michel Fichant has identified Leibniz’s 1678 text, De Corporum Concursu, as containing the first formulation of the principle of continuity, a mere two years after the composition of Pacidius to Philalethes, and the apparent first use of the principle of continuity in an argument

¹⁵ DM §18. ¹⁶ DM §18. ¹⁷ A 2.2.179/LA 116. ¹⁸ See Mouy, Le Développement de la Physique Cartésienne, 300–2. ¹⁹ DM §16. See also letter to Arnauld, April 30, 1687 (A 2.2.179/LA 116), Leibniz’s fifth letter to Clarke, §107 (G 7.416/LC 90–1) and T §249 (G 6.265). For more discussion of this view of miracles, see §3 of chapter 1.

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 ’     against the Cartesian laws of motion and impact were in a letter of June 1679.²⁰ But the locus classicus of Leibniz’s principle of continuity is his “Letter of Mr. Leibniz on a General Principle Useful in Explaining the Laws of Nature through a Consideration of the Divine Wisdom: to Serve as a Reply to the Response of the Rev. Father Malebranche,” which was published in the Nouvelles de la République des Lettres in July 1687. (I will refer to this text as “PG.”) I will not here trace the development of the principle of continuity between Pacidius to Philalethes, written in 1676, to the published letter to Malebranche in 1687. It is clear that Leibniz developed his “general principle” very soon after Pacidius and made use of it in his arguments against Cartesian laws of motion. However, the public announcement of this principle was Leibniz’s 1687 letter—that is the formulation of the principle of continuity that Leibniz refers back to again and again—and so a closer attention to the context and argument of that letter will sufficiently demonstrate Leibniz’s reasons for adopting the principle of continuity and the utility that he thought it to have in discovering a fully natural theory. One of Leibniz’s main avenues of attack against the Cartesian principle of the conservation of motion was to appeal to a principle of equipollence. The principle of equipollence says that “the entire effect is equipollent to the full cause.”²¹ Leibniz was entertaining this principle around the same time as his writing of Pacidius Philalethi (1676).²² In the earliest writings, Leibniz uses the principle of equipollence to demonstrate plenitude,²³ but he also quickly sees the application to the theory of impact.²⁴ As is well known, Leibniz employed the principle of equipollence to directly engage the Cartesian laws of motion, culminating in his 1686 publication, “A Brief Demonstration of a Notable Error of Descartes,”²⁵ in which Leibniz argues that the Cartesian conservation principle is false and replaces it with what he regards as the correct conservation principle (i.e., the conservation of mv²). In that essay, Leibniz

²⁰ Michel Fichant, La Réforme de la Dynamique: De Coporum Concursu (1678) et Autres Textes Inédits, trans. Michel Fichant (Paris: J. Vrin, 1994), 213 and 216–18. See also Daniel Garber, “Leibniz: Physics and Philosophy,” in The Cambridge Companion to Leibniz, ed. Nicholas Jolley (Cambridge: Cambridge University Press, 1994), 314–16. ²¹ A 6.3.584/DSR 107, a formulation repeated in many different texts. ²² See “Three Primary Axioms” (summer 1675–autumn 1676?, A 6.3.427), “A Chain of Wonderful Demonstrations about the Universe” (December 12, 1676, A 6.3.584/DSR 107), “Notes on Metaphysics” (December 1676, A 6.3.400/DSR 15), and “Concerning the Equipollence of Cause and Effect” (1677–78?, A 6.4.1963–4). ²³ See especially A 6.3.400/DSR 15, where Leibniz says, “From the principle that the entire effect must be equipollent to the full cause, it is demonstrated that all things are full.” Leibniz’s argument here is not clear, and he later argues for plenitude not from the principle of equipollence but from considerations of divine wisdom and power. ²⁴ For discussion of the function of the principle of equipollence in Leibniz’s early criticisms of the Cartesian laws of impact, see Fichant, La Réforme de la Dynamique, 277–302 and Garber, Leibniz: Body, Substance, Monad, 235–50. ²⁵ See “A Brief Demonstration of a Notable Error of Descartes and Others Concerning a Natural Law, According to Which God is Said Always to Conserve the Same Quantity of Motion; a Law which They Also Misuse in Mechanics” (Acta Eruditorum March, 1686; GM 6.117–19/A 6.4.2027–30/L 296–301).

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recognized the equipollence of cause and effect, which, when measured by mv² rather than by quantity of motion (m|v|), represents the true conservation law.²⁶ In a more lengthy defense of the “Brief Demonstration” in a letter to Foucher, Leibniz says that “all can be reduced to this principle,” namely the principle of equipollence,²⁷ and, elsewhere, Leibniz expresses confidence that this principle provides the bridge between geometry and physics.²⁸ He takes up the principle in his correspondence with Bossuet,²⁹ and it was one of only two axioms in Leibniz’s 1692 Essay on Dynamics.³⁰ Additionally, scholars have recognized this principle as fundamental to Leibniz’s natural science.³¹ In sum, Leibniz fairly early saw the promise of the principle of equipollence. While it is an enriching study to consider Leibniz’s reasons for endorsing the principle of equipollence, I refer interested readers to other good studies.³² What is interesting to me is that in his correspondence with Cartesians and occasionalists, the principle of equipollence is eventually supplemented with the principle of continuity. And since this is the context that—I argue—Leibniz develops his naturalizing constraints, it is worth considering why he needed to introduce additional principles. My thesis is that both the principle of equipollence and the principle of continuity ground certain ways of making nature intelligible. Leibniz at one place restates the principle of equipollence in the following way: “from the mere knowledge of the effect one may come to the knowledge of the cause, and from the mere knowledge of

²⁶ For more on this controversy and the principle of equipollence, see Carolyn Iltis, “Leibniz and the Vis Viva Controversy,” Isis 62 (1971) and Garber, Leibniz: Body, Substance, Monad, 144–55 and 235–50. In a text as late as 1682–84, Leibniz remained open to the possibility of the conservation of the quantity of motion, even after stating the principle of equipollence: the power of the effect and of the cause are equal to each other, for if the effect were greater, we should have mechanical perpetual motion, while if it were less, we should not have continuous physical motion. It is worth showing that the same quantity of motion cannot be conserved but that the same quantity of power is. Yet we must see whether there will not also be conserved in the universe the same quantity of motion also. (L 279) At this point, Leibniz seems uncertain. Loemker notes the variations in Leibniz’s views: in the “Brief Demonstration” Leibniz “rejects the Cartesian principle of the conservation of quantity of motion,” but in his later comments on Descartes’s Principles of Philosophy, “the conservation of total quantity of motion in a system is reaffirmed, on condition that directions of motion are treated algebraically” (L 290n9). ²⁷ Letter to Foucher in 1687 (A 2.2.206–7; see also A 2.2.203). ²⁸ See letter to Melchisédech Thévenot, August 24 (Sept 3), 1691 (A 2.2.444). ²⁹ See the letters of October 23, 1693 (A 2.2.747–8) and July 12, 1694 (A 2.2.827). ³⁰ Fichant, La Réforme de la Dynamique, 277–302. The second axiom, Leibniz says, is provable from the first, and so in fact the principle of equipollence is the only axiom. ³¹ See, for example, Pierre Costabel, Leibniz and Dynamics: The Texts of 1692, trans. R.E.W. Maddison (Ithaca, NY: Cornell University Press, 1973), 112–13: the key “to a possible conciliation between the empirical laws of motion and an a priori principle of conservation . . . consisted in the principle of equivalence between full cause and entire effect. One must find a way of capping the rules of impact between colliding bodies, empirical generalizations, with theoretical laws by deploying an integrative system of equations to represent the efficient causes involved.” See also François Duchesneau, “Leibniz’s Contribution to Natural Philosophy,” in The Continuum Companion to Leibniz, ed. Brandon C. Look (London: Continuum, 2011), 241–2 and Garber, Leibniz: Body, Substance, Monad, 144–55 and 235–50. ³² In addition to the texts referred to in the footnotes above, see also Michel Fichant, “Leibniz et les Machines de la Nature,” Studia Leibnitiana 35 (2003).

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 ’     the cause to the knowledge of the effect.”³³ Since the entire effect is included in the whole cause, the knowledge of the effect is contained in the knowledge of the cause.³⁴ We can see here in the principle of equipollence seeds for Leibniz’s complete concept theory of substance and for his frequent claims that “the present is pregnant with the future.”³⁵ Similarly, the principle of continuity will provide for a certain kind of explanation. In particular, while the principle of equipollence preserves the full cause in the total effect, the principle of continuity guarantees a certain kind of structural or functional ordering, a dependence of the ordering of the effect upon the ordering of the cause. As we will see, this will ground a heuristic for natural theories and a guide for reasoning by analogy that will guide discovery.

1.3. Development of the principle of continuity All of this was developed in dialogue with several Cartesians and, especially, Malebranche. Malebranche published a paper in the April 1687 Nouvelles de la République des Lettres, conceding that Leibniz’s critique of his laws of motion “seems quite fair,”³⁶ admitting that he (Malebranche) should have stopped short at criticizing Descartes’s rules of motion rather than endorsing others, which are “not quite right.” Nevertheless, Malebranche does not grant Leibniz’s fundamental point about the conservation of force. In the Search after Truth, Book 6, Part II, chapter 9, Malebranche provides an account of the motion of bodies based on divine volition, arguing that rest is merely the privation of God’s volition that the body move, given that bodies themselves have no force of their own. So, motion and rest are fundamentally different in kind. In his reply to Leibniz, Malebranche says that the motions of objects are “arbitrary and depend on the Creator” and argues that experience is the way to access God’s will.³⁷ As André Robinet points out, “in advancing the arbitrariness of God in the explanation of motion, Malebranche renders physics independent from divine wisdom in its natural course.”³⁸ This highlights a fundamental point of disagreement between Leibniz and Malebranche. In July 1687, Leibniz published his response in the Nouvelles de la République des Lettres.³⁹ Leibniz proposes a “principle of general order” that would ground any investigation into natural changes. This principle holds, Leibniz says, because “the sovereign wisdom, the source of all things, acts as a perfect geometrician,”⁴⁰ and so our reasoning about the actions of God need not depend primarily on our experience of the operations of nature. Given that God acts in orderly ways, this principle of general order will be useful to investigations in physics, and it demonstrates the weakness of Descartes’s physics prior to any empirical inquiry.⁴¹

³³ “Concerning the Equipollence of Cause and Effect” (A 6.4.1963). ³⁴ Spinoza, of course, held to a similar principle, cf. Ethics Ia4. ³⁵ M §13. ³⁶ RML, 251. ³⁷ RML, 252. ³⁸ RML, 245. ³⁹ PG 351–3. There is also an extended Latin version of the letter at A 6.4.2031–9. ⁴⁰ PG 351. ⁴¹ PG 352. For an example of how the principle of continuity demonstrates the error in Cartesian physics, see Larry M. Jorgensen, “The Principle of Continuity and Leibniz’s Theory of Consciousness,” Journal of the History of Philosophy 47 (2009): section 2; Duchesneau, “Leibniz on the Principle of Continuity,” 158–9; and Garber, “Leibniz: Physics and Philosophy,” 314–16.

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Now, it may not be entirely fair to Malebranche to regard his theory of motion as arbitrary. As several commentators have noted, Malebranche regarded the interactions between bodies fully in terms of laws of nature and general volitions of God rather than in terms of whim and particular volitions as this characterization makes it seem.⁴² But even so, Leibniz thinks things have gone awry, since God’s laws would be irregular laws, allowing for disorder and discontinuity in natural transitions. As Leibniz notes, Malebranche “continues to believe that since the laws of motion depend on the good pleasure of God, God could therefore have established laws as irregular as these.”⁴³ In a 1687 letter to Arnauld, Leibniz summarizes what he sees as the status of the dialectic between himself and Malebranche: [Malebranche] seems to acknowledge that some of the laws of nature or rules of movement that he had put forward may be hard to defend. But he thinks the reason to be that he based them on infinite hardness, which does not exist in nature; whereas I believe that, even if it did exist, these rules would still be impossible to defend. And it is a weakness of his and M. Descartes’s arguments that they have not considered that every statement about motion, inequality and elasticity must also be verified when one assumes that these things are infinite or infinitely small. In that case motion (infinitely small) becomes rest, inequality (infinitely small) becomes equality; and elasticity (infinitely rapid) is nothing else but extreme hardness; more or less as all the proofs of the ellipse undertaken by geometers are verified about a parabola when it is thought of as an ellipse whose other focal point is infinitely distant. And it is strange to see that almost all M. Descartes’s rules of movement offend this principle, which I consider to be as infallible in physics as in geometry, because the author of the world acts as a perfect geometer. If I answer Father Malebranche, it will be mainly to bring this principle to notice, for it is very useful and has scarcely yet been considered in its generality, to my knowledge.⁴⁴

There are two particularly interesting aspects of this summary. First, notice that Leibniz is rejecting Malebranche’s claim that rest and motion are radically different. Or, more precisely, Malebranche argued that Descartes’s mistake had been to believe that rest has force. In contrast, Malebranche regarded rest as the mere privation of force. Leibniz’s position is more nuanced than either: rest can be conceived as an infinitely small degree of motion. And the rules of motion must apply to infinitely small motions just as well as to intermediate degrees of motion. The second thing to notice in this summary is that Leibniz expresses unequivocally the application of geometry to physics, and he gives a foundation for the claim. The principle is “as infallible in physics as in geometry because the author of the world acts as a perfect geometer.” Here Leibniz is providing the bridge between geometry and physics—the mathematical mindset of the creator (in contrast to arbitrary volitions). As Leibniz sees it, these are two deep differences between Malebranche

⁴² For more on the relation between Malebranche and Leibniz, see Jolley, “Leibniz and Occasionalism”; Rutherford, “Natures, Laws, and Miracles”; R.C. Sleigh, Jr., Leibniz and Arnauld: A Commentary on their Correspondence (New Haven, CT: Yale University Press, 1990), 161–70; and Sean Greenberg, “Malebranche and Leibniz,” in The Bloomsbury Companion to Leibniz, ed. Brandon C. Look (London: Bloomsbury, 2011), 68–85. ⁴³ PG 352. ⁴⁴ Letter to Arnauld, July 22/August 1, 1687 (A 2.2.219–20/LA 130–1).

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 ’     and himself, and they result in significant differences in how physics (and other empirical sciences) should be approached. But in order to make his case for this, Leibniz needed to introduce a principle beyond an equivalence principle. Malebranche’s account of motion allows Malebranche to appeal to God’s activity in directing motion, and so the equivalence of force could be preserved even in cases of discontinuous motion. What Leibniz requires here is a principle that preserves a dependency of ordering of effects on causes, and this is what he introduces in his 1687 letter. Leibniz’s reply to Malebranche, “Letter of Mr. Leibniz on a General Principle Useful in Explaining the Laws of Nature through a Consideration of the Divine Wisdom: to Serve as a Reply to the Response of the Rev. Father Malebranche,” was published in the Nouvelles de la République des Lettres in July 1687.⁴⁵ Leibniz refers to this paper repeatedly in later years as supporting what he then calls “the principle of continuity” or “the law of continuity.”⁴⁶ At the time of composition, however, the principle does not appear to have taken shape under this heading. The first reference to the name, “the law of continuity,” that I have found is in 1692, in Leibniz’s “Critical Thoughts on the General Part of the Principles of Descartes,” where he says that he “usually” calls this principle “the law of continuity.”⁴⁷ Since he says this is usual for him, there may be other references around that time that I have not discovered. But prior to 1692 (and even, in some cases, later), Leibniz does not give it this name. Instead, he describes it as an instance of a more “general principle”⁴⁸ that is useful in physics. Nevertheless, Leibniz’s thinking was clearly guided by the principle of continuity, and he referred often to the 1687 “General Principle” article as its source.⁴⁹ (Note: although Leibniz frequently refers to the principle as the “law of continuity,” he does also call it the “principle of continuity.” Today it is more commonly referred to as the “principle of continuity,” and I will continue the practice in this volume.) In the 1687 essay, Leibniz defines what he calls a “principle of general order”: Principle of General Order: ordered also.”

“As the data are ordered, so the unknowns are

Under Malebranche’s theory of motion, natural changes would include what Leibniz regarded as disorder, sudden changes that cannot be explained by the objects in motion themselves. The principle of general order identifies a dependency of ordering of the unknowns on the known. ⁴⁵ PG 351–3. ⁴⁶ See, for example, “A Specimen of Dynamics” (GM 6.249/AG 133); Letter to Bernoulli, July 2 (12), 1697 (A 3.7.479–80); “Reply to . . . ‘Rorarius’ ” (G 4.568/WF 123); and the preface to the New Essays on Human Understanding (A 4.6.56/NE 56). ⁴⁷ G 4.375/L 397. ⁴⁸ In the Nouvelles letter and in a Letter to Foucher, end of 1688 (A 2.2.284). ⁴⁹ Leibniz even sent a version of the principle of continuity to Paul Pelisson-Fontanier, who passed it along to be evaluated by the Royal Academy of Sciences in Paris. Pelisson passed the paper along to Claude Mallement, who called it “very dangerous,” saying that it could be good or bad depending on how it is used (A 2.2.505–6). Leibniz complains about this response, saying that his claims were not well understood and, if he had known it was going to be passed along, he would have written it out more fully (A 2.2.509–10 and A 2.2.524). (It actually seems incredible to me that Leibniz might not have known it was being passed along.)

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The principle of general order, by itself, does not guarantee continuity, since the data may not be ordered in a continuous series. And if the data were not continuously ordered, neither would the unknowns be ordered. But Leibniz provides another formulation, which he comes to call the “principle of continuity”: Principle of Continuity: “When the difference between two instances in a given series or that which is presupposed can be diminished until it becomes smaller than any given quantity whatever, the corresponding difference in what is sought or in their results must of necessity also be diminished or become less than any given quantity whatever.” This is a technical way to express the principle, but Leibniz provides a more friendly version: Principle of Continuity (friendly): “When two instances or data approach each other continuously, so that one at last passes over into the other, it is necessary for their consequences or results (or the unknown) to do so also.” To put it formally, for any function, f(x), if |x₂–x₁|