Possibility, Agency, and Individuality in Leibniz's Metaphysics (The New Synthese Historical Library)

POSSIBILITY, AGENCY, AND INDIVIDUALITY IN LEIBNIZ’S METAPHYSICS

The New Synthese Historical Library Texts and Studies in the History of Philosophy VOLUME 61

Managing Editor: SIMO KNUUTTILA, University of Helsinki Associate Editors: DANIEL ELLIOT GARBER, Princeton University RICHARD SORABJI, University of London Editorial Consultants: JAN A. AERTSEN, Thomas-Institut, Universität zu Köln ROGER ARIEW, Virginia Polytechnic Institute E. JENNIFER ASHWORTH, University of Waterloo MICHAEL AYERS, Wadham College, Oxford GAIL FINE, Cornell University R. J. HANKINSON, University of Texas JAAKKO HINTIKKA, Boston University PAUL HOFFMAN, University of California, Riverside DAVID KONSTAN, Brown University RICHARD H. KRAUT, Northwestern University, Evanston ALAIN DE LIBERA, Université de Genève JOHN E. MURDOCH, Harvard University DAVID FATE NORTON, McGill University LUCA OBERTELLO, Università degli Studi di Genova ELEONORE STUMP, St. Louis University ALLEN WOOD, Stanford University

The titles published in this series are listed at the end of this volume.

POSSIBILITY, AGENCY, AND INDIVIDUALITY IN LEIBNIZ’S METAPHYSICS by OHAD NACHTOMY Bar-Ilan University, Israel

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To my Parents

Contents Acknowledgements ..................................................................................... ix Abbreviations ............................................................................................. xi Introduction................................................................................................. 1 Part I: Chapter 1: Chapter 2: Chapter 3: Chapter 4: Part II: Chapter 5: Chapter 6: Chapter 7:

Possibility Leibniz’s Combinatorial Approach to Possibility ................9 Possible Individuals..............................................................51 The Individual’s Place in Logical Space ..............................85 Individuals, Worlds and Relations ......................................105 Agency Possibility and Actuality ....................................................123 Agency and Freedom..........................................................145 Agency and Necessity .......................................................167

Part III: Individuality Chapter 8: Aggregates..........................................................................189 Chapter 9: Nested Individuals..............................................................215 Chapter 10: Possibility and Individuality...............................................237 Conclusion................................................................................................249 References ................................................................................................255 Index .........................................................................................................265

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Acknowledgements In writing this book I have benefited enormously from a live and stimulating dialogue with many Leibniz scholars who share the Leibnizian spirit of exchange and cooperation. In particular, I have benefited from discussions and exchanges with Andreas Blank, Marcelo Dascal, François Duchesneau, Alan Gabbey, Dan Garber, Martine de Gaudemar, Sean Greenberg, Emily Grosholz, Glenn Hartz, Mark Kulstad, Mogens Laerke, Elad Lison, Brandon Look, Yitzhak Melamed, Christia Mercer, PierreFrançois Moreau, Marine Picon, Jean-Baptiste Rauzy, Donald Rutherford, Ayelet Shavit, Justin Smith, Achile Varzi, David Widerker, Catherine Wilson, and Elhanan Yakira. I am especially indebted to Andreas Blank, Emily Grosholz, Justin Smith, Pauline Phemister and Roslyn Weiss who read and commented on the whole manuscript, sometimes on more than one version. I have also greatly benefited from the works of Massimo Mugnai and Michel Fichant. I owe special thanks to Christia Mercer who not only introduced me to the world of Leibniz but also followed the project and helped along the way. In the fall of 2004, an early version of this book was presented, chapter by chapter, at the weekly meetings of the faculty seminar of the philosophy department at Lehigh University. I have greatly benefited from these discussions and I would like to thank all the participants of the seminar for their contributions, criticism and generous encouragement. I would like to warmly thank Roslyn Weiss for her extremely helpful editorial work. An early version of chapter 2 appeared in Studia Leibnitiana, 30, 1998; an early version of chapter 3 appeared in Studia Leibnitiana 34, 2002; an early version of the first part of chapter 4 appeared in The Leibniz Review, 11, 2001.

ix

Abbreviations A

G. W. Leibniz: Sämtliche Schriften und Briefe, Darmstadt/Leipzig/Berlin, Edition of the German Academy of Sciences 1923- , Cited by series, volume, and page. If not otherwise indicated, the reference is to series 6, volume 3. AG G. W. Leibniz: Philosophical Essays, D. Garber and R. Ariew (eds. and trans.) Indianapolis, Hackett, 1989. Arthur G. W. Leibniz, The Labyrinth of the Continuum. Writings on the Continuum Problem, 1672-1686, translated by R. Arthur, New Haven and London, Yale University Press, 2001. C Opuscules et Fragments inédits de Leibniz, L. Couturat (ed.), Paris, Olms, 1961. CCL The Cambridge Companion to Leibniz, N. Jolley, (ed.), Cambridge, Cambridge University Press, 1995. Confessio Sleigh, R. C., JR., (ed. and trans.), Confessio philosophi, Papers Concerning the Problem of Evil, 1671–1678, New Haven, Yale University Press, 2005. Ethics Baruch Spinoza, Ethica, Roman numerals indicate part; a: axiom; p: proposition; s: scholium, followed by Arabic numerals. FC Nouvelles lettres et opuscules inédits de Leibniz, A. Foucher de Careil, (ed.), Paris, August Durand, 1857; reprinted Hildesheim, Olms, 1971. GP Die Philosophischen Schriften von G. W. Leibniz, C. I. Gerhardt, (ed.), 7 vols. Berlin, Weidmann, 1875-90; reprinted Hildesheim, Olms, 1978. GM Die mathematischen Schriften von G. W. Leibniz, C. I. Gerhardt, (ed.), Berlin: Winter, 1860-1875. Grua G. W. Leibniz: Textes inédits d’après les manuscrits de la Bibliothèque provinciale de Hanovre, G. Grua, (ed.), Paris, 1948. L G. W. Leibniz, Philosophical Papers and Letters, translated by L. E. Loemker, 2nd edition, Dordrecht, Kluwer, 1969. LA The Leibniz-Arnauld Correspondence, H. T., Mason, (ed. and trans.), Manchester, Manchester University Press, 1967. LR G. W. Leibniz, Discours de métaphysique et correspondance avec Arnauld, George Le Roy, (ed.), Paris, Vrin, 1970. NE G. W. Leibniz, Nouveaux essais sur l’entendement humain, cited by book chapter and section, translated by P. Remnant and J. Bennett, Cambridge, Cambridge University Press, 1981. xi

xii

Abbreviations

PLP SR Theodicy

G. W. Leibniz: Logical Papers, Parkinson G. H. R. (trans. and ed.), Oxford, Clarendon Press, 1966. G. W. Leibniz: De Summa Rerum: Metaphysical Papers 16751676, (trans. and ed.), G. H. R. Parkinson, New Haven and London, Yale University Press, 1992. G. W. Leibniz: Essays on the Goodness of God the Freedom of Man and the Origin Evil, (trans.), E. M. Huggard, La Salle, Illinois, Open Court, 1993, first published by Routledge & Kegan Paul, London, 1951.

Introduction

Leibniz’s notion of possibility is one of his most significant contributions to philosophy as well as one of the cornerstones of his metaphysics. This work attempts to bring out the intrinsic subtlety of Leibniz’s approach to possibility and to explore some of its important repercussions in his metaphysics. This project involves an examination of some of the most difficult questions in Leibniz‘s metaphysics from this vantage point. The book consists of three parts, the first focusing on Leibniz’s notion of possibility, the second on his notion of agency, and the third on his notion of individuality. Leibniz’s preoccupation with the notions of possibility, agency and individuality is evident in his early writings as well as in his later ones. His combinatorial insights regarding the notion of possibility as a model for creating the world, his commitment to the traditional doctrine that activity constitutes being, and his view that individuals are the only true beings are among the formative and persisting tenets of his metaphysics. This work explores these tenets in some detail and seeks to highlight the connections between them. The first part of the book presents Leibniz’s approach to possibility by exposing his early presuppositions about the status and nature of possibilities (chapter 1); his notion of possible individuals (chapter 2); and his notion of possible worlds as constituted by the relations among possible individuals (chapters 3 and 4). The second part discusses the transition from possibility to actuality through the notion of agency. In chapter 5, I take up the question of actualization and divine agency. In chapter 6, I discuss the notions of moral agency and freedom of action in the human context. In chapter 7, I discuss the relation between agency and necessity in comparison to Spinoza who denies possibilities altogether. The third part discusses Leibniz’s notion of nested, organic individuals in distinction from his notion of aggregates. In chapter 8, I discuss Leibniz’s notion of aggregates and how their unity differs from that of genuine individuals. In chapter 9, I examine Leibniz’s notion of nested individuals and their organic unity. In the final chapter I attempt to highlight the way in which Leibniz’s notion of possible individuals helps clarifying the unity and simplicity of actual, nested individuals. 1

2

Introduction

In drawing attention to the connections between possible individuals and actual ones through the notion of agency, I attempt to highlight a thread that runs through Leibniz’s metaphysics — one which Leibniz himself for the most part presupposes but does not state. I present this thread — by no means the only thread that runs through Leibniz’s metaphysics — by developing his definition of possible individuals and exploring some of the roles it plays in his metaphysics. I suggest that Leibniz defined a possible individual through a combinatorial rule that generates a unique and maximally consistent structure of predicates in God’s understanding. Such a rule may be viewed as a program for action. I use this definition to clarify Leibniz’s notion of actualization as endowing such a program with primitive force or power of action; his notion of moral agency and moral necessity by reflecting on the relation between the individual’s concept and the agent realizing it; his distinction between individual substances and aggregates, and his notion of organic individuals, which have a nested structure to infinity. I conclude by arguing that Leibniz’s definition of a possible individual as a program of action helps clarifying the type of unity he ascribes to a unique structure of nested individuals. My choice of texts reflects the central role Leibniz’s approach to possibility plays in his metaphysics. I present Leibniz’s early presuppositions about possibility by focusing on his early texts and, in discussing other topics, I focus on texts in which Leibniz’s views are either formative or very clearly expressed. While my main concern in this book is not a detailed and linear story of Leibniz’s development, generally speaking, the book does progress (with some important exceptions) from his early to his later writings. The story of Leibniz’s metaphysics I present here is not meant to be comprehensive. Rather, it starts with his suppositions about possibility and continues to examine central themes which are either interestingly related to it or which are intrinsically difficult and whose consideration against the context of his theory of possibility may contribute to our understanding of them (such as freedom and contingency, striving possibilities, unity of nested individuals). Some of chapters are also internally related (e.g., chapters 6 and 7, as well as 8 and 9) so that my discussion of the one motivates my discussion of the other. At the same time, the main conviction that informs the structure of this work is that there are intrinsic and interesting connections between Leibniz’s logical theory of possible individuals and his theory of actual, organic ones. In some more detail, the contents of each chapter are as follows. Chapter 1 presents the context in which Leibniz develops his approach to possibility. Leibniz’s approach to the status of possibilities is situated

Introduction

3

within the Platonic tradition in Christian philosophy. The Christian tradition reconciles the Platonic realm of eternal and immutable essences with its view of God as an active creator. It places the realm of ideal essences in the mind of God and sees these as exemplars of an ideal model for creation. Christian philosophy commonly viewed the formal model for the creation as thoughts in the creator’s mind. Leibniz’s view of possibility can be seen as a modification of this traditional model: he sees the individual exemplars not as some kind of entities but rather as logical possibilities, that is, as consistent thoughts in God’s understanding that he may or may not realize. Given this context, I examine how God's thinking (his mental activity) produces such possibilities. I argue that Leibniz understood this question in combinatorial terms. His insight is that the combinatorial nature of thinking produces possibilities as mental composition of simple constituents produces complex concepts. According to this view, God produces possible things by thinking the combinations among his simple forms, which Leibniz identifies with God’s simple attributes. God’s successive and reiterative combinatorial operations yield more complex forms, which are successively and indefinitely recombined, to yield diverse and infinite structures of predicates. God’s combinatorial activity thus generates complex structures of predicates and each consistent structure of forms is deemed possible. On the basis of Leibniz’s presuppositions about possibility, I examine his views of predication, truth, and his projects to construct a universal language and a real characteristics. In chapter 2, I attempt to clarify how individual concepts or possible individuals are formed in the context of God’s combinatorial activity. I suggest that Leibniz identified the concept of an individual with the combinatorial rule that generates a unique and maximally consistent structure of predicates in God’s understanding. I term this rule the “production rule of the individual”—the method of producing a complex and unique structure of predicates by combining simple forms in God’s understanding. The production rule unifies many predicates into one whole and constitutes the logical subject of an individual. While the production rule constitutes the individual’s subject, the forms that make it up constitute its predicates. Such a rule corresponds to one of God’s “modes” of intelligible activity. All the modes of God’s activity that produce unique and consistent structures of predicates correspond to basic concepts of individuals. Since all concepts of individuals derive from God’s simple forms and his combinatorial operations, they reflect God’s essence and constitute the exemplars that are candidates for actualization. God’s mental activity consists in reiterative reflection on the relations among its forms; it is neither temporal nor causal and no real production takes place—only mental composition in God's understanding.

4

Introduction

Within this picture of possibility and the formation of individual concepts, I examine in chapter 3 how possible worlds are formed as compossible sets of individual concepts. This task involves Leibniz’s view of relations. However, there seems to be a severe tension between Leibniz’s commitments to a metaphysics of individuals and his use of relations among possible individuals as constitutive of a possible world. On the one hand, Leibniz’s notion of compossibility among possible individuals presupposes relations between them. On the other hand, Leibniz believes that only individuals exist and that each individual has a concept so complete that all the truths about an individual, even such a truth as being compatible with other individuals, can be derived from the concept of that individual. I approach this tension by presenting it in the context of possibilities. In the context of possibilities in God’s mind, relations have a natural place: relations among possible individuals arise as God considers several individuals at the same time. This view does not imply that relations exist or that they are properties of God. Rather, following Mugnai, I suggest that, for Leibniz, the ontological status of relations is not that of entities but of mental/logical co-considerations of various relata in the same thought or, as I prefer to call it, in the same logical space. Thus possibilities and relations have similar ontological status. I note that Leibniz’s view of relations formulated in his correspondence with Arnauld reveals an additional tension: while relations are required for the notion of possible worlds, such relations are also required to complete the individuation of concepts of individuals. I note that Leibniz’s use of relations seems to conflict with his nominalism and his denial of the reality of relations. The resolution of this conflict, however, leads to a severe problem of circularity: on the one hand, Leibniz believes that interindividual relations presuppose individuals, but, on the other hand, he uses such relations for the very individuation of individuals. I seek to resolve this circularity by using the notion of the “logical space of possibilities” and the individual’s place within it. The individual’s place within logical space is both constitutive of its concept and a relational notion. Due to Leibniz’s view of relations, the concepts of individuals and the logical space turn out to be mutually constitutive notions, which points to a way out of the circularity. Chapter 4 develops the suggestion that complete possible individuals and possible worlds are mutually constitutive by responding to an objection Catherine Wilson raises, namely, that worlds logically precede individuals. Wilson argues that the notion of a world conceptually precedes that of an individual substance. Instead of a world produced by

Introduction

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conjoining individuals, Wilson suggests that individuals are produced by breaking down an already complete world. My response to this argument leads to the conclusion that we can avoid the question of whether individuals precede worlds or vice versa since we can take the position, which I favor, that these notions are mutually constitutive. I suggest that possible worlds are formed at the moment that the relations between incomplete concepts of individuals are considered. It is only at this moment that the complete concepts of individuals, as well as of worlds, are formed in God’s mind. In the second part of the chapter, I extend my reconstruction of Leibniz’s position to the role that relations play in individuation. In light of the distinction between complete and incomplete concepts, I consider two recent approaches (those of Cover and O’LearyHawthorne (1999) and Mugnai (2001) to the role of relations in individuation. According to Cover and O’Leary-Hawthorne, relations play no metaphysical role in individuation; according to Mugnai, they play an essential role. I argue that Leibniz’s mature view of individuation is a reconciliation of these positions. Chapter 5 takes up the question of actualization. I consider the actualization of a possible world in terms of the actualization of possible individuals. As I argued in chapter 2, a possible individual is partly defined by the rule of activity that produces a unique structure of predicates in God’s mind. The production rule thus defines the essence of an individual and constitutes its logical subject. Such a notion of a possible individual may be seen as a unique program of action, that is, a course of action that God conceives in his mind. A Leibnizian actual individual, however, acts on its own – it is a spontaneous agent. To become an active agent, a possible individual needs power of action. I suggest, therefore, that actualization involves endowing a rule of action with primitive power of action. A program for action and power of action yield an active agent who has a unique course of action. Upon creation, the agent’s activity, implemented according to its rule, produces the sequence of predicates prescribed by the production rule. The agent’s production rule thus regulates its development and unifies its various states from within. The agent’s activity, according to its production rule, renders it a self-sufficient individual substance. Whereas the intelligible activity in God’s mind is atemporal and immutable, the activity of actual individuals involves change. The intelligible activity in God’s mind produces possible individuals, while the activity of created minds realizes (some of) these possibilities in the world. Thus the transition from possible individuals to actual ones can be understood against the background of the Platonic contrast between the realm of Being and that of becoming.

6

Introduction

Chapter 6 examines the tension between Leibniz’s definition of the individual by a complete concept and his insistence that rational individuals act freely – what Leibniz calls the labyrinth of human freedom. In light of the view of possible individuals presented in chapter 2, and in light of the view of actualization presented in chapter 5, I suggest a prescriptive reading of the individual’s concept as an explication of Leibniz’s notion of moral necessity. My approach is based on a distinction between descriptive and prescriptive aspects of Leibniz’s notion of the complete concept as well as on the distinction between concepts and actions. A complete concept may be seen as a comprehensive picture of the individual’s activities and properties and it may also be seen as prescribing the reasons for the individual’s course of action. In this way, the reasons may be seen as intrinsic to the individual’s concept while there remains a logical possibility that they would not be the causes of the individual’s actions. This reading may help clarify Leibniz's distinction between necessary and intrinsic predicates as well as his claim that reasons “incline” the rational individual’s actions without necessitating them. The prescriptive reading I develop helps to explicate Leibniz’s notions of contingency and moral necessity and shows that the notions of possibility and agency, and particularly the notion of rational agency, play a significant role in his insistence on human freedom. Chapter 7 contrasts the views of Leibniz and Spinoza. According to Leibniz, rational agency presupposes contingency or logically possible alternatives. Spinoza, however, holds that the notion of contingency merely attests to human ignorance and delusion regarding the truly necessary course of events (e.g., Ethics I p 29). He famously writes that, “a thing is called contingent only with regard to a defect in our knowledge” (Ethics I p 33 s2). Since Spinoza denies contingency, his metaphysics offers a very interesting context in which to examine a notion of agency as separated from the notion of possibility—that is, a context in which agency is strongly related to necessity. I examine the relation between activity and necessity in Spinoza against the background of Descartes’ mechanistic view of res extensa and I outline an interpretative approach according to which, for Spinoza, God’s activity is constitutive of his essence, rather than entailed by it independently of his activity. This approach depends on a generative notion of essences and concepts, common to both Spinoza and Leibniz (but much more explicit in Leibniz). I suggest that the use of generative definitions may make clearer the relation between activity and necessity in Spinoza and that Leibniz’s extensive use of generative definitions lends support to the central role agency plays in his view of substance as well as to the intrinsic relations he conceives between the notions of possibility, agency and individuality.

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Chapter 8 focuses on Leibniz’s notion of aggregates and their distinction from individual substances. In contrast to Descartes, Leibniz describes extended bodies as at once semirealia and semimentalia. Such bodies differ from true beings (individual substances) as well as from mere phenomena. They occupy a curious middle position between true beings and fictions and are aptly termed “well-founded phenomena”. In effect, such extended bodies are aggregates of non-extended substances. In applying Leibniz’s view of relations presented in chapter 3, I suggest that Leibniz’s notion of aggregate presupposes a mental/logical operation through which many substances are united. While the unity of the aggregate derives from a mind performing the operation, its reality is grounded in real substances. Thus, according to Leibniz, extension is understood as a relational property that presupposes a uniting operation of the relata. I argue that this extent of mind-dependence does not imply an anti-materialist (or entirely idealist) view of material bodies. Rather, it requires that claims about material bodies will be seen as involving relations among substances and a mind perceiving these relations. I conclude that the status of aggregates as well-founded phenomena derives primarily from their relational and external unity. By contrast, individual substances have internal (substantial) unity. In effect, this difference is strongly related to a range of features that also serves to distinguish organic from non-organic beings. In contrast to aggregates, true beings, which Leibniz identifies with individuals, are characterized by their substantial (i.e., enduring and necessary) unity. Among Leibniz's paradigmatic examples of individual substances are organic unities such as animals and plants. It is remarkable, however, that, in Leibniz's view, such organic unities consist of other individual substances nested within them. Thus chapter 9 examines Leibniz’s notion of nested individuals and their unity, which is characteristic of organic units alone. As it turns out, this structure of creatures nested within creatures typifies the Leibnizian notion of individuality, so that nested individuals turn out to be the constituents of other individuals. This radical and fascinating model of individuality contrasts with most of the traditional models (starting from Aristotle’s) as well as with contemporary models of individuality and involves some severe difficulties. Since Leibniz defines substances as true units and as self-sufficient, it is not at all clear what makes such an ensemble of creatures, nested within each other, one substance. In other words, it is not at all clear what distinguishes the supposed unity of substances from the lack of unity in aggregates – which also comprise a plurality of true units. I suggest we approach this difficult question by examining the precise sense in which

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Introduction

Leibniz employs the notions unity and nestedness. Following a remark by Ishiguro, I suggest that the unity in question is not the cohesiveness of parts or (primarily) that of spatio-temporal unity but rather the unity of agency. It is a unity deriving from activation in the sense of functional organization that gives unity to the substance. Thus, a living being is united by virtue of a single principle of functional organization that also orders its activity in accordance with a certain end. In chapter 10, the insights from Leibniz's view of possibility are used to further clarify his notion of nested individuality. In particular, the observations on how a possible individual is formed in God's mind are used to illuminate the simplicity and infinite structure of nested individuals. I suggest that the structure of individuals nested one within another is consistent with the notion of a possible individual presented in chapters 2 and 3. Like an algorithm, the production rule generating a unique structure of predicates in God’s mind may include many nested sub-rules as constitutive components. If a "divine combinatorics" gives rise to concepts of individuals through the notion of a production-rule for unifying and ordering predicates, it may also be used to explain the relation of functional organization and domination between an individual substance and the individual substances nested in it. In this way, the production rule may be used to account for the unity as well as the simplicity of nested individuals. Thus Leibniz’s views of possibility and actuality are not only intrinsically connected but may also be used to shed light on each other.

Chapter 1 Leibniz’s Combinatorial Approach to Possibility 1.1 Leibniz’s Motivation Leibniz’s preoccupation with the notion of possibility is generally recognized. Yet some of his presuppositions as well as some of its implications are not. The main purpose of this chapter is to present these presuppositions. Leibniz’s presuppositions have metaphysical, theological, logical and mathematical aspects, which very naturally integrate into his thought about possibility. Although most of these presuppositions are individually quite familiar to Leibniz’s scholars, a less familiar approach to the question of possibility emerges when they are considered as a whole. This approach, which is deeply rooted in metaphysical and theological contexts, amounts to a rich and original philosophical analysis of possibility, in which possibility is primarily understood in combinatorial terms. Leibniz’s notion of possibility, its centrality as well as its rich development, are some of the most distinctive features of his philosophy. Leibniz’s notion of possibility and its employment clearly distinguish his system from the major philosophical systems in the modern period.1 Before presenting Leibniz’s original approach to possibility in detail, I would like to examine some of the reasons that motivate him to develop it. While Leibniz’s approach to possibility stand out in the modern era, his motivation can be best understood in contrast to the views of other philosophers in his period, especially with the view of Spinoza. As Martine de Gaudemar very aptly noted, Spinoza’s philosophical system is characterized by the notion of necessity, while Leibniz’s system is characterized by the notion of possibility. While the early Leibniz was very curious and intrigued by Spinoza’s metaphysical system,2 he was deeply troubled by its necessitarian consequences.3 The way his philosophy could avoid these consequences was by means of a theory of possibility that would make sense of contingency and of reasoned choice.4 At the same time, Leibniz’s concern about Spinoza’s necessitarian system was in fact indicative of a broader and deeper philosophical concern in which Spinoza occupied a distinctive role.

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Chapter 1

Leibniz is deeply concerned by a broader tendency (present to some extent in the views of Hobbes and Descartes) re-emerging with the modern philosophical picture – a naturalist tendency that, according to Leibniz, leaves no room for morality, goodness and ultimately, for rationality itself. In short, in this naturalistic picture, there is no room for norms. This point is made explicitly in Spinoza’s Ethics, appendix to book I. Leibniz identifies this type of naturalism with a new form of Stocism (GP VII 33236; AG 281-84) whose most prominent and acute voice in his time is Spinoza (AG 282). For Spinoza, the moral and the normative domains are grounded in human features and needs, which are considered to be purely natural. For example, Spinoza identifies the good with the useful. According to him, the right, the beautiful and the orderly merely express human concerns.5 This shift away from a philosophical world-view in which being and reality express moral truths, to a naturalized morality grounded in human nature will receive an explicit expression in the prevalent theory of moral sense in the 18th century. In contrast, Leibniz attempts to account for an eternal, rather than merely human, notion of morality (and more broadly of normativity) grounded in a divine source. For Leibniz, the notion of possibility constitutes a necessary condition for such an account. Its development, therefore, is strongly motivated by moral and theological concerns. Let me rephrase this point in some more detail. In Descartes’ rejection of the natural world as embedding values, final causes and purposes, in his striving for a purely scientific and quantitative picture of the natural world, the notions of internal activity and life were given up. For Descartes, the natural world was to be understood as pure geometric-like extension, i.e., bits of matter in motion, to be described in quantitative terms alone. Spinoza radicalizes this turn. For him, there is nothing over and above the natural, viewed as God or Nature (Deus sive Natura). As Leibniz wrote in his comments on Spinoza’s Ethics: “Spinoza begins where Descartes left off: in naturalism” (AG 277). Since Spinoza accepts Descartes’ scientific standards for describing nature, an adequate description of reality, for him, reduces to facts, entirely governed by necessity (both causal and logical) in which there is no room for moral or normative notions. The world as a whole is to be seen as morally neutral. Hence, any ascription of value to it can only derive from a human source and interest rather than to an adequate description of nature.6 While Leibniz shared the scientific spirit of Descartes and Spinoza, he was deeply opposed to its sweeping application. In particular, he was concerned about the implication that all intelligible reality reduces to causal connections since, according to him, in such a view of reality, there is no room for values, morality and rational deliberation. In this sense,

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much of Leibniz’s philosophical work can be seen as an attempt to form an alternative to Spinoza’s naturalist picture. Since, in Spinoza, there is only a unique and necessary course of nature, and hence no alternatives, it would seem that there is no room for moral deliberation and reasoned choice among them.7 Leibniz’s notion of possibility counters this philosophical predicament by attempting to make sense of alternatives. While it remains open at this juncture whether these alternatives are possible worlds, possible individuals or possible actions of individuals in the world, the main challenge for Leibniz is a conception of the world in which various possibilities make sense, and there is not a necessary result – be it logical and/or causal – which, for Spinoza, produces one and the same reality. If there are various ways in which the world could be, or more exactly, various possible worlds, which are equally possible but not equally good, then a choice between them makes sense. In Leibniz’s view, without alternatives, there is no room for rational deliberation or reasons to prefer one alternative over another. In short, for Leibniz, a notion of possibility is required for a world-view in which moral choice and moral reasoning according to norms make sense. Very broadly speaking, this is also the motivation behind Leibniz’s commitment to his “two great principles” – the principle of contradiction and that of sufficient reason. Leibniz is using his two great principles in a complementary way: the principle of non-contradiction defines all possibilities and that of sufficient reason allows decision among these possibilities.8 As we shall see, the story is much more subtle and complex. Having sketched the motivation behind Leibniz’s approach to possibility, let me turn to its presentation. As we shall see, his approach to possibility includes a set of commitments that inform his views of logic, truth, contingency, individuality, agency, space, time, and others. This is why Leibniz’s combinatorial approach to possibility is the point of departure in this work. It provides an essential background for many of Leibniz’s metaphysical doctrines. In elaborating his early presuppositions regarding possibility, we shall thus gain some insight into the constitution of his metaphysical system. This point seems to hold both in a historical and a conceptual sense. Leibniz’s notion of possibility was one of the earliest philosophical notions that he presupposed and it may have led him to develop other related notions. However, I will not argue for the historical case in this work. It is only suggested here.9

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1.2 Background: Platonic Forms, Divine Thoughts and Logical Possibilities The first supposition I will explore is that possibilities are conceived in God’s mind. This supposition mainly concerns the status of possibilities (that is, the notion of possibilitates, in the scholastic jargon) rather than the question what type of things are considered to be possible (the question of possibilia, in the scholastic jargon). Exploring this supposition will also help us to place Leibniz’s view of possibility in its historical context. In following Augustine’s lead in the Christianization of Plato, the neoplatonic tradition interpreted the Platonic realm of Being – the eternal and invariable Forms – as a realm of divine thoughts. In this interpretation, the Platonic self-sufficient Forms came to be seen as the objects of thought of an active and all-knowing mind, namely that of God. In the Christian platonic tradition, God was seen as an active agent whose intelligible activity consists of the conception of all true Beings. The notion of Being, which is primarily ascribed to God in this tradition, is grounded in his intelligible activity – i.e., in his thought. In the early modern period, it became common practice to explicate God’s intelligible activity by means of mathematical and logical activity (e.g., Galileo, Spinoza). Just as for Plato mathematics was the paradigm for understanding the eternal Forms, so for the early moderns, mathematics was the paradigm for understanding God’s intelligible and creative activity. Yet the notions of Being and activity have undergone dramatic changes since the early modern era. While we now tend to associate activity and being primarily with spatio-temporal and causal change, in the pre-modern era, Being was seen as entirely distinct from spatio-temporal and causal activity. It was seen as an atemporal and immaterial type of activity, i.e., as intelligible thought.10 The best model of such activity is indeed mathematical or logical. It is primarily this type of intelligible activity that permeates Leibniz’s presuppositions about the divine realm as the locus of possibilities and truths. In the Christian Platonic tradition, the Greek distinction between Being and becoming, the intelligible and the sensible, was transposed into a distinction between the objects of God’s thought – seen also as the ideal model of creation – and the created world. This transposition has significant consequences: it introduces the notion of agency into both the notion of the creator as well as that of creatures. An active Creator thinks all forms and exemplars of the things he may realize in material form. According to this tradition, God creates the material world of change and becoming according to an invariable model of Forms (or essences seen as ideal exemplars), which he conceives in his mind. This is roughly the

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Christianized version of the Timaeus myth (29a) in which the demiurge produces the material world according to the ideal model of Forms. Likewise, in this tradition creation may be interpreted as a shift from intelligible atemporal type of activity to material temproal type activity (more on this in chapter five). The modern notion of possibility is first articulated against this background. Leibniz’s approach to possibility is grounded in this view of thoughts in God’s mind. In Leibniz’s view, however, one can already detect explicit separation between the notion of being in God’s mind and the notion of pure logical possibility. Knuuttila nicely summarizes some of the most important points in the history of modern modal notions and in particular pinpoints the moment at which the ontological basis for possibility was given up. He writes: In ancient metaphysics, modality and intelligibility were considered as real moments of being. A Christian variant of this doctrine can be found in such thirteenth century Parisian scholars as Thomas Aquinas, Bonaventura, and Henry of Ghent. They thought that God’s infinite act of understanding contains the ideas of all conceivable kinds of beings. Ideas, as possibilities have an ontological foundation, however, because God’s act of thinking consist of understanding the infinite ways in which his essence could be imitated by finite beings. Because the ontological foundation remains as such unknown to men, it is claimed that we usually cannot decide whether an alleged unrealized possibility really is a possibility at all. In Duns Scotus’s modal theory, the ontological foundation of thinkability is given up. The area of logical possibility is characterized as an infinite domain of thinkability which, without having any kind of existence, is objective in the sense that it would be identical in any omniscient intellect thinking about all thinkable things. This theory of the domain of possibility as an absolute precondition of all being and thinking was accepted by Ockham and many other medievals, and through Suarez’s works it was commonly known in the seventeenth century, too (Modern Modalities (ed.) S. Knuuttila, viii). It is very clear that Leibniz’s view of possibility is rooted in this tradition. Leibniz follows the Suarezian view in which the domain of possibility is seen as an absolute precondition of all being and thinking. Already in his Confessio (1673), in which he explicitly connects the nature

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of things with the ideas of these things and with the essence of God, he writes: I say, therefore, that the will of God is not the reason why God wills something (for what leads someone to will is never his willing to will but his believing that the thing merits it); the reason why God wills something is rather the nature of the things themselves, contained in ideas themselves of these things, i.e., in the essence of God (A 6.3 124; Confessio 49).11 Leibniz makes it clear that God’s essence entails the nature of things, as well as the eternal truths, by virtue of his thinking and understanding them (Confessio, 61 and his Paris notes A 6.3 572; SR 91). In short, the nature and essence of all things is expressed by the contents of God’s thoughts. As in the Christian tradition described above, Leibniz sees the Platonic forms as thought by God: "God, who is necessarily a thinking being" (A 6.3 476; SR 29) thinks the ideas of all things and it is in this sense that, "the divine mind consists of the ideas of all things."12 So far there is nothing surprising or exceptional in Leibniz’s view of possibility. Leibniz continues the tradition stemming from Scotus’s logical interpretation of modal notions. However, he did not just continue this tradition – he also radicalized and systematized it. For Leibniz, the ontological background of possibilities was not only unnecessary, as it was for Scotus, it was also misleading. For Leibniz, the neo-platonic realm of Essences and intelligible Entities becomes a realm of pure logical possibilities. This subtle and seemingly innocuous change bears dramatic consequences. In fact, it signifies a crucial turn in the history of the notion of possibility. Possibilities need no longer be seen as entities subsisting in God or as some type of shadowy entities. Rather, Leibniz does not see possibilities as entities at all; he sees them as mere thoughts in God’s understanding.13 With this change, the very notion of intelligibility is transformed as well: from its platonic sense of true Being to that which is conceivable by a perfect mind – regardless of whether it exists or not.14 As we shall see, the connection between possibilities and thoughts is very interesting. Parts of this chapter and the following one are devoted to explicating and developing the way in which Leibniz conceives of this relation. Leibniz sees possibilities as pure essences that may or may not exist. However, the Leibnizian notion of essence is distinct from that of a platonic-like essence as well as from that of spatio-temporal existence. One might say that, for Leibniz, the traditional distinction between essence and existence becomes a real distinction, not just a distinction of

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reason. Simply put, possibilities do not exist; they are merely thought or conceived by God. At the same time, they serve as a precondition for worldly existence. It is remarkable that Leibniz ascribes similar conceptual status to truths, numbers and relations.15 In contrast to the Platonic interpretation, for Leibniz, truths need not be seen as entities. It suffices that they are conceived in God’s understanding. The significance of separating the realm of truth and possibility from that of reality can hardly be overstated. It produces a conceptual separation between the thinkable and the possible on the one hand, and the real, on the other. It also leads quite naturally to the distinction between two kinds of truths – truths of reason, which pertain to the realm of the thinkable, and truths of fact, which pertain to the realm of actual existence. Likewise, this distinction corresponds to a distinction Leibniz draws early on between two notions of possibility and impossibility: “one from essence, the other from existence or, positing as actual.” (A 6.3 464; SR 7). In addition, Leibniz’s logical interpretation of possibilities implies a dramatic rejection of the dominant interpretation of modal terms during the early modern era, namely, the Aristotelian temporal interpretation of modalities. In fact, the significance of Leibniz’s view of possibility can be fully grasped only in contrast to the Aristotelian view of possibility. According to the Aristotelian view, possibilities roughly correspond to potential states of existing things.16 According to this view, a state of affairs is possible if it occurs in the present, will occur in the future or has occurred in the past. If a state of affairs has not occurred, does not occur, and will not occur, then, in the Aristotelian view, it is considered impossible. If it occurs at all times, it is considered necessary. In the end, all possible states of affairs, i.e., all potentialities, are to become actual, or, in other words, every genuine potentiality will play itself out.17 Following Knuuttila, it is instructive to characterize the Aristotelian view according to the principle: "no genuine possibility can remain unrealized".18 In this view, the modal terms (i.e., possible, impossible, necessary and contingent) are defined in direct reference to time. For example, if there is a moment in time in which a statement is true, then it is possible; if a statement is false at all times, then it is impossible; if a statement is true at all times, then it is necessary; if a statement is true at some time and false at another, then it is contingent.19 Due to its essential reference to time, the Aristotelian view may be termed a temporal view of possibility. Leibniz’s denial of the temporal interpretation has an additional significant implication, viz., the denial of the principle that every possibility will be realized. For obvious reasons, the principle that any

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genuine possibility will be realized has been viewed (by Knuuttila et al) as the adequate rendering of the principle of plentitude. Leibniz’s own version of the principle of plentitude will be qualified so that only compossible individuals are seen as candidates for creation while there remain infinitely many unrealized logical possibilities. It is remarkable that, through this rejection, Leibniz disagrees with most of his contemporaries, including Hobbes, Descartes and, Spinoza. From this partial list it can be seen that, although the logical view of possibility has become evident to us today, in the early modern period, it was certainly an exception – especially among the great modern philosophers and scientists. 1.3 Possibilities as Self-Consistent Thoughts On the basis of this background, I now turn to investigating Leibniz’s other suppositions in more detail. I will begin with a familiar and seemingly innocuous supposition, namely, that possibilities correspond to selfconsistent thoughts. “Possibile est, quod non implicat contradictionem.” “Possibile est quicquid clare distincteque cogitabile est” (A 6.2 475). Possible is that which does not imply a contradiction; that which can be thought clearly and distinctly.” This is the heart of the logical interpretation of possibility. We have already noted that Leibniz understands possibilities in terms of divine thinkability and intelligibility. The supposition of self-consistency provides the crucial constraint on his notion of intelligibility. The notion of self-consistency immediately places the notion of possibility in a conceptual realm (for it presupposes consistency among terms) as opposed to the realm of real entities. A contradiction cannot arise among entities, only among terms. By analyzing the supposition of self-consistency in its Leibnizian context, we will discover some less familiar presuppositions. Note that this supposition demonstrates how the notions of thinking and possibility are intrinsically connected.20 Leibniz defines genuine thoughts in terms of possible, i.e., self-consistent, concepts and he defines possibilities in terms of the intelligible activity in the divine understanding. A clear statement of this view makes an early appearance in the Confessio philosophi of 1673, in which Leibniz writes: Now I have defined the necessary as something whose contrary cannot be conceived; therefore, the necessity and impossibility of things are to be sought in the ideas of those very things themselves, not outside those things. It is to be sought by

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examining whether they can be conceived or whether instead they imply a contradiction (A 6.3 128; Confessio 57). Leibniz defines both possibility and impossibility in terms of intelligibility: either the concepts of things can be thought, in which case they are selfconsistent, or they cannot be thought since they imply a contradiction. In the first case, they are possible; in the second case, impossible. Something is possible only in the case that its concept can be conceived, i.e., its concept is self-consistent. It will later become clear that, concerning the question of possibilia or what is possible, Leibniz presupposes the above “something” to be individuals. Leibniz goes on to define the modal notions as follows: I will designate that as necessary, the opposite of which implies a contradiction or cannot be clearly conceived... Those things are contingent that are not necessary; those are possible whose nonexistence is not necessary. Those are impossible that are not possible, or more briefly: the possible is what can be conceived, that is (in order that the word can not occur in the definition of possible), what is conceived clearly by an attentive mind; the impossible – what is not possible; (A 6.3 127; Confessio 55). 21 The subtle shift from “what can be conceived” to “what is understood by an attentive mind” is significant. It indicates an actualist strand in Leibniz’s theory of possibility. The notion of pure logical possibility is grounded in the actual thoughts of God. Since I don’t know how to rephrase Leibniz’s point more clearly, let me simply emphasize it: “the possible is what is understood clearly by an attentive mind”. Assuming, as Leibniz did, that God’s mind is perfectly attentive, the point becomes more powerful. Since Leibniz identifies the possible with what is conceived in God’s mind, he is entitled to consider the essence of a given thing as independent of its existence. As we shall see, he does this by interpreting the essence of a thing as the concept or the possibility of that thing. … if the essence of a thing can be conceived ... (e.g., a species of animal with an uneven number of feet, also a species of immortal beasts), then it must already be held to be possible, and its contrary will not be necessary, even if its existence may be contrary to the harmony of things and the existence of God, and consequently it never will actually exist.... Hence all those who

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call impossible (absolutely, i.e., per se) whatever neither was nor is nor will be are mistaken (A 6.3 128; Confessio 57).22 Leibniz alludes here to the traditional Aristotelian sense of possibility that is grounded in the past or future existence of things. By contrast, his distinction between essence and existence gives rise in effect to two distinct notions of possibility. As he writes in his Paris notes: ‘Impossible’ is a two-fold concept: that which does not have essence, and that which does not have existence, i.e., that which neither was, is, nor will be because it is incompatible with God, or with the existence or reason which brings it about that things exist rather than do not exist. One must see if it can be proved that there are essences which lack existence, so that it cannot be said that nothing can be conceived which will not exist at some time in the whole of eternity. (A 6.3 463; SR 7) His response to his own query is clear: “The origin of impossibility is twofold: one from essence, the other from existence or, positing as actual” (A 6.3 464; SR 7). In these passages we see a straightforward denial of the Aristotelian principle that every genuine possibility will be realized. There are many genuine possibilities, i.e., logically possible things, that will never come to exist, as there are many possible situations that are intelligible but never occur in our world. Many creatures and things that do not exist may be conceived. As Leibniz notes, “when we dream of palaces, we rightly deny that they exist” (A 6.3 464; SR 7). While such things do not exist, they are possible. Here is another example. It is the mark of an elegant poet that he fabricates something that is false but nevertheless possible. The Argenis of Barclay is possible i.e., is clearly and distinctly imaginable.... The Argenis would not be impossible, although she had not yet existed. Those who think otherwise necessarily destroy the difference between truth and possibility, necessity and contingency.... (A 6.3 128129; Confessio 57-59) Any non-contradictory thought is logically possible in itself but not all such possibilities are realized in the created world. Thus a distinction is drawn between truth and possibility. Consequently, there are many statements (e.g., hypothetical ones) that need not refer to existing things at all.23 One can speak of the properties of the Argenis of Barclay without being committed to the Argenis’ existence, given that she is logically

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conceivable. In other words, there is a concept of the Argenis just as there are concepts of the palaces in the Arabian Nights. Fabricated characters are not impossible – whether they exist in our world or not. If it is conceivable, one may talk about it and reason about it. Let us not lose sight of the fact that, when Leibniz ties together the notions of conceivability and possibility, such that "the possible is what can be conceived," it is primarily God's ability to conceive that he has in mind. “God is that which perceives perfectly whatever can be perceived” (A 6.3 520; SR 81). Since God is all-knowing and his mind is infinite, any conceivable thing will be conceived by him. This characterization gives an actualist touch to Leibniz’s theory of possibility since possibilities are understood in terms of God’s actual thoughts.24 As we have seen, humans are limited in their capacities to think and understand ideas. For example, it requires some intellectual work for humans to realize that "the number of all numbers" does not express a genuine notion. Leibniz believed that the methods of analysis and synthesis enable and facilitate such intellectual work for humans. God's omniscient intellect, however, is not limited in this way: God sees at once that the combination of ideas, "the ‘number’ of all ‘numbers’", implies a contradiction. Therefore it cannot be "distinctly conceived."25 Thus, there is no notion of it or its notion is impossible (see, for example, A 6.3 463; SR 7, A 6.3 520; SR 79). In other words, the above combination of terms is not a part of God’s thoughts.26 When Leibniz defines his modal notions in terms of intelligibility or conceivability, it is not human capacities that he primarily has in mind but God's.27 Thus when Leibniz says that God thinks all things or entails the ideas of all things, he means that God conceives all non-contradictory ideas or all possible notions.28 Let me summarize this point. Leibniz’s analysis of possibilities as thoughts allows for the crucial constraint of his logical interpretation, namely that of non-contradiction, so that self-consistent concepts express possibilities and inconsistent concepts point to impossibilities or impossible notions (such as the largest number, a mountain without a valley or a square circle). In fact, it seems more precise to say that impossibilities do not correspond to concepts at all or to any divine thoughts. Impossible notions correspond to a combination of terms in the mind of humans, which fail to represent concepts or ideas in God’s mind. 1.4 Consistent Thoughts, Complex Concepts and Simple Constituents Since all self-consistent concepts are the objects of God's thought and since they all form an intelligible model for creating the world, we may say

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that Leibniz explicates the traditional realm of forms, the thoughts of God, in terms of self-consistent concepts.29 However, we need to qualify this point. As it turns out, self-consistency does not apply in the limit case, that is, in the case of God’s most simple forms. Leibniz presupposes that complex concepts are composed of simple ones, which he identifies with God’s simple forms. However, owing to their simplicity, the relation of self-consistency cannot apply to simple forms. A simple constituent ‘A’ cannot be either consistent or inconsistent simply because it is not complex. Because it has no constituents, there are no relations among its constituents. This observation points to another Leibnizian presupposition. If possibility is to be ascribed to self-consistent concepts, i.e., concepts whose (simple) constituents are compatible, then it may only be ascribed to complex concepts. The compatibility relations between the terms (or constituents) can only apply to concepts composed of certain terms, such as “‘the’ ‘greatest’ ‘number’”; “‘the’ ‘most’ ‘rapid’ ‘motion’”; “‘a’ ‘winged’ ‘horse’”; and the like, but it cannot apply to absolutely simple or atomic concepts. For this reason, Leibniz’s approach to possibility presupposes compatibility (and incompatibility) relations among constituents of complex concepts (their terms in the traditional jargon), as well as their coconsideration in God’s mind. As it turns out, Leibniz also presupposes simple elements as the basis of all compositions. The simplest concepts, though, cannot be seen as possible in the same sense as the complex since they do not satisfy a necessary condition for logical possibility, that is, self-consistency. Instead, God’s simple forms may be seen, in accordance with Leibniz’s theological commitments, as actual. The presupposition of God’s mind and its simple forms are part of the actualist basis for Leibniz’s theory of possibility. Leibniz’s criterion of self-consistency also presupposes a mental notion of co-consideration or composition in God’s understanding. 30 As selfconsistent concepts, possibilities are produced by the mental composition of simple conceptual constituents into complex ones. In other words, Leibniz’s notion of possibility presupposes simple terms and their mental combination in various ways. While the consistent results of these mental compositions are seen as possibilities, inconsistent ones are seen as impossibilities. Note that the notion of combination plays an essential role in the production of possibilities. As we have seen, possibilities must be composed according to Leibniz. This, in turn, seems to imply that they must be composed of simpler terms or constituents. Hence, for Leibniz, complex concepts presuppose simple concepts as their constituents. As we shall see, this is consistent with Leibniz’s notion of natural order, going from the simple to the more complex.

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The following passage from the Combinatorial Art reveals some of Leibniz’s early presuppositions regarding the compositional nature of concepts: Since all things which exist, or which can be thought of are in the main composed of parts, either real or at any rate conceptual, it is necessary that those things which differ in species differ either in that they have different parts – and here is the use of complexions – or in that they have a different situation – and here is the use of dispositions. The former are judged by the diversity of matter; the latter, by the diversity of form. With the aid of complexions, indeed, we may discover not only the species of things but also their attributes. Thus almost the whole of the inventive part of logic is grounded in complexions – both that which concerns simple terms and that which concerns complex ones (L 130; CCL 228). Leibniz’s supposition concerning the compositional structure of concepts motivates and informs his enterprise to discover and analyze all complex concepts. In turn, the discovery of all possibilities and impossibilities motivates the analysis of concepts as well as the discovery of new concepts. There is nothing exceptional or extraordinary about Leibniz’s supposition that the structure of concepts is compositional. On the contrary, this was the dominant view at the time. However, the conjunction of this supposition with a logical notion of possibility, according to which possibilities are seen as self-consistent concepts (thoughts in God’s mind), provides the foundation for an original philosophical system. Rutherford nicely brings out Leibniz’s supposition of the combinatorial nature of concepts in the Combinatorial Art: In [the Combinatorial Art] we meet full-blown the theory of the combinatorial nature of concepts – the doctrine that all complex concepts are composed from, and analyzable into, simpler concepts – a constant feature of all of Leibniz's later writings. It is evident that he regards this theory as following from more general metaphysical principles. In his view, all things and thus all concepts, are defined in terms of the parts they contain (their "matter") and the specific arrangements of these parts (their "form"). Differences of parts ... are differences of "complexion";

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differences in the arrangement of parts are differences of "situation" or "disposition" (CCL 227-8). Leibniz's notion of "matter" refers to the elements that constitute a complex concept while his notion of "form" refers to the various ways in which the elements (i.e., matter) may be arranged or ordered. What Leibniz calls difference of “disposition” is roughly what we would now call a difference of permutation or configuration of a given number of elements (i.e., the matter). For example, there may be different spatial arrangements of the same elements since different orders of the same elements give rise to different sequences.31 Roughly speaking, in a written language, the letters – that is, the alphabet – may be seen as the basic elements while the words may be seen as various configurations of letters and sentences as configurations of words. Leibniz’s master insight about the notion of possibility, however naïve, can already be stated in these terms: Given a number of simple concepts, call them ‘matter’, possibilities may be accounted for by virtue of variations in form. As I will argue in the next chapter, the central role of Leibniz’s notion of form, the order and arrangement of the elements, in his notion of possible individuals has been largely underestimated by Leibniz commentators. Leibniz’s presupposition regarding the complex structure of concepts and possibilities and his distinction between complex and simple terms above points to another presupposition: If Leibniz supposes that complex concepts are composed of simple ones, does this not also commit him to presupposing that there are conceptually simple elements at the basis of composition – elements that are not themselves composed? Though this assumption is not logically entailed in the suppositions we noted above (for it may be argued that the conceptual elements are analyzable to infinity and that simplicity would admit degrees) 32, there is strong textual evidence showing that Leibniz in fact presupposes it.33 Leibniz often remarks in his Paris notes that the simple elements are unanalyzable and indefinable (A 6.3 572); that “there necessarily exist simple forms” (A 6.3 514); and that “nothing can be said about forms on account of their simplicity” (A 6.3 514; SR 69). 1.5 The Simple Forms are the Attributes of God It is interesting to observe that this presupposition relates to another: Leibniz identifies the simple conceptual elements, which he calls simple forms or perfections (A 6.3 575, 578), with the simple attributes of God. He writes that, “God is the subject of all absolute simple forms” (A 6.3

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519; SR 79) and adds that, “[a]n attribute of God is any simple form” (A 6.3 514; SR 69). This supposition provides the basic assumption for his proofs that a most perfect being is possible and consequently that a most perfect being exists (A 6.3 572-579). 34 As we shall see later in more detail, Leibniz’s proof that all positive perfections that belong to the concept of God are compatible (inter se) is grounded in the supposition that these perfections are simple (and positive).35 While this identification may seem surprising, it is consistent with Leibniz’s approach to possibility that I sketched above. The divine simple forms may be seen as the material or the actual basis out of which possibilities arise in his mind by virtue of God’s mental combinations and reflections. Leibniz’s supposition of simple forms as the “elements of thinking” suggests that his combinatorial approach to the construction of concepts and possibilities has an ultimate starting point. As we shall see later, this supposition of ‘logical atomism’ (if I may use the term) plays a substantial role in Leibniz’s approach to possibility. While its full significance will only become apparent later, let me make some observations at point: (1) The presupposition of absolute simple forms accords with Leibniz’s notion of a natural order, that is, proceeding from the simple to the complex in the construction of possibilities; (2) The postulation of different simple forms might help Leibniz to account for negations and the incompatibility relations among predicates of complex concepts. 36 As Fichant argued convincingly in “L’origine de la négation”, it would be impossible to account for exclusion relations among complex concepts unless a variety of simple forms is supposed. For this reason, it is also the ultimate source of incompossibility relations among possible individuals. Without such a supposition, it would hardly seem possible to account for the variety of possible individuals and the compossibility relations between them, which are necessary for the formation of possible worlds. All this will be spelled out later in much greater detail. (3) As we shall see in the next chapter, Leibniz has strong arguments for assuming such simples as the prima possibilia, which he identifies with the absolute forms or perfections of God. Leibniz’s identification of simple forms with the perfections or the simple attributes of God, which he defines as “the subject of all absolute and positive perfections” (A 6.3 577; SR 101), is intrinsically related to the metaphysical and theological contexts of Leibniz’s approach to possibility. Leibniz sees possibilities as self-consistent thoughts in God’s omniscient mind. On the basis of Leibniz’s presuppositions presented above, we may interpret this point as follows: Seen as the “subject of all perfections” and as an active (thinking) agent,37 God thinks the various combinations

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among his simple forms so that complex concepts or possibilities arise in his mind (see A 6.3 514; SR 71). 1.6 Divine Thinking Implies Reiterative Reflection Let me now develop this point by examining God’s thinking. I will suggest that God’s thinking is inherently reflective. Though somewhat speculative, my explication of the production of possibilities in terms of God’s reflective activity is supported by numerous remarks in the Paris notes and elsewhere about the significance (as well as the beauty) of reflection in general, and of God’s reflection, in particular. For example, Leibniz writes: “A necessary being acts on itself, or, it thinks. For to think is nothing other than to sense oneself” (A 6.3 587; SR 113). 38 At least since 1671, Leibniz viewed thinking and reflection as intrinsically connected. For example, he defines thinking as “action on oneself” and adds that, “Thinking is internal action on itself, perception with reflection” (A 6.2 493).39 In his notes from Paris Leibniz again identifies reflection as action on oneself (A 6.3 480; SR 37). As we have already noted, according to Leibniz, God acts primarily by thinking. As we can now see, to think, according to Leibniz, is to act on oneself or to reflect. As we shall see in a moment, these are consequential definitions. While it is well known that self-reflection is the defining feature of rational beings, it is not well understood that divine reflection plays a crucial role in Leibniz’s view of possibility and intelligibility. As noted, Leibniz explicates possibilities as that which is understood in God’s mind. But he also writes that, “God understands because he acts on himself” (A 6.3 465; SR 11). In other words, God, who is a thinking being, a mind, primarily thinks on himself or reflects. Leibniz curiously remarks that, “If some mind thinks nothing in particular, but thinks nevertheless, it would be God, or, it would think all things” (A 6.3 512; SR 65).40 He also notes that, “[e]verything that thinks, (cogitans) thinks something. The most simple thing is that that which thinks that it think itself; and thinking is absolute when that which thinks itself is all things” (my italics) (A 6.3 518; SR 75).41 The relation between the divine mind who thinks all things and his reflection upon himself is evident. Leibniz writes: “It must be shown that God is a person, i.e., an intelligent substance. It must be demonstrated rigorously that he senses his own action on himself, for nothing is more admirable than for the same being to sense and to be affected by itself” (A 6.3 475; SR 27). We might ask why is this reflective property so admirable

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in Leibniz’s eyes. The answer, I propose, is this: In attributing reflective thinking to God, Leibniz connects the traditional view that God thinks all intelligible things with his own interpretation of the intelligible objects of God’s thought as logical possibilities. God’s reflections may be seen as mental operations on his simple forms or attributes, so that he is thinking or conceiving all the permutations and combinations among them. In this way, God’s thinking on himself constitutes the realm of all logical possibilities. Given this notion of divine reflection, let us reformulate our previous point as follows: by reflecting upon his simple forms or attributes, God thinks their various relations and combinations. Being an infinite and logically omniscient mind, God perceives all the combinations and the conceptual relations among his forms. However, this is not all that Leibniz ascribes to divine reflection. As we shall now see, the claim that God thinking is reflective implies that, in effect, God thinks infinitely many consequences stemming from these conceptual relations as well. From the very notion of reflection, that is, the notion that a mind thinks about itself, it seems to follow that reflection has an iterative structure, i.e., that God also reflects upon his reflections. It turns out that this feature of iterative reflection plays a crucial role in the production of possibilities in God’s mind. Let me first present some evidence (mainly passages in the Paris notes and in the Confessio) indicating that, for Leibniz, reflection is iterative. We have already observed that, for Leibniz, a rational mind reflects, i.e., thinks on itself. However, Leibniz also holds that such a mind reflects on its own thoughts, and then reflects on those reflections, and so on. For example, in a note on Reminiscence and on the Mind’s Selfreflections (A 6.3 515-18), Leibniz writes: The following operation of the mind seems to me to be most wonderful: namely, when I think that I am thinking, and in the middle of my thinking I note that I am thinking about my thinking, and a little later wonder at this tripling of reflection. Next I also notice that I am wondering and in some way I wonder at this wonder … (A 6.3 516; SR 73). This remarkable passage testifies to Leibniz’s iterative view of reflection. Leibniz continues with the following example: When it happens that he cannot sleep, let him begin to think of himself and of his thinking and of the perception of perceptions… and so the perception of a perception to infinity is

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perpetually in the mind, and in that there consists its existence per se, and the necessity of the continuation (A 6.3 517; SR 7375). Although the mind discussed in these passages is a human mind, the feature of reflexive perception clearly applies to the most perfect mind as well. Note that the very existence (per se) of the mind lies in the perpetual perception of perception to infinity, which is necessarily continued. The analogy between the human mind and God’s mind (in this very respect) as well as the iterative character of self-reflection and its metaphysical significance are nicely presented in the following passage: The harmony of things requires that there should be in bodies beings which act on themselves [i.e., minds]. On the nature of a being that acts on itself: it acts by the simplest means, for in that there is harmony. Once it has begun, it is eternal. There are ideas in it of those things it has sensed and done, as there are in God; the difference is that in God the ideas are of all things and are simultaneous. The mind never forgets anything, since the ideas in the mind are indestructible. Motion, once given, is necessarily continued. Thought, or the sensation of oneself, or action on oneself, is necessarily continued (A 6.3 588; SR 113).42 Several points in this passage are remarkable: (a) The mind is characterized as a being that acts on itself; (b) The mind’s activity on itself is eternal and necessarily continued; (c) This activity is analogous to God’s activity though it is limited and not simultaneous. The most significant point for my purposes here is that thought as reflection is necessarily continued. It may be argued that the continuation Leibniz has in mind here is a continuation in time rather than the continuation of reflection on previous reflections. However, it seems that the very nature of reflection is such that, if it continues, it would include reflection on previous reflections. If the mind acts on itself and, if it never forgets anything and there is within it ideas of the things it has perceived and done, then it would reflect upon them, and, in turn, upon those reflections, and so on. Thus, if I am thinking about my thinking, “the perception of perception is infinitely and perpetually in the mind”. With the supposition of the iterative character of God’s reflections we can now amend the picture of the production of possibilities. God reflects on his simple forms, then reflects on his reflections, and then further on these resulting reflections, and so on to infinity. When we add this feature of divine thinking to Leibniz’s view that God thinks all possibilities as

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complex, self-consistent thoughts, we get the following picture: God’s reflections on his simple forms and his iterative reflections on the results of his previous reflections may be seen as compositional in a mental sense. That is, God‘s reflections may be seen as his thinking all the combinations among his simple forms and as perceiving the relations among them. The iterative form of reflections may be seen as a progressive construction of more and more complex thoughts or concepts in God’s mind. 1.7 Reflection Proceeds in a Natural Order Let us now observe that, as part of this picture of the production of possibilities, Leibniz presupposes a well-defined notion of order, starting from the simplest forms and proceeding to more and more complex structures of them. This corresponds to what Leibniz calls natural order. As he writes: “natura prius est involutum simplicius” (A 6.4 180-81). This point comes up explicitly in his brief note Quid sit natura prius? — what is prior by nature? (A 6.4 180-81). I would like to suggest that the natural priority Leibniz presupposes is due to his supposition of the priority of the simples in the formation of concepts in God’s mind. As Rauzy remarks, natural order constitutes a general matrix to which one can refer in considering the order of things rather than the order of human discoveries (Rauzy, 1995 40). The various senses of order and various modes of priority and posteriority can be explicated by the notion of natural order (A 6.4 180-81; Rauzy, 1995 40 n. 26). By ‘natural priority’ Leibniz means a priority of the simple over the complex in the context of composition.43 That Leibniz interprets the notion of simplicity in the context of composition is clear in the following passage: Prior by nature is a term which consists of terms less derived. A term less derived is equivalent to one [which includes] a smallest number of primitive simple terms (A 6.4 180-81).44 The tight connection between the simplicity of terms and the order of composition comes up in another passage: “A term which is anterior by nature is one which is obtained by substituting the simples for the composed. Or what is the same: naturally prior is produced by analysis; naturally posterior by synthesis” (C 241; Rauzy 1995, 34).45 In fact, the supposition of natural order is strongly suggested by the presuppositions noted above. If Leibniz presupposes simple conceptual elements, and if he supposes God’s reflexive thinking on these elements and if, in addition, he supposes iterative reflections on reflections, then it

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seems to follow that God’s thinking, as described above, proceeds in order from the simple to the more complex, which is precisely what he calls natural order. While most Leibniz scholars have ignored his notion of order, assuming that it has no significant role in his logic, I will try to show that it plays an important role. Though its full significance will only become apparent later, let me anticipate several points: (1) As I shall argue in the next chapter, the order of forms within a complex structure plays an essential role in the individuation of complex concepts. Similarly, the very complexity of a given structure also plays a role in its individuation. (2) The direction of construction, from the simple to the complex, also indicates what Leibniz says explicitly in the Meditation on the Principle of the Individual (1676) and elsewhere, namely, that the method of production plays a constitutive role in individuation. This will allow Leibniz to provide a generative (or causal definition of the concept of an individual i.e., a definition of the rule generating a unique concept in God’s understanding. (3) The order of production from the simple to the complex also indicates an increase in the degree of perfection (which is interestingly related to the degree of individuality and of being). (4) Leibniz associates such an increase in perfection with the end or telos built into the concept of an individual. I will develop points 1 and 2 in the next chapter and points 3 and 4 in chapter 9. In the next chapter I will argue that Leibniz’s presupposition of the natural order from the simple to the complex – and of order in general – plays an essential role in the composition and individuation of complex concepts. The question of priority of the simple over the complex or vice versa will continue to occupy us in other contexts as well, such as the relation between individuals and worlds, which I will discuss in chapters 3 and 4. At this point, one might object that the notion of natural order does not make much sense in the context of God’s intelligible activity. Since we are considering an a-temporal, logical context of activity, what sense can be made of order in this context? 46 Let me make this point in another way. We have seen that Leibniz presupposed a compositional structure of concepts. This is consistent with Leibniz’s view of synthesis and analysis as two inverse methods. One can construct concepts by composing elements into more complex concepts (e.g. ‘rational’ and ‘animal’ into ‘human’) or by analyzing complex concepts into their simpler constituents (e.g. ‘human’ into ‘rational’ and ‘animal’). These two methods seem symmetrical and, from a formal point of view, it seems to make little difference whether one produces complex notions from simple ones or whether one starts from complex notions and breaks them down into their constituents. But Since Leibniz presupposes that there are simple elements

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of thinking, there does seem to be an asymmetry between going from the simple to the complex and going from the complex to the simple. The simple provides a natural starting point for the construction of concepts. Given the historical context, there is nothing peculiar about assuming a natural order from the simple to the complex; on the contrary, as the works of philosophers such as Descartes and Locke clearly testify, this was a common view. 1.8 An Illustration Leibniz, like many other thinkers in the 17th century, presupposed that complex ideas or concepts are composed of simpler ones. Many texts since “The Art of Combination” testify to his current use of this supposition. For example, as Couturat already noted: The combinatorial structure of concepts and the method for investigating them is illustrated and exemplified by the decomposition of complex numbers into their primary factors. The number 210 can be represented as a product of the following couples: 42 x 5; 35 x 6; 14 x 15; etc., but these may be further divided until the number 210 is represented as a product of its primary factors, namely, 2 x 3 x 5 x 7 = 210 (GP IV, 65; Couturat, 1961 41 n. 1). As Couturat notes, the first step in applying Leibniz’s combinatorial method is to reduce all complex concepts to their simplest constituents. In this way, a certain number of simple concepts which are irreducible and indefinable is obtained. These simple elements are considered to be the terms of the first level. The combinations of pairs of simples yields those of the second level; the combinations of three simples yields those of the third level; the combinations of four simples yields the terms of the fourth level, as follows: First level:

2, 3, 5, 7.

Second level:

2 x 3 = 6, 2 x 5 =10, 2 x 7 =14, 3 x 5 =15, 3 x 7 =21, 5 x 7 =35.

Third level:

2 x 3 x 5 =30, 2 x 3 x 7 = 42, 2 x 5 x 7 =70, 3 x 5 x 7 =105.

Fourth level:

2 x 3 x 5 x 7 = 210.

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In this example, all the factors of 210, both complex and simple, are considered to be the logical predicates of 210. For example, 2 x 3 = 6, being a factor of 210, is considered to be a predicate of 210. Assuming that all complex concepts have such a compositional structure, and that each constituent is considered to be a logical predicate of the whole, one can find all the predicates of a given subject by analyzing a complex concept or its definition. Since Leibniz supposed that all concepts have simple compositional structure, he also supposed that any concept (at least in principle) can be analyzed into its simple constituents, and that by composing all simple concepts in all consistent ways, all concepts may be obtained. As already noted, the construction of all consistent concepts explicates the production of all possibilities or all intelligible notions according to Leibniz. Another example of the application of this general scheme is Leibniz’s attempt to compare simple concepts to primary numbers, so that the result of their multiplication yields a complex concept consisting of simple concepts. One of Leibniz’s famous examples is as follows: combining ‘rational’ and ‘animal’ yields ‘rational animal’, which he takes as analogous to: 3 x 2 = 6. This implies that the proposition ‘a human is a rational animal’ is represented by the mathematical proposition 6 = 3 x 2. This indicates that Leibniz takes the copula in a proposition to be analogous to numerical equivalence. Drawing on these examples, Couturat aptly summarized Leibniz's combinatorial method as follows: First, all complex concepts have to be resolved into simple concepts by analysis analogous to the analysis of numbers to their prime factors; and they (the complex concepts) can be inversely obtained by a progressive combination of the simple concepts. Next, the simple concepts or categories, which are the constitutive elements of all others, are of small enough number to engender the innumerable multitude of complex concepts, thanks to the marvelous fecundity of the combinatorial art (Couturat 49). Thanks to Couturat’s pioneering presentation (however one-sided) in La Logique de Leibniz, we possess a clear and comprehensive exposition of Leibniz’s unique use of his combinatorial method and its relation to logic. Couturat demonstrated the extreme generality of Leibniz’s combinatorial art and especially its inclusion of mathematics and logic. Yet Couturat’s exposition misses a crucial aspect of Leibniz’s combinatorial method,

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namely, that it explicates the notion of possibility as the underlying structure of thought in general – both human and divine. In other words, Couturat places Leibniz’s combinatorial art entirely in the context of the human sciences. By contrast, I am convinced that the extreme generality of Leibniz’s combinatorial method derives from his supposition that it aims to capture the notion of the intelligible – that which can be thought. As we have seen, the notions of thought and possibility are intrinsically related in Leibniz. In the broader context of Leibniz’s metaphysics, this implies that the combinatorial presuppositions I have described above regarding the nature and formation of concepts pertain not only to human thought but also to God’s. Once placed in the context of divine thought, Leibniz’s combinatorial presuppositions can be seen as explicating his logical approach to possibility and as constituting a theory about the nature and formation of concepts. This is not only consistent with Couturat’s point that the combinotoire underlies Leibniz’s logic; in a sense it explains it. The generality of logic and the combinatorial art derives from their object, namely, the nature and formation of concepts in God’s mind.47 The principle of contradiction and the related notion of compositional structure of concepts is what Leibniz supposes to be the common ground between the realm of divine thought (i.e., the realm of pure concepts) and the human representation of it. As we shall see in the next section, this supposition motivates Leibniz to develop a universal and philosophical language. To sum up this point, whereas, for Couturat, Leibniz’s logic is primarily a human affair, I think that it also applies to thought in its most general form, i.e., whatever can be thought or conceived. As we have seen, Leibniz identifies the thinkable with the intelligible and the possible. Leibniz’s Approach to Possibility – A Summary Let me summarize Leibniz’s presuppositions presented above. First I noted that possibilities are situated in a conceptual realm and are seen as thoughts in God’s mind. More precisely, possibilities are seen as consistent thoughts in God’s mind. Consistent thoughts are explicated in terms of complex thoughts or complex concepts, whereas complex concepts presuppose simple elements so that consistency relations hold between the terms of complex concepts. We have seen that Leibniz presupposes logically simple elements that are indefinable and unanalyzable. Interestingly, Leibniz identifies these logically simple elements with God’s attributes or God’s simple forms. At

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the same time, God is seen not merely as “the subject of all simple forms” but also as an active, thinking mind. More precisely, God is seen as the most perfect mind whose primary activity is thinking and self-reflection. In addition, Leibniz sees God as reflecting on his simple attributes or forms. God’s reflections on his simple forms may be seen as mental combinations of his simple forms that produce complex forms. Likewise, God’s reflective operations are iterative, implying that he reflects upon his reflections. In this way God thinks the combinations among his simple forms, so that more and more complex concepts arise in his mind. This implies that God combines the simple forms in a natural order – from the simple to the complex – and, in this sense, Leibniz’s system of possibility is recursive. These suppositions agree with Leibniz’s (and his generation’s) assumption that any complex concept is composed of simple ones and can, at least in principle, be analyzed into its constituents. The very simple constituents, though, cannot be analyzed and constitute the basic elements, which are at the foundation of Leibniz’s combinatorial approach to possibility. Since the basic elements are seen as the attributes of God, both God’s simple attributes and his mental operations constitute the actualist aspect of Leibniz’s approach to possibility. As we shall see in the next chapter, the results of God’s reflections on his forms are infinitely many concepts and each one of them may also be seen as an infinite structure. On the basis of these presuppositions, we may ascribe to Leibniz a combinatorial approach to possibility which explicates the very notion of possibility through different and consistent combinations of unique elements. Leibniz’s approach to possibility is conceptualist in the sense that he sees possibilities as the thoughts of God’s intellect, not as entities and not as potential states of existing things.48 It is a logical approach to possibility in the sense that it is divorced from the temporal notion of potentiality and inherent capacities of existing things, so central to the Aristotelian notion of possibility. Leibniz’s approach is also actualist (in Adams’, 1979, sense), to the extent that it presupposes an actual basis, viz., God’s mind and his simple attributes. 1.9 Truth, Predication, and Symbolic Representation In some of his optimistic moments, Leibniz seems to have believed that, through the complementary methods of analysis and synthesis, it would be possible to construct all possible concepts as well as to discover all truths. 49 On what basis did Leibniz believe that it would be possible to assess the truth or falsity of all propositions? I would like to point out that,

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given the presuppositions presented above, Leibniz’s optimism, even if somewhat overstated, is understandable. The crucial point in this respect is to see how the notion of possibility is related to that of truth. As I already noted, Leibniz clearly saw and emphasized the distinction between truth and possibility (which cannot be said of some of his commentators, e.g., Couturat 1961, 196). For Leibniz, possibility or intelligibility is a precondition for truth. As a precondition for assessing the truth of propositions, Leibniz sought real definitions of concepts, i.e., demonstrations that these concepts are possible or self-consistent. The paradigmatic example of Leibniz’s practice is his attempt to prove the possibility of the notion of Ens Perfectissimum as a precondition for asserting its existence.50 For Leibniz, the question of reasoning about certain notions or using these notions for making assertions such as ‘God exists’ presupposes the possibility or the self-consistency of these notions. He held that, given the real definitions of all concepts, one could go on to discover all truths. In other words, his view of truth presupposes his view of possibility. His view can be justified along the following line: Anything that can be said – either truly or falsely – presupposes a proposition. A proposition presupposes predication, that is, an ascription of a predicate-term to a subject-term. As we have seen, Leibniz presupposes that all complex concepts have logical predicates. More precisely, the logical predicates of a complex concept are its logical constituents or the various conceptual elements that make it up. In the example given above, each one of the factors of the number 210 may be seen as one of its predicates. In this intuitive sense, a predicate (of a true proposition) is seen as included in its subject. Obviously, a constituent is included in that which it serves to constitute. This is partly analogous to the way a part is included in the whole of which it is a part. Hence, in order to find out whether a proposition (understood as an ascription of a predicate term to a subject term in the canonic form of an affirmative proposition) is true, one has to analyze the concept of the subject into its constituents and see whether the predicate is included therein or not. In case the predicate is included in the concept of the subject, the proposition is true; in case that it is not, the proposition is false.51 In the latter case, the proposition ascribes to the subject a predicate that it does not include. For example, in order to examine the proposition ‘a human is an animal’ one has to analyze the concept ‘human’ into its constituents and see whether it includes the concept of animality or not.52 From our current perspective, this view seems somewhat naïve, not to say simple-minded, but there is little doubt that Leibniz presupposed such

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a view of the relations between possibility, truth, and predication. Furthermore, there is little doubt that this picture constitutes an essential part of the background for the theory of truth he explicitly develops in 1679, as well as for his well-known doctrine, according to which each individual is defined through its complete concept, presented in his Discours de Métaphysique in 1686. In fact, given Leibniz‘s commitment to the existence of individuals, not much is missing to develop this doctrine. If God conceives all possible things in his mind, and if these things are seen as individual things, then it would seem to follow that God must have a conception of every possible individual – whether it is to be realized or not. In this way, we can see how Leibniz’s curious idea of concepts of individuals, each of which is composed of its logical predicates, would naturally emerge from his suppositions about possibility. In light of the above presuppositions regarding the notion of possibility, the emergence of the complete concept doctrine in the years before the Discours seems to be a natural development. I will leave this interesting topic for a more detailed discussion in the next chapter. At this point, I would like to turn to the interesting connection between Leibniz’s approach to possibility and his attempts to develop a universal language and a real characteristics. 1.10 Combinatorial Possibility, Universal Language and Real Characteristics Since most Leibniz scholars have not paid sufficient attention to the connection between Leibniz’s use of combinatorial methods and his view of possibility, they have not seen the intrinsic (if subtle) connection between his view of possibility and his attempts at constructing a universal language and a real characteristic. As we have seen, Leibniz’s presuppositions add up to a fairly crystallized view of possibility. The combinatorial suppositions, seen in the context of divine thoughts, give both an explication of the notion of possibility and an account of its ontological status. In addition, these presuppositions position Leibniz’s view of modalities within the tradition and point to his break from it. The consequences of Leibniz’s presuppositions and the influence they exerted on his later projects – especially the universal language – are too important to ignore. In his groundbreaking work, Couturat did not fail to see that Leibniz’s project of an alphabet of human thought is based on the supposition of the compositional structure of concepts and the subordination of logic to the combinatorial method. However, Couturat did fail to see that the compositional structure of concepts and the combinatorial method of analyzing concepts arise in the context of a general theory of intelligibility.

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Although Couturat’s elegant presentation of Leibniz’s Combinatoire stresses its relation to his logic, he overlooks the relation between Leibniz’s logic and his view of possibility. 53 For this reason, he also fails to see that Leibniz’s theory of possibility provides the basis and part of the impetus for developing a universal language as well as a theory of symbolical representation. Briefly put, I suggest that Leibniz saw the universal language as a necessary instrument for humans to represent the purely intelligible realm of possibilities in God’s understanding. The objective of this project is to provide humans with a research tool that enables them to approach and model the true nature of concepts. In other words, the alphabet of human thought is intended to help us gain insight (to the extent that this is possible) into the divine combinatorial activity that produces all intelligible concepts. Leibniz’s supposes that the realm of God’s thought or the realm of all intelligible concepts constitutes an a priori and universal basis for the construction of any language whatever. This supposition underlies the project of a universal language. This supposition also explains Leibniz’s optimistic belief that such a task is possible. Indeed, it is precisely in this respect that Leibniz’s project radically differs from those of his predecessors (especially Wilkins and Dalgarano).54 Leibniz’s project is not based on existing languages but rather on the supposition of an ideal realm of pure and universal concepts common to all possible languages (that is, to anything that could be thought and represented). Both Leibniz’s motivation and his unrestrained optimism for this project are better understood in light of his presupposition of a universal conceptual realm of all intelligible concepts. In this sense, the project for designing a universal language derives its inspiration and raison d’être from his view of possibility. In addition, Leibniz’s universal language is complementing his view of possibility by devising the means for representing concepts and possibilities to humans. Without means of representation, the investigation of concepts, as well as of truths, would be totally unfeasible for humans. As Leibniz writes: When the table of categories of our art of complication has been formed, something greater will emerge. For let the first terms of the combinations of which all others consist be designated by signs; these signs will be a kind of alphabet... If these are correctly and ingeniously established, this universal writing will be easy as it is common ... and, at the same time, all knowledge will be obtained (A 6.1 202; PLP 11).

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To form the alphabet of human thoughts, one needs to assign to each of the simple concepts a simple sign.55 The method of composing a complex symbol out of its simple constituents (the simple signs) is meant to reflect the order and method of composition in the complex concept being symbolized. If the similarity of structure between a symbol and its concept is not preserved, symbolical representation would not be possible. As Couturat pointed out, in order to form the alphabet of human thoughts we need to assign a simple sign to each simple concept and, by combining the signs in the same manner as the corresponding concepts, all others notions could be expressed. Thus, logic or, more precisely, the art of invention, entirely depends on the combinatorial method, which enables us to find all the possible combinations (or their signs) and to determine their exclusion and inclusion relations, that is to say, to discover all the truths pertaining to a certain concept. This gives rise to the idea of a universal characteristic, that is, an algebraic logic that would replace all concepts by combinations of signs (Couturat 1961, 49-50). This is the basis for Leibniz’s view of symbolic representation (also clearly expressed in his Quid sit idea, 1677). A language is an adequate means of representing ideas and concepts because a language, like concepts, has a compositional structure. It is worth stressing that the role of the alphabet of human thinking is to represent the ideas in God’s mind (i.e., all intelligible ideas) in a way accessible to humans, viz., through sensible symbols or characters. Thus, we clearly see that, for Leibniz, the development of a symbolic system presupposes the compositional structure of concepts. Yet the connection between Leibniz’s view of possibility and his various projects for symbolic representation is not just a logical one but a functional one as well. For it is only by means of symbols that humans can represent and investigate ideas and concepts. The intrinsic connection between Leibniz’s approach to possibility and his project to develop a universal language has several interesting implications. In his La Sémiologie de Leibniz (chapter VII) and in his article “Signs and Thought in Leibniz’s Paris Notes” (Dascal, 1987, 47-61), Dascal raises the following interesting question: [A]re signs mere instruments, mere psychotechnical devices which increase the efficacy of our reasoning or else are they its constitutive elements, inseparable of reasoning itself, which would then be nothing but a process of a manipulation of signs? (Dascal, 1987, 48).

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Dascal points out that there is evidence in Leibniz’s writings from the Paris period that he held both positions and that he “oscillated” between them. He has argued that Leibniz’s approach to the role of signs and his view of the relations between symbols and thought is ambiguous. Given the theory of possibility presented above and the supposition that concepts are conceived in God’s mind, we are in a position to account for the source of this systematic ambiguity. This ambiguity derives, at least in part, from the distinction between divine and human thinking. Continuing with Dascal, let us examine the example of (the concept of) a circle. He writes: Leibniz asserts categorically that we cannot have the idea of a circle. We can have images of the circle, the definition of a circle, the ideas of each one of the properties that each circle must have. But since we cannot conceive all of them simultaneously, we do not have the idea of a circle. Only God can have the ideas of complex things, since he is able to think of everything simultaneously. We are condemned, in view of our finitude, to know the essence of a circle – and other composed things – only partwise. But how can we be sure of the possibility of such an idea, i.e., of the compatibility of the ingredients present in it, if the very condition of possibility of a complex idea is the joint simultaneous conceivability of all its components? The answer is: by means of characters and sensible things.56 … the appeal to characters becomes necessary because the ‘ideas’, this supreme object of knowledge, are defined in such a way as to render them practically beyond our reach (Dascal, 1987, 51). Dascal points both to the necessity for humans to use characters as well as to the limitations imposed by their use. When we recall that the eternal ideas and truths and all complex concepts are primarily thought by God in a domain of pure possibilities, the reasons for their inaccessibility to humans become clear. Only an infinite mind, perfect and all knowing, can perceive all concepts directly without the mediation of symbols or characters. There are two specific reasons why humans cannot come to fully know the ideas in God’s mind and therefore must use symbols as mediators. First, as noted above (and, as I will argue at length in the next chapter), the simple elements are unknowable to humans. Second, as Dascal pointed out, infinitely complex concepts are also unknowable to humans. Given these two factors, the inaccessibility of the realm of pure concepts to

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humans is clear enough. The need for symbols and characters as a means of human representation is clear as well. In the context of God’s thoughts, however, symbols are not necessary. In fact, they are redundant. God intuits directly all the relations and combinations among his forms without any need for representation. Humans are limited in their ability to comprehend the infinitely small as well as the infinitely complex. The second limitation derives from the finitude of our mind, which is unable to comprehend the infinitely complex. In this context, the indispensability of using symbols is evident. The difficulty of knowing the simple ideas also reveals the need for symbolic representation. Since we cannot perceive the true simple elements directly, we have to assign simple symbols or characters to stand for them. Like the letters of the alphabet or the natural numbers, such simples constitute the basis of any representational system. On the one hand, as human beings with limited cognitive capacities who operate in time, we cannot directly perceive ideas. On the other hand, Leibniz is very keen to show that we are not doomed to a state of complete ignorance, let alone desperation. Even if humans cannot directly perceive ideas, either on account of their complexity or on account of their simplicity, they can, nevertheless, represent them by means of symbols, and, thus, to some extent, perceive them. Humans must use symbols to substitute for both fundamentally simple concepts and for infinitely complex ones. Since any meaningful and representable concept is complex, symbols play a constitutive role in the context of human thinking,. Humans have no way to conceive of ideas other than through the mediation of symbolic systems of language. As it turns out, the combinatorial structure of concepts, described in the first part of this chapter, shows why the ideas of intelligible things (which are either simple or very complex) must remain inaccessible to the human mind. But this very structure also reveals something about the extent to which, and the way in which, ideas and concepts may become accessible to the human mind. While Leibniz supposes that, in God’s mind, the formation or production of concepts is immediate, intuitive and atemporal, the human mind can only partially represent ideas in a temporal and pictorial manner by using symbols. This very constraint on human thinking, viz., the constitutive role of symbols and systems of symbolization (notations and language) suggests that neither can we gain access to the primary elements in God’s mind.57 As Dascal notes, we also cannot have direct access to complex ideas on account of their infinite richness and complexity. However, the relation between the finite human mind and God’s infinite mind does not in any way imply helplessness or ignorance on our part. Rather, the recognition of

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this gap sets the stage for investigating and representing the ideas in God’s mind. Consequently, an essential part of the project is to construct adequate notation systems. This can partly be achieved by substituting the variables in the general combinatorial scheme with elements and operations in specific domains, such as mathematics, music, chemistry, etc. Such notational systems constitute a necessary instrument of investigation as well as a model for preserving knowledge and facilitating reasoning in specific domains. The language of mathematics remains the best example of such a system in that we use the mathematical symbols to expand our knowledge of mathematical concepts. This is why Leibniz sees the human project of constructing notations as an integral part of the investigation of pure concepts and possibilities. In this way, the project (or rather the family of projects) of the universal language is conceptually related to Leibniz’s combinatorial approach to possibility. While Leibniz’s universal language is based on the a priori and universal notion of the divine conception of possibilities and logic, it is also conceptually related to its application in particular domains of human knowledge. In fact, it is only in applying the general scheme to specific domains that the project takes on its full meaning. This explains why Leibniz’s writings on the project of universal language contain examples from a variety of disciplines. The examples do not indicate any confusion on Leibniz’s part but rather illustrate the nature of the project. Using the terminology made famous by Berlin we might say that, in this respect, Leibniz is both a hedgehog and a fox. He acknowledges a unifying formal basis for all concepts and possible objects of knowledge, but this thin structure is only fully realized when applied to a variety of domains and disciplines.58 In short, there is both unity and multiplicity in the sense that all particular notations and domains have a common and universal foundation. The project of universal language calls for the design of particular notations for its very realization. Ultimately, the main point of designing particular notions is to improve and enhance the representation of concepts. Let me illustrate this point using the concept of the natural numbers. Following are three ways to represent natural numbers: 1. i ii iii iiii iiiii… 2. I II III IV V… 3. 1 2 3 4 5….

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According to Leibniz, all three of these symbolic systems represent the concept of natural numbers. At the same time, Leibniz holds that the Arabic numeric system is the superior of the three (see GP VII, 192; L 184) since it facilitates the representation of large numbers, reflects the decimal basis of the natural number system and enables complicated calculations. In this sense, the development of a symbolic system (or notation) provides not only a method of judging the truth and falsity of propositions, but also a method of research for the discovery of new propositions and concepts. This implies that Leibniz views notations not merely as an instrument for storing information but also for expanding the existing state of knowledge. In other words, it turns out that the universal language and the real characteristics are not only means for preserving and representing knowledge but also for acquiring knowledge. The dependence of knowledge on certain means of representation also implies the expansion our representation systems, i.e., the development of new terms and concepts, as the investigation of concepts may require modifying their modes of representation. In Leibniz’s favorite example, mathematical language not only enables the representation of the current state of knowledge but also the formulation of questions, hypotheses, and new methods of proof. A new method of proof sometimes requires a certain modification in the notation. In fact, Leibniz’s own infinitesimal calculus illustrates this point very well. As Couturat pointed out, Leibniz’s invention of infinitesimal calculus “consists in effect in its presentation, by appropriate signs, notions and operations which are no longer arithmetical, and its subsumption of them under a formal algorithm” (Couturat 1961, 85, translation from Wilson 1989, 32).59 1.11 Does Leibniz’s Characteristics Presuppose Complete Knowledge We have already noted that Leibniz's project of the universal characteristic, and his optimism towards it, rely on a set of basic assumptions. As Rutherford accurately observes,60 It is evident that a set of more basic assumptions about the relationship between language, thought, and reality underlie Leibniz's project of a universal characteristic. For this project to make sense it must be supposed from the start that reality has an intelligible structure that can be expressed in terms of combinations of atomic concepts, and that this structure is in principle accessible to the human intellect (CCL 257).

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Yet Leibniz’s basic assumptions concern not only the relations between language, thought and reality but also between these notions and the notion of possibility, which is clearly distinct from that of reality. Rutherford goes on to question whether Leibniz’s assumptions are justified: [C]ould such a characteristic ever be realized? Arguably not. To carry out the aims that Leibniz foresees for it, its characters would, from the start, have to be constructed such that they exactly express the composition of the concepts they are meant to replace. This implies that rather than aiding the philosophical analysis of concepts, the formulation of a universal characteristic, in fact, presupposes a complete analysis of concepts into their simplest parts (CCL 231-2). As in turns out, Descartes already raised a similar criticism of the project of a philosophical language. Descartes argued that a universal language presupposes a "true philosophy," i.e., a complete knowledge of nature. Leibniz was well aware of this criticism and, although at times he doubted that his project was humanly feasible, he never gave up his basic assumptions and his conviction that the project was, in principle, possible (C 429-30; CCL 232-3). His response to Descartes’ charge is that the very composition of such a characteristic is an essential part of the logic of discovery. For Leibniz, the invention of the characteristic is an integral part of the human quest for knowledge. This is not to deny Rutherford's point that Leibniz "presupposes a complete analysis of concepts into their simplest parts”; rather, I’d like to stress that a complete analysis need not be currently available to human beings; nor is it required to pursue this project. Leibniz indeed presupposes a "complete analysis of concepts". His supposition, however, does not pertain to the human mind but rather to God's. Such an analysis may gradually become available to humans by using the very "instrument of reason" Leibniz suggests to construct, viz. the universal characteristic. For Leibniz, the construction of the characteristic is an essential part of the human quest for knowledge. Constructing the characteristic is a matter of acquiring a symbolic system in which all intelligible concepts can be represented. Once concepts are represented, they (and their interrelations) can become the object of human investigation, just as the language of arithmetic enables the investigation of numbers, their qualities, and their interrelations. In short, the Universal Characteristic is primarily an instrument that makes reasoning and investigation possible; it is not a result of such investigation. It is not primarily a body of knowledge; rather,

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its primary function is to serve as a means of representing and pursuing human knowledge. In this light, one may express Leibniz's "basic assumptions" roughly as follows: Although only God sees all truths and possibilities intuitively and immediately, human beings are not doomed to a state of ignorance; rather, humans are capable of knowledge and reasoning. For humans, unlike for God, acquiring such knowledge requires time, method, and labor. Due to the limitations of our mind, we can proceed only step by step and necessarily by using symbols. Therefore, Leibniz believes that a substantial part of the quest for knowledge is the design of symbolic systems to facilitate and enhance our investigations and reasoning. Since Leibniz believes that knowledge of the universe leads to a better understanding of God and his reasons for creating this world (C 136; GP VII 425), the broader objective of Leibniz's characteristic is to encourage and contribute to this pious pursuit. A major goal of Leibniz's schemes is to provide a human counterpart to divine thinking, as far as that is possible. His schemes represent a human attempt to model and thereby to investigate the realm of conceptual intelligibility. His Universal Characteristic is intended to provide an instrument for investigating all possible things and their relations and does not presuppose a complete knowledge of them (see L 258). Leibniz seeks to model divine combinatorial activity – the production of all possible things in God’s mind. It is this realm of divine thinking that Leibniz's universal characteristic both presupposes and seeks to represent. 1.12 Conclusion I started out by presenting Leibniz’s early presuppositions regarding the notion of possibility. I have shown that, from very early in his career, Leibniz was working with a rich and original approach to possibility, embedded in a metaphysical context. I also noted that Leibniz’s preoccupation with the notion of possibility was partly motivated by moral and theological concerns and that he used it as a major instrument in his effort to resist a naturalized and necessitarian world view. I developed Leibniz’s approach to possibility in some detail, arguing that it includes the following commitments: Possibilities are situated in a conceptual realm, understood as consistent thoughts in God’s mind. Consistent thoughts are explicated in terms of complex thoughts or concepts, whereas complex concepts consist of simpler elements. Leibniz also presupposes logical simples, indefinable and unanalyzable, which he identifies with God’s simple attributes (or God’s simple forms). At the

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same time, for Leibniz, God is an active mind whose primary activity is thinking and self-reflection. God’s reflections on his simple attributes are mental combinations of his simple forms that produce complex forms. Likewise, God’s reflective operations are iterative, so that he reflects upon his reflections. Thus God thinks the combinations among his simple forms, and more complex concepts arise in his mind. In this view, God combines the simple forms in a natural order – from the simple to the complex – and, in this sense, Leibniz’s system of possibility is both recursive and yields the production of infinite concepts. These presuppositions taken as a whole characterize Leibniz’s approach to possibility and provide the point of departure in this work. As we have seen, it affords some insights into a number of questions and difficulties in Leibniz’s metaphysics. For example, we have seen that Leibniz’s view of possibility is closely linked to his projects of the universal language and the real characterstica, which can be seen as a human effort to model and comprehend the realm of divine ideas and concepts by means of symbol systems. In turn, the compositional structure of concepts and possibilities clarifies Leibniz’s view of representation and symbolization by means of one-to-one correspondence between the components of a concept and the components of a symbol of it (at well as between their methods of production). Leibniz’s view of possibility also clarifies that the construction of various notation systems rather than a unique universal language is the adequate realization of the project, as Leibniz’s examples amply testify to. In turn, these notation systems play a role not only of representing concepts but also of enabling the acquisition of new concepts and the discovery of new knowledge. For human knowledge requires language and notation as a means of partially representing and improving our insights into the realm of pure concepts in God’s mind as well as into its realization in the created world. I have also pointed out that Leibniz’s view of truth as the inherence of the predicate term in the subject term is very naturally related to his view of concepts and possibility. If possibility is understood as self-consistency among terms (so that it pertains to concepts rather than to things), and if concepts are formed by a unique combination of constituents, then predication, as well as the nature of propositions, is naturally understood (along its traditional form) as an ascription of a predicate term to the subject term. Such an ascription yields a true proposition just in case the predicate term is included in – i.e., is one the predicates making up – the concept of the subject; and it yields a false proposition if it is not included therein. In the next chapter, I will examine God’s intelligible activity in

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more detail and examine how, according to Leibniz, the notion of a possible individual arises in this context.

1 For example, while there are many predecessors to Leibniz’s logical notion of possibility, the other major philosophers in the early modern period did not accept the notion of unrealized possibilities. 2 For a recent thorough investigation (as well as a judicious judgment) of Leibniz’s attitude towards Spinoza, see Mogens Laerke Leibniz lecteur de Spinoza. La genése d'une opposition, forthcoming, especially the first part which adequately captures Leibniz’s attitude as “La curiosité métaphysique”. 3 For example, Leibniz writes: “what he says about the intellectual love of God (Ethics part IV, proposition 28) is only a sop to the masses, since there is nothing capable of being loved in a God who necessarily produces all good and bad indiscriminately. True love of God is grounded not in necessity but in goodness” (AG 281). 4 It should be noted that Leibniz became familiar with Spinoza’s views expressed in his unpublished Ethics during his stay in Paris (1672-1676) mainly through the mediation of Tschirnhaus. Thus, it may well be that some of the presuppositions I present in this chapter were already formed before he became familiar with Spinoza’s views. My point is that he used these presuppositions to produce a cogent alternative to the danger he perceived in Spinozism. 5 “[W]hatever seems immoral, dreadful, unjust, and dishonorable, arises from the fact that [one] conceives the things themselves in a way which is distorted, mutilated, and confused” (Ethics IV, p73 s). See also Ethics IV, propositions 64c and 68. 6 In the 18 th century this trend further developed such that the whole moral domain could be ascribed to human psychology, which accounts for the emergence of moral sentiments, in general, and of the moral sense, in particular. This becomes very explicit in Hume. According to him, the only possible source of moral judgments is to be found in human psychology. 7 I stress here the aspects that horrified and challenged Leibniz. In fact, Spinoza’s view is more subtle and complex. He sees his philosophy as an ethical endeavor that consists in recognizing and realizing our peculiar place, as beings capable of self-reflection, in nature. By becoming aware of our nature and our place in Nature, we can liberate ourselves from prejudices and illusions such as that we have alternatives and free choice among them. 8 For a very interesting presentation of the complementary role these principles play in Leibniz’s metaphysics, see Grosholz and Yakira 1998. 9Arguing for the historical case would require a different approach from the one I am taking in this work.

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10 As Mugnai notes, “there are no ideas without the intellectual activity of someone thinking (be it God or man or some other rational being).” Leibniz Theory of Relations, 1992, 25. 11 “For every ratio, proportion, analogy, proportionality arises from God’s nature or, what is the same, from the idea of things and not from the will of God” (A 6.3 122; Confessio 43). 12 See A 6.3 521, SR 81: “Ideas exist in God ...as properties result from an essence”. 13 While this point may be controversial, I hope to show that Leibniz’s logical interpretation implies that possibilities pertain to what can be the case rather than what is the case. 14 Given this definition, it is easy to see how the development of this notion would go: if God’s mind drops out of the picture, ‘intelligible’ would come to mean that which in principle can be understood. 15 “Numbers, modes, and relations are not entities” (A 6.3 463; SR 7). 16 This view was articulated by Aristotle and I label it “Aristotelian,” following Hintikka and Knuuttila. However, in Aristotle’s writings, one finds other views as well. Roughly speaking, the view that any genuine possibility will be actualized was also held at least by Spinoza and Hobbes. Regarding this point, see the first section of Hintikka's "Leibniz on Plenitude, Relations, and the 'Reign of Law" in Frankfurt, (ed.) 1961. 17 See Aristotle's Metaphysics, Theta 4; 47b3. 18 See The Cambridge Companion to Later Medieval Philosophy, 1982, 344, for the formulation of this principle. 19 See The Cambridge Companion to Later Medieval Philosophy, 1982, 344. 20 In the De Summa Rerum he also says that, “everything possible is thinkable” (A 6.3 475; SR 27-9). 21 The passage continues as follows: “the necessary – that whose opposite is impossible; the contingent – that whose opposite is possible.” See also “On Freedom and Possibility” (1680-82): “all truths that concern possibles or essences and the impossibility of a thing or its necessity rest on the principle of contradiction...” (Grua 287; AG 19). 22 This is, of course, a reference to the temporal notion of possibility noted above. 23 See Letter to Simon Foucher of 1675: [w]e cannot deny that the very truth of hypothetical propositions in themselves is something outside of us and independent of us. For all hypothetical propositions assert what would or would not be, if something or its contrary were posited; consequently, they assume...the possibility or impossibility ... of something. ...So, of all the things

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Chapter 1 which actually are, the possibility or impossibility of being is itself the first. But this possibility or this necessity form or compose what are usually called eternal. And we are right in calling them this, for there is nothing so eternal as that which is necessary. Thus the nature of a circle with its properties is something which exists and is eternal, that is, there is some constant cause outside of us which makes everyone who thinks about a circle discover the same thing,…. But although existence of necessities comes before all others in itself and in the order of nature, I nevertheless agree that it is not first in the order of knowledge (L 2356, my italics).

24 See 24 Metaphysical Theses n. 2, Rauzy 1995, 466; C 534; GP VII 289. 25 See A 6.3 583; SR 105-7. It seems that, for Leibniz, what can be "distinctly conceived" is that which can be conceived by considering the concepts, regardless of their instantiation in the world. 26 It is an interesting question whether the thought that “X is impossible” is a thought of God. 27 These definitions apply to humans as well, though in a limited sense. This is why humans can benefit from philosophical and logical investigations and why we should devise the combinatorial and logical calculi. 28 In the next sections I will suggest that Leibniz’s projects of a Universal Language and a Real Characteristic are premised on this presupposition. They are roughly human attempts to model and investigate divine thoughts. 29 In this respect, Leibniz is extending the conceptualistic approach to the question of relations (and truths) to the domain of possibilities. It is not surprising therefore that Leibniz views the ontological status of truths, relations and possibilities as similar. 30 Given Bisterfeld’s notion of “mental multiplication” and Hobbes’ notion of “mental addition,” there is nothing surprising in Leibniz presupposing a notion of mental combination. Rather, the notion of combination is all embracing for him, such that it includes all types of mental activity. 31 The question whether order, for Leibniz, is necessarily spatial order is particularly interesting. The order of elements in a sequence may be seen as neither spatial nor temporal but rather as a mathematical or formal order. 32 It is fairly clear that Leibniz thought that such a view leads to absurd consequences, though it is very interesting to note a striking disanalogy with his views on the divisibility of matter to infinity. Of course, Leibniz makes the point that there is a disanalogy between the real and the ideal in this respect. 33 See Fichant 1998, 103-4 and Cover and O’Leary-Hawthorne 1999, 264. 34 “Attributum Dei est, forma simplex quaelibet ” (A 6.3 514). See also A 6.3 522. In the context of proving that “a most perfect being exists”, which he defines as “a being which is a subject of all perfections” (A 6.3 577; SR 101), he writes:

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“Perfections, or simple forms, or absolute positive qualities, are indefinable or unanalyzable” (A 6.3 575; SR 97). “I term a ‘perfection’ every simple quality which is positive and absolute, or, which expresses without any limits whatever it does express. But since a quality of this kind is simple, it is therefore indefinable or unanalyzable” (A 6.3 577, SR 99). See also A 6.3 578 and GP VII 261. 35 See GP IV, 296. I explore Leibniz’s argument for the consistency of this definition in detail in the next chapter. 36 “Every purely affirmative attribute is infinite; or, it is as great as it can be, or contains all the things that belong to its genus. There are necessarily several affirmative primary attributes; for if there were only one, only one thing could be understood. It seems that negative affections can arise only from a plurality of affirmative attributes – for example, thought and extension” (A 6.3 572-73; SR 93). 37 “There is a uniquely active thing, namely, God” (A 6.2 489; cited from Mercer 2001, 347). 38 See also, A 6.3 475; SR 27 and A 6.3: 465, 480, 495, 509, 515-17, 518. 39 The translation is from Mercer 2001, 354. 40 “Si Mens quaedam nihil cogitet particulare, sed cogitet tamen, erit Deus; seu cogitabit omnia“ (A 6.3 512). 41 “Omne cogitans cogitat utique aliquid. Simplicissimum est, id quod cogitat cogitare se ipsum; et cogitatio absoluta est, cum id quod cogitat se ipsum, omnia est” (A 6.3 518). 42 Note that, in A 6.3 399; SR 115, Leibniz draws an interesting analogy between reflection of reflections and relations of relations, both of which, as Leibniz’s example shows, go to infinity. 43 See also Leibniz’s comments on Spinoza’s Ethics, proposition 1: “’To be prior by nature’ can be defined in this way, however, as that which can be conceived without the other being conceived, while the other thing cannot, on the contrary, be conceived without the concept of the former. But, to tell the truth, to be prior by nature is a little more general even than this. For example, the property of the number 10 to be 6 + 4 is posterior to that of being 6+3+1, because this latter property is closer to the first property of all; ten is 1+1+1+1+1+1+1+1+1+1. Still it can be conceived without the second property, and, what is more, it can be proved without it. I add another example. In a triangle the property that the three internal angles equal two right angles is posterior in nature to the property that two internal angles are equal to the exterior angle of the third. Yet the former can be understood without the latter and, indeed, can be demonstrated without it, though not as easily” (L 303). 44 “Sed si sic definias: Natura prior est terminus qui constat ex terminis minus derivatis. Terminus autem minus derivatus est, qui paucioribus simplicibus primitivis aequivalet” (A 6.4 180-81).

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45 “Terminus natura prior (posterior) est qui prodit pro composito (simplicibus) substituendo simplices (compositum). Sive quod idem est, natura prior prodit per analysis, natura posterior per synthesis: alter ex altero” (A 6.4 180). 46 Leibniz raises a similar question to himself in his Quid sit natura prius (A 6.4 180-81). 47 This point also shows that Couturat’s claim that Leibniz’s metaphysics is entirely grounded in his logic cannot be correct. As the remarks above makes clear, Leibniz’s notion of logic involves a number of metaphysical presuppositions. 48 For the precise sense of Leibniz’s conceptualism, see Mugnai (1992) Leibniz’s Theory of Relations 24-25. 49 In some of these moments Leibniz is clearly overstating his achievements in what seems to be an attempt to impress influential figures, such as Oldenburg. 50 “A real definition is one according to which it is established that the defined thing is possible, and does not imply a contradiction. For if this is not established for a given thing, then no reasoning can be safely taken about it, since if it involves a contradiction, the opposite can perhaps be concluded about the same thing with equal right. And this was the defect in Anselm’s demonstration, revived by Descartes, that the most perfect or the greatest being must exist, since it involves existence. For it is assumed without proof that a most perfect being does not imply a contradiction; and this gave me occasion to recognize what the nature of real definition was.” (A Specimen of Discoveries (circa 1686), cited from Arthur (ed. and trans.), 2001, 305-07. 51 Leibniz’s view of possibility and concept formation presented above is consistent with his general view of truth, viz., that there is a single paradigmatic form of truth based on the principle of logical inclusion. 52 Parkinson illustrates Leibniz's early assumptions on predication as follows: “Suppose that a, b, and c are first terms and when combined they constitute the concept x. We may predicate of x any one of these first terms – e.g. a – or any combination of these first terms belonging to the second class [of combinations] – e.g. ab. In saying that these derived terms are 'nearer to' first terms, Leibniz may mean that they are nearer to first terms than x is, since x (which is equivalent to abc) belong to the third class [i.e., it is a combination of three elements]. Leibniz adds that we may predicate of a subject its entire definition; in this case, we may say of x that it is abc. This view of predication was of greater importance for Leibniz than he first realized. ... [O]ne may say of x that it is a, b, c, ab, ac, bc, or abc. From this it follows that one may not say of x that it is d, if d is a term which is not equivalent to a, b, c, or any combination of them. This suggests that a proposition is true when it is of the form 'abc is abc', 'abc is bc', 'abc is c', etc., which Leibniz was to express later in the assertion that a true proposition is

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reducible to an identical proposition. Further, in saying that (for example) 'x is a' one will be saying that a is one of the concepts constituting x, or, as Leibniz was to put it later, one will be saying that the predicate a is included in the concept of the subject, x” (PLP, Introduction). 53 I suppose that this substantial omission from Couturat’s otherwise wellinformed work is due to his commitment to a logicist interpretation of Leibniz. 54 “I have considered with attention the great work on Universal Character and Philosophical Language of Monsieur Wilkins; I find that he has put there an infinity of nice things, and we never have had a more accomplished table of predicates; but the application to characters and language does not at all conform to what one could and should have done. I have considered this matter before reading the book of Monsieur Wilkins, when I was a young man of 19 years, in my small book On the Art of Combinations, and my opinion is that the truly real and philosophical characters must respond to the analysis of thoughts …” (Leibniz to Thomas Burnett, 24 August 1697, GP III, 216). 55 Letter to Oldenburg, August 27, 1676 (GP VII 11); Confessio Naturae contra Aetheistas, 1669 (GP IV 103); De Scientia universali (GP VII 199). 56 Dascal cites this passage: “When we do not possess an idea, its functions are fulfilled by some sensible image or by a definition, i.e., a set of characters … The place of the idea is always fulfilled by some image (phantasma), which is completely perceived at once.” 57 A detailed argument for this claim is presented in the next chapter. 58 “The pure sciences such as mathematics are seen as the source of a river, a rather dry and meager source, but from it water descends continuously into the most fertile rivers of mixed sciences like acoustics, optics, and mechanics which in turn flow out into a sea of various uses and applications” (De rationibus motus, 7, A 6.2, 160, cited from Beeley, 2003, 83). 59 As another example of the significance of notation systems, one thinks of the system of chemical notation as enhancing the study of chemical elements and their interactions. 60 In his illuminating article “Philosophy and Language in Leibniz” in CCL, 22469.

Chapter 2 Possible Individuals 2.1 Introduction As we have seen, Leibniz presupposed a fairly clear view of possibility. It does not follow from his view of possibility, however, which things he considers as possible, that is, what are the things that may become actual. As a matter of fact, we know that he considers worlds to be possible1 and, for him, there are many possible worlds, the best of which is the actual one. A possible world, however, consists of possible individuals. More precisely, a possible world consists of a compossible set of individuals or a set of individuals whose co-existence is possible. Likewise, the actual world is a set of compossible, realized individuals. This point accords with Leibniz’s nominalistic view that ‘individuals and their properties’ are the only things that exist.2 Given that individuals exist, it is clear that they are also possible. Although possible individuals entail simpler constituents, Leibniz’s version of nominalism suggests that only compossible individuals are candidates for actualization, which points to the central role possible individuals play in Leibniz’s metaphysics. How do we understand Leibniz’s notion of a possible individual? As Fichant notes, “Leibniz moved from [Suarez’s] conception of individuation through the ‘total entity’ (in 1663), the form and matter of a thing, to a conception of individuation by means of a complete notion”.3 Mugnai recently noted that “[o]ne of the main features of which distinguishes Leibniz’s account of individuation from the more orthodox views of the scholastic type is that it expresses the principle of individuation in purely logical terms”. 4 From 1679 on, Leibniz defined an individual through a complete concept that entails its predicates and thus includes every truth about it.5 Mates suggested that the complete concept of an individual corresponds to a possible individual.6 Mates’ suggestion to identify possible individuals with their complete concepts significantly contributes to our understanding of possible individuals. First, this identification places Leibniz’s notion of possibility within its proper context, namely, the realm of intelligible thoughts in God’s understanding. Second, it clarifies that possibilities are not obscure entities since they are not seen as entities at all. Rather, possibilities are thoughts of a perfectly 51

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rational mind. And third, Mates’ observation points to an internal connection between divine thinking and the emergence of possibilities, which I develop below. The connection between thought and possibility is evident in the theological context of God’s understanding where all candidates for creation are conceived, but it also derives, for Leibniz, from the compositional structure common to both thoughts and possibilities. As we have seen in the previous chapter, according to Leibniz, thinking involves combining simple elements into complex ones (or, inversely, analyzing complex concepts into simple ones). We have seen that this compositional notion of thinking helps explicating the emergence of possibilities in God’s understanding. As God combines simple elements into complex ones, possibilities or complex thoughts arise in his understanding. The composition of simple elements into complex concepts is constrained by Leibniz’s commitment to a logical notion of possibility, that is, the internal consistency among the terms that make up a complex concept. In accordance with the combinatorial nature of thinking, possibility is understood in terms of the conceivability of an ensemble of self-consistent terms or complex concepts. In the previous chapter, I have argued that Leibniz’s presuppositions concerning possibility include a logical notion of possibility; a compositional structure of concepts; 7 a natural ordering of concepts from simple to complex8; and God’s understanding, seen as an active mind performing combinatorial operations. 9 On the basis of these presuppositions, it seems natural to suggest that Leibniz explicates not only the notion of possibility in general, but also the notion of possible individuals, in particular, in combinatorial terms. 10 This claim is brought out in passages such as this one: “There can be as many singular substances as there are diverse combinations of all compatible attributes. And this is the source of the principle of individuation, about which so many disputes took place among the Scholastics”.11 Since Leibniz states that, ‘there can be as many singular substances’, it is clear that he thinks of possible individuals or complete concepts rather than of actual individual substances. Leibniz’s combinatorial principle of individuation stated above differs considerably from the ‘total entity’ suggested in his early work on the principle of the individual (1663). We have noted that Leibniz has moved to express the source of individuality in logical and combinatorial terms. But what is the source of individuation

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that arises in the context of the ‘diverse combinations among compatible attributes’ and how it is formed as a concept of an individual in God’s understanding? While Leibniz’s notion of a complete concept has received much attention, the question of its formation in God’s understanding has received very little.12 In this chapter, I address this question by focusing on the period (roughly 1672-1679) during which Leibniz developed the notion of a complete concept as an explicit definition of an individual.13 During this period, Leibniz applied his general approach to possibility (understood in terms of divine conceivability) to characterize possible individuals in terms of complete concepts.14 For this reason, a close consideration of Leibniz’s texts from this period would be useful in revealing his presuppositions regarding the formation of possible individuals or complete concepts. The main texts I will consider here are Leibniz’s notes written during his stay in Paris and the logical papers composed in the late 1670s. In the first part of the chapter I will sketch the connection between the combinatorial activity in God’s mind and the ‘production’ of possibilities in general. In the second part, I will suggest how this activity might give rise to concepts of individuals. I must clarify at the outset that my attempt to sketch the formation of individual concepts goes only as far as the monadic (one place) predicates of individual concepts are concerned. Such concepts may be termed ‘thin’ or ‘incomplete’ and they are the main focus of investigation here.15 There is an interesting story concerning the relations between such concepts and how they contribute to complete the individuality of concepts. But this story will have to wait for the next chapter. My thesis concerning the formation of ‘thin’ individual concepts in God’s understanding involves three claims: (1) Leibniz sees an internal connection between composing simple concepts into complex ones and the individuation of concepts, so that the complexity of concepts also contributes to their uniqueness and hence their individuality. (2) An individual concept should not be identified with a set of predicates (as most commentators hold); rather, it should be seen as a unique structure of predicates, in which the order of predicates plays an essential role. (3) An individual concept should not to be correlated only with a unique structure of predicates but also with the combinatorial rule that generates such a unique structure of predicates in God’s understanding. Such a rule orders and unifies various forms in a unique way and, in this sense, it may be considered as the source of unity and individuality of an individual concept. I will conclude that the production rule of a complete concept in

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God’s understanding may be considered as its source of individuation and that an individual is thus given a generative definition. As we shall see in subsequent chapters, this generative notion of the individual plays a crucial role in Leibniz’s view of creation, of created substances, the extent of their freedom, the way they are nested one within the other, and the way they differ from aggregates. 2.2

God’s Combinatorial Activity

Let me begin by exploring some aspects of God’s combinatorial activity. We may think of God’s understanding as a kind of a combinatorial mechanism that constructs complex concepts by combining simple ones. The simple things God mentally combines are his ‘simple forms’.16 God’s simple forms can be compared to logical atoms, that is, basic conceptual elements. Leibniz makes it clear that such simple forms play a role in the ‘production’ of possibilities in God’s mind. He says that “a perfect analysis of concepts” terminates in prima possibilia, and he identifies these first possibilities with the “absolute attributes of God”.17 In addition, he defines God as the most perfect being or as the being which contains all affirmative attributes or as “the subject of all absolute simple forms”.18 God entails all the prima possibilia as his simple attributes. The results of God’s activity are all the consistent combinations and recombinations of his simple forms. As noted, such consistent combinations are considered to be possible.19 God as the Subject of all Simple Forms In 1676, Leibniz set out to prove that the definition of God as ‘a most perfect being’ or one that has ‘all absolute simple forms’ is possible. 20 Let us consider some implications of characterizing God who thinks all possibilities as ‘the subject of all simple forms’. Leibniz writes: “I seem to have discovered a demonstration that a most perfect being – or one which contains all essence, or which has all qualities, or all affirmative attributes – is possible, or does not imply a contradiction. This will be evident if I show that all (positive) attributes are compatible with each other. But attributes are either analyzable or unanalyzable; if they are analyzable they will be aggregates of those into which they are analyzed. It will therefore be sufficient to have shown the compatibility of all primary or unanalyzable attributes, or, of those which are conceived through themselves. For if individual

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attributes are compatible, so are several attributes, and so therefore are composite attributes. It will therefore be sufficient to show only the intelligibility of a being which contains all primary attributes, or, to show that any two primary attributes are compatible with each other”.21 To show this, Leibniz uses a reductio ad absurdum argument. He wishes to show that the supposition that some primary attributes are incompatible implies a contradiction. His proof goes as follows: if two attributes (which are, we presume, arbitrarily chosen), A and B, are incompatible, then one of them is negative, or one of them is analyzable into a negative one. But the argument assumes that both A and B are positive and unanalyzable. Hence, the supposition that the two attributes are incompatible is false; hence, its negation, that A and B are compatible is true. By generalization, Leibniz infers that “any two primary attributes are compatible with each other”, and concludes that “a being which has all attributes is possible [i. e. self-consistent]”.22 Both the validity and the implications of this argument are of great interest and deserve closer examination23. For my current purposes, I will focus on the following points: (a) Leibniz defines God (the most perfect being) as possessing all positive and simple attributes; (b) these attributes cannot be defined or analyzed; 24 (c) the combination of God’s simple forms gives rise to composite forms or affections; 25 and (d) composite forms may be compatible inter se. What is difficult to see in this picture is how composite forms may be incompatible. This implication raises a serious threat to the intelligibility of producing a variety of distinct concepts by combining God’s simple forms. If all the attributes – simple and complex – are compatible, how could this process produce more than one big concept, consisting of all attributes? This problem of accounting for incompatibility among God’s forms is in the background of my discussion below and some of the points are developed with this question in mind.26 Our Ignorance of God’s Simple Forms At this stage, the question, what are the basic elements Leibniz identifies as the simple attributes of God, clearly arises. Disconcertingly, Leibniz holds that we cannot know what they are. The logically simple elements of his combinatorial scheme are indefinable and unknowable. He says that, “[a]n analysis of concepts by which we are enabled to arrive at primitive notions, i.e., at those which are conceived through themselves,

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does not seem to be in the power of man”. 27 In considering Leibniz’s reasons for his avowal of ignorance on this question, we may shed some light on the status of the simple elements. A theological argument: Since the elements in question are God’s attributes, it may seem impious for Leibniz to either speculate what they are, or worse, to presume to know what they are. Professed ignorance regarding the divine attributes is deeply rooted in the Judeo-Christian tradition. It goes back to Philo and is forcefully presented by Maimonides in his Guide for the Perplexed. An argument from symbolization: According to Leibniz, the relation between human symbols and divine concepts has both arbitrary and necessary aspects.28 A necessary condition for symbolical representation is a structural similarity (isomorphic relation) between the composition of a concept and the composition of its symbol.29 Leibniz explicates this structural resemblance in terms of one-to-one correspondence between the elements of a complex concept and the elements of the representing symbol. The way in which a concept is composed of its simple constituents must be preserved in the symbol representing it. This view of representation implies, however, that the elementary constituents cannot be represented and can only be given arbitrary names. Since the elements are logically simple, they lack compositional complexity.30 If they are not a part of compositional complex, the elementary constituents lack the necessary condition for being represented, namely, possessing a common structure with a symbol. Since the elements do not belong to a structure to begin with, they cannot structurally resemble any symbolical expression. Therefore, they cannot be represented directly.31 An empirical argument: Leibniz’s avowal of ignorance regarding the logical elements may have had an additional justification. We may view his approach as laying out the logical framework of concepts (a priori) which is to be supplemented with empirical material derived from experience. From this point of view, logic may postulate the existence of basic elements, but it is the task of empirical science to figure out (a posteriori) what these elements are. 32 The philosopher’s task is not to substitute the logical variables with the real constituents of our world but to provide the logical scheme for such substitution by empirical science. Leibniz does not articulate his approach in these terms, but his endorsement of both logical considerations and empirical experimentation as essential elements of the scientific enterprise is compatible with such an approach. In addition, his view of substitution may allow for the elements

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of formal propositions to be substituted by empirical content in particular contexts. God’s Intelligible Activity However disconcertingly, we are left with the conclusion that God’s simple forms are unknowable to humans. Thus, for Leibniz, God is the subject of all compatible but unknowable forms. This characterization, however, is not all there is to Leibniz’s notion of God. Leibniz states that God is “necessarily a thinking being”,33 and that, “God is not a Metaphysical something, imaginary, incapable of thought, will, action, as some make out, so that it would be the same as if you said that God is nature, fate, fortune, necessity, the World; but God is a Substance, Person, Mind. [...] It should be shown that God is a person or intelligent substance”.34 For Leibniz, God is an active mind 35 whose activity consists in thinking. Most important to the production of possibilities is that God’s thinking is reflexive. This means that God thinks and reflects on his own forms. 36 Furthermore, God also reflects on his own reflections and combines them in various ways. In this way, God’s reflexive activity can produce more and more complex thoughts. As I noted above, in this context, complex thoughts may be considered as possibilities. Let me illustrate this point: If A and B are among God’s simple forms, then, by reflecting on them, God forms the complex thought {A, B} or, in other words, the possibility of {A, B}. God may reflect again upon this and some other complex thoughts (e. g., {C, D}, assuming that C and D are among his simple forms) to produce more complex thoughts, such as {{A, B}, {C, D}} and so on to infinity. For God’s reflexive activity implies that he reflects on the results of his own thoughts or, in other words, that he operates on the outcomes of his operations. 37 Since God can operate on the outcomes of his primary operations, and then again on the outcomes of any successive operation, increasingly complex thoughts arise in his mind. God’s reflections begin with his simple forms and progress to more complex combinations of them. By virtue of continued reflection, increasingly complex structures of forms can be constructed in his understanding. This productive activity yields infinitely many structures, each of which may be infinite as well.38 Let me connect the above set-theoretical illustration with a linguistic analogy that Leibniz’s often uses. We can take the simple forms (the logical elements) as analogous to letters of an alphabet, as Leibniz does in

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his Art of Combinations and Universal Language. 39 In this analogy, the complex forms, which result from the first-level operation, are combinations of letters. They can be seen as analogous to the terms of a language.40 In the second-level operation, God thinks of combinations of complex forms which may be seen as analogous to propositions (seen as combinations of terms).41 In the third-level operation, God thinks of sets of sequences of complex forms which can be seen as analogous to sets of propositions. We can regard certain sets of propositions as corresponding to concepts of individuals, namely, sets of predicates predicated on the same subject. In the fourth level, God thinks of sets of concepts of individuals which can be viewed as analogous to possible worlds.42 This illustration suggests that reflexive combinatorial operations of God’s understanding can generate an infinite number of complex concepts, which may be organized as the realm of possibility. The Generality of God’s Combinatorial Activity Before providing further illustrations of God’s combinatorial activity, let us reflect on one remarkable but frustrating feature, namely, its extreme generality. The combinatorial scheme sketched above assumes (a) logically simple elements and (b) operations performed on the elements. Whereas the elements may be seen as God’s simple attributes, the operations may be seen as God’s ways (or modes) of thinking. This supposition is supported by statements such as “God thinks out infinitely many things in infinitely many ways”. 43 In comparison with arithmetic, from which Leibniz draws much of his inspiration, the elements can be viewed as the units and the operations as addition, multiplication, division, etc. However, since we do not know what the simple elements and the operations are, Leibniz’s combinatorial scheme seems vague, if not entirely obscure. 44 Since the elements and operations are not specified, the claim that all the combinations among logically simple elements are possible does not seem very informative. Leibniz’s vagueness, however, is due to the extreme generality of his project. As Russell pointed out, both the logical elements and the methods of their combination (the operations) in Leibniz’s scheme are not constants but variables.45 Unlike algebra, for example, in which the operations are constant 46 and the variables may take different values, in Leibniz’s scheme, both the elements and the operations are variables. These variables may be seen as placeholders for any operation and for any logically simple element. I do not wish to suggest, however, that the simple elements postulated by Leibniz are

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‘colourless’ in the sense that they lack internal characteristics. I suggest that in different domains of application we shall find different elements and different operations. Though there is a universal structure to all rational methods, each method may differ with respect to its subject matter. Leibniz is explicit about this generality. He writes that, “Combinatory treats of calculus in general, or of general signs or characters (such as A, B, C, where any one could be taken for another at will), and of the various laws of arrangement and transition, or of formulas in general. The algebraic calculus is a certain species of the general calculus, [in which], for example, there is a law of multiplication. [...] Not all formulas signify quantity, and an infinite number of ways of calculating can be conceived”.47 Leibniz sees his combinatorial scheme as the most fundamental and most universal form of all calculi. In his letter to Oldenburg, (dated December 28, 1675), Leibniz writes: “I have come to understand that everything of this kind which algebra proves is only due to a higher science, which I now usually call a combinatorial characteristic, though it is far different from what may first occur to someone hearing these words”. 48 As I noted earlier, Leibniz believes that combinatory underlies the very structure of thinking since both analysis and synthesis presuppose the compositional structure of concepts. In his groundbreaking work, La logique de Leibniz, Couturat takes a similar position. He writes: “En définitive, la Mathématique proprement dite, c’est-à-dire la Logistique, est subordonnée à la Combinatoire, et celle-ci à la Logique elle-même. La Combinatoire paraît même faire partie de la Logique; en tout cas, l’une et l’autre réunies composent la science des formes. Et par là il faut entendre, non seulement les formules mathématiques et les ‘formes’ algébriques, mais toutes les formes de la pensée, c’est-à-dire les lois générales de l’esprit. La Combinatoire ainsi conçue est la partie générale et formelle des Mathématiques; elle étudie toutes les relations qui peuvent exister entre des objets quelconques, et leur enchaînement nécessaire et formel. En un mot, c’est la science générale des relations abstraites”.49 Due to its abstraction from specific objects and operations, combinatory can investigate the forms of thought and its laws in general.50 If the combinatorial characteristic is supposed to model the divine thinking that

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produces every intelligible concept, then it must be applicable to any domain. As a formal scheme, the elements and operations of particular disciplines can substitute its symbols and variables. Leibniz’s notion of substitution may render the application of his general scheme to particular domains feasible. Thus the extreme generality of Leibniz’s combinatorial scheme is in fact required for the role it plays in his approach to possibility, namely, to produce every possible thing or every intelligible concept. Some Illustrations If it is applicable to every domain of knowledge, one can illustrate God’s combinatorial activity with examples from particular domains. These examples must be regarded as specific illustrations that need not be generalized. Leibniz provides a variety of examples, including deductive systems, such as Euclidean geometry and arithmetic, and non-deductive systems, such as law, written language, Chinese characters, chemical notation, musical notation, and others. Due to their axiomatic nature, arithmetic and Euclidean geometry can be presented by means of very simple concepts, i.e., assumptions and operations. In arithmetic, Leibniz follows Euclid’s definition of numbers and takes units as the fundamental assumptions. Various operations on these units, such as addition, subtraction, multiplication and division, yield an infinity of natural numbers as well as negative numbers, rational numbers, real numbers, imaginary numbers and complex numbers. For example, negative numbers are obtained when a larger number is subtracted from a smaller number (e. g., 3 - 4 = -1); rational numbers are ratios of numbers and may be produced by divisions of two numbers, and so on. In geometry, Leibniz thinks of points and dimensions as fundamental assumptions and of constructions as operations. Thus geometrical figures can be produced and the relations among them can be further investigated. Both arithmetic and geometry assume few elementary concepts which turn out to be very fertile ground for many consequences and theorems. Leibniz’s binary notation provides another illustration of how successive combinatorial operations on two simple elements – 0 and 1 – can produce infinitely many numbers. Leibniz also considers an interesting example of relations. He writes: “[...] suppose that there is a relation between a and b, and that that relation is called c; and let a new relation be considered between a and c, and let that relation be called d, and so on to infinity”. 51 A simple operation like relating two objects allows for an infinite hierarchy of relations.52 While Leibniz marvels at the capacity of reiterative and reflexive operations to

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produce infinite results, he is cautious about their ontological status. He says that, “all relations or reflections are not distinctly understood; for they are imaginary and have nothing that corresponds to them in reality”.53 The above examples illustrate how few elements (such as basic numerical units, points or elements) and several operations can produce a great variety of results. In all these examples, the results are complex concepts produced by combinatorial operations on simple elements. A Numerical Analogy Let us consider another analogy Leibniz frequently uses in the context of producing possibilities in God’s mind. In a number of passages from the Paris notes, Leibniz employs a numerical analogy to illustrate both the origin of things from God and the origin of properties from an essence. He writes: “It seems to me that the origin of things from God is of the same kind as the origin of properties from an essence; just as 6 = 1 + 1 + 1 + 1 + 1 + 1, therefore 6 = 3 + 3, = 3 x 2, = 4 + 2, etc. [...] So just as these properties differ from each other and from essence, so do things differ from each other and from God”.54 The various combinations of the units of six, produced by different operations (e. g., 3 + 3, 3 x 2), are considered to be different properties of the same essence (6).55 The example shows that various combinations of simple elements can produce a variety of things and that they differ from each other merely in the internal organization of the elements. In another passage, Leibniz goes as far as saying: “I cannot explain how things result from forms other than by analogy with the way in which numbers result from units – with this difference, that all units are homogeneous, but forms are different”. 56 I take this to mean that, unlike numerical units, elementary forms are not of the same type and that each of them is unique. Therefore, before any combination or permutation takes place, the degree of diversity is much richer than in the case of numbers. In these passages, Leibniz draws an analogy between a whole number and God’s essence. While the units are analogous to God’s simple forms, the whole number is analogous to God’s essence. This suggests that Leibniz uses the notion of essence in two senses here: in a minimal sense, ‘essence’ means all the simple forms; in a full sense, it means the variety of combinations of these forms. 57 Note that this distinction corresponds to Leibniz’s distinction between the matter and the form mentioned above. The numerical analogy purports to show how God’s reflexive and

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combinatorial activity may transform his essence in the minimal sense to an essence in a full sense. Whereas the minimal sense is the logical sum of the simple forms, the full sense involves various operations and reflections on the simple forms. These operations and reflections result in a variety of arrangements and configurations, all of which account for the production of intelligible things in God’s understanding. Furthermore, Leibniz points out that even though the sum of 3 + 3 and the multiplication of 3 x 2 are numerically the same, they should be seen as different things because they are produced in different ways. This suggests that, for Leibniz, a complex concept is partly individuated through its method of production and internal organization – a point I shall develop below.58 A similar analogy appears in the Confessio philosophi (1673) in which Leibniz says that (the vision of) the essence of God can increase so as to entail all intelligible things. The opponent, Theophile, vigorously protests: “I do not grasp how vision of the divine essence can increase, for if it is of the essence, it is complete; and if it is complete, it cannot increase”.59 Although this response seems decisive, Leibniz, far from conceding the point, replies: “Even knowledge that is complete can increase, not through new material but through new reflection. If you consider nine units displayed before you, then you have comprehended completely the essence of the number nine. However, even if you had knowledge of the material basis for all its properties, you would nevertheless not have knowledge of its form or reflection. For even if you do not observe that three times three, four plus five, six plus three, seven plus two and a thousand other combinations, are nine, you have nonetheless thought the essence of the number nine. I say nothing about the comparison of the number nine with other unities outside itself, because in this way not only the form, but the material of the thoughts is changed”.60 When the number of constituents (the units in this case) is fixed while the number of internal properties increases as a result of the various combinations of the constituents, we have novelty of reflection. Once again we see in this example that the internal organization of the forms plays a crucial role in increasing the variety of concepts. By analogy, we see how ‘essence’ in the minimal sense can be extended by virtue of combinations and the resulting internal ordering of the same basic elements. Once again, we see how the variety of intelligible things can be multiplied by virtue of form and reflection.

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However, the analogy between a number and God’s essence breaks down at this point: “God …cannot be compared with anything outside himself, since he has everything within himself ”. 61 For this reason, Leibniz gives another example: “I will give an example of a finite thing displaying infinite properties, without any comparison with external things. Here is a circle: If you know that all the lines from the center to the circumference are equal, then in my opinion, you have comprehended its essence sufficiently clearly. Still that does not mean that you have comprehended innumerable theorems, for as many diverse figures and, indeed, regular ones, can be inscribed in a circle (i.e., even if they are not marked out, they are already contained therein) as there are numbers. Thus there are infinitely many figures contained therein of which there is none that does not supply the investigator with prodigious material for theorems”.62 An omniscient being sees all the consequences and theorems that follow from the essence of a circle immediately.63 Likewise, God sees all the consequences that follow from reflection on his own essence. Furthermore, God sees all the relations among the products of his reflection. In this way, God’s reflections on his own essence (i. e., all his positive qualities) produce all intelligible concepts in his mind.64 Accordingly, Leibniz states that: “A most perfect being [...] is capable of ideas and of thoughts, for this multiplies the varieties of things, like a mirror. Therefore God, who is necessarily a thinking being, even if he is not a being which thinks everything, will be more perfect by that very fact”. 65 Since his reflexive thinking multiplies the number and variety of things, Leibniz says that God will be most perfect by that very fact.66 The Structure of Leibnizian Complexes Given the general outline of the combinatorial activity in God’s mind, let us consider whether the internal ordering of forms is essential to Leibnizian complex concepts. To clarify this point, let me use two contemporary notions: a set and a sequence. While the internal ordering of elements is irrelevant in a standard set, it is essential in a sequence. We may think of Leibnizian complex structures as sets of predicates, or as sets of sets of predicates, or as a sequence of predicates, or as a sequence of sets of predicates, or as other combinations of those. Of course, the notions

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of ‘set’ and ‘sequence’, as currently defined, were not available to Leibniz. Nonetheless, we can use them as examples and illustrations of Leibnizian intuitions and presuppositions. 67 This is worthwhile since the main approach to interpreting Leibniz’s complete concept seems to be unsatisfactory. The main approach among commentators (e. g., Mates, Fichant, Adams) has been to view an “individual concept as a set of attributes ” 68 and accordingly to reduce Leibniz’s combinatorial operations to logical conjunction and negation.69 However, reducing Leibniz’s combinatorialism to the single operation of logical conjunction has important implications for his notions of inclusion in a complete concept, predication and truth. For example, such a reduction implies that the inclusion relation of a predicate in a subject reduces to mere logical inclusion. This means that all one can say about a predicate is whether it is included in a concept or not. As an illustration, think of a complete concept (c) as a set, and of the membership relation as defining the inclusion relation, so that a predicate (P) can be truly asserted of (c) if P is a member of c. The membership relation of an element in a set does not involve an internal order between the members of the set or the method by which it is produced. However, we can think of a different model in which ordering the same predicates in different ways would constitute different complex concepts. In such a model (consider a sequence as an example), the internal order of the predicates also matters. This would affect the way we conceive of the inclusion of predicate in a subject (the inesse principle). In a sequence, the inclusion of a predicate is qualified since it is included in a certain place. Likewise, we can conceive of structures more complex than a sequence, such as ordering forms in various dimensions.70 The textual evidence considered above suggests that Leibniz takes considerations of ‘form’ and the method of production – i. e., the method of composition – as constitutive of the formation of concepts as well. This conclusion informs my thesis regarding the nature and formation of individual concepts. 2.3 Some Remarks on the Composition of Individual Concepts Given the picture of God’s productive thinking sketched above, let me raise a few suggestions as to how it may give rise to concepts of individuals. Given this picture of the composition of simple elements into complex concepts in God’s understanding, I will examine whether an increase in complexity may contribute to the individuality of concepts.

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An Intensional Approach Leibniz’s article Elements of a Calculus (April, 1679),71 offers some hints for approaching this question. Concepts of individuals may be represented in terms of the propositions that describe the predicates included in them. A proposition consists of two terms, which Leibniz defines as “the subject or predicate of a categorical proposition”, that is, something of the form ‘A is B’. 72 Unlike many in the Scholastic tradition, he holds that terms should be taken in intension rather than in extension. As Parkinson notes, Leibniz is contrasting his own ‘intensional’ approach to the proposition with the ‘extensional’ approach. His reason for preferring the former is that concepts “do not depend on the existence of individuals”. 73 “So if, for example, gold were a purely mythical metal, it would still be true to say that all gold is metal”.74 In my view, Leibniz’s motivation for taking the intensional approach is connected to his commitments regarding possibility. According to him, the scope of logic and metaphysics extends beyond concepts of existing individuals.75 Both his logic and his metaphysics presuppose all possible things as their proper objects. In contrasting himself to the Scholastics, Leibniz is focusing on concepts of individuals rather than “instances which are brought under universal concepts”.76 He is focusing on the content (or comprehension) of concepts of individuals, not merely on the extension of universal concepts (their instances). Each individual concept comprehends all its predicates conceptually in a manner analogous to the way in which the concept ‘gold’ comprehends the predicate ‘metal’ and the concept ‘human’ comprehends the predicate ‘rational’. Complexity and Individuality With its focus on the comprehension of individual concepts, Leibniz’s intensional approach plays a substantial role in the composition of individual concepts. This may be presented against the background of the Aristotelian classification system of existing things and the extensional interpretation of terms related to it. The Aristotelian classification system is hierarchical and assumes descending degrees of generality: from the most universal genera, to the less general species and all the way down to particular instances.77 For example, ‘living creatures’, ‘animals’, ‘mammals’, ‘swimming mammals’, ‘whales’, ‘white whales’, and finally an individual whale. Unlike the Aristotelian system, Leibniz is concerned with the classification and composition of concepts, that is, the composition of possible things in God’s mind. He is concerned with the

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classification and analysis of “universal concepts, i. e., ideas, and their combinations”. 78 As I noted earlier, the ‘combination of universal concepts’ results in complex concepts and Leibniz’s following remark reveals that the increase of complexity in concepts contributes to their individuality. “So I say that gold is greater than metal, since more is required for the concept of gold than for that of metal and it is a greater task to produce gold than to produce simply a metal of some kind or other. Our language and that of the Scholastics, then, is not contradictory here, but it must be distinguished carefully”.79 By generalizing the above example, we can illustrate Leibniz’s inversion80 of the Scholastic extensional model as follows: In the Scholastic model, the terms ‘material things’, ‘solids’, ‘metals’ and ‘golden things’, denote classes of things in which the above predicates are instantiated, namely, the class of material things, which is larger than the class of solids, which is larger than the class of metals, which is larger than the class of golden things. By contrast, in Leibniz’s model, the terms ‘matter’, ‘solid’, ‘metal’ and ‘gold’, denote universal concepts included in a more particularized concept: the concept of matter is included in the concept of a solid; the concept of a solid in the concept of metal; and the concept of metal in that of gold; and all the above are included in the concept of a particular golden thing. While the universal concepts are combined in various ways, individual concepts are formed as a unique combination and internal organization of universal concepts. In turn, universal concepts figure as the predicates of an individual concept (e. g., ‘metallic’ in a golden ring). When Leibniz says that ‘it is a greater task to produce gold than some kind of metal’, he is not making a point in alchemy, or a remark on manufacturing gold; rather, it is a remark about the composition of concepts in God’s mind. Since the concept of gold is more inclusive and more complex, it is also more particular than the concept of metal. Since the concept of gold includes some universal concepts that distinguish it from the concept of metal, it is more particular.81 As Leibniz clarifies, “The concept of metal, regarded absolutely and taken in itself, does not involve the concept of gold; for it to do so, something must be added. This ‘something’ is the sign of particularity; for there is some certain metal which contains the concept of gold”. “[...] for although metal does not by itself contain gold, nevertheless some metal, with some addition or specification

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(e. g., ‘that which makes up the greater part of a Hungarian ducat’) is of such a nature as to involve the nature of gold”.82 This compositional view of individual concepts assumes Leibniz’s view of inclusion, that is, that simpler conceptual constituents are included in more complex concepts. 83 Leibniz says that, “when ‘metal’ is the subject and ‘gold’ the predicate” (as in ‘some metal is gold’) the concept of the predicate and the concept of the subject will be related “as a part to the whole” (i.e., the concept ‘metal’ is a part of the concept ‘gold’). As Parkinson remarks, “[t]o say that the concept of P is included in the concept of S is to say that the concept of P is among those concepts that constitute the concept S”.84 The concept of metal is among the concepts that constitute the concept of gold and is included therein. In this sense, the concept of an individual is always more inclusive than the universal concepts that make it up. 85 The concept of an individual is more inclusive because it is composed of many universal concepts, structured in various ways, as its constitutive parts. In this compositional view of concepts, the more complex a concept, the more specifying predicates it includes. In this sense, complexity contributes to individuality. Two Notions of Composition It is time to observe that two notions of composition (which correspond to two different notions of inclusion and predication) run together in the Leibnizian approach presented above. Let me distinguish between viewing the combinatorial activity as a purely formal mechanism whose products are formal structures (such as sets, sequences, etc.) and viewing these products as concepts that also bear semantic and logical relations to one another. The formal notion is suggested by several Leibnizian examples in which arbitrary letters or units stand for the simple elements which are combined and configured in various ways. The semantic notion is suggested by the linguistic examples and by the illustration of the intensional model just considered. In these examples, the relations between incomplete concepts (such as solid, metal, gold) play a substantial role. In the semantic case, the entailment of a predicate (e. g., of ‘metal’ in the concept ‘gold’) is not simply the entailment of a part in a whole.86 Leibniz’s attempt in his Numerical Characteristic of 1679 to assign numbers to notions (and particularly prime numbers to simple notions) suggests an attempt to reconcile these two notions of composition.87 It seems to me that the conjunction of the semantic and the formal notions of composition does not indicate a confusion on Leibniz’s part; rather, it

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serves the particularization of individual concepts. The semantic notion implies a crucial element lacking in the formal one, namely, relations of accord and exclusion among the predicates of complete concepts. Without such relations, it is hard to see how the notion of self-consistency (which is so central for Leibniz) could even play a role in the construction of concepts. Further, if all simple forms were positive and compatible, the result of any logical conjunction of them would be compatible. If this were the case, self-consistency, as a constraint on the construction of concepts, would be empty and redundant. In addition, without exclusion relations, there wouldn’t be different individual concepts but one big concept consisting of all attributes. The Leibnizian examples noted above and the point just made suggest that, in Leibniz’s eyes, the two conceptions of composition are reconcilable. This supposition, however, seems to involve a difficulty. If the simple elements themselves lack semantic content, how do complex notions have such content? In response, one may suggest that the semantic content of complex notions may be related to the composition of elements. Whereas the simple forms lack semantic content, their products may acquire such content through their composition with others. In current terminology, we might say that semantic content emerges from the complexity. In our context, this means that the composition of constituents contributes something to the resulting product which is more than the mere sum of the constituents. As an analogy, consider the letters of the alphabet as elements lacking semantic content. On the basis of something like Frege’s context-principle (namely, that only in the context of a proposition do words have meaning), and the premise that the meaning of single words is their contribution to the truth value of the proposition, we can say that words by themselves (which are, formally speaking, combinations of letters) are not fully meaningful and that only sentences (that is, combinations of words) have full semantic content. Similarly, we might consider the suggestion that complex notions acquire semantic content by virtue of their combination with other elements. Part of the meaning of the elements may be understood through the complex structures they serve to construct. Only in the context of a complex structure, does it make sense to talk about the contribution of its constituents. Such a view suggests not only a reconciliation of the two notions of composition noted above (the formal and the semantic) but also their mutual contribution to the production of concepts. This suggestion implies that the notion of composition through combinatorial operations may itself play a role in the emergence of the semantic content of terms and concepts.88

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Universal Forms and Individual Forms 89 As noted, Leibniz conceives of individual concepts as complex combinations of universal forms or predicates. Combinatorial operations on the universal forms produce conceptual complexes which, being unique structures of predicates, may be regarded as concepts of individuals. Whereas the relation between a universal form and its instantiations (the things in which the form is instantiated) is one-to-many, the relation between an individual form and its instantiation is one-to-one. In Leibniz’s view of possibility, both types of forms play an essential role; they need not, therefore, be considered as mutually exclusive but rather as complementary. According to the Leibnizian view sketched above, individual forms are the products of God’s operations on his universal forms. As I have already suggested, Leibniz interprets God’s simple attributes as universal forms in the sense that they are instantiated in many concepts of individuals. As such, God’s simple forms hold a one-to-many relation to individual concepts and, of course, to created individuals as well, (e. g., as the concept ‘solid’ is related to concepts of solid things and to created solid things). The relation between an individual concept and its created counterpart, if it is created, is one-to-one. This allows Leibniz to accept universal forms (albeit in a somewhat idiosyncratic sense) and to see individual forms as combinations of them.90 God’s Combinatorial Activity Redescribed The combinatorial activity in God’s mind thus produces: (a) complex concepts out of simple ones, that is, complex structures out of structureless elements; (b) representable concepts out of unrepresentable simple forms (as a consequence of Leibniz’s view of representation); (c) individual concepts out of universal concepts; and (d) possible individuals out of actual universal forms. 2.4 A Divine Production Rule and the Concept of an Individual As we have seen, Leibniz holds that an individual concept entails many – in fact, infinitely many – predicates. It is natural, of course, to seek a definition of an individual concept as a sum of its predicates.91 This view raises the following question: how can an infinite number of predicates be characterized such that they are seen as one whole and are all included in one subject? Enumerating or considering the sum of an infinite number of predicates is clearly unhelpful, as Leibniz is acutely aware.92 What seems

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required here is something that would both unify and entail all the various constituents. Leibniz writes: “Whenever it is said that a certain infinite series has a sum, I am of the opinion that all that is being said is that any finite series of the same rule has a sum, and that the error always diminishes as the series increases, so that it becomes as small as we would like” (A 6.3 503). As Levey remarks, “’Infinite series’ are thus construed as uncollected, or at most finitely collected, multitudes of numbers obeying a certain rule. Such a rule is what he will often refer to as “the law of the series” (Levey 1998, 139). We might therefore consider the rule that generates an infinite sequence of predicates in God’s mind rather than the sum of predicates as a candidate for individuation. The rule according to which God mentally combines his forms may serve to characterize an infinite whole (which corresponds to an individual concept) and to distinguish it from other (finite and infinite) complexes. Such a rule can be seen as akin to an algorithm that compounds predicates so that a unique and complete combination of forms results in God’s mind. According to this view, individual concepts will always differ in their method of production – that is, in the rule generating their unique structure. This points to the essential role the method of production plays in individuation according to Leibniz.93 Let us examine whether the method of producing individual concepts can be related to the notion of rule of action in God’s mind. In the De Summa Rerum, Leibniz defines a rule [regula] as “an instrument of action, determining the form of the action by the perpetual and successive application of the agent to the parts of the instrument”.94 As Mercer and Sleigh note, “a rule”, according to Leibniz, “not only specifies what the actor does, but the order in which she does it”. 95 It is also important that, in this context, Leibniz distinguishes a rule (regula) from a law (lex). 96 According to Leibniz, there could be a law which is not a rule, since a rule is a principle which involves an agent as distinct from a mere mechanical operation. For Leibniz, God is an active agent. He states that God is ‘a person, a mind’ who is “absolutely active”. 97 Given this view of God as an active agent, we may ascribe the above description of ordered, rule-governed action to God’s intelligible activity. If we take the ‘agent’ in the passage cited above as God, ‘parts of the instrument’ as God’s forms, and ‘perpetual and successive application’ as God’s operations on himself, we obtain the view of divine action that I have ascribed to Leibniz with one important addition: God’s activity is now seen as rule-governed and as unifying many predicates into one whole. For each one of God’s rules of action corresponds its ordered result, that is, an

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infinite structure of predicates produced by the ‘perpetual and successive application of the agent to the parts of the instrument’. Each individual concept is seen as a unique structure of predicates which is produced according to a certain rule of thought in God’s understanding. The reiterative operations implied by the notion of a rule generate an infinite structure of predicates. In this way, the rule can be said to entail all the predicates that its application generates. We can conceive of such a rule as similar to formulas of mathematical series whose definition yields an infinite extension. However vague, this notion of a production rule may serve Leibniz in characterizing the principle generating and unifying all the non-relational predicates of an individual concept. As the unifying principle of a maximally consistent structure of predicates, the rule can be regarded as the source of unity and individuality of an individual concept. 2.5 Conclusion As we have seen, attempting to describe the combinatorial activity in God’s mind in detail is a frustrating affair. Leibniz treats both the elements and the combinatorial operations as variables which are to be substituted according to their application in particular domains. As we have also seen, Leibniz has good reasons for doing so. His commitment to isomorphic relations between a symbol and the thing symbolized rules out the possibility of representing structureless atoms. As the source of all possible things, God’s combinatorial activity is inherently general and thus defies specification. In order to illustrate Leibniz’s combinatorial scheme we must use analogies and examples which can serve as partial illustrations. Nevertheless, the general outlines of the combinatorial activity in God’s mind allow us to draw a rough sketch of Leibniz’s view of the formation of concepts and to raise some suggestions regarding the formation of individual concepts. In his view, the progressive combination of simple forms produces complex concepts. This progressive composition assigns an infinite number of predicates with various degrees of complexity to distinct complex structures. The unification of predicates into unique structures, according to their rules of production, serves to construct concepts of individuals. As the degree of complexity of predicates and the structures in which they are included increases, the particularization of the complex concept increases as well. This applies in both the formal and the semantic senses of inclusion. Through their composition, complex concepts become more and more particularized. Particularization is

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achieved not only by virtue of the predicates that constitute the complex structures but also by virtue of their internal organization. Furthermore, through their composition, the terms of complex concepts may acquire semantic content and logical relations between them, which may help to account for exclusion relations among them. Thus a basic individual concept should not be seen as a mere set or conjunction of predicates; rather, it should be seen as an ensemble of predicates which is unified and structured in a unique way according to a unique rule, i. e., its method of production. I have suggested that the internal ordering of individual concepts results from the rules that generate them. These rules of God’s thinking incorporate predicates into consistent, ordered and unique conceptual wholes. Such concepts are saturated in the sense that no predicate needs to be added in order to make them unique. 98 The production rule gives such a concept its unity and individuality. In this sense, the production rule may be seen as the logical subject of a possible individual and its source of individuation. The logical subject of a possible individual includes all its predicates and thus provides the basis for Leibniz’s view of the complete concept. I should stress, however, that it only provides the basis for a complete concept of an individual. For the individual concept as described in this chapter includes only monadic or non-relational predicates. To arrive at a complete concept, the issue of relations has to be brought into the picture. As I will argue in the next chapters, individuality is completed, according to Leibniz, through relations to other such basic concepts. As we shall see, it is equally important to stress that these relations are grounded in the non-relational predicates, whose formation as concepts in God’s mind I illustrated above. In closing, let me anticipate two points that I will take up in chapters 5 and 6: (1) A complete concept constitutes a unique program for the activities and eventual development of an individual substance – as Rescher puts it, a ‘conceptual blueprint for possible things’. As we shall see in chapter 5, this suggestion coheres with Leibniz’s definition of an actualized individual substance in terms of an internal source of activity that defines its unique course of action. Upon creation, the production rule that generates a possible course of action in God’s mind may also serve to realize this course of action in a created, individual substance. The production rule of an individual may be considered as the forerunner of the source of unity and activity in created substance – what the tradition (Leibniz attempts to rehabilitate in 1695) assigned to the substantial form.99

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(2) As we shall see in chapter 6, viewing the complete concept of an individual as a program of action may help to approach Leibniz’s claim that human actions are entailed in their concepts and yet need not be seen as necessary consequences of them.

1

See GP II, 40. For a more comprehensive description of Leibniz’s Nominalism, see Fichant’s “De l’individuation à l’individualité universelle”, in Fichant, Science et metaphysique dans Descartes et Leibniz, 1998, p. 147. 3 Fichant: “De l’individuation”, in Fichant 1998, p. 148 (my translation). In his early work Metaphysical Disputation on the Principle of the Individual (Disputatio metaphysica de principio individui, 1663), Leibniz concluded that an individual should be identified with its “complete or total entity”. For details, see McCullough: “Leibniz’s Principle of Individuation in his Disputatio metaphysica de principio individui of 1663”, in Barber and Gracia (eds.), Individuation and Identity in Early Modern Philosophy, 1994, pp. 201-217. 4 Mugnai: “Leibniz on Individuation: From the Early Years to the ‘Discourse’ and Beyond”, Studia Leibnitiana 33, 2001, p. 43. 5 For details of Leibniz’s development up until the Discourse on Metaphysics in 1686, see Mugnai, “Leibniz on Individuation”, (2001); Rauzy, La doctrine leibnizienne de la vérité, Paris 2001, pp. 299-308; Mercer and Sleigh, “Metaphysics: The Early Period to the Discourse on Metaphysics”, in Jolley (ed.), The Cambridge Companion to Leibniz, Cambridge 1995, pp. 67-123. 6 Mates suggests that “we interpret the term ‘possible world’ as referring for Leibniz to a set of individual concepts, and not to a set of individuals. In that way he can avoid introducing a shadowy realm of ‘possible individuals’ […]” (Mates, “Leibniz on Possible Worlds”, reprinted in Woolhouse (ed.), G. W. Leibniz. Critical Assessments, 1994, vol. 1: pp. 210-211. Recently Rescher formulated this point as follows: “A possible substance is – and must be – individuated through its complete description, its individual notion” (Rescher, “Leibniz on Possible Worlds”, Studia Leibnitiana 28, 1996, p. 132). 7 A 6.1 202; Leibniz: Logical Papers: A Selection, (trans. and ed.), Parkinson, 1966 (PLP), p. 11. 8 Couturat: La Logique de Leibniz, Paris 1901 (reprinted Hildesheim 1961), p. 241. See J. B. Rauzy: “Quid sit Natura Prius”, in Revue de Métaphysique et de Morale 100/I (1995), pp. 31-48. 9 The appeal to God’s thinking should not be confused with any kind of psychologism, especially not in the present context of producing (or thinking) all possibilities. Rather, God’s thinking is much closer to our sense of logic than to our sense of psychology. I wish to stress, however, that Leibniz’s view of logic and his view of the definition of concepts involves a thinking agent. It seems to me that the notion of God as a thinking agent plays an important role in his logic – 2

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a role that cannot be dismissed merely on account of Leibniz’s theological assumptions. 10 See GP IV, 65; Couturat: La Logique de Leibniz, p. 41 note 1. 11 “Item tot posse esse substantias singulares quot sunt diversae combinationes omnium attributorum compatibilium. Et hinc patet principium individuationis, de quo irritae habentur multorum Scholasticorum concertationes” (A 6.4. 306). 12 The most important exception familiar to me are the works of Fichant, collected in Fichant: Science et metaphysique (1998). It is not surprising that commentators have avoided examining this topic thoroughly. As we shall see, it is quite frustrating. Nevertheless, the project is worth pursuing as it yields some deep insights into the conceptual and historical foundations of Leibniz’s philosophy. 13 For a survey of Leibniz’s philosophical commitments from his youth to the Discourse of Metaphysics (1686), see Mercer and Sleigh: “Metaphysics” in CCL. 14 See Fichant: “De l’individuation”, in Fichant 1998, pp. 148-149. 15 This distinction has been noted by several commentators. For example, G. Brown, “Compossibility, Harmony, and Perfection in Leibniz”, 1987, p. 184; Cover and O’Leary-Hawthorne, Substance and Individuation in Leibniz, 1999. 16 In the De Summa Rerum, Leibniz also calls them the “elements of thinking”, e.g., A 6.3 504; SR, p. 53, see also GP IV 296. 17 A 6.4 590; GP IV, 425; L, 293. According to Leibniz, “[a]n ‘attribute’ is a necessary predicate which is conceived through itself, or, which cannot be analyzed into several others” (A 6.3 574; SR p. 95). 18 A 6.3 520; SR, p. 79. 19 Rescher made this point as follows: “Every substance-descriptive permutation and combination of properties that is internally coherent – consistent with the laws of logic – will figure in the wider scheme of things that is represented by the manifold of possibility-at-large” (Rescher, “Leibniz on Possible Worlds”, 1996, p. 134). 20 Leibniz’s aim was to support the proof that derives God’s existence from his concept. Descartes and his predecessors did not prove the premise that the concept of ‘the most perfect being’ is consistent. In order to derive God’s existence from the concept of God, one has to first show that that concept is possible (i. e., selfconsistent). 21 “Demonstrationem reperisse videor, quod Ens perfectissimum, seu quod omnem Essentiam contineat, seu quod omnes habeat Qualitates, seu omnia attributa affirmativa, sit possibile, seu non implicet contradictionem. Hoc patebit si ostendero omnia attributa (positiva) esse inter se compatibilia. Sunt autem attributa aut resolubilia, aut irresolubilia, si resolubilia sunt erunt aggregatum eorum in quae resolvuntur; suffecerit ergo ostendisse compatibilitatem omnium primorum, sive irresolubilium attributorum, sive quae per se concipiuntur, ita enim si singula compatibilia erunt, etiam plura erunt, adeoque et composita. Tantum ergo suffecerit ostendere Ens intelligi posse, quod omnia attributa prima contineat, seu duo quaelibet attributa prima esse inter se compatibilia”; A 6.3 572; SR, p. 91-93. As Leibniz is well aware, this is far from being self-evident. He exposes the contradictions that arise in notions such as ‘the number of all

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numbers’ and ‘the most rapid motion’. He is clearly aware of the logical similarity between the structure of these notions and that of ‘the most perfect being’ or ‘the subject of all positive attributes’ and attempts to argue that in the latter notion, a contradiction may be avoided. For a discussion of this point, see Nachtomy, “Leibniz on the Greatest Being and the Greatest Number”, The Leibniz Review, 2005, pp. 49-66 22 A 6.3 573; SR, p. 93. 23 For a detailed analysis of this argument, see Adams, Leibniz. Determinist, Theist, Idealist, 1994, pp. 142-151. For other critiques, see Russell, A Critical Exposition of the Philosophy of Leibniz, 1937, and Fichant, Science et metaphysique 1998. For example, the argument makes the questionable assumption that the compatibility relation among simple forms is transitive. In his “L’origine de la négation” (in: Fichant: Science et metaphysique 1998, pp. 85119), Fichant has argued explicitly and convincingly that it is not transitive. The argument also assumes that the compatibility of composite forms depends on the compatibility among the simple forms. However, if this point is generalized, it is hard to see (a) why Leibniz insists on self-consistency among the constituents of a complex concept and (b) how a variety of concepts may arise. If complex concepts cannot exclude one another, then the result of their combination would be one large concept consisting of all forms. 24 In his complementary proof, “A Most Perfect Being Exists” (“Ens perfectissimum existit”), he writes, “[p]erfections, or simple forms, or absolute positive qualities, are indefinable or unanalyzable” (A 6.3 575; SR, p. 97). Interestingly, Leibniz adds a variation of this point in terms of thinkability. He continues the passage as follows: “or, the thought which is had of them cannot be analyzed into other more simple thoughts” (ibid.). I take it that it is primarily the thoughts of God that he has in mind here. 25 See A 6.3 574. 26 It may be objected that this problem arises because we suppose that individual concepts are produced by combinations of simple forms and that, in fact, Leibniz presupposes backwards order so that God starts with complete concepts and analyses them into simpler constituents. In response, let me first remark that the order in question is, of course, not temporal but logical or mathematical-like. Now from this formal point of view, it may seem that it does not matter at all whether one goes from the simple to the complex or vice versa. However, I think that Leibniz’s stress on the notion of natural priority of the simple over the complex speaks strongly for my recursive construal of the production of possibilities. Yet I admit that the issue is far from clear cut and that it requires further investigation. 27 “Non videtur satis in potestate humana esse Analysis Conceptum, ut scilicet possimus pervenire ad notiones primitivas, seu ad ea quae per se concipiuntur”; A 6.4 530 (C, 514); the translation is in Leibniz: Philosophical Writings, ed. and trans. M. Morris and G. H. R. Parkinson, London 1973, p. 8. 28 “[…] although characters are arbitrary, their use and connection have something which is not arbitrary, namely a definite analogy between characters

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and things, and the relations which different characters expressing the same thing have to each other” (“Nam etsi characteres sint arbitrarii, eorum tamen usus et connexio habet quiddam quod non est arbitrarium, scilicet proportionem quandam inter characteres et res; et diversorum characterum easdem res exprimentium relationes inter se”; A 6.4 24 (GP VII, 193); Loemker, p. 184; see also C, 151152). For more details, see Rutherford: “Philosophy and Language in Leibniz”, in Jolley: Cambridge Companion to Leibniz, 1994, pp. 224-269. 29 See “What is an Idea” (“Quid sit idea”); A 6.4 1369-1371 (GP VII, 263264), and Rutherford: “Philosophy and Language” (1994). 30 This does not imply that the simple elements lack peculiar characteristics and must be regarded as mere placeholders. Rather, as Fichant argued, the elements must differ from one another in order to account for the exclusion relations between them. “Leibniz says that ‘there are no purely extrinsic denominations’ because the reasons why things enter into certain relations stems from their ‘internal structure’, what they are. There are no purely externally imposed relational structures”. What I wish to point out here is that, if considered in themselves, the simple elements cannot be represented. 31 A similar argument is put forward by Rutherford in his “Philosophy and Language” (1994). From a contemporary point of view, this argument is not entirely convincing. A simple element can still have an internal structure and it can also be considered through its role in complex structures. For example, one can identify an atom indirectly through its contribution to the molecules in which it appears and the molecules in which it can appear. 32 A recent example of such an approach can be found in L. Wittgenstein’s Tractatus Logico-Philosophicus, 1922. 33 A 6.3 475; SR, p. 29. 34 “Deus non est quiddam Metaphysicum, imaginarium, incapax cogitationis, voluntatis, actionis, qualem nonnulli faciunt, ut idem futurum sit ac si diceres Deum esse naturam, fatum, fortunam, necessitatem, Mundum, sed Deus est Substantia quaedam, Persona, Mens. [...] Ostendendum est Deum esse personam seu substantiam intelligentem”; A 6.3 474-475; my translation. See also Loemker, p. 158; SR, p. 27. 35 A 6.3 520; SR, p. 70. 36 A classical source for the reflexive activity of a mind is Aristotle’s notion of ‘Nous’ – a mind contemplating itself. In the Paris notes, Leibniz often remarks on the beauty and philosophical importance of self-reflection. For example, in a paper dated April 1676, entitled “On Reminiscence and on the Mind’s Self-Reflection” (“De reminiscentia et de reflexione mentis in se ipsum”), he writes: “The following operation of the mind seems to me to be most wonderful: namely, when I think that I am thinking, and in the middle of my thinking I note that I am thinking about my thinking, and a little later I wonder [...] at this wonder, and fixed in one contemplation I return more and more into myself, alternately as it were, and often elevate my mind through my thoughts” (“Operatio mentis maxime mira mihi illa videtur, cum cogito me cogitare, et inter cogitandum, hoc ipsum jam

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noto, quod de cogitatione mea cogitem, et paulo post miror [...] ipsam admirationem, obtutuque defixus in uno, velut per vicem magis magisque in me redeo, et saepe cogitationes ipse meas animum elevo”; A 6.3 516; SR, p. 73). After considering further “reflections of reflections” he says at the end of this paper: “[...] the perception of a perception to infinity is perpetually in the mind” (A 6.3 517; SR, p. 75). 37 I use the notation of set theory in order to illustrate how reiterative operations on simple elements may produce infinite structures. The analogy with set theory has its limits though, especially with respect to the unique character of the simple elements noted above. 38 With this conception of God’s activity, we can clarify some of Leibniz’s otherwise obscure remarks. For example, he says that, “[i]f some mind thinks nothing in particular, but thinks nevertheless, it will be God, or, it will think all things” (A 6.3 512; SR, p. 65). God does not think particular things but rather his own forms. Leibniz also says that, “thinking is absolute when that which thinks itself is all things” (A 6.3 518; SR, p. 75); and that, “God is the perfect mind, and that mind is the cause of its own perceptions” (A 6.3 516; SR, p. 71). God’s reflexive operations bring about his own [complex] perfections by composing them out of simple ones (see A 6.3 475; SR, p. 29). 39 “But when the tables or categories of our art of complication have been formed, something greater will emerge. For let the first terms, of the combination of which all others consist, be designated by signs; these signs will be a kind of alphabet. [...] If these are correctly and ingeniously established, this universal writing will be as easy as it is common, and will be capable of being read without any dictionary; at the same time, a fundamental knowledge of all things will be obtained” (“Verum constitutis Tabulis vel praedicamentis artis nostrae complicatoriae majora emergent. Nam Termini primi, ex quorum complexu omnes alii constituuntur, signentur notis, hae notae erunt quasi Alphabetum. [...] Ea si recte constituta fuerint et ingeniose, scriptura haec universalis aeque erit facilis quam communis, et quae possit sine omni lexico legi, simulque imbibetur omnium rerum fundamentalis cognitio”; A 6.1 202; PLP, p. 11). 40 In drawing this analogy, however, we should observe that, to some extent, one smuggles some of the syntax and formation rules of natural language into the combinatorial scheme. This analogy tacitly introduces the notion of ordering the letters in certain ways: for instance, in linear sequences of rows and columns, to be read from right to left or from left to right. 41 Note that this analogy tacitly introduces the notions of subject and predicates which Leibniz indeed seems to presuppose. 42 There is an additional restriction on the production of worlds, namely, the compossibility among individuals. As Fichant (in his “L’origine de la négation” in Fichant 1998) argues, compossibility among individuals is different from compatibility among simple forms. 43 A 6.3 515; SR, p. 71.

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In fact, being formal, it seems almost empty of information. This of course, is among the very characteristics of a symbolic or logical calculus. Hence, this is not a criticism. What is curious is that, in spite of the formal (or the quasi-formal) character of his scheme, Leibniz thinks that, on the one hand, it lays down the general rules of producing all things and, on the other, it is the key to obtaining knowledge of all things. Moreover, Leibniz seems to hold the view that one can move from formal to empirical knowledge by substituting general symbols with empirical statements in particular domains. 45 In Russell, “Recent Work on the Philosophy of Leibniz”, in Frankfurt (ed.), Leibniz: A Collection of Critical Essays, 1972, p. 379. See also A 6.4 196 (C, 50 § 5); PLP, p. 18: “we shall use letters (such as a, r, [...]) when numbers are either not available, or they are at any rate being treated generally and not considered specifically. This we must do here, when we are establishing the elements of the subject. The same thing is done in algebra [...]”. 46 That is not to say that constants cannot stand for numbers in algebra. 47 “Combinatoria agit de calculo in universum, seu de notis sive characteribus universalibus (quales sunt a, b, c, ubi promiscue alter pro altero sumi potuisset) deque variis legibus dispositionis ac processus seu de formulis in universum. Calculus algebraicus est species quaedam certa calculi generalis, lex verbi gratia multiplicationis est, ut quaevis pars multiplicantis, cuivis parti multiplicandi combinetur”; A 6.4 511 (C, 556); Rutherford: “Philosophy and Language” (1994), p. 238. 48 “Ego vero agnosco, quicquid in hoc genere praebet algebra, non nisi superioris scientiae beneficium esse, quam nunc combinatoriam, nunc characteristicam appellare soleo, longe diversam ab illis, quae auditis his vocibus statim alicui in mentem venire possent”; A 6.3, 331; Loemker, p. 166; my italics. 49 Couturat: La Logique de Leibniz (1961), pp. 299-300; my italics; see also the citations on pp. 299, 288, 287 note 2. While Couturat believes that this applies primarily to human thought, I believe that, in the context of possibility, the combinatorial scheme serves to model God’s thought, even if humans must pursue this task by means of symbols. 50 I believe that this conception of logic as intrinsically related to the combinatorial activity of God’s mind shows that the question of whether Leibniz’s metaphysics derives from his logic or vice versa is misguided. 51 A 6.3 399; SR, p. 115. 52 There is a very close connection between the question of the relation of all relations, the number of all numbers (which Leibniz raises in the same passage) and Russell’s paradox of the set of all sets. It is of historical interest to know whether Russell’s paradox was inspired in some way by his extensive study of Leibniz’s texts. For Leibniz, ‘the number of all numbers’ was a paradigmatic example of a contradiction. Russell was clearly influenced by Cantor and it is noteworthy that, if one thinks of numbers as sets, Leibniz’s ‘number of all numbers’ paradox and the ‘set of all sets’ paradox have very similar structures. 53 A 6.3 399; SR, p. 115.

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A 6.3 518-519: SR, p. 77. See also A 6.3 523; SR, p. 83; A 6.3 512; SR, p. 67 for similar analogies and A 6.3 521; SR, p. 81. 55 In the “Confessio philosophi” of 1673 (A 6.3 115-149), Leibniz explicitly intends to exemplify the essence of God with his numerical analogy (see A 6.3 139-140. Like any analogy, this one has its limits: in some places, Leibniz says clearly that God’s forms are infinite, but in others he tends to minimize the number of elementary forms. 56 A 6.3 523; SR, p. 85. It is crucial that the forms be different. As Fichant argues, the diversity of forms is the only source of negations and incompatibility relations among forms. In other words, diversity in the forms makes exclusion relations among the forms possible. 57 Note that an individual essence is seen here as entailing many properties and truths, which points to the type of complexity Leibnizian individuals admit. 58 In “Meditation on the Principle of the Individual” (“Meditatio de principio individui”), A 6.3 490-491; SR, pp. 51-53, Leibniz clearly argues that two forms that seem identical must differ in their method of production. 59 “[...] quomodo divinae essentiae visio crescere possit non capio, nam si essentiae est, exacta est; si exacta est, crescere non potest”; “Confessio philosophi”; A 6.3 139 (translation in Confessio, Sleigh 2005, p. 85). 60 “Potest crescere etiam exacta cognitio, non materiae sed reflexionis novitate; si novem unitates expositas habeas, exacte novenarii essentiam comprehendisti, proprietatum autem omnium etsi materiam haberes, at non formam tamen seu reflexionem, nam etsi ter tria, quatuor et quinque, sex et tria, septem et duo esse novem et mille alias combinationes non observes, non eo minus essentiam novenarii cogitasti. Nihil addo de collatione novenarii cum aliis extra ipsum unitatibus, quia ita non forma tantum sed et materies cogitationum variatur, [...]”; “Confessio philosophi”; A 6.3 139 (translation by Sleigh, p. 85). 61 “[...] quod in Deo, qui cum omnia intra se habeat, nulli extra se comparari potest, [...]”; “Confessio philosophi”; A 6.3 139 (translation by Sleigh 2005, p. 85). 62 “Dabo igitur exemplum rei finitae, infinitas proprietates, sine ulla cum rebus extraneis comparatione, praebentis. Ecce circulum intuere, si scias omnes lineas a centro ad circumferentiam esse aequales, satis lucide opinor essentiam eius, non ideo et theoremata innumerabilia comprehendisti, nam tot figurae diversae, eaeque regulares, circulo inscribi possunt (id est etsi non designentur, jam tum insunt) quot sunt numeri, ergo infinitae, quarum nulla est, quae non ingentem theorematum materiem suppeditaret indaganti”; (“Confessio philosophi”; A 6.3 139-140, translation by Sleigh 2005, p. 85). 63 As Dascal notes “[w]e [humans] cannot have the idea of a circle, only a definition of it. The full idea – including all its consequences – can be only conceived by God simultaneously” (La Sémiologie de Leibniz, 1978, p. 183). 64 See also A 6.3 523; SR, p. 85. 65 “On the Secrets of the Sublime, or on the Supreme Being” (“De arcanis sublimium vel de summa rerum”); A 6.3 475; SR, p. 29. God does not think

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everything because the conjunction of all things, taken as a whole, may evoke a contradiction. See Parkinson’s comments on this passage in SR, p. 129 notes 18 and 19. 66 “Ideas exist in God in so far as the most perfect being arises out of the conjunction in the same subject of all possible absolute forms or perfections; but from the conjunction of simple possible forms there result modifications, that is, ideas, as properties result from an essence” (A 6.3 521; SR, p. 81). 67 Note that in the context of producing all possible things, there is no reason to exclude any one of these models since a unique model does not achieve the aim of producing all intelligible concepts. 68 Mates: “Individuals and Modality in the Philosophy of Leibniz”, 1972, pp. 89, 110. 69 In his “Individuals and Modality in the Philosophy of Leibniz”, Mates writes: “If, with Leibniz, we consider Adam’s concept to be just the set of his simple attributes […]” (Mates 1972: “Individuals and Modality”, p. 110). In “Leibniz on Possible Worlds” section 2, he writes: “Thus a complete individual concept is a set of simple attributes jointly satisfiable by exactly one individual” (Mates: “Leibniz on Possible Worlds”, p. 210). In his “De l’individuation a l’individualité universelle” Fichant writes: “La doctrine combinatoire du concept permettait de définir le concept du sujet unique S d’une suite quelconque de propositions vraies ‘S est P1’, ‘S est P2’, ‘S est Pn’, etc.” (Fichant: “De l’individuation” (1998), p. 149). See also Adams: Leibniz. Determinist (1994), p. 65. 70 To illustrate this point, consider a biological example, namely, the DNA molecule. We know that a sequence of four basic nucleotides (A, G, C and T), which, in effect, reduces to two couples (since they form two pairs in the sequence), is sufficiently rich to encode the genetic information of any set of properties of a biological individual. The capacity of the DNA molecule to contain such a huge amount of information in each individual and allow for great variety among individuals by changing the order of a few elements is quite remarkable. This example emphasizes the point that to construe Leibniz’s combinatorial method of producing concepts as a mere logical conjunction would be to miss one of his most profound insights, namely that of internal ordering. Even for finite sequences such as that in DNA, the order is a rich enough source of information and variety. As a referee to this journal remarks, “ordering is not merely linear (the kind of order that logic prefers) but spatial. The linear ordering of DNA is indeed important for its ‘meaning’ and causal efficacy, but the efficacy and communicative ability of biological molecules generally lies in their complex spatial configurations, as does incidentally the intelligibility of the things of geometry”. I think that the significance of spatial order contributes to appreciate Leibniz’s insight that considerations of form are of great importance for individuation. 71 “Elementa calculi”; A 6.4 195-205 (C, 49-57); PLP, pp. 16-24. 72 A 6.4 195 (C, 49); PLP, p. 17. Leibniz adds that “the categorical proposition is the basis of the rest, and modal, hypothetical, disjunctive and all other propositions presuppose it” (A 6.4 195 (C, 49); PLP, p. 17).

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A 6.4 200 (C, 53); PLP, p. 20. Parkinson: “Philosophy and Logic”, in: Jolley (ed.), Cambridge Companion to Leibniz (1994), p. 201. 75 Moreover, as a nominalist, he does not believe that uninstantiated universals exist. The universal forms we are considering as part of Leibniz’s realm of possibilia are instantiated in possible individuals and possible individuals do not exist other than as thoughts of God. For this reason, I think that Leibniz’s position with respect to possibility is better characterized as conceptualism rather than nominalism. 76 A 6.4 200; C, 53; PLP, p. 20. 77 “The finger is in the hand and generally the part in the whole” (Aristotle: Physics, n, 3 210a - 15-16). “Man is in animal and generally the species in the genus” (Physics, n, 3 210a 18), Categories, chapter 5. There are other pronouncements in Aristotle’s corpus which do not fit the above model. The purpose of using the Aristotelian classification system here is only to facilitate the presentation of a Leibnizian view of individual concepts. 78 A 6.4 200; C, 53; PLP, p. 20. 79 “Itaque dico aurum majus metallo, quia plura requiruntur ad notionem auri quam metalli, et majus opus est aurum producere, quam metallum qualecunque. Nostrae itaque et scholarum phrases hoc loco non quidem contradicunt sibi, distinguendae sunt tamen diligenter”; A 6.4 200 (C, 53); PLP, pp. 20-21. 80 “[...] we could prove all the rules of logic by a calculus somewhat different from the present one – that is, simply by a kind of inversion of it” (A 6.4 200; C, 53; PLP, p. 20). As Couturat notes, this inversion does not work in the syllogism. 81 Cf. “Nouveaux essais” (NE) 4.17.8; A 6.6, 486. 82 “Ita notio metalli absolute spectata et in se sumta non involvit auri notionem; et ut involvat addendum est aliquid. Nempe signum particulare: quoddam metallum, est enim certum quoddam metallum quod auri notionem continet”; “[...] licet enim metallum per se non contineat aurum tamen quoddam metallum cum addito seu speciale (exempli causa id quod majorem ducati Hungarici partem facit) ejus naturae est, ut naturam auri involvat”; A 6.4 198-199 (C, 51-52); PLP, p. 19. Cf. Adams: Leibniz. Determinist (1994), p. 59. 83 “[T]he concept of gold and the concept of metal differ as part and whole; for in the concept of gold there is contained the concept of metal and something else – e. g., the concept of the heaviest among metals” (“[...] notio auri et notio metalli differunt ut pars et totum; nam in notione auri continetur notio metalli et aliquid praeterea, exempli causa notio ponderosissimi inter metalla”; A 6.4 199-200 (C, 52-53); PLP, p. 20). 84 Parkinson: “Philosophy and Logic” (1966), p. 201. Parkinson also notes that the corollary to this view is the view of a true proposition as identity; not identity in the sense of equality – A is A – but in the sense of inclusion as in “AB is A”, e. g., “a white man is white” (ibid., p. 202). 74

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Conversely, “the concept of the genus is formed simply by casting off [abjectio] from that of the species” (A 6.4 204 (C, 57); PLP, p. 24). According to my interpretation, what is being cast off are universal concepts. See also NE 4.17.8 and Fichant’s comments in: “Leibniz et l’exigence de démonstration des axiomes: ‘La partie est plus petite que le Tout’”, in: Fichant: Science et metaphysique (1998), pp. 329-371, pp. 345-346. 86 Cf. Adams: Leibniz. Determinist (1994), pp. 65-67. 87 A 6.4 221-227; C, 84-89; AG, pp. 10-14. 88 A different way to put this is that Leibniz’s notion of possibility and his notion of meaning are intimately related. Let me just note that this point seems to merit some further examination. 89 Leibniz sometimes discusses this point under the terminology of ‘abstracts’ for universals and ‘concrete’ for particulars. See A 6.3 169-188 where he identifies the abstract with “simple incomplete” and the concrete with “composed (or complex) complete”. 90 The reconciliation of universal and individual forms also permits to view Leibniz’s notion of the individual as a reconciliation of the Platonic notion of abstract essences with Aristotle’s notion of individual essences since Leibniz conceives of individual concepts as combinations of universal essences. 91 See, for example, Rutherford’s Leibniz and the Rational Order of Nature, 126 and the critique of Cover and Hawthorne in Substance and Individuation in Leibniz (1999), 284. 92 This is clear in his observations that the notion of infinite number is impossible since it involves a contradiction (e.g., A 6.3 477; SR 31-33; A 6.3 463; SR 7, A 6.3 168). 93 “In my view, a substance or a complete being is that which, by itself, involves everything, i. e., that for the perfect understanding of which the understanding of anything else is not required. […] Because any complete being whatsoever may be produced in only one way, the fact that figures can be produced in different ways is a sufficient indication that they are not complete beings” (“Substantia seu Ens completum mihi est illud quod solum involvit omnia, seu ad cuius perfectam intelligentiam nullius alterius opus est intellectione. [...] Unumquodque Ens completum non nisi uno modo produci potest: Figurae quod diversis produci possunt modis, satis hoc indicio est non esse Entia completa”; A 6.3 400; my translation. See also SR, p. 115). Concerning Leibniz’s commitment to the connection between the method of production and individuality of complete beings, see also “A Meditation on the Principle of the Individual” (in SR). All possible things are “modes” of God (A 6.3 573; SR, p. 93) and each one corresponds to a unique method of production. 94 A 6.3 483; SR, p. 39. 95 A 6.3 483; SR, p. 39. Mercer and Sleigh: “Metaphysics” (1994), p. 95; my italics. 96 A 6.3 483; SR, p. 39. 97 A 6.3 520; SR, p. 79.

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The question of whether one concept of an individual can be instantiated in another is very interesting. Traditionally, instantiability has been considered a criterion for individuality (see T. M. Lennon: “The Problem of Individuation among the Cartesians”, in: Barber and Gracia: Individuation and Identity (1989), pp. 13-39, pp. 33-36). Despite the compelling intuition of this criterion, I am not sure that Leibniz accepted it in its traditional sense. After all, Leibniz suggests that individuals are nested in other individuals all the way down (e. g., “Monadology” §§ 67-70; GP VI, 618-619). 99 Rescher: “Leibniz on Possible Worlds” (1996), pp. 131-132. See Adams: Leibniz. Determinist (1994), p. 80 and Mercer and Sleigh: “Metaphysics” (1994).

Chapter 3 The Individual’s Place in Logical Space 3.1 Introduction According to Leibniz, the created world consists of individuals and their properties alone. Each individual is self-sufficient. These individuals are causally independent of one another, so that the activity of one individual does not affect the activity of another. In effect, the individuals which constitute the fundamental substance of the world – are characterized by a unique principle of activity, which constitutes the cause and explanation of their properties. Since the activity of one individual does not interfere with the activity of another, perfect harmony reigns among the activities of the individuals. This harmony is pre-established in the sense that God considers the courses of action of all possible individuals in advance of the creation and chooses to create the set of individuals whose realization will bring about maximal harmony.1 As we shall see, God produces possible worlds by considering the compatibility and incompatibility of the eventual activities of all possible individuals in his mind. In this sense, possible worlds can be seen as compossible sets of possible individuals, that is, individuals whose would-be activities are compatible inter se. Thus the causal independence among created individuals implies strict conceptual dependence among possible individuals (of the same world). In other words, the nonexistence of causal relations between real individuals requires compatibility relations between the respective set of possible individuals.2 This is why the context in which the question of interindividual relations arises in Leibniz’s metaphysics extends not only to relations between real, created substances but also to possible ones. As we shall see in the next chapter, this approach will provide some insights into the notion of possible worlds as well. Since Russell’s critique (in 1900), the question of relations among real individuals intrigued many of Leibniz’s commentators (e.g., Rescher, Hintikka, Ishiguro, Mates, and Mugnai, to name a few). Russell argued that Leibniz’s metaphysics cannot accommodate relations and that he must therefore reduce all relational truths to non-relational ones, a reduction which cannot but fail.3 Little effort, though, has been dedicated to the question of relations between possible individuals, which I undertake here. Focusing on relations among possible individuals may help to relieve some of the severe difficulties that are supposed to infect Leibniz’s view of 85

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relations. In the context of possibility – where Leibniz needs relations in order to allow causal independence among real individuals – the ontological status of relations is less problematic, and so is Leibniz’s use of them. In what follows I will discuss primarily the relations between possible individuals. I believe that this perspective affords an interesting and fruitful approach to Leibniz’s notion of relations and to his notions of possible individuals and possible worlds. As I noted earlier, the term ‘possible individuals’ does not indicate real entities, let alone mysterious or shadowy ones. For Leibniz, possibilities are not entities; rather, they are thoughts or concepts. More precisely, possibilities are complex thoughts that are conceived primarily in God’s mind. My point of departure in this chapter is Leibniz’s view of relations as it is formulated in his correspondence with Arnauld (1686-87). Considering the example of the relations between the concept of Adam and the concepts of his posterity (discussed between Leibniz and Arnauld), reveals the following presuppositions in Leibniz’s view of relations: 1. There are relations between the complete concepts of individuals. 2. These relations play a central role in the “construction” of possible worlds, where possible worlds are seen as sets of compossible individuals. 3. Such relations not only play a role in the “construction” of possible worlds but also in the very individuation of the complete concepts of individuals. As we shall see, for Leibniz, the individuation of an individual concept cannot be complete without considering its relations with other individual concepts. Each one of these presuppositions (1-3) is problematic and requires thorough clarification. It is not clear whether these theses are compatible among themselves, let alone with other Leibnizian commitments. My strategy in this chapter is to examine whether the first presupposition (1) is consistent with Leibniz’s nominalistic metaphysics of individuals. Whereas (1) states that “there are relations among complete concepts of individuals”, Leibniz denies the reality of relations. The reconciliation of these two Leibnizian commitments implies that inter-individual relations presuppose the individuals between which they stand (the relata). But this leads to a severe problem of circularity; for, according to (3), the complete concepts of individuals include and, therefore, presuppose relations between them. The attempt to clarify this circularity will place us in a position to clarify Leibniz’s view of relations and the crucial rule they play in individuation.

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3.2 The Example of Adam and His Posterity in the Leibniz-Arnauld Correspondence I now turn to present Leibniz’s view of relations through the example of the relations between Adam and his posterity. On February 1686, Leibniz asked Landgrave Ernest de Hesse-Rheinfels to forward to Arnauld the summary of his Discourse on Metaphysics. Arnauld was immediately intrigued by Leibniz’s claim (13) that “the individual notion of each person includes once and for all everything that will ever happen to him”. Arnauld argued that, if each individual includes all its predicates – past, present, and future – then, such an individual is not free. Arnauld writes: “Si cela est (13), Dieu a été libre de créer Adam ou de ne pas créer Adam; mais supposant qu'il l'ait voulu créer, tout ce qui est depuis arrivé au genre humain, et qui lui arrivera à jamais, a dû et doit arriver par une nécessité plus que fatale. Car la notion individuelle d'Adam a enfermé qu'il aurait tant d'enfants, et la notion individuelle de chacun de ces enfants tout ce qu'ils feraient et tous les enfants qu'ils auraient : et ainsi de suite.” (LR 83)4 Arnauld uses the notion of Adam to illustrate Leibniz’s view of the individual’s notion and its consequences. Arnauld's example also illustrates clearly the question of the relations between the notion of one individual, namely, Adam, and the other notions of individuals which belong to the same world, namely, his posterity (96). He observes that Leibniz's view of an individual leads to a seemingly absurd consequence, namely, that Adam's notion entails (enferme) those of his posterity, and all that they will ever do, and all their posterity, and all that they will ever do, and so, such a notion of Adam presumably entails all the history of mankind. Leibniz's response to Arnauld's example and its allegedly “absurd” consequences is very instructive: Leibniz does not see any absurdity in a concept of Adam so complete that it implies all its posterity, even if it might be an infinite series of individuals; to the contrary, Leibniz accepts Arnauld’s formulation and illustration of his position without reservation.5 What Leibniz does dispute with Arnauld is whether such a view of the individual is compatible with freedom of action. However interesting, the question of freedom is not our present concern. Our concern is what Leibniz and Arnauld presuppose in the sequel of their correspondence, namely, that a notion of an individual is related to the notions of other

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individuals that belong to the same world, such that the creation of one individual necessitates the creation of the other individuals. This view implies that the Leibnizian individuals are related inter se conceptually. For example, a concept of Adam that is not related to Eve as the mother of their children is not the concept of Adam; it is the concept of a different individual who has different posterity and who belongs to a different possible world (LR 108). To distinguish the concept of Adam from other “possible Adams”, one has to specify particular names of other individuals (e.g., Eve), places (e.g., the Garden of Eden), and other particular circumstances with which it is related and which “complete its individuality” (“autre circonstances qui achévent l’individualité”, LR 108). Leibniz says that God did not choose to create an "Adam vague" (87), that is, an indefinite notion of Adam which entails only general characteristics (conceived sub ratione generalitatis). Rather, God chose to create a specified and well-defined notion of Adam. Leibniz writes that, “the nature of an individual [‘which he finds completely formed in his understanding’ (LR 109)] must be complete and determined” (LR 108). For example, that Eve is the mother of his children is constitutive of the complete concept of Adam and, as it turns out, of the complete concept of any member of humankind. Already as a candidate for creation, the content of an individual notion is entirely specified and fixed (LR 116). Furthermore – and this is what really pertains to our present interests – a notion of an individual is specified and determined precisely by its relations with the other individuals and their particular events. In Adam’s case: his presence in the garden of Eden, that he ate a certain apple, that Eve gave birth to his children, and others are constitutive features of the notion of Adam. “Car par la notion individuelle d'Adam, j'entends certes une parfaite représentation d'un tel Adam qui a de telles conditions individuelles et qui est distingué par là d'une infinité d'autres personnes possibles fort semblables, mais pourtant différentes de lui.... Il y a un Adam possible dont la postérité est telle, et une infinité d'autres dont elle serait autre; n'est-il pas vrai que les Adam possibles (si on les peut appeler ainsi) sont différents entre eux, et que Dieu n'en choisit qu'un, qui est justement le nôtre?” (LR 88). Even if Leibniz uses the misleading terminology of different “possible Adams” 6 , it is clear, as Arnauld shows with the example of “divers mois” that each possible Adam is a different individual with a different

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posterity.7 What Leibniz means is that the individual conditions noted above distinguish the first man of our world (Adam) from first men in other possible worlds (LR 108). As we noted, the “individual conditions” include relations with other particular things. Leibniz writes that “il [Dieu] n’a pris aucune résolution à l'égard d’Adam, sans en prendre à l'égard de tout ce qui a quelque liaison avec lui” (LR 114). “Dieu choisissant non pas un Adam vague, mais un tel Adam dont une parfaite représentation se trouve parmi les êtres possibles dans les idées de Dieu, accompagné de telles circonstances individuelles et qui, entre autres prédicats, a aussi celui d'avoir avec le temps une telle postérité; Dieu, dis-je, le choisissant, a déjà regard, à sa postérité et choisit en même temps l'une et l'autre...” (LR 87). To illustrate that God's decision to create Adam (one individual) is, in effect, a decision to create all the other individuals with which it is related, Leibniz uses the following analogy: “Un prince sage qui choisit un général dont il sait les liaisons choisit, en effet, en même temps, quelques colonels et capitaines qu'il sait bien que ce général recommandera et qu'il ne voudra pas lui refuser pour certaines raisons de prudence, qui ne détruisent pourtant point son pouvoir absolu ni sa liberté” (LR 87). When a wise prince chooses a general, he considers the general’s contacts, among which are the individuals the general will assign as his colonels and captains. Thus, when the prince chooses the general he also chooses the general's circle which “comes with him”. Likewise, when God chooses to create a certain individual he chooses, in effect, all the other individuals that are related to that individual. In short, the choice of an individual is at the same time a choice in the world to which it belongs. And as we noted, an individual’s belonging to a world depends on its relations to other individuals. Now, for Leibniz, possible individuals must be related mainly through their reciprocal predicates (such as love, perception, being a father of, being a sibling of, etc.). Since each concept of an individual is selfconsistent, only relational predicates can account for the compatibility and incompatibility among concepts of individuals. It is thanks to compatibility and incompatibility relations that sets of possible individuals split into

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different possible worlds. Without compatibility and incompatibility relations among possible individuals, all possible individuals would collapse into one possible world – namely, the set of all possible individuals. Without several possible worlds, God would have no reason to prefer one world over another and Leibniz’s notion of possibility, which is central to his metaphysics and theodicy, will collapse into necessity. Consequently, his notion of choice and with it his notion of contingency – which distinguish his system from that of Spinoza – will collapse as well. For these reasons, Leibniz cannot give up his fundamental commitment to various possible worlds. But, as we noted, his notion of possible worlds presupposes relations among the possible individuals who make up these worlds. Thus, it seems clear, that (1) Leibniz presupposes relations among possible individuals; (2) such relations are required for his notion of possible worlds; and (3) such relations are also required to complete the individuation of the concepts of individuals. Assuming that these points are indispensable for Leibniz’s view of relations between possible individuals, I now turn to examine whether the first point is compatible with Leibniz’s nominalism. 3.3 Does Leibniz’s View of Relations Coheres with His Nominalism As Russell pointed out, the fundamental role relations play in Leibniz’s logic and metaphysics seems incompatible with his metaphysics of individuals. 8 Leibniz adheres to a nominalist view according to which only individuals and their properties (individuals cum accidents) exist. This view denies the reality of relations in general, and the reality of interindividual relations, in particular. In other words, Leibniz is committed to the view that predicates with more than one place such as love and fatherhood do not denote real entities. According to Russell, Leibniz’s commitment to a subject/predicate logic or, more precisely, to an ontology which is described solely by means of monadic predicates commits him to reduce statements with relational predicates to statements with monadic predicates. 9 Russell’s interpretation is based on Leibniz’s view of truth, namely that, in any true statement, the notion of the predicate is included in that of the subject. If one identifies the subjects of propositions and the individuals, as Russell does, one arrives at the conclusion that all truths have a single form, namely, the ascription of a monadic predicate to a subject that denotes an individual. According to this interpretation, Leibniz must express any relational truth in terms of monadic predicates inhering in concepts of individuals. For example, the statement “Paris loves Helen”

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should be reduced to ascription of monadic predicates to the concepts of Paris and Helen. Indeed, Leibniz provides an analysis that goes one step in this direction: he rewrites “Paris loves Helen” thus: “Paris loves and eo ipso Helen is loved” (C 286-90). The result of this analysis is indeed two statements that ascribe a predicate to an individual and are connected by the operator eo ipso. But Leibniz stops what is supposed to be a reduction at that. Russell can argue that this testifies to the impossibility of a successful reduction of relational to monadic predicates. For the predicates “loves” and “being loved” are at least tacitly relational: if Paris loves, then he loves someone; if Helen is being loved, then someone loves her. Thus, in Leibniz’s analysis, the relational predicates are not eliminated. However, one can also argue, as Hintikka and Ishiguro did, that Leibniz’s ascription of relational predicates to concepts of individuals shows not that his attempted reduction failed but that he did not attempt such a reduction in the first place. As Hintikka noted, it would be particularly ironic if such a reduction were successful; for such success would render his notion of compossibility, and with it his notion of possible worlds, incoherent.10 As Ishiguro stressed, Leibniz does not hesitate to ascribe relational predicates such as “lover” and “father” to individuals without attempting further analysis.11 And as we illustrated above with the example of Adam, the problem cuts even deeper: Leibniz needs relations not only for his notion of possible worlds but also for the full individuation of an individual (such as Adam). For these reasons, it seems clear that a Leibnizian metaphysics needs relations. Russell was quick to denounce Leibniz’s system as inconsistent, but the challenge he posed to the more patient interpreter is to try to reconcile Leibniz’s view of relations with his view of truth and with his metaphysics of individuals. The Status of Leibnizian Relations I will suggest that, due to the peculiar ontological and logical status of Leibnizian relations, one can reconcile his use of relational notions with his view of truth and his metaphysics of individuals. To a large extent, altering the focus of the discussion from real individuals to possible ones plays a significant role in relieving this tension. For, in the first place, we discuss the relations between concepts rather than between real entities. After all, it is precisely the relations between concepts of individuals that are needed for the harmonization of the activities of real individuals. That is to say, it is the conceptual relations among possible individuals that allow the causal independence among the activities of real individuals.

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In my view, Russell’s influential critique that Leibniz attempted an impossible reduction of relational truths to monadic ones misses its target. Russell and his followers ignore the subtlety of Leibniz’s approach to relations, which is not purely formal. A relation, for Leibniz, is not merely an ntouple; nor is it an entity or a property of an entity. His view of relations should be seen not only against the new logic of Frege and Russell, but also against the subtle discussions of the status of relations in the medieval tradition. As Mugnai suggested, Leibniz’s view of relations may be characterized most precisely by a term taken from the conceptualist position in the medieval tradition – namely, consequentia (for details, see Mugnai 1992).12 Following Mugnai’s work, I suggest that Leibniz sees relations as consequences of considering two things at the same time (or at one thought). According to this view, a relation results when two separate elements are considered together or are united within the same logical space – what he calls a concogitabilitas.13 A relation, for Leibniz, is neither an entity in its own right nor is it a property in the mind which considers it; rather, it is a result of a mental and logical operation, viz., the operation of mentally uniting two elements. For example, by relating two points, a line may result; by relating several stars, a constellation may result; by comparing two magnitudes, relations like “bigger than” “smaller than” “the same as” may result; by regarding two colors that are juxtaposed, a third may result (as in Van Gogh’s famous paintings). This should not be confused with a psychological, subjective operation. Although this operation requires a mind (and, in this sense, it is mental), it pertains primarily to God’s mind – a perfect and all-knowing mind. And, in this sense, it is primarily a logical operation, not a psychological one. Such relations are grounded in the relata, but they result in thoughts that are logically irreducible to the mere sum of the components related. As Leibniz noted, “A new thing is always determined by two other things taken together” (C 539).14 Although the relata may be said to imply (in the sense of a material implication) a relation via their co-consideration, they do not entail it if they are considered separately. Two points considered in isolation are not logically equivalent to the line that would result from their simultaneous consideration; likewise, the number three and the number four do not entail the “bigger than” relation. The logical operation of considering such two elements in the same logical space produces something additional to the things considered. Even though a relation derives from and supervenes on the relata, it is not reducible to them. The very union of the relata adds a specific aspect under which the relata are compared and/or united. For example, two individuals can be

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compared with respect to their length, strength, endurance, etc.; two numbers can be compared in their numerical value, their divisibility, etc.; two points can be related by infinitely many lines.... Thus, a relational proposition normally states the result of a comparison under a certain aspect (e.g., “four is bigger than three”). This is why there is no logical equivalence between the relations (the co-consideration) and the things related, as Mates (1986) noted. Thus relational truths presuppose the relata (individuals, in our case15), their co-consideration, and the particular aspect under which they (the individuals) are considered. This is why, for Leibniz, the truth conditions of an inter-relational proposition can be traced to the concepts of individuals but cannot be fully reduced to them. Ontologically speaking, only the individuals really exist; relations result from a logical operation – the mutual consideration of the individuals – but remain ontologically transparent. Leibniz’s denial of the reality of relations is not a denial of the fundamental role they play in establishing the notion of compossibility (in sorting individuals into worlds), and the individuality of a complete concept. In other words, that the ontological status of relations supervenes on that of the relata, need not affect the logical role they play. Even if relations are entirely dependent on the individuals, it does not hinder them from playing a substantial role in Leibniz’s metaphysics and logic.16 A Problem of Circularity It seems, however, that this conclusion regarding the status of relations conflicts with the third presupposition we discerned in the first section. I have just proposed that relations derive from their relata; that relations among the individuals depend on, and thus presuppose the individuals. But, as we have seen through the example of Adam and his posterity, relations are also required for the complete individuation of the individuals and, as such, relational predicates are indispensable to the concepts of individuals. But if relational predicates are indispensable to the concepts of individuals, then the complete concepts of individuals depend on and presuppose such relations. These two claims, however, lead to an embarrassing circularity in the Leibnizian view we have developed. On the one hand, individuals presuppose their relations; on the other hand, relations also presuppose the individuals they relate – a truly embarrassing circle. As we have seen, however, there are very strong arguments in favor of both claims. Individuals presuppose their relations because, without them, they are not fully individuated; and, on the other hand, relations

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presuppose individuals because a relation, for Leibniz, supervenes on the relata. Holding these two propositions, however, seems circular, if not utterly contradictory. Since there are compelling reasons to hold both claims, I want to examine whether there is a way out of this circularity? I will try to do this by examining some of the presuppositions – or the philosophical context – that give rise to this circularity. 3.4 The Individual’s Place in Logical Space Before we approach the circularity between possible individuals and their relations, let me briefly review some of the background regarding the “construction” of possible individuals in God’s mind. As we have seen in chapter 1, according to Leibniz, possibility is defined in terms of selfconsistency. More precisely, a possibility is defined in terms of logical conceivability (or intelligibility), that is, the thought of self-consistent terms (or forms) in God’s mind. For Leibniz, it is God – seen as an omniscient agent – who thinks all logical possibilities. In turn, some of God’s thoughts are regarded as complete concepts of individuals or possible individuals that are candidates for creation. A concept of an individual may be partially defined as a unique structure of monadic predicates. More precisely, it may be partially defined by the combinatorial rule according to which a unique structure of predicates is thought in God’s understanding. Such a structure of predicates is generated (in the mental sense) by reiterative reflections and combinations of God’s forms. This logical production of possibilities is recursive and proceeds according to what Leibniz calls natural order17: it starts from logical atoms and produces, by continuous combinations, more complex forms. Such complex forms are further combined and may form very complex structure. Such an ensemble of predicates is structured and united by a unique production rule. The production-rule of the individual may be seen as an algorithm (a prescription) for combining and ordering forms such that a unique structure of predicates results. While the forms that make up the structure may be regarded as the predicates of the individual, its production-rule may be regarded as the individual’s logical subject. The production of a possible individual may be said to begin with simple and universal forms (the logical atoms). The combination of such atoms yields more complex and, at the same time, more particular forms. This combinatorial notion of production integrates two distinct aspects – complexity and particularity – that serve the constitution of individual concepts. As the complexity of a concept increases, it becomes more particular and distinct from other common notions. In a sense, it is the very

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complexity of the structure and its internal organization that makes it individual or unique concept. A unique organization of universal forms may result in individual and unique concepts. In this sense, the complexity (of the structure) increases the particularity of the concept. For example, “gold” is more complex than “metal”, for it includes both the concept of metal and that of gold. 18 At the same time, the concept “gold” is also more particular than the concept “metal”. The concept of a “rational animal” integrates the concept of animality and that of rationality. The concept of a “rational animal”, although generic, is more particularized than both the concept of “animality” and that of “rationality”. The concept of an individual person, however, must include a variety of other predicates which distinguish it from all other rational animals and thus individuate it as a unique individual. In other words, more concepts (some of which relate to other individuals) have to be included in the concept of a rational animal in order to make it a specific and unique individual, as we have seen in the case of Adam. Logical Space and the Constitutive Role of Relations This view of possibility, according to which God recursively thinks all possible individuals as distinct and unique structures of predicates, has a consequence that pertains to the question of circularity. This consequence can be stated very roughly as follows: given the above-mentioned view, each possible individual occupies (and in a sense constitutes) a unique place within the logical space of possibilities.19 Since God’s mental activity produces all unique structures of predicates, each individual constitutes exactly one of many possible structures, and the ensemble of possible things (which is itself structured) constitutes the whole logical space of possibilities. Given the recursive nature of the construction of individuals, the whole space of possibilities is, in effect, itself structured. Although the view of possibility mentioned above does not commit itself to specify the exact structures of individuals or even to say what the simple forms are, it does suggest an ordering of the individuals according to their degree of complexity, ranging from the most simple to the most complex. This ordering of the individuals is similar to the logical order of their production and corresponds to what Leibniz calls “natural order”. Now, if all the possible individuals are ordered, then they are not independent of one another, at least in a sense. They are not independent of one another because there is a general framework – namely, the order – in which they figure and which, taken together, they also constitute. Moreover, since each individual is unique and since logical space is

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constituted by all possible individuals, each one of the individuals occupies a unique place therein. To say that the individuals are not independent of one another is of course to say that they are related to one another. To illustrate this point, consider the following Leibnizian analogy. Suppose that God’s mental activity consists of combining single units such that all the natural numbers result from this activity. 20 This activity produces what may be called a numerical space (in the limited sense of the natural numbers). The numerical space has the structure of a sequence within which each number occupies a unique place. In the numerical space, the place is clearly essential to the properties a certain number has. In this case, one can go as far as saying that the place in the sequence fixes what a number is. If the notion of a certain number, say, of three, is to be abstracted from its place in the sequence of natural numbers, it would lose some of its essential properties, if not become completely meaningless. One can say that the place in the sequence figures in the definition of a number. At the same time, the number three or three units contribute to the constitution of the numerical space. Note that the notion of “a place within a space” is thoroughly relational. And this is precisely the point I try to illustrate. In analogy to numbers within a numerical space, the relations of a certain individual to the others, particularly its place within a space of possibilities, plays a constitutive role in fixing the concept of a given individual. In other words, the individual’s place in the space of possibilities figures in its definition and “enters” into its concept. 21 For example, the place the concept of Adam holds among all concepts of individuals fixes it not only as a man in our world but also as the first man of our world – a thoroughly relational predicate which thereby becomes a part of its concept. Even if each individual is, by definition, logically possible in itself and in this sense independent of all others, its occupying a particular place within the space of possibilities implies that it is also (conceptually) related to the other individuals. This is due to the fact that all the individuals share (and at the same time construct) a common logical space. The space in question is, of course, not a real space; it is a conceptual space that is conceived in God’s mind. Such a general notion of a space of possibilities may seem trivial. But the notion of an exhaustive and structured space of possibilities, consisting of a plurality of distinct individuals, implies that each individual constitutes a unique place within this space. This may turn out to be very consequential for resolving the problem of circularity that infects Leibniz’s view of relations. The most pertinent point is that the place an individual occupies within this logical space turns out to determine some of its

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essential features and, at the same time, it is relational. As described above, the notion of an individual involves a subtle duality: while a notion of an individual contributes to the definition of the logical space, it is also partially defined by means of its place in it. The key to the resolution of the circularity is that there is no priority to the individual’s place nor to the whole space; rather, these are mutually constitutive concepts. The notions of “place” and “space” used above are clearly general, not to say vague. The notion of a numerical space is not the same as that of a musical space, which is partially defined by the distances between the tones, or a space of colors, which is also partially defined by the relations between primary and derivative colors. These spaces are sharply distinct from the notion of a place within a geometrical space and surely from the real space. Yet, there is something common and more general about these cases that justifies our terminology: the notion of a place within a logical space is semantic; it pertains to the essential characteristics of a given concept among others, and it points to conceptual dependencies among the elements which constitute a given space. In this sense, the use of the notion of a logical space used above is not just metaphorical. It points out that a number of concepts unified by a logical space serve the full definition of one another. As the cases of numbers, colors, and tones (think of terms like a musical scale, modus, accords, all of which are defined in terms of the mutual relations between the tones), the dependencies are conceptual in the sense that they serve to define the very concepts of the individuals (e.g., as yellow may be defined in terms of red and green). Let us now connect this point to the Leibnizian status of relations noted above. Since, according to Leibniz, God has an intuitive view of the whole space of possibilities, the relations among the concepts of individuals are transparent to him. But even for God, seeing these relations requires an additional logical step, namely, the mutual consideration of the individuals. In light of this point and in light of the semantic sense of “place in space” noted above, we can try clarifying Leibniz’s ascription of relational predicates to concepts of individuals. Since the place of possible individuals determines some of their properties, from a perspective of an omniscient God, the very individuation of a given individual presupposes the place it holds within the whole space. For example, the individuation of the concept of Adam requires the whole set of individuals with which it is compatible (and in a sense, those with which it is not compatible). To this extent, we can say that the mutual consideration of individual concepts in God’s mind gives them their relations. In this sense, the complete concept of an individual presupposes the concepts of other individuals and its relations with them enter, as it were, into its concept. This is not to say that

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the individuals are not distinct from one another; rather, it is to stress that the way an individual is related to other individuals is constitutive of it and, therefore, it figures in its complete concept. For example, if individual X includes more simple forms than individual Y, this relational predicate (“have more simple forms than Y”) presupposes the comparison of X and Y and may be ascribed to X’s proper concept as an essential predicate. Let me try to exemplify some of the points made above, namely, the semantic sense of “place in space”, its relational character, and its relation of mutual constitution by considering Leibniz’s notion of magnitude and change of magnitude. According to Leibniz, “magnitude consists in comparison” (C 107-108; Mates, 1986 225). The magnitude of an individual is fixed by its comparison to other individuals (relative to which a scale of magnitudes is to be formed). The case of change of magnitude is of particular interest. In rephrasing Socrates’ remark (in Theaetetus, 155C) that he has become smaller than Theaetetus without himself being changed, Leibniz remarks: “When someone, by growing, becomes bigger than me, then some change occurs in me as well, since a denomination of mine is changed. In this way, all things are in a way contained in all things" (SR 85).22 When someone grows, and thereby becomes bigger than me, I do not, in Leibniz's eyes, remain the same. Although my actual size does not undergo any real (in the physical sense) change, a denomination of mine is nevertheless changed. Here is a simplified example of this case, presented in my terminology. Suppose a logical space of three individuals with three different magnitudes at t 1: A, B, C. Suppose that A grows and becomes A. Then we have at t 2 : A, B, C. Note that, even though only A grows, some change occurs in B and in C as well. Although B did not change, a denomination 23 of it did change: while B was of medium magnitude at t1, it becomes small at t2 (after A grows). Similarly, a denomination of C, namely, its similitude to A with respect to size, has arisen. As Leibniz says, “...my similitude to someone else arises without any change in me, solely by change in the other person” (C 107-108; Mates 1986, 225). Clearly, while A has undergone a real change, the changes B and C have undergone are due to their new places within the space (or scale, in this case) of magnitudes.24 In turn, their new place fixes an internal predicate of theirs, namely, being small or big.

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In this sense, the relations to other individuals produce a change in the very predicates of an individual. In Leibniz’s words, “extrinsic denominations, which arise and disappear without any change in the subject itself but only because a change comes about in something else, appear to pertain properly to Relation; thus a father becomes a father when the child is born, even if he happens to be in India and thus is not affected. Thus my similitude to someone else arises without any change in me, solely by change in the other person. It must be admitted, however, that speaking rigorously there is no extrinsic denomination in reality, since nothing happens anywhere in the universe which does not affect every existent thing in the universe” (C 107-108; Mates 1986, 225). 3.5 Conclusion I have suggested that Leibniz’s view of relations should be seen against the background of the following presuppositions: (a) A combinatorial view of possibility; (b) A view of relations as mental/logical products of the relata; (c). That God thinks all possibilities and consequently considers all the relations among them; (d). That God’s co-consideration of the individuals gives rise to logical space; (e). That a possible individual occupies a unique place within the space of possibilities; (f). That the individuals’ place in the space is a relational notion and that it plays a constitutive role in the individuation of possible individuals and in completing the concept of an individual. On the basis of these points, my approach can be summarized as follows: I suggest that a possible individual occupies a unique place within the logical space of possibilities, a space which is itself constituted by all the individuals considered together. While the notion of an individual is defined as a self-consistent and unique structure of predicates, the notion of logical space is constituted by God’s considering all the individuals at once. This co-consideration of individuals in God’s mind gives rise to the relations between individuals and particularly to the compossibility relations among them. I would like to stress that the individual’s place within the logical space is a relational notion and that it is constitutive of what an individual is. I use this duality to explain Leibniz’s seemingly circular logic of relations. I propose to avoid the circularity by noting the difference between considering each individual in isolation and considering the ensemble of other individuals at the same time – a

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consideration that gives rise to the logical space and assigns each individual a unique place therein. Whereas the first operation is based on self consistency among the monadic predicates of the individual (and fixes it as logically possible in itself), the second operation is based on comparisons and gives rise to the relations with other individuals. Note that, in considering an individual in isolation and in considering an individual together with other individuals, one does not consider exactly the same thing; rather, a consideration of an individual in isolation depicts a structure of monadic predicates 25 and it is the co-consideration of individuals that gives rise to the logical space within which all individuals are related and within which they are also fully individuated. To say that relational predicates enter into the concepts of individuals is not to say that relational truths are reducible to monadic ones. Rather, relational truths presuppose God’s mental operations such as comparisons and the logical space these operations constitute. Relational truths presuppose non-relational truths because a relation is grounded in the relata. We can therefore conceive of a notion of an individual considered in isolation, which consists of non-relational predicates alone, and the complete notion of an individual, which, in a semantic sense, may be said to include relational predicates as well. This distinction provides the point of departure for my discussion in the next chapter.26

1 The exact criteria of maximal harmony are not relevant to my purposes here. One can think of it as the maximization of individuals under the constraint of compatibility among the activities of individuals. Leibniz also talks about the maximization of individuals (or essences) within the simplicity (i.e., minimization) of laws. On this see Rescher, The philosophy of Leibniz, (1967). 2 In fact, and as I shall indicate in section 3.3, it also implies exclusion relations with all the other possible individuals who do not belong to the same world. On this point, see Rescher’s “Leibniz on Possible Worlds”, 1996, section 7. 3 For more details, see section II and Russell’s A Critical Exposition of the Philosophy of Leibniz, 1937, chapter I. 4 If not otherwise indicated, page references in this chapter are to Georges Le Roy ed., Leibniz, Discours de métaphysique et correspondance avec Arnauld (Paris, Vrin 1993). 5 Since the notion of Adam is related to the notions of other individuals who share the same world, the creation of Adam implies the creation of all the other individuals who belong to our world, that is, the notions of other individuals with which it can coexist. “Or chaque substance individuelle de cet univers exprime dans sa notion l’univers dans lequel il entre. Et non seulement la supposition que

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Dieu ait résolu de créer cet Adam, mais encore celle de quelque autre substance individuelle que ce soit,...” (LR 107). 6 Leibniz's terminology is misleading because the use of a proper name "Adam" is incompatible with the claim that there are many of them. A proper name normally designates a single individual, rather than a kind or a plurality of them. Leibniz clearly notices the discrepancy. After writing that each possible Adam differs from the other, he remarks "if one may so call them". It seems to me that Leibniz uses the notion of Adam not as a proper name but as a generic term, designating the first man in every possible world in which there is a first man (see LR 108). 7 To conceive of “several possible me(s) is certainly inconceivable.... The reason is that these different me(s) would be different from each other, otherwise there would not be several me(s). There must therefore has been one of me(s) which is not me, which is an evident contradiction” (LR 97). 8 Russell, B. A Critical Exposition of the Philosophy of Leibniz, 1937, chapter I. 9 As Russell observed, from a formal point of view, such a reduction cannot succeed. 10 Hintikka, "Leibniz on Plenitude, Relations, and the 'Reign of Law'", in Frankfurt, ed., (1972), pp. 155-190. 11 Ishiguro writes: “All that I am anxious to stress is that there is no elimination of relational properties in what is expressed in the rewritten result. Not only is there a relational expression (viz., a comparative) in each of the sentences expressing the constituent propositions; the two propositions are claimed to be related in a non-extensional way. The original proposition – Paris loves Helen – is shown to be logically a “compendium” of two propositions ... linked by the logical connective 'eo ipso'. And each of the two propositions is still a relational proposition in the sense that it is expressed by a sentence that conceals a two-place predicate ... It is part of their truth conditions that there is someone whom Paris loves and someone who loves Helen. Thus ...in each of the propositions expressed by the rewritten result, relational predicates are still ascribed to the subject, relating him to another person” (Leibniz's Philosophy of Logic and Language, 1972, 121. 12 Leibniz’s Theory of Relations (1992). 13 “A relation is an accident which is in several subjects and is only a result or supervenes with no change made on their part if several things are thought at once; it is concogitabilitas “ (C 74r, 1679). “A relation is the concogitabilitas of two things” (C 35, June 1679). “A relation is that according to which [secundum quod] two things are thought of at once” (C 47, April, 1679). Cited from Mates, 1986, pp. 222-6.

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14 “Ex duobus quibuslibet simul sumtis semper aliquid novi determinatur” (C,539). 15 There are also intra-individual relations, which I ignore in this context. 16 Regarding the question of truth, one need not conflate the grammatical subject of a relational proposition with the metaphysical subject (an individual). There is no simple one-to-one correspondence between the two. 17 See “Quid sit natura prius” (A 6.4 180-81) and “La conception leibnizienne de l’ordre”, Rauzy,1995 p. 37). 18 See C 53; PLP 20. 19 In this context, the logical space just means that which spans all possibilities. 20 "I cannot explain how things result from forms other than by analogy with the way numbers result from units – with this difference, that all units are homogeneous, but forms are different" (A 6.3 523; SR. 85). There are, of course, other ways to define the sequence of natural numbers by the method of its production, notably, via the successor relation. See also: “Mihi videtur origo rerum ex Deo talis esse, qualis origo proprietatum ex essentia, ut senarius est 1+1+1+1+1+1, ergo 6= 3+3, = 3 x 2, = 4+2, etc.” (A 6.3 518-9; SR 77). 21 That a place in a logical space is constitutive of i ndividual concepts is, of course, not peculiar to the sequence of natural numbers. On the contrary, this point could perhaps be generalized. Think of a color spectrum as the space within which, and by means of which, distinct colors may be defined. For example, orange is not defined absolutely but as lying between red and yellow; it can also be defined as the color a mix of yellow and red would produce. The same, I think, applies to the prime colors. Their identification may depend on the particular spectrum which their composition yields. Even black and white, being the two limit cases, may be defined respectively as the lack of color and as the composition of all colors. In any one of these cases it is clear that a color is defined by virtue of its place in the spectrum, that is, in relation to all the other colors. This point is illustrated even better if one considers the range of musical tones where the tones are defined by virtue of their intervals within the octave and where different moduses are obtained by varying the number and intervals between them. 22 See also SR 135 n.4 and p. xli. 23 A predicate corresponds to a denomination. 24 The more radical point is that the very notion of magnitude is constituted by the whole space, or, in other words, by the comparison of the individuals. While each individual contributes to the space (i.e., it plays a constitutive role in it), the magnitude of each individual is also fixed by its place in the space. This implies that, for Leibniz, there is no independent criterion to measure magnitudes rather than the comparative magnitudes of the individuals. Another way to make this point is that the system of individuals provides its own system of reference (or its

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own measuring scale). Even if God’s mind does provide a privileged perspective, the privilege consists precisely in the view of all individuals at the same time, not in having some external criterion. For Leibniz, even an all-knowing God has no measuring rod which is independent of the magnitudes of the individuals. 25 It may be termed, following Gregory Brown (in his “Compossibility, Harmony, and Perfection in Leibniz” (1987) as a “monadically complete individual concept”. However, I find this terminology misleading because a concept with monadic predicates alone is not complete. 26 The view developed above has two noteworthy consequences. The first concerns the question of compatibility. By virtue of its inner structure, each individual may be said to entail its possible connections with other individuals. This view presupposes that a unique individual is considered within a space of individuals, some of which are compatible with it and some of which are not compatible with it. Loosely speaking, the world into which an individual fits can be seen as the structure that complements it. In a similar sense, the notion of an individual can be said to involve its complementary parts, and in that sense, relational predicates. The second consequence concerns the relations between logical space and geometrical space. The logical place an individual occupies within the range of all possibilities is analogous to the geometrical place a created individual occupies within the created world – what Leibniz calls a unique point of view. In both cases, the unique place in space contributes to individuation. Whereas in the context of possible individuals, God sees all individuals together, in the context of created ones, each individual perceives the whole world from its unique point of view.

Chapter 4 Individuals, Worlds and Relations 4.1 The Priority of Worlds In a stimulating article, Catherine Wilson has developed a powerful alternative to the recursive approach to the notion of possible worlds I have espoused thus far.1 In the previous chapters I assumed that Leibniz’s view is recursive in the sense that God constructs concepts of individuals and possible worlds as conjunctions of them. Wilson articulates an opposing approach. She considers the moment of worlds-making in Leibniz’s philosophy and raises the following question, “How do possible substances give rise to possible worlds?” 2 She considers (section 2) two approaches to the question. According to the first, possible individuals logically precede possible worlds and possible worlds are constituted either by combinations of possible individuals (model 1) or by mechanically checking the compossibility relations among them (model 2). According to the second approach, worlds logically precede individuals. Wilson argues that since the two accounts of the transition from individuals to worlds (i.e., the combinatorial model and the compossibilitychecking model) are unsatisfactory, the order presupposed by these models should be reversed. “The notion of a ‘world’, she writes, conceptually precedes the notion of a substance” (Leibniz Review, 10, 2000, p. 10). Instead of a world produced by conjoining individuals or by checking whether an already given set of individuals is compossible, as I supposed thus far, Wilson suggests an inverse picture according to which breaking down an already complete world produces individuals. In using the analogy of a jigsaw puzzle in which possible individual substances are broken down from a complete world, she writes: “The claim here is simply that the puzzle-piece model is the most coherent account of his [Leibniz’s] creation-story, preserving most of the theses he held dear” (14-15). By “the theses he held dear” Wilson designates the following eight “criteria for a Leibniz world” (1): (1) A given substance exists in only one world. (2) Our world is the richest and fullest of all possible worlds. 105

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(3) Our world does not contain every possible substance. (4) If and only if substances A...n can (all) exist together in some possible world, they are compossible. (5) Substances A...n are compossible if and only if each perceptually represents (all) the others. (6) If A...n are compossible, and if any element of that set is compossible with any member of the compossible set B...k, then A, B...n...k are (all) compossible and conversely. (7) Our world is morally-aesthetically optimal. (8) Our world is the only actual world. Wilson reccomands that we take these as constraints on a “rational reconstruction” of Leibniz’s creation-story. I will adapt these theses as constraints on a rational reconstruction of Leibniz’s creation-story but will reject Wilson’s conclusion that Leibniz’s notion of a world is conceptually prior to his notion of individuals. I will do so by responding to Wilson’s main and most interesting argument against the compossibility model in which God examines the compossibility relations among all possible individuals (A…n), which is the model that I have been working with in the previous chapters. Wilson argues as follows: Suppose A happens to be the possible substance Julius Caesar, and the next substance God picks up to compossibility-test is Judas. We know a posteriori that Judas is compossible with Caesar, for both exist in our actual world. But is there a possible world consisting of the 2-tuple {Caesar, Judas}? There cannot be: for if Judas and Caesar exist in our world, they cannot exist in some other world too by (1). What prevents Judas and Caesar from forming a possible world “prematurely” if they are compossible? We should not succumb to the temptation of rewriting (4) as a conditional, for it is in fact true that if two substances are compossible they are found together in a possible world. The premature assembly of tiny worlds of compossible objects needs to be precluded by the account we give (6-7).3 On the basis of this thought experiment, Wilson observes that “Such collections as {Judas, Caesar} or {Adam, Judas, Caesar} or {Adam, Judas, Caesar, CW} can only be torn-off pieces of worlds, fragments of worlds that have fallen apart, or potential parts of possible worlds” (7), and argues that, “the ideal account should show us why, in the absence of an appropriate quorum of other compossibles, two compossibles do not stick together in a world-like way” (8-9).

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This leads Wilson to the following suggestion: “Perhaps the problem solved by the ‘striving possibles’ is not how to agglomerate, but how to fill in a given outline with pieces so that there are no gaps. This idea is expressed in Leibniz’s comparison between creation and the solution of a building or tiling-problem” (9). In following up her argument of tiny worlds, Wilson arrives at the puzzle piece-model in which “the problem of tiny, premature worlds does not arise” (10), and concludes: “…our world, and every possible world, is in a sense, given in advance. To make a puzzle, we start with a photograph or drawing, glue it to a backing and then cut it up with a jigsaw. And this, I submit, is what Leibniz’s theory of the striving possibles comes to” (10). While this agument leads to an important insight, note that the jigsaw puzzle analogy faces the following problem: In order to “cut up” a world into the individuals that fill it up, one has to follow some non-arbitrary lines of division. Leibniz’s principle of sufficient reason surely precludes an arbitrary division into the possible substances that make up a world. But if the lines are non-arbitrary, then they are not conceptually dependent on the division but rather conceptually prior to it. I will present an alternative model for the moment of world-making in which the problem of the premature assembly of tiny worlds of compossible individuals is also precluded. More precisely, in the model I develop the problem does not arise. In my view, Wilson rightly focuses our attention on the crucial moment of world-making in Leibniz’s philosophy. I think, however, that this moment can be better captured in terms of the relations between possible individuals and possible worlds. This terminology is more appropriate since it makes clear that the picture of “possibles striving for existence” is somewhat misleading to the extent that it implies that there may be a direct mechanical transition from possible individuals to the actual world. Rather, an actual world presupposes all possible worlds, which precede God’s choice of the morally best one. This is one of the central points in Wilson’s article and I will take it for granted here. I will focus on the subtle relations between possible individuals and possible worlds and, more specifically, on Wilson’s claim (b) that “individual substances presuppose completed worlds” (1). I wish to point out that, in suggesting the reversal of the order of composition (from worlds to individuals), Wilson overlooks an interesting and plausible alternative for the “production” of possible worlds. Although this alternative model is difficult to articulate, I wish to draw a rough and preliminary sketch of it. Developing this model will, curiously enough, lead to the conclusion that the question of logical precedence (between

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possible individuals and possible worlds) is somewhat misleading. Even more curiously, the model leads to partial agreement with Wilson’s conclusion that “individual substances presuppose completed worlds” (1) and to an interesting explication of this claim. The model I develop focuses on the relations between possible individuals (as presented in the previous chapter) and attempts to construct possible worlds as constituted by such relations. More precisely, it focuses on the moment when relations among incomplete individuals, which include only monadic properties, are constituted. As it turns out, this model lends support to the conclusion that complete possible individuals and possible worlds are mutually dependent or, in other words, that possible worlds and complete individual concepts are mutually constitutive. This conclusion is based on the view presented in the previous chapter that complete individuality can only arise in the context of the complex net of relations with other possible individuals. In order to clarify the notion of a possible world, we need to carefully consider the notion of a possible individual. This is the approach I have been taking in this work. In the model I am trying to sketch here, one must at least distinguish between an incomplete (or a thin) individual and a complete (or a thick) individual. Whereas the former consists of nonrelational predicates alone, the latter involves relational predicates as well. 4 I stress the word ‘complete’ because in this model incomplete concepts of individuals do precede worlds, although complete concepts of individuals do not; rather, complete concepts, as well as possible worlds, result from the relations among incomplete concepts of individuals. That is to say, incomplete concepts of individuals are required for worldformation. At the same time, worlds (viewed as compossible sets of individuals) are required for the formation of complete individuals.5 Thus the completion of individuals’ concepts through the emergence of interindividual relations constitutes, at the same time, possible worlds. This is why the question of logical precedence is somewhat misleading. As we shall see, this distinction allows a new and (as is typical of Leibniz) a conciliatory approach to the question of whether individuation is extrinsic or intrinsic – and whether and to what extent it depends on relations. In other words, on the basis of this distinction we will be able to describe more precisely the role that relations play in individuality. Given the distinction between incomplete and complete concepts, we can begin the story of world-formation from incomplete possible individuals. 6 The relations among possible individuals arise “when” God considers all possible incomplete individuals in his mind. At the moment when God considers all possible individuals simultaneously, their inter-

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relations arise in his mind. As a partial illustration, suppose God considers the numbers 3 and 4 at the same time. At that moment, the relation ‘3 is smaller than 4’ (among others) arises in his mind. The simultaneous consideration of the relata gives rise to relational truths (such as ‘3 is smaller than 4’). Likewise, suppose God considers the incomplete concepts of Paris and Helen at the same time. At that moment, the relation ‘Paris loves Helen’ (among others) arises in his mind. As I argued in the previous chapter, the consideration of all incomplete individuals by God results in the constitution of the whole logical space of possibilities in his mind. Each possible individual, consisting of only monadic predicates, may be seen as a possibility per se, that is, something which on purely logical grounds may exist, while all possible individuals taken together make up the whole space of possible things. Once God considers them all in one thought, their interrelations emerge as thoughts (or secondary intentions in the scholastic jargon) in his mind. Let me describe this complex and consequential moment in another way: a moment “after” God forms all incomplete (monadic) concepts of individuals in his mind, he considers them (all) simultaneously. The coconsideration of all individuals constitutes the whole logical space, that is, the space of all possible things. At the same time, it constitutes something more as well, namely, the way in which all possible things are related to one another. Hence, in this moment, the space of logical possibilities (per se) serves as the basis for the relations among them (and for the relational propositions describing these relations). As we have seen, in this logical space, each incomplete individual already occupies a unique “place”. Such a unique “place” is fixed by the non-uniform system of relations among the (incomplete) individual concepts. A unique place for each individual is ensured by virtue of the fact that each incomplete concept is unique and therefore its relations to other individuals must be unique. This view is consistent with Leibniz’s theory of relations (advocated by Mugnai)7 that I deployed in the previous chapter. As already noted, the moment when all the basic concepts of individuals are considered simultaneously has great significance. Once the relations among individuals are conceived in God’s mind, the compossibility relations among all individuals emerge as well. In turn, once the compossibility relations among the individuals are conceived, possible worlds are in effect formed. Recall that according to the standard interpretation, worlds are compossible sets of possible individuals. This approach allows us to take incomplete individuals as fundamental and, by considering the relations among them, arrive at possible worlds. As Wilson argues, the compossibility relations do not result from a mechanical

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procedure that processes all individuals; rather, they require some sort of intellectual perception by an infinite mind of all relations among possible individuals. Furthermore, once the relations among all individuals are constituted, their individuality can be completed. By virtue of their place in logical space and their simultaneous consideration, incomplete individuals acquire, so to speak, relational predicates that express their relations to other individuals. Such relational predicates “complete” the basic concepts and allow them to “achieve” full individuality. Let me illustrate how relations complete the individuality of individual concepts. Consider again Arnauld’s example of the concept of Adam. The concept of Adam is related to the concept of Eve as the father of her children, to the Garden of Eden, and to the concepts of other human individuals in the world as the first among them. Any concept which is not related to the concepts of Eve, the Garden of Eden and to the concepts of other human individuals in this way is not the concept of Adam; it is the concept of a different individual who has a different posterity and belongs to a different possible world. 8 Leibniz states clearly that in order to distinguish the concept of Adam from other “possible Adams”, one has to specify the particular names of other individuals (e.g., Eve), places (e.g., the Garden of Eden) and particular circumstances to which it is related and which “complete its individuality” (“autre circonstances qui achévent l’individualité”).9 In my view this phrase reveals something deep and interesting about Leibniz’s complex view of individuality. In this vein, Leibniz states that God did not choose to create an "Adam vague",10 that is, an indefinite notion of Adam which entails only general characteristics (conceived sub ratione generalitatis). Rather, God chose to create a specified and well-defined notion of Adam. As a candidate for creation – a possible individual – the content of an individual notion is entirely specified and fixed.11 In particular, the notion of an individual is specified and determined precisely by its relations with other possible individuals and particular events.12 For example, a would-be married Arnauld would not be the same person as the non-married Arnauld, since his relations to other individuals would be different. According to this view, relations to other (incomplete) individuals play a constitutive role both in forming worlds and in completing the individuality of possible individuals. I will now use this point to respond to Wilson’s powerful argument for the precedence of worlds over individuals. Wilson argues that if one assumes that worlds are formed by conjoining individuals, it is not clear why subsets of compossible individuals, such as the set {Adam, Eve}, do

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not form a world. We can now offer the following answer: if the names Adam and Eve are seen as referring to complete individuals, then their very individuation requires the concepts of the other individuals with which they are related, such as their descendents. However, in that case, these individuals must be included in the same world. For example, Adam’s sons figure in his complete concept as giving rise to some of his essential predicates (such as paternity). Hence, the subset {Adam, Eve} cannot form a world. If, on the other hand, ‘Adam’ and ‘Eve’ do not refer to complete individuals but only incomplete ones or possibilities per se, then surely they are not even candidates for being constituents of a world since worlds require at least compossibility relations (or the conditions for perceptual representation) among individuals. In addition, if ‘Adam’ and ‘Eve’ are seen as incomplete (i.e. relationless) individuals, they cannot be anything like the complete individuals that these names refer to and with anything that we could identify as individuals. In the model I outline here, relations with other individuals are constitutive of the very concepts of individuals. Boldly put, an individual is not fully individuated unless its relations to all other individuals are considered. A partial set of compossible individuals, e.g. {Adam, Eve}, does not form a world since if the names Adam and Eve refer to complete individuals, there would have to be many more individuals – in fact all the individuals in the world. Only a set formed by considering all the relations among all possible individuals can be considered a world. Such a world is a set which satisfies compossibility relations which, upon creation, translate into perceptual relations among existing substances. As it turns out, the model sketched above partly confirms Wilson’s main point that worlds precede individuals. However, if the model is adequate, Wilson’s point must be qualified in that it only applies to complete individuals. In any event, the point is better stated as a thesis of mutual constitution between complete individuals and possible worlds. The main point I have tried to make here is that the “moment” of world-making can be described according to an alternative model. I have tried to show that there is another option worth considering before concluding that a world logically precedes individuals. I have argued that we can gain some insight into the question of world-making by focusing on the crucial role that relations between incomplete concepts of individuals play in the construction of possible worlds and in completing the individuality of basic individual concepts. In the next section I will further examine the role of relations in the individuation of complete concepts as well as some problems with this model of world-making.

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4.2 Relations and Individuality In this section I extend the rational reconstruction of Leibniz’s position to the role of relations in individuation in light of the distinction between incomplete and complete concepts. First, I will address some objections Wilson’s raised 13 and then I will briefly consider two recent approaches (Cover and O’Leary-Hawthorne (1999)14 and Mugnai (2001)15 to the role relations play in individuation. I will argue that Leibniz’s mature view of individualtion is nicely captured as a reconciliation of these positions. As Wilson accurately observes, the key idea in my model “is that uncreated substances may be taken as complete or as incomplete individuals. As incomplete individuals, they possess only monadic predicates, and it is as incomplete individuals they are considered by God before the world comes into being” (125-26, my italics). One point of clarification is required here: since ‘before’ is ambiguous (due to the transitivity of precedence), let it be clear that it is meant to refer to a moment not only before the actual world comes into being but also to the moment before possible worlds are formed in God’s mind. In associating incomplete individuals with ‘vague’ ones, Wilson writes: “But, if I understood the proposal as intended, it is just such an Adam vague who, along with an Eve vague, a Caesar vague, a Judas vague, a Serpent vague, an apple-tree vague, are considered by God before the moment of world realization” (126, my italics). Again, I wish to stress that this refers not only to the moment before the world is realized but also to the moment before possible worlds are formed in God’s mind. In fact, (and as Wilson also notes 16 ), my position is better stated by considering two phases of candidacy. Yet I must stress that these two phases of candidacy are also two different types of candidacy. The first phase involves the candidacy of an incomplete individual for being in a possible world, which is essentially the candidacy of a merely possible thing to be compossible with others. In the second phase, the concepts of individuals can already be viewed as being related to others and therefore as complete. In this phase, the candidacy is of complete concepts of individuals for being created or actualized as members of a world (which is not the case for the first phase of candidacy). In other words, the first phase is a candidacy for belonging to a possible world while the second is for belonging to the real world (or for selecting the best of possible worlds for actualization). Leibniz’s creation story may be broken down into several distinct moments. First (logically speaking, of course), there is the formation of

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incomplete concepts of individuals in God’s mind. This moment involves several phases, as I presented in the second chapter. Second, there is the co-consideration of all incomplete concepts of individuals. This moment involves the formation of relations between individuals which, at the same time, turns out to constitute possible worlds and to complete the basic individual concepts. Third, all possible worlds are considered for actualization. And fourth, the elected world is created. This moment will be discussed in the next chapter. There is also a fifth phase in which created individual substances realize their possibility or essence spatiotemporally, which I shall discuss in subsequent chapters. As it turns out, Wilson’s argument against a vague concept of Adam as a candidate for actualization is consistent with my position. It is precisely my point that we cannot refer to the thin concept of Adam. Our concept of Adam is essentially different from its thin or basic concept, precisely because it involves relations with other individuals. In order to ‘refer’ to Adam’s incomplete concept, we must abstract from our concept of Adam and, only in abstracto, subtract its relational predicates. In this way, we can talk about the individual’s monadic or thin concept. However, this is a pure abstraction. As Wilson argues, any individual which is recognizable to us as such would necessarily have relational predicates such as parenthood, being a member of its species, likeness to others, and so on. Thus there is more agreement between our positions than first meets the eye. 4.3 Relational and Non-Relational Predicates There remains the most substantial problem in the model I presented above which Wilson nicely brings out in her comment, namely, the vagueness of the distinction between monadic and polyadic predicates. The challenge is to clarify this distinction. Yet I believe that the distinction between monadic and polyadic predicates is as difficult to articulate as it is indispensable to Leibniz’s philosophy. At the same time, I doubt that such clarification can be achieved through a technical analysis of relational statements and relational predicates. In fact, attempting to clarify the distinction along merely syntactical and formal lines seems to me rather misguided. 17 Instead, clarifying this distinction requires a philosophical discussion of Leibniz’s complex and subtle view of relations, as well as the metaphysical context in which relations (and relational predicates) arise. What further complicates the issue is that, to some extent, Leibniz’s view of relations defies generalization and therefore this distinction would in this sense remain vague. If the only standard of clarity we accept is a

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Frege-like analysis of the formal structure of relations, this might seem like a serious problem. But as I have already hinted, the presumption that this is the only adequate standard of clarity is a mistaken one, at least in the case of Leibniz. In any event, whether we can arrive at a clear formal definition of Leibnizian relations or not, it remains certain that Leibniz’s philosophy cannot do without a distinction between the relational and the nonrelational – however vague and context-dependent it may be. This distinction is required both in the conceptual and the actual contexts. In the conceptual context, we have seen in chapter one that Leibniz postulates a domain of logically simple forms whose relations and combinations constitute the realm of possibiliites and eternal truths in God’s mind. In the actual context, the plurality of created substnaces implies relations between them. In this context, created substances may be taken as non-relational relata. In addition, there is a more straightforwad and convincing argument which stems from Leibniz’s view of relations, namely, that any relation presupposes the things it relates. Leibniz is very explicit in denying the very possibility of a relation without a foundation.18 Thus Leibniz’s approach requires both relations and non-relational foundations of them. Wilson rightly argues that all allegedly monadic predicates applicable to living creatures are implicitly relational. However, it does not follow that all monadic predicates applicable to ‘thin’ concepts of individuals are relational as well. Moreover, and this is my main point, even if it is true that all our examples of monadic predicates are implicitly relational (Wilson, 127), it would still be true that, according to Leibniz, relations in general and relational predicates in particular presuppose non-relational facts or non-relational predicates. This follows from what Leibniz takes to be the most fundamental feature of relations. As Mugnai has persuasively shown, a relation, according to Leibniz, derives from its relata; it results from a mental act of relating two objects or predicates – a co-thinking (cogitare) of two things at the same time.19 If this is the case, then it seems that, at some level of abstraction, we must accept some distinction between relational and non-relational predicates. In other words, if relations supervene on the non-relational relata (or terms), it seems to follow that, if there are relations, there are also non-relational elements (at least in a given context). On the other hand, if there were non-relational elements, then, given the comparative activity in God’s mind, relations would result. Thus in the context of Leibniz’s metaphysics of relations, it seems that both relations and non-relational elements are presupposed.

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Another reason for the difficulty of exemplifying and generalizing the distinction between monadic and polyadic predicates is the unknowability of the ultimate non-relational simples in Leibniz’s system. As I noted in the second chapter, the absolute simple terms in Leibniz’s metaphysical system are identified with the attributes of God and are unknowable to humans.20 Leibniz had a number of reasons for holding this position. Since I already presented these arguments in chapter 2, there is no need to elaborate this point here. I will only recall one of these arguments that should suffice for our current purposes, namely, the argument from symbolization. If the way in which a concept is composed of its simple constituents must be preserved in the symbol representing it, the elementary constituents themselves cannot be represented. Since the elements are postulated to be logically simple, they lack compositional complexity. If they lack compositional complexity, they cannot have common structure with a symbol because they have no structure at all. Hence, they cannot be represented. Since the elements cannot be represented, we cannot (epistemically) reach the ultimate simples, whether conceptual or real, and may never be able to exemplify the ultimate ground floor of relational predicates. This is no doubt frustrating and difficult to accept. Yet, as we have just seen, Leibniz has a good argument to justify the human inability to know in this case. An additional reason for the vagueness of the distinction between the relational and non-relational, in general, and between monadic and relational predicates, in particular, is the relative character of relations. This point is another direct consequence of Leibniz’s view of relations. If relations are constituted as consequences of the relata, then the nature of a specific relation necessarily depends on the specific relata in question. For example, the relation of marriage between two individuals depends on the two individuals in question. Note that, to a large extent, this analysis corresponds to our common sense intuition about the marriage relation. Otherwise, it wouldn’t make much difference whom we marry. Most of us, of course, tend to believe that the quality of a certain marriage does depend on the individuals thus related. This illustrates how the very nature of a relation depends on the individuals being related. Friendship and paternity are similar in this respect. These examples show that relations are intrinsically context-sensitive and that it could be problematic to deal with relations in a general way. For these reasons, it is dangerous to generalize from particular cases. For example, even the relation of paternity between Isaac and Esau (his first born son) is not the same as the paternity relation between him and Jacob

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(his second son). This is not to deny that there are similarities among all paternal relations but simply to note the complexity of the issue. In fact, the similarity or difference between various paternal relations is already a comparative relation between relations, which might have an altogether different structure. A correlate of this point is that a syntactical and formal approach to Leibnizian relations is insufficient precisely because it abstracts from the specific relata in question. Again, I do not claim that relations do not have certain features in common. Rather, relations are all the results of a mental operation or comparison. Yet, each case must be treated separately. I trust these points illustrate the difficulty in providing a general and as it were syntactically ‘clear’ definition of the distinction between monadic and relational predicates. At the same time, for all its inherent vaguness, the distinction remains indispensable to Leibniz’s philosophy. 4.4 Relations and Individuation Let me turn to a brief discussion of the role of relations in individuation. More specifically, the question is whether, and to what extent, relations play an essential role in Leibniz’s view of individuation.21 In Scholastic terms, the question may be formulated as whether the source of individuation is internal or external to the individual (i.e., whether it is relational or not). In the picture Wilson draws, worlds logically precede individuals. This seems to imply that individuation is primarily external since individuals are seen as ‘cut-off pieces’ from worlds. As Mugnai has aptly noted, “[t]o understand Leibniz’s thought concerning individuation, it is necessary to put some emphasis on the distinction between individual substances on the one hand and complete concepts on the other” (Mugnai, 2001, 52). Hence, it is all-important whether one is discussing the individuality of substances or the individuality of their complete concepts. Bearing Mugnai’s point in mind, I would like to stress that, according to Leibniz’s mature view, individuation may be seen as both internal and external, that is, as partly internal and partly external. In my view, the formulation of the question in its Scholastic terms as presenting mutually exclusive options, namely, whether individuation is either extrinsic or intrinsic, is misguided. This disjunction oversimplifies Leibniz’s complex view of the issue. Instead, I think that both internal and external considerations play an indispensable role in Leibniz’s view of individuation.22 This point is intrinsically related to the distinction between complete and incomplete individual concepts noted above. While the individuation

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of incomplete concepts is internal , 23 the individuation of complete concepts requires relations and, in this sense, it is external. A complete individual acquires its full range of proper predicates from two sources: (a) from within, through its unique structure of monadic predicates, and (b) through its comparison to other individuals, which give rise to relational predicates. If so, Leibniz’s view of individuation clearly involves both intrinsic and extrinsic elements, which complement rather than exclude one another. This is consistent with Leibniz’s view of relations, according to which the relational presupposes the nonrelational. In supposing the complete/incomplete distinction Leibniz can reconcile these seemingly opposed views. As a matter of fact, one finds both external and internal views of individuation in Leibniz’s texts. It is also clear that Leibniz’s view of individuation has underwent several stages of development in the course of his career. 24 Nevertheless, commentators have tended to adopt one view and argue against the other. They consider the two views to be mutually exclusive. By employing the incomplete/complete distinction, as I suggested above, one can see why this polemic arises and how it can be resolved. For example, this question is discussed by Cover and O’Leary Hawthorne (1999), who write: “as far as individuation goes, we shall argue that, in the mature Leibniz, relations drop out of any metaphysical role” (Cover and O’Leary Hawthorne, 1999, 62). In particular, they write that “relations cannot individuate substances” (257) and conclude that, “Leibniz does not wish to put relations to serious metaphysical work” (Cover and Hawthorne, 1999, 217). By contrast, Mugnai (in Studia Leibnitiana, 2001) argues that Leibniz’s position is more complex and involves a duality in his view of individuals. He writes: “... we may have two descriptions of an individual substance: a) a description which includes all properties inhering in the substance, and b) a description which includes, besides the properties inhering in the substance, the ‘concept of everything else in the universality of things’ [GP II 226]. Leibniz calls the description corresponding to b) a ‘perfect concept’. Both kinds of description give rise to a principle of individuation: they differ only in that b) simply makes explicit what in a) is implicit; a) corresponds to a description which involves a given individual only, with its internal states and dispositions as well, whereas b) calls into the picture the entire world to which the individual belongs” (53).25

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The duality Mugnai is pointing to is systematic and, as we have seen in chapter 3, it holds in the conceptual context as well. In the conceptual context (as distinct from that of actual substances), Mugnai’s distinction may be captured in terms of the distinction between the incomplete and complete concepts of individuals. According to Leibniz, and in contrast to the Scholastic tradition, individuation also pertains to concepts which may remain mere possibilities. Cover and O’Leary-Hawthorne are right insofar as relations are insufficient to individuate. However, this point must be qualified as follows: Given a non-relational core, relations may complete individuality. In my view, relations (but not primarily those of time and space) are constitutive of complete individual concepts. 26 At the same time, there is a non-relational core of individual concepts which allows that “things are nevertheless distinguishable in themselves” (cited from Mugnai 2001, 50). As I will make explicit in the next chapter, I agree with Cover and O’Leary-Hawthorne that this core may be identified with the law-of-series that defines the inner states of a created individual. Yet, as I argued in the second chapter, I think that an individual concept may be identified with the law that generates its incomplete concept in God’s mind and that the relations with other individual concepts (not substances) are required to complete its individuality. 27 As I shall suggest in the next chapter, the relations between created individuals emerge as a result of their creation. Given Leibniz’s view of relations, a non-relational core is a necessary condition for relations to emerge (though primarily in God’s mind). On the other hand, Leibniz’s notion of a world as a plurality of compossible individuals presupposes relations between them. In my view, a subtle and complementary interplay between relational and non-relational aspects is required in order to adequately capture Leibniz’s complex view of individuation. Likewise, internal individuation provides only one part of the story while the external (or better, relational) individuation completes the story of individuation. According to the view of possible individuals presented in chapter 2, internal relations among the inner constituents of possible individuals arise. I suggest that the internal relations of a given individual also imply its possible connections with other individuals, namely, the individuals with which it is compatible and the individuals with which it is not compatible. Although the notion of compatibility among possible individuals presupposes their simultaneous consideration in God’s mind, the grounds for the compatibility of a given individual with other individuals are found in the inner structures of the individuals. Given this

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view of relations, possible worlds are, in effect, implied by the way all possible individuals are constructed. For the inner structure of each individual implies its possible connections with others. Observe that this is part and parcel of Leibniz’s combinatorial approach to possibility in which possibility is understood as the compatability or fitness of components in a larger structure. As we shall see in chapter 9, this has also substantial implications for Leibniz’s view of nested individuality.

1 “Plenitude and Compossibility in Leibniz”, The Leibniz Review, 10, 2000, p. 1. The first part of this chapter is based on Nachtomy, “Individuals, Worlds, and Relations: A Discussion of Catherine Wilson's 'Plentitude and Compossibility in Leibniz'", The Leibniz Review, 11, 2001, pp. 117-125. 2 I do not deal with Wilson’s second question, “How does one of the worlds become the actual world” and her claim that there may be a plurality of actual worlds. 3 There may be a technical way of addressing the issue by modifying the notion of possible world as a maximally compossible set of possible individuals but there is a deeper issue at stake here that I want to bring out. 4 The need for and usefulness of such a distinction has been noted by several commentators. For example, see G. Brown, "Compossibility, Harmony, and Perfection in Leibniz", (1987) p. 184. This distinction has been also extensively discussed in Cover and O’Leary-Hawthorne, Substance and Individuation in Leibniz (1999). I will further defend this distinction in the sequel to this chapter. 5 For some elaboration of this point, see chapter 3. 6 As I noted in the second chapter, I believe that the story begins a moment ‘earlier’ when such thin concepts are formed in God’s mind. 7 Leibniz’s Theory of Relations, (1992). Mugnai argued that Leibniz considered relations to be the consequences of considering (at least) two relata at the same time. A relation results when two (or more) separate elements are considered together and united in thought – what Leibniz calls a concogitabilitas. 8 Georges Le Roy, (ed.), Leibniz, Discours de métaphysique et correspondance avec Arnauld, Paris: Vrin 1993, (108). 9 Ibid. 108. 10 Ibid. 87. 11 Ibid. 116. 12 For another vivid illustration, see Leibniz’s response to Arnauld’s claim that whether he marries or not does not affect his identity.

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13 In subsequent discussion (The Leibniz Review, 11, 2001 125-29) Wilson raised a number of questions and objections, some of which I try to clarify in this section. 14 Substance and Individuation in Leibniz (1999). 15 "Leibniz on Individuation : From the Early Years to the ‘Discourse’ and Beyond", Studia Leibnitiana, 1, 2001, 36-54. 16 See footnote 2 of her response. 17 For a criticism of a syntactic approach to relations in Leibniz, see also Cover and O’Leary-Hawthorne, 1999, 67. 18 “implicare contradictionem ut implicat relation sine fundamento” (GP II 420). 19 Mugnai (2001) writes that “he [Leibniz] states that relations result from the existence of singular things with their (non-relational) properties” (47); and that “[R]elations are parasitic on the features of related things” (49). 20 "[a]n analysis of concepts such that we can reach primitive concepts, i.e., those which are conceived in themselves, does not seem to be within human power" (C 514; PLP xxxviii). 21 For a strong textual case for the indispensable role relations play in individuation (circa 1686) see Mugnai, 2001, section VII pp. 49-50. 22 Likewise, while relations supervene on their relata (or better, result from their co-consideration) a reductionist approach is misguided since the nature of a relation or the content of a relational statement cannot be reduced to the separate natures (or contents) of the relata. The very operation of relating two relata adds something that is not found in the relata. As Leibniz puts this, “A new thing is always determined by two other things taken together”. “Ex duobus quibuslibet simul sumtis semper aliquid novi determinatur” (C 539). 23 Let me note in passing that the very notions of individuation and uniqueness make implicit reference to other individuals (i.e., are relational). To be unique, an individual must differ from all others. 24 Well informed reviews of the development of Leibniz’s view of individuation are presented in Cover and O’Leary-Hawthorne (1999), in Mugnai (2001), and in Rauzy (2001). 25 “I do not think that there is any substance that does not involve a relation to all the perfections of any other” (GP II 239). See also Fichant 1998, 132. 26 “The essential ordering of individuals, that is, their relation to time and place, must be understood from the relation they bear to those things contained in

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time and place, both nearby and far, a relation which must necessarily be expressed by every individual so that a reader can read the universe in it, if he were infinitely sharp sighted” (Letter to De Volder, GP II 275-78; AG 183). 27 “Cette loi de l’ordre, qui fait l’individualité de chaque substance particulière, a un rapport exact a ce qui arrive dans toute autre substance, et dans l’univers toute entier” (GP IV 518).

Chapter 5 Possibility and Actuality 5.1

Introduction

In previous chapters I examined Leibniz’s notion of possibility in some detail. Since Leibniz’s metaphysics recognizes only individual things as candidates for actualization, I have given special attention to the notion of possible individuals. We have seen, however, that, in Leibniz’s eyes, individual concepts and possible worlds are intrinsically related. The basic concept of an individual is completed within the context of a world – that is, in the context of the other individual concepts compossible with it. With this view of possibility in mind, let us now consider the transition from a possible world to the actual one or, in other words, the question of actualization. It is significant that, in Leibniz’s metaphysics, the notion of actualization is understood within the context of creation. Creation, according to Leibniz, is not a natural event; rather, it is a divine act that constitutes the natural world. At the same time, the issue of creation involves several questions, such as the criterion for goodness in the best world and God’s choice of it, which go beyond the scope of this chapter. My focus in this chapter is the issue of actualization. I concentrate mainly on clarifying the transition from the realm of possibility (discussed in the first part of this work) to that of actuality, which I shall briefly describe in this chapter. In what follows I assume that possible worlds are not equally good and that God chooses the best among them for actualization. Since a possible world consists of compossible individuals, our question reduces in effect to the actualization of possible individuals. According to Leibniz, all the features of the created world (including extension, space and time) emerge from the creation of individual substances. The worldly features of the created world emerge as a result of the relations between individuals, discussed at length above. The relations that belong to the individuals’ complete concepts emerge as a result of the actualization of the individuals. As Mugnai (1992) put it, “once God has created certain objective realities, he cannot prevent given relations as a result.” (Leibniz’ Theory of Relations 26). We noted that such realities are individual substances. Hence, “In creating individuals, God conceives of them in their 123

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reciprocal relationships, and this act of thought ‘brings to birth’, so to speak, all possible relations and all the truths that can be asserted concerning those individuals” (Leibniz’ Theory of Relations 21). For this reason, the actualization of the best world can be reduced to the actualization of its individual members. Since the creation of the world reduces to actualizing the individuals that belong to the best world, the question of the actualization of the world can be narrowed down to that of individuals.1 Since possible individuals are understood in terms of their complete concepts, the question may be phrased as follows: how are complete concepts turned into actual substances? Or, what are the essential gaps between complete concepts and actual substances? That Leibniz’s metaphysics involves such gaps is clear. As Cover and O’LearyHawthorne nicely point out, “…substances are created, contingent, causally active individuals while concepts are eternal, necessary, passive items in the mind of God” (Cover and O’Leary-Hawthorne, 1999, 217). Thus our question may be rephrased as follows: how passive concepts become active agents? As we shall see, Leibniz’s notion of actualization implies the notion of individual agents. The notion of individualized activity, which I emphasize here by the notion of agency (as distinct from mere activity), is central to Leibniz’s view of actual substances as well as to their actualization. I will suggest that the concept of agency best accounts for the transition from merely possible things to actual ones. My strategy for developing this point is as follows: first I will present Leibniz’s relevant suppositions regarding the notion of actual substances. Once the main characteristics of actual substances are presented, I will compare them with the characteristics of possible ones (as presented in chapters 1-4). Then we shall be in a position to approach the question of how possible individuals become actual. The structure of this chapter is as follows: in the first section I present Leibniz’s suppositions about actual substances; in the second I argue that actualization is achieved by rendering a unique program of action active, whereby a self-sufficient agent is created. In the third section, I consider an objection to this view that arises in the context of Leibniz’s statements that possibilities strive to exist. I attempt to reconcile these statements with the view of actualization developed in the second section. 5.2 Leibniz’s Suppositions About Actual Substances Let me begin by noting some of Leibniz’s most fundamental commitments regarding actual substances. Since most of these commitments are recognized and well documented by other scholars, I will keep my presentation here brief.2

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1. Individuality. According to Leibniz, the only things that truly exist, that are actual substances, are individuals.3 The world consists of individual substances alone and whatever else there is derives from the existence of individuals and their properties. In his metaphysics of substance, Leibniz follows Aristotle. As already noted more than once, in this respect, Leibniz is a nominalist. Since this point is widely recognized and noncontroversial, there is no reason to dwell upon it here. It is interesting, however, to clarify how Leibniz’s complex motivation for maintaining his commitment to nominalism is related to his fundamental commitment to the active nature of individuals. 2. Activity. According to Leibniz, substances are intrinsically active. More precisely, they contain their own source (principium) of activity or are spontaneous. Leibniz adheres to the traditional relation between activity and Being, so that every substance acts and any active thing is a substance. Leibniz’s early commitment to this thesis is defended and developed at length in Mercer’s (2001) extensive study on Leibniz’s early writings. In his article “L’ontologie leibnizienne de l’action” (pp. 2-3), Fichant eloquently makes this point with respect to Leibniz’s later texts: La liaison essentielle de l’action et de la substance est constamment réitérée dans tous les textes de la dernière période, 4 celle qui est instaurée par la constitution du concept de “ dynamique ” en 1690. Au “ Tout ce qui est proprement une substance ne fait qu’agir ” des Nouveaux Essais (II, 21, § 72) répond le “ ce qui n’agit point ne mérite point le nom de substance ” de la Théodicée (§ 393); les deux se concentrent en: “ Il n’y a que les substances qui agissent et il n’y a point de substances qui n’agissent pas” (Lettre à Le Long, 14 mars 1713, citée dans André Robinet, Malebranche et Leibniz. Relations personnelles, Paris, Vrin, 1955, p. 423). While this supposition is widely recognized and hardly controversial, it requires some qualifications and an additional degree of precision. First, according to Leibniz, being active is clearly not reducible to being externally moved or being efficiently caused. Leibniz’s notion of internal activity cannot be reduced to efficient causality; rather, Leibniz’s notion of spontaneity stresses a metaphysical sense of activity and distinguishes it from the mechanistic views in fashion among the new philosophers of his time. For Leibniz, having an internal source of activity entails a number of significant implications. It includes both Aristotelian notions of final and

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formal cause, entailing an end (seen as a program) and potentia.5 In this sense, an intrinsic source of activity includes the program for the individual’s development as well as some resources for its realization. 6 In other words, the source of activity has both an end and some sort of power. Second, while the notion of spontaneous activity is ascribed both to God and to created substances, it is not ascribed to them in the same sense. While in the case of God activity is intelligible and invariable (i.e., it is mathematical or combinatorial as described above); in created substances activity is sensible and variable. While God is invariable and eternal, creatures develop and change their states and properties.7 As we shall see, there is also something constant and invariable in created substances – viz., the very law of change and what Leibniz calls primitive force. 3. A Plurality of Substances. It follows from the above suppositions that substances for Leibniz are active individuals. Since all substances are individual and since all substances are active, all substances are active individuals. It is an individual that contains its own source of activity. Yet it does not follow from these suppositions that there are such individual substances other than God. After all, these suppositions are also acceptable to Spinoza who holds that there is only one substance, no genuine possibilities, and no creation. Therefore, it is worth making explicit Leibniz’s supposition that God creates the world as a plurality of distinct substances.8 4. Activity pertains to subjects (Actiones sunt suppositorum). From the suppositions noted above, namely, (1) that substances are individuals; (2) that substances are active; and (3) that there are substances other than God, it follows that Leibnizian substances not only act but that each acts in a unique way and constitutes a unique source of activity. 9 This implies that the very notion of activity according to Leibniz is individualized, so that there is no activity in general but only the actions of actual individuals. In the traditional terminology Leibniz employs in the Discourse on Metaphysics 8 and On Nature Itself (paragraph 9, AG 160), actions are the actions of subjects. This is intrinsically related to the Scholastic notion of an individual as a self-subsisting substance. As Fichant explains, Un étant subsistant par soi est ce qui a en soi un principe d’action. En effet un étant subsistant par soi ou cette substance-ci ou celle-là, prise individuellement, est un suppôt (car les Scolastiques définissent ordinairement le suppôt comme individu

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substantiel). Or les actions sont actions des suppôts. Le suppôt a donc en soi un principe de mouvement ou agit. C’est pourquoi un étant subsistant par soi a en soi un principe d’action (A 6.1, 508; Fichant 1997, 4). This point is also nicely brought out by its converse, which Leibniz clearly maintains: Whatever acts is, by definition, an individual substance or a unique agent. In addition, note that to act implies to produce a determinate result.10 According to Leibniz, there is no undetermined activity; rather, activity is necessarily an activity of subjects whose actions derive from a unique inner source and are thus determined by their intrinsic nature. Like God, any created substance is also an agent endowed with power to act. Unlike God, who is pure and unlimited activity, created substances also suffer and are acted upon. In other words, created substances are also passive. An essential aspect of their being limited is that they always act in a unique and determinate way (whereas God acts in all possible ways). They have a unique place or perspective that expresses God’s essence in a unique way (see chapters 3 and 4). In this sense, created substances determine and delimit God’s infinite power. Leibniz makes it very clear that the ascription of actions to individual subjects follows from the very notion of action. He writes: “To the extent that I have made the notion of action clear to myself, I believe that the widely received doctrine of philosophy, that actions pertain to supposita, follows from that notion and is grounded in it. Furthermore, I believe that we must grasp the fact that this must hold reciprocally, so that not only is it the case that everything that acts is an individual substance [substantia singularis], but also that every individual substance acts without interruption, including even body itself, in which one never finds absolute rest” (On Nature Itself par. 9, AG 160). I have noted earlier that, for Leibniz, activity and being are intrinsically related, so that whatever is, acts and whatever acts, is. It now becomes clear that both activity and being are also individualized for Leibniz; they must pertain to individual actors or agents. This, in turn, implies that agents are spontaneous, i.e., their actions stem from their own depths or inner sources. It is this determinate and spontaneous type of activity that I designate here by the notion of agency.11 I emphasize the notion of agency because I believe that it provides the clue for understanding the passage from possibility to actuality. Leibniz’s

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notion of creation involves several interrelated aspects – all of which have great philosophical significance: (1) the actualization of possibilities; (2) the transition from one necessary Being (i.e. God) to many substances whose existence is contingent upon his decision to create them; (3) the transition from the realm of Being (God’s intelligible activity) to the realm of becoming (sensible and variable activity of created agents); (4) the determination of power and activity through the production of diverse and self-sufficient subjects which individualize and limit God’s infinite power. We have already seen that God’s essence can be individualized in the sense that individual essences or concepts can be conceived of in it as pure possibilities. However, these essences are mere thoughts of God. Active subjects or agents are required as diverse determinations of God’s power and activity. Without active and spontaneous agents, there would only be the infinite power of one agent without the creation of other substances. In fact, this is precisely the case in Spinoza’s metaphysics, in which there is no creation and no substances other than God. According to Spinoza, particularization is understood through the different modes or ways in which God acts. Strictly speaking, however, there is only one individual – God or Nature. Such a view, of course, is unacceptable to Leibniz.12 In Spinoza’s system, there is no room for the Leibnizian notions of possibility, diversity of individuals and their actualization. For Spinoza, there is only one, purely actual substance. 5. Two Senses of Spontaneity. I have already stressed that, for Leibniz, actual substances contain their own sources of activity – which Leibniz often terms the first entelechy (On Nature Itself par. 11, AG 162). While this notion of spontaneity is an essential feature of what I call agency, it involves two distinct aspects. According to Leibniz, possessing an internal source of activity implies both (a) an internal law of action and (b) primitive force or power of action. As he writes: “I recognize in the active force ... the primitive entelechy or, in a word, something analogous to the soul, whose nature consists in a certain perpetual law” (GP II 171; L 517). “The essence of substances consists in the primitive force of action, or in the law of the sequence of changes” (GP I 347; L 155). “And so, we must add a soul or form analogous to the soul, or a first entelechy, that is, a certain urge [nisus] or primitive force of acting, which itself is an inherent law, impressed by divine decree” (GP IV 512; AG 160-61, On Nature Itself 1698).13

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Although Leibniz’s notion of a source of action often confuses the notion of primitive force with that of an internal law of changes, the two are conceptually distinct and each constitutes a distinct requirement for the self-sufficiency of substances.14 While the law prescribes a course or program of action, primitive force is required to enable the execution of the program. While each agent has an undifferentiated power of action, the rule of action contributes the individualizing information to make it a unique substance (Theodicy 291). As we shall see, the distinction between power of action and the rule of action is crucial for Leibniz’s view of actualization (as well as for his notion of freedom that I will discuss in the next chapter). It is also important to note that Leibniz is careful to distinguish between force and activity. He writes in “On Nature Itself” that, “action and power are different things, the former successive, the latter persisting” (AG 160). Since “each [substance] follows the inherent force and laws of his own nature” (AG 161), “in all substance, there is natural constancy opposed to change” (AG 161). Inherent and constant force is required in each substance enabling it to change itself and develop its states according to its individual law. As Leibniz argues against “certain Cartesians, who think that things do not act, but that God acts directly on things…and who thus think that things are occasions, not causes,” (AG 160), inherent force is a defining feature of active substance precisely because it must persist and thus constitutes the ground of being. For this reason, inherent force may be seen as a divine aspect present in each created substance, which is a being by virtue of its constant law and force and, at the same time, is becoming by virtue of its changing states. 6. Inherent Force. Leibniz’s rehabilitation of substantial forms in reaction to Descartes’ purely mechanistic picture of inert matter as geometrical extension also involves the notion of passive forces.15 In opposition to the inert character of material substances according to Descartes, Leibniz places the notion of force – both active and passive – at the heart of his notion of substance.16 The notion of inherent force is the non-extensional and true essence of substance. It is the only feature that is truly indivisible (for it is non-extensional in the first place) and therefore, unlike extension, can constitute true substantial unity. As Wilson nicely put this, “For Leibniz, the refusal to ascribe active force to created things amounted to a denial of the independent reality of the world” (Wilson C. 1987, 165). Likewise, the independent reality of the world requires that creatures would possess active force.

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7. Law of Action. While both active and passive aspects are necessary for a Leibnizian substance, they do not have equal status with respect to the metaphysical functions they perform. While the role of the passive force is not to be played down, the major metaphysical tasks are performed by the active principle, which Leibniz variously calls the soul, the entelechy or the form of a substance.17 As we have noted, a crucial aspect of this active principle is to provide the inherent law of action. The law of action gives each substance a unique course of action and consequently a unique sequential organization of properties over time.18 As a principle of organization, the law also unifies the various constituents of a substance as one entity; as a principle of change and development in a substance, the law remains the invariable essence of a substance that serves to fix its identity over time.19 While the law informs the substance’s change of states, the law itself, like the force its application requires, remains invariant. The active form is not only responsible for the individuality, unity, and identity of substances; it also constitutes the reason for their indestructibility, indivisibility and, interestingly, their simplicity. According to Leibniz, indestructibility follows directly from continuous activity. As Leibniz writes, "[w]hatever acts cannot be destroyed; for at least it endures whilst it acts, therefore it will endure forever" (A 6.3 521; SR 81). Thus, as long as a substance acts, it is indestructible. Since its very nature is to act, it is imperishable. As I shall argue later (in chapter 10) in more detail, I think that indivisibility and simplicity also follow from the intrinsically active nature of substances and their definition by a unique law of action. Since the individuality and unity of a substance are defined by means of the specific law of action (with its implication of infinite series of states), the rule itself must be seen as a unity that cannot be divided or disrupted, for this would destroy the identity and individuality of the substance whose development it informs. The indivisibility and simplicity Leibniz attributes to active units – whether he calls them monads or substances – derive from these features of the law of action. It is for this reason that his notion of simplicity (deriving from the intrinsic agency of substances) does not conflict with their complexity, as I will suggest in chapters 9 and 10. 8. Passivity. In spite of the great importance of the active aspect in Leibniz’s notion of a substance, the entelechy, it provides only part of the story. In adapting the basic hylomorphic structure of Aristotelian substance, Leibniz also presupposes a material principle of passivity (primary matter). A passive principle is required in order to receive the

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action and thus complement the active principle. In this Aristotelian conception, both principles – active and passive, forming and being formed, determining and being determined, organizing and being organized – are necessary conditions for a complete substance.20 For Leibniz, the law takes the role of a substantial form or soul that informs and organizes passive matter. As we shall see in chapter 9, this is also the point at which the similarity with Aristotle’s view breaks down. Leibniz’s view is far more complex and the basic hylomorphic structure of Leibnizian substance requires significant modifications.21 9. A Complete Concept. Finally, let me explicitly note the well-known doctrine that a substance is also defined by a complete concept that uniquely specifies all its true predicates (explicitly noted in DM 8, 13). In chapter 2, I noted that a complete concept could be seen as defining a possible course of action or an individuated and unique essence that is conceived in God’s mind – a God’s-eye view of all the would-be actions and passions of the individual. I also suggested in chapter 2 that such a complete concept is individuated by the combinatorial rule that generates a unique and infinite structure of predicates in God’s mind. I shall now turn to examining how such a concept or possibility is actualized, so that it becomes an active and self-sufficient agent. 5. 3

Actualization

Having presented the main features Leibniz ascribes to actual substances, let me now consider the question of their actualization. As we have seen above, actualization, for Leibniz, can be seen as a transition from an individual concept to an active agent. Following Adams,22 I think that the best way to approach this question is to consider the following thought experiment: compare Leibniz’s notion of actual substance with his notion of a possible one and consider what the actual has that the possible lacks. In this way, we shall be able to see what is required for a possible substance to become actual. While it may seem surprising, the results of this thought experiment are clear and decisive. Since the concept of an individual is complete, so that it provides a comprehensive and detailed specification of all its predicates and the ground for true assertions about the individual, and since the basic concept of an individual is defined by its production rule in God’s mind (so that its relational predicates derive from its comparison to other individual concepts), it seems that the main thing a possible individual needs in order to become actual is power or force to activate the rule. Since, on the one hand, the

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production rule provides a complete source of information concerning the content of the individual’s actions and properties, but since, on the other, it is entirely impotent to act on its own (since, after all, it is a mere thought in God’s mind), it must be given power or force of action. Furthermore, as we have seen, since actions pertains to supposita, it follows that, in order for x to act, x must be a subject or an individual. As Leibniz stated in his notes on Spinoza’s Ethics: ideas do not act – only minds (or subjects) do. 23 Let me restate this point: As far as the content or essence of an individual is concerned, the concept of the individual is already complete. 24 Yet a concept does not have power to act. A concept is not an agent. Rather, a concept is a mere possibility in God’s mind. For this reason, actualization requires that a unique and well-defined course of action, corresponding to a possible individual, be given power to act and thereby make it actual. The constitution of a self-sufficient agent that acts on its own requires both a law of action and power to act. As noted, self-sufficiency has a dual sense for Leibniz: it requires both an internal law prescribing what to do and constant power to enable its execution. If the agent has a complete program specifying what to do and what to perceive and an inner source of action in the sense of power or force, it would be self-sufficient as it would need nothing from the other substances making up the created world. The requirement of individual forces in Leibniz’s view of actualization explains the central role the notion of force plays in his metaphysics as well as in his physics. Force is the constant core of being in every created substance. Hence, it is conserved and remains constant through change. At the same time, it also points to the need to individualize and delimit God’s infinite power, so that it is expressed through diverse subjects or agents. In this picture, actualization may be seen as ascribing divine-like powers to pure thoughts in God’s mind. In turn, the diversity of rules of action restricts God’s infinite power with limitations, determinations and specific orientations. In this way, unique information serves to individualize unlimited power. After all, mere unlimited power lacks determination.25 “[No] one could object if the substance in abstracto is taken to be the primitive force which always remains the same in the same body and brings about, successively, accidental forces, and particular actions, which are all nothing but the nature or primitive subsisting force applied to things. …Nevertheless, it is true that the substance, in concreto, is something other than force, for it is the subject taken with this force” (Letter to Pellisson, 1692, A 1.7 249).

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“…to say that, in creation, God gave bodies a law for acting means nothing, unless, at the same time, he gave them something by means of which it could happen that the law is followed; otherwise, he himself would always have to look after carrying out the law in an extraordinary way. But, indeed, his law is efficacious, and he did render bodies efficacious, that is, he gave them an inherent force” (GP IV 393-400; AG 253-54, 1702). Since a rule in itself is impotent, a pure possibility, only a conjunction of power to act and a rule of action can constitute a self-sufficient individual substance. Thus actualization is understood as endowing a production rule with primitive force. Force makes the law active. While the law in itself is entirely impotent, its conjunction with force renders it not only potent but also actual in the sense that the agent can produce by itself the series of actions (or accidents) it entails. 26 From this crucial moment of creation, the intelligible activity in God’s mind is also expressed as sensible and variable, that is, as the variation of accidents in created substances. Such activity, though, does not belong to God, who is invariable, but to created substances alone who develop their series of accidents from their internal sources. The unnatural moment of creating the natural world is, of course, not a moment in time. Rather, it constitutes time as an order among created individuals. At the same time, this moment of creation also constitutes space as an order among created individuals.27 This account makes sense of Leibniz’s notions of possible individuals, that is, of merely possible (non-actualized) individuals and of actual individuals. A possible individual, though complete with respect to its information or content, does not exist because it does not act; an actual individual is inherently active and its activities may be described through its complete concept and production rule. Actualization, therefore, consists of the divine act of uniting the two to create spontaneous agents. It follows from this view of creation that “God produces substances, but not their actions” (AG 281). Created substances are agents who produce their accidents spontaneously. This is a significant point to keep in mind while we explore the Leibnizian labyrinth of human freedom in the next chapter. 5.4

Striving Possibles and the Divine Choice to Actualize the Best Possible World

Before I turn to examine the question of human agency and freedom in the next chapter, I would like to briefly consider what seems to constitute an alternative account of actualization, namely the theory of striving

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possibles – the idea that there is an inherent tendency to exist in possibilities themselves. This theory has important implications regarding the status of divine freedom and agency in the context of actualizing the best world. I will try to show that an adequate interpretation of this idea has important implications concerning Leibniz’s understanding of rational agency – both divine and human. It is well known that in several places Leibniz writes as if possibilities have an inherent inclination or exigency towards existence and that they engage in some kind of struggle for existence, in which the best set wins, that is, it becomes actual. One of the clearest (and most influential) pronunciations of this idea is stated in “On The Ultimate Origination of Things” (GP VII 302-8, 1697), where Leibniz writes: “…there is a certain urge for existence or (so to speak) a straining towards existence in possible things or in possibility or essence itself; in a word, essence in and of itself strives for existence. Furthermore, if follows from this that all possibles, that is, everything that expresses essence or possible reality, strive with equal right for existence in proportion to the amount of essence or reality or degree of perfection they contain, for perfection is nothing but the amount of essence“ (AG 150).28 This doctrine is intriguing, curious and – it goes without saying – controversial. Interpreters such as Blumenfeld and Rescher argued that Leibniz is using this notion as a metaphor. 29 Other interpreters such as Shields and Belaval argued that Leibniz’s words should be taken more seriously. 30 While I cannot enter into the details of this controversy here, I wish to note a few reasons why the literal reading of “possibilitas exigat existentiam” is highly problematic. Let me first point out that, as stated, the doctrine is vague. It is unclear whether by possibilitas or possibilia Leibniz refers to possible individuals or to possible worlds or to both. If, as I argued at length in the first chapter, the status of possibilities is similar to that of ideas and concepts in the mind of God, then possibilities, according to Leibniz, are not agents. If so, possibilities or essences cannot actively strive for anything (let alone to exist) they lack the capacity to act (a capacity Leibniz ascribes only to substances). Taken literally, the theory of striving possibles violates Leibniz’s fundamental distinction between the realm of logically possible things and necessary truths, which is governed by the principle of contradiction and is seen within the domain of God’s understanding, and the realm of desirable or the moral and contingent truths, which is governed by the principle of sufficient reason and involves

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God’s will. It is central for Leibniz that the realm of the moral (what ought to be) presupposes the realm of the logical (what can be). As I noted in chapter 1, the rationale behind Leibniz’s theory of possibility is that, only once possibilities are defined, a moral choice among them would make sense. For this reason, I assumed above that all possible worlds are equally possible but not equally good. Only at the moment of selecting a world among many possible ones the principle of sufficient reason can play the role (in the context of divine agency) of selecting the best among them. In this sense, the per se possibility of x is independent from x’s moral value. If the theory of striving possibles is taken literally, some disturbing consequences follow: (a) if the struggle for existence among possibles is seen as a process of self-selection whose result is existence, the role of God as the creator of the best world becomes redundant. (b) The passage from possibility to actuality becomes a purely logical procedure, which (c) would make one of Leibniz’s great principles, the principle of sufficient reason or the principle of the best, redundant as well.31 Likewise, (d) it would make Leibniz’s central idea that the created world is contingent upon God’s choice to create it (rather than another) groundless. It goes without saying that, if this were the case, (e) Leibniz would be in a difficult position preventing his system from collapsing into Spinozism (for, in this case, the actual world would be a necessary result of the struggle of the possibles to attain existence). For these reasons, it seems to me that, if the theory of striving possibles is taken literally, the very thrust of Leibniz’s philosophy (at least as I understand it) is seriously endangered. While it is undeniable that Leibniz ascribes to possibilities a propensity or tendency to exist (e.g., A 6.4 1443), it is quite different from ascribing to possibilities the power to actualize themselves. Leibniz’s reluctance to ascribe the power of self actualization to possibilities is clearly expressed in the following passage: “If there were a certain force in possible things to put themselves into existence, this group [i.e., the maximally consistent group] of four would incontestably win, for in this combat, necessity would make the best choice possible, as we see in machines in which nature always chooses a most advantageous part. But, possible things having no existence, they have no power to make themselves exist, and as a result, it is necessary to seek the choice and reason for their existence in a being whose existence is necessary and fixed on its own.”32

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Rather than understanding the notion of creation on the model of Platonic emanation, Leibniz is clear that the reason for the existence of worldly things must be found outside those things. Otherwise, there could never be an answer to the question why this world exists rather than another. In other words, the series of worldly things could never provide the reason for its existence. In fact, it is precisely with this thought that Leibniz begins his “On The Ultimate Origination of Things”. He writes that “…we cannot find in any of the individual things, nor even in the entire collection and series of things, a sufficient reason why they exist” (“On the Ultimate Origination of Things”, GP VII 302; AG 149). For this reason, the “One Being who rules the universe, not only rules the world but also fashions or creates it; he is above the world, and, so to speak, extramundane, and therefore he is the ultimate reason for things” (AG 149). In the same paper where he most clearly articulates his view of striving possibles he is also very clear that God is “the ultimate reason for things.” Note that the notion of a reason for the existence of this world implies that other worlds are possible. However, if possible things would attain existence in a process of self realization Leibniz’s motivation for postulating possibilities in the first place would be frustrated. For Leibniz, the raison d’être of possible worlds is that they allow reasoned choice and moral justification of the actual world. It is also for this reason that God is postulated as the only necessary being or the unique being whose essence involves existence. “Creatures are contingent, that is, their existence does not follow from their essence” (Grua 302; AG 28), which is why an act of creation is needed. If this is more or less the way to reconstruct Leibniz’s philosophical motivation, how can one account for his pronouncements that possibilities strive to exist? Fortunately, there is a better way to interpret the notion of the striving possibles. As Adams noted, the correct interpretation of Leibniz’s talk about the “possibles” striving for existence is that, “it is in the mind of God that they strive, and it is the power of God that gives reality to their tendency to exist” (Adams, 1994, 168). Likewise, Blank (2005) recently argued that we can think about the claim or exigency of possibles to exist as the extent to which their essence affects God’s choice to select them for actualization. 33 The extent to which the realization of a certain possible would maximize reality and perfection in the world (relative to other worlds) is also the extent to which it may be said to strive to (or better, to have a claim for) existence. The claim is clearly made upon God. This interpretation makes no concessions to the passive nature of possibilities and to their status as pure concepts in God’s mind. Rather, in this interpretation, God remains the only agent in Leibniz’s story of creation.

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At the same time, it is undeniable that the essence or the logically fixed nature of each possible thing constitutes the reason for God to choose (or not choose) it for actualization. As we have seen in chapter 4, the way an individual is constituted also figures in the reasons whether it would belong the best world or not. I suspect that Leibniz’s notion of striving possibilities responds to a related but different question, namely why there is something rather than nothing, or why a world is to be created at all. I am not sure that the theory of striving possibles provides a good answer but I also do not know if Leibniz has a better one. Here is one place where he addresses this issue: “since something exists rather than Nothing, it is necessary that in Essence itself, or in possibility, something is contained from which actual existence follows, and therefore that reality or possibility brings with it some propensity [propensio] to exist” (A 6.4 1362-1363). Let me observe that, with slightly different emphasis, the notion of striving possibles can be seen (as I think it should) as requiring (rather than making redundant) the need for a sufficient reason in God’s choice to realize the best possible world. If we do not stress the very exigency of possibles to exist but rather Leibniz’s point that they “strive with equal right for existence” (“On the Ultimate Origination of Things”, AG 150), we shall see that this is precisely what Leibniz needs, assuming that all possibles are not compossible, to argue that a reasoned choice among them is required. 34 If all possibles demand existence, they can be distinguished by their perfection, goodness or moral value rather than by being possible. This view is easy to reconcile with Leibniz’s position that possibility is defined in God’s understanding by the principle of contradiction and that the choice to actualize the best world involves God’s will and moral deliberation according to the principle of the best. In this way, the distinction between the realm of pure logic (possibility, essence, and necessary truths) and the realm that involves moral considerations (perfection, goodness, contingent truths and existence) remains in tact. As Leibniz writes in the same piece, “…just as possibility is the foundation [principium] of essence, so perfection or the degree of essence (through which the greatest number of things are compossible) is the foundation of existence” (“On the Ultimate Origination of Things”, AG 151). Because all worlds are equally possible but not equally good, a moral choice between them has to be made. Leibniz does not leave much room to

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doubt who makes this moral decision (see, e.g., 24 Metaphysical Theses, nos. 3 and 4) and who makes possibles actual. It is much less clear how God makes this decision. Leibniz often presents this choice as a decision procedure with fixed parameters and desiderata, along the following lines: God wishes to realize the most perfect world. The most perfect world is the one in which there is the greatest amount of essence or the maximal number of things and the minimal number of laws. Without getting into the details here (see Rescher 1967 and Blumenfeld, 1994), it is clear that Leibniz presents this decision as a solution to an optimization problem of maximizing certain parameters (number of possibles) and minimizing others (the laws). Leibniz stresses with many examples, such as a straight line among curved ones, that there is a determined and unique solution to this problem (e.g., “The Source of Contingent Truths” (1685-89) AG 101; C 534). But if there is such a unique solution, it would seem that God is not free to choose but rather necessitated to choose and create the best world by such decision procedure. While it is important to clearly distinguish between the necessity imposed on selecting the best world and the decision to create it (which may be seen as an independent act of will), the same objection applies to both: Since God is good and desires to bring goodness, and (we assume that) it is better to create rather than not, and it is better to create the best (rather than the second best), Leibniz’s God is necessitated to create the best world. Indeed, Leibniz freely ascribes such kind of necessity to God. For example, in On Contingency 1686?, he writes: “it is necessary for God to choose the best” (AG 30). However, he claims that God’s mode of operation in this context is not characterized by logical necessity but rather by the necessity of the wise to choose the best. He makes it clear that he views such necessity as compatible with freedom. “If the necessity of the wise person to choose the best destroyed freedom, it would follow that God does not act freely when he chooses the best among many alternatives. The essences of things are like numbers. Two numbers are not equal; similarly, two essences are not equally perfect.” (A 6.4 1352; Sleigh 2005, 139, circa 1677) Leibniz’s reasoning goes along the following lines: God is morally necessitated to choose the best because it is the best, not because there are no alternatives. Rather, only because there are alternatives, God can be said to choose the best among them according to the principle of reason. It is crucial for Leibniz’s philosophical project that such choice would be a

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reasoned choice (DM 3; AG 37). Famously, the reasons for God’s choice, according to Leibniz, “incline without necessitating” (DM 13; AG 44). Since the “wise always follows the best inclination”, God, who “always acts with the mark of perfection or wisdom” (AG 30), will always choose the best (DM 13; AG 46). The following example nicely illustrates the way Leibniz conceives of God’s choice: “..as with the wise person, so with God, the first decree and intention is that everything happens with the best reason. And so, if we were to imagine the case in which it is agreed that a triangle of given circumference should exist, without there being anything in the givens from which to determine which one could determine what kind of triangle to create, we must say that God would create an equilateral triangle, freely, of course, but without a doubt. There is nothing in the givens which prevents another kind of triangle from existing, and so, an equilateral triangle is not necessary. However, all that it takes for no other triangle to be chosen is the fact that in no triangle except for the equilateral triangle is there any reason for preferring it to others” (“On the Source of Contingent Truths”, AG 101; C 3) “[T]hough it is certain that God always chooses the best, this does not prevent something less perfect from being and remaining possible in itself, even though it will not happen,..” (DM 13; AG 46). Thus God’s choice to realize the most perfect world, while morally necessary, is not logically necessary since choosing less perfect worlds (or triangles in the example above) remains logically possible. As Blank pointed out, “The doctrine of striving possibles is closely connected with Leibniz’s view that the laws of rational deliberation involve reasons that incline without necessitating. According to Leibniz, reasons that incline without necessitating not only govern the Divine evaluation of possible worlds, but also govern the series of thoughts of human beings.” (Blank 2005, 155) In the following chapter I investigate in some detail the notion of reasons that incline without necessitating in the context of human agents and their alleged freedom of action.

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1 Leibniz’s notion of actualization has some interesting implications. It implies, for

instance, that the world is not an ens per se; rather, the world’s existence derives from (or supervenes on) the existence of its individual members. This is also the main reason for Leibniz’s rejection of the notion of a unique world soul (GP VI 52938). 2 The most comprehensive study of Leibniz’s early commitments is Mercer (2001). Cover and O’Leary-Hawthorne nicely summarize Leibniz’s commitments regarding individual substance, as follows: “Central to the mature Leibniz’s account of individual substance are two categories of notions: First is a set of general defining features of substance, familiar from the Aristotelian tradition and firmly fixed by the intension of ‘substance’ as then conceived: (a) that which is independent of other things; (b) that which is the subject of predication, but is not predicated of another; (c) that which contains within a principle of activity; and (d) that which persists through change. Second is a set of core notions deployed with their Leibnizian glosses: complete individual concept, law-of-the-series, active force, form and soul or entelechy”, Cover and O’Leary-Hawthorne, 1999 217. See also, Martine de Gaudemar, De la puissance au sujet 1994, Adams, Leibniz: Determinist, Theist, Idealist, 1994, and Jalabert, La theorie leibnitienne de la substance, 1948. 3 It is worth noting that this commitment holds both for created things as well as for the creator – all beings are individuals. 4 Both Fichant’s article and Mercer’s extensive study of Leibniz’s early commitments make it evident that Leibniz maintained a similar position throughout his life. 5 I take it for granted here that finality is built into the notion of a program. 6 One might also see in it the neo-platonic notion of the informative type of causality. 7 This internal change is the very foundation of time while the co-existence of a plurality of substances is the foundation of extension and space. 8 This is especially pertinent in light of the debate about whether the early Leibniz was a substance monist. See, for example, Kulstad 2000 and Blank 2001. 9 “…the very substance of things consists in a force for acting and being acted upon. From this it follows that persisting things cannot be produced if no force lasting through time can be imprinted on them by the divine power. Were that so, it would follow that no created substance, no soul, would remain numerically the same, and thus nothing would be conserved by God, and consequently everything would merely be certain vanishing or unstable modifications and phantasms, so to speak, of one permanent divine substance” (On Nature Itself, AG 159-60). 10 See M. de Gaudemar, 1994, 81. 11 The notion of inherent force of action also demonstrates how different Leibniz’s notion of activity is from that of Descartes. Created substances are not moved

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from the outside as in Descartes’ mechanistic picture; rather, they possess the force (as well as the information) to change themselves from within. I discuss this point in more detail in chapter 7. 12 “For this view [of occasional causes] is so far from increasing the glory of God by removing the idol of nature that, quite to the contrary, it seems with Spinoza to make of God the very nature of things, while created things disappear into mere modifications of the one divine substance, since that which does not act, which lacks active force, which is robbed of discriminability, robbed finally of all reason and basis for existing, can in no way be a substance” (On Nature Itself, AG 16566). 13 See also: “Primitive force, which is nothing but the first entelechy, corresponds to the soul or substantial form, but for this very reason it relates only to general causes which cannot suffice to explain phenomena” (Specimen of Dynamics L 436). 14 This point is controversial. Cover and O’Leary-Hawthorne (1999, 227) identify the substance with its law-of-the-series, arguing that the law-of-the-series is itself causally active. They write: “What is law enforcing is causally active: the substantial form is the law-of-the-series, the substance itself” (227). However, this proposal lacks the resources to account for Leibniz’s view of possible individuals along the lines I have suggested above and for his view of actualization. As I will suggest in the next chapter, there are other reasons to reject the view that, in itself, the law is causally active. 15 GP VI 511. 16 “The other question is whether creatures can properly and truly be said to act. Once we understand that the inherent nature is no different than the force of acting and being acted upon, this question reduces to the earlier one. For there can be no action (actio) without force for acting and, conversely, a power [potentia] which can never be exercised is empty” (On Nature Itself, AG 160). 17 “For forms are for me nothing but activities and or entelechies, and substantial forms are primitive entelechies” (to Bernoulli, 18 November 1698, AG 168). 18 See Leibniz’s letter to Arnauld March 23 (L 198) and his reply to Bayle’s criticism of the New System: “The law of order... constitutes the individuality of each particular substance” (GP IV, 518; L 493). In the Theodicy (291) Leibniz writes that “every simple substance has perception, and that its individuality consists in the perpetual law which brings about the sequence of perceptions”. 19 “For me nothing is permanent in things except the law itself… The fact that a certain law persists, which involves the future states of what we conceive to be the same – this is the very fact, I say, that constitutes that same substance” (GP II 26364; L 534-35). 20 In this context, the ‘incomplete’ is “the active without the passive or the passive without the active” (To Bernoulli, September, 1698, AG 167). For an elaboration of this thesis in the early Leibniz, see Mercer 2001; for the later Leibniz, see Phemister 2005 pp. 40-46.

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21 “I understand matter as either secondary or primary. Secondary matter is,

indeed, a complete substance, but it is not merely passive; primary matter is merely passive, but it is not a complete substance. And so, we must add a soul or a form analogous to a soul, or a first entelechy, that is, a certain urge [nisus] or a primitive force of acting which itself is an inherent law, impressed by divine decree” (AG 162-63). 22 In fact, my approach differs from Adams’ only to the extent that I apply it to individuals rather than to worlds (since creation of the world just is creation of its individual members). Adams writes: “Let us imagine ourselves in the position of Leibniz’s God. In His infinite understanding, He has a perfect knowledge of infinitely many possible worlds, each of them completely determinate (presumably in infinite detail). One of them is the single world on which He has conferred actuality: the actual world. But what is it that He has conferred on that world in actualizing it? What does that world have by virtue of being actual that the other possible ones do not have? In what does the actuality of the actual world consist?” “Theories of Actuality” in The Possible and the Actual, Loux (ed.) 1979, p. 190. 23 “Ideas are purely abstract things, like numbers and shapes, and cannot act” (AG 277). “L’âme n’est pas idée mais source (fons) d’innombrables idées. Car elle possède, outre l’idée présente, quelque chose d’actif, c’est-à-dire la production de nouvelle idées” (Réfutation inédite de Spinoza par Leibniz, ed. Foucher de Careil, Paris, 1854, 46). See also A 6.4, 1713. 24 It is very interesting to note in this context that, in this respect, Leibniz precedes Kant who explicitly stated that existence is not a predicate. As Russell noted, Leibniz too held this view except in the unique case of God. Given the context of creation and actualization, the reason is clear – it is God, in thinking the concepts of all individuals, who confers power of action on some of them. For this reason, God himself must be seen in this system as the unique being whose existence is necessary or belongs to his essence. “…si l’Être par soi est impossible, tous les êtres par autrui le sont aussi, puisqu’ils ne sont enfin que par l’Être par soi : ainsi, rien ne saurait exister” (Sur la démonstration cartésienne de l’existence de Dieu du P Lamy, GP IV 406). 25 As Martine de Gaudemar eloquently put this, “La leçon leibnizienne concernant la puissance est brève: sans détermination ni orientation, il n'y a pas de puissance” (1994, 80). 26 “Thus, in my view, each substance (already expressed in advance) produces in orderly fashion all that will ever happen internally to it… (Letter to the Marquis de l’Hospital, 1695; GM II 295, my translation). 27 “Space and time are orders of things, not things” (AG 257). 28 De rerum originatione radicali, 23 November 1697; GP VII, 303. See also GP VII 289 where Leibniz says that “possibilitas exigat existentiam”, Rauzy 1998

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466; C 534. However, it clear that it is only within the context of God, seen as ens necessarium est Existenficans, who makes the possibilities actual that possibilities may be said to demand existence. 29 Blumenfeld, “Leibniz’s Theory of the Striving Possibles” (1973); Rescher, “Leibniz on Creation and the Evaluation of Possible Worlds” (1981). 30 Shields, “Leibniz’s Doctrine of the Striving Possibles”, 1986 ; Belaval, “Note sur Leibniz et Platon”, 1995. 31 For a discussion and references to Leibniz’s use of these principles in the De Summa Rerum (1675-76), see Parkinson introduction to SR pp. xxii-xxv. 32 Dialogue between Theophile and Polidore, 1679?, Grua Textes inédites, I: 286, translation from C. Wilson, 1989 42-43. See also Grua 324 for a very clear statement of this point from 1683-86. 33 “Thinking the degree of goodness of a possible substance, for the Divine mind, is identical with being inclined to a certain degree to create this substance. Because inclinations involve presumptions towards a certain course of thought or action that can be overruled, not all inclinations of the Divine mind result in creating actual substances” (Blank 2005, 154). As this citation makes clear, the inclination is God’s but it derives from the essence of the possible thing. 34 It is interesting to note that in a text from 1677?, entitled A Demonstration that God Understands All Possibles (A 6.4 1353), Leibniz is using a similar illustration, namely, that of “a liquid that is restrained and that tries to flow out. It is manifest that on every occasion the liquid will probe all possible routes. However, it will succeed only by finding the easiest of all possible routes. That all routes are probed is evident … because the most suitable route is not determined except by comparison with all routes” (Sleigh, 2005 141). If we draw the analogy with the striving possibles then here, too, God would have to consider all possibilities in order to find the best.

Chapter 6 Agency and Freedom 6.1 Introduction I have argued above that Leibniz’s notion of created individuals involves a rule of action that defines a unique program of action and primitive power to act. This view of the individual, however, gives rise to a problem that Leibniz famously (and very aptly) characterized as a labyrinth, namely, the labyrinth of human freedom.1 The problem is how to reconcile Leibniz’s definition of an individual through its complete concept – a concept which entails all the individual’s predicates of past, present, and future actions – with his claim that rational individuals may perform these very actions freely. In some early texts but more explicitly in his later ones, Leibniz describes free human actions in terms of moral necessity, which he distinguishes from logical and metaphysical necessity. According to Leibniz’s notion of moral necessity, the wise is morally necessitated to do the best while it is logically possible not to do the best. In section 5.3 we have seen that considerations of moral necessity inform Leibniz’s view of God’s decision to actualize the best world. In this chapter I examine the extent to which the notion of moral necessity can be applied in the context human agency. I suggest that something similar, which may be called the principle of the apparent best, holds in the human context. The reading I develop below shows that Leibniz’s notions of possibility and agency, particularly that of rational agency, are crucial for understanding his insistence on human freedom. 6.2 Leibniz’s View of a Created Individual and its Alleged Freedom of Action Throughout his career Leibniz defined an individual substance as entailing its own source (principium) of activity.2 As we have seen, for Leibniz, an individual is essentially active, both in the sense that its nature is to act and in the sense that its activity brings about the changes in its properties. In the late 1670s, Leibniz began to define an individual through the notion of a complete concept that includes all the individual’s predicates, and thus specifies everything that would happen to the 145

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individual.3 A complete concept may be seen as God’s view of an individual, which includes foreknowledge of all the individual’s properties and activities ((Discourse on Metaphysics 13, AG, 45). Yet, if each individual is defined by such a concept, then, as Leibniz notes, “by considering the individual's notion, one can see there everything that can truly be said of it” (Discourse on Metaphysics 13, AG, 44). In presenting this definition of the individual in the Discourse on Metaphysics Leibniz notes that it seems to conflict with the individual’s freedom of action (30). If one can deduce from the complete concept of an individual (such as Caesar) all its predicates in the same way that one can discern in the nature of a circle all the properties that can be deduced from it, then “it would seem that there will be no place for human freedom, and that an absolute necessity would rule all the actions as the other events in the world” (DM 13, AG 44-45). When the complete concept of an individual is seen as a general concept, great difficulties arise for the individual's freedom of action. The difficulty becomes only more acute as Leibniz goes on to analyze the relation between an individual’s complete concept and its predicates in terms of the relations between the subject term and the predicate term in propositions such as “Caesar will cross the Rubicon”. He writes that, ...if someone were able to carry out the whole demonstration by virtue of which he could prove the connection between the subject, Caesar, and the predicate, his successful undertaking, he would in fact be showing that Caesar’s future dictatorship is grounded in his notion or nature, that there is a reason why he crossed the Rubicon rather than stopped at it and why he won rather than lost at Pharsalus and that it was reasonable, and consequently certain, that this should happen. But this would not show that it was necessary in itself nor that the contrary implies a contradiction (DM 13, AG 45). Note that, in each of the two passages cited above from the Discourse on Metaphysics, the notion of necessity is qualified: first as “absolute” and second as “in itself”.4 Note also that Leibniz’s claim that Caesar’s action (his crossing the Rubicon) was certain is grounded in the claim that the action is reasonable. This reasonableness may derive from God’s choice to create Caesar but it also applies to the rationality of Caesar’s action. Leibniz’s claim that Caesar’s action was not necessary in itself is grounded in the claim that a contrary action (not crossing the Rubicon) does not imply a contradiction and, in this sense, it is contingent.

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Leibniz’s typical line of defense of the contingency of Caesar’s action runs as follows: God’s choice to create Caesar is contingent upon God’s choice to create the best world, in which Caesar is a member. Since Caesar’s existence and, consequently, all Caesar’s activities, are contingent upon God’s choice to create him, they are not absolutely necessary. Rather, Caesar’s activities are considered to be hypothetically necessary because they depend on the hypothesis that God would choose to create the world in which Caesar exists. In other words, it is true that, if God chooses to realize a world in which Caesar exists, Caesar will cross the Rubicon.5 Given that Caesar has been created, it follows that Caesar will cross the Rubicon. But since Caesar’s creation is contingent upon God’s choice to create this world, Caesar’s actions are contingent as well.6 Since Arnauld to present day readers of Leibniz, his insistence on considering Caesar’s action contingent, let alone free, has intrigued many and convinced few.7 Leibniz’s notion of freedom requires that the contrary act of an individual, say that ‘Caesar will not cross the Rubicon’ would be logically possible, that is, would be, metaphysically speaking, not necessary but contingent. However, as Blumenfeld notes, ...Leibniz makes clear in numerous discussions that the contingency condition he has in mind for freedom is not satisfied merely by the agent’s non-existence. What is at stake is the agent’s possibility to behave differently. Thus Leibniz says that, in virtue of our liberty, the will ‘has the power to act otherwise or also to suspend its action entirely, since both alternatives… are possible’ (L 322; GP IV 454).8 The mere possibility of Caesar’s non-existence seems insufficient to justify the claim that it would be logically possible for Caesar to act otherwise. Yet, as Blumenfeld (1988) and others have argued, it is extremely difficult to reconcile the claim that various courses of action are open to an individual with the claim that the individual’s concept fully specifies and determines the individual’s unique course of action, since, as we have seen, the individual's complete concept also defines the individuality and identity of that individual. Consequently, it seems that the doctrine of the complete concept of the individual conflicts with human freedom of action. Yet, as we have seen, Leibniz does not think so. Rather, he thinks that the doctrine of complete concept is compatible with human freedom of action and his insistence still baffles his students.9 I think that it is instructive to remind ourselves at this point that Leibniz characterized this problem as a labyrinth. I am undecided whether he thought that he knew

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the way out of this labyrinth or not. It seems likely that he saw it differently at different times. Be this as it may, his insistence commends our attention and I will make a modest attempt here to contribute to our understanding this formidable and fascinating labyrinth. While Leibniz's doctrine of the complete concept has been thoroughly investigated by contemporary scholars, it seems to me that an interesting point has been overlooked, viz., the relation between concepts and agents. While the relation between a subject concept and a predicate concept is a relation between concepts and thus admits of logical necessity, the case might be different for the relation between a predicate concept contained in the individual’s concept and the action an actual individual performs. Furthermore, given the status of complete concepts as possibilities in God’s mind, it seems that the complete concept may have two distinct (but complementary) senses. In the context of possibility, we might see the complete concept as a specific description of the individual’s would-be activities and properties (if it is created). This is the sense I used above to describe the concept of an individual as it is conceived in God’s mind. Yet I would like to suggest that the doctrine of the complete concept is also morally relevant, both in the context of God’s choice of the best world (as I noted in section 5.3) and in the context of human action. In the context of human action, we might see the complete concept as intrinsically related to Leibniz’s notions of the principle of reason and that of moral necessity. In this context, the individual’s complete concept may be seen as including the reasons according to which a rational agent would judge what seems to him the best course of action. By drawing on the notion of an agent as consisting of both a program for action and an inherent source of action presented above, I will suggest that this distinction can be used to shed some light on Leibniz’s use of the notion of moral necessity in the context of human agency, viz., the “moral principle that all minds will pursue what appears best to them” (Remarks on Arnauld’s Letter, May 1686, AG 70). 6.3 The Inclination of Reason Let me begin with an example that Leibniz employs in both divine and human contexts. In “The Source of Contingent Truths” (C 1-3, 1685-89), immediately after the example of the equilateral triangle we have considered in section 5.3, Leibniz writes: Circumstances are the same if one were ordered to draw a line from one given point to another, without being given anything by which to determine what kind of line or how long a line to draw.

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Surely it would be a straight line, but it would be drawn freely, for just as nothing prevents a curve, nothing recommends one either (C 3; AG 101).10 Leibniz‘s example provides a clear illustration of his view of rational agency as informed by the principle of reason: Given two points, one is to draw a line between them. Since infinitely many curved lines satisfy this requirement, and since “nothing prevents a curve”, it is clear that all lines are equally possible. Yet, according to Leibniz, only one line – viz., the straight line – is the optimal solution to the problem and is therefore recommended by reason.11 While there are many possible courses of action here, only one has a “reason for preferring it to others” (AG 101). “For, as with a wise person, so with God, the first decree and intention is that everything happens in accordance with the best reason” (AG 101). It is worth stressing that the notion of a “best reason” makes sense only if reasons for alternative courses of action are (at least logically) possible. As Leibniz notes in the same paper, the principle according to which reason is applicable to contingent truths (and not to necessary ones) is that “there is more reason for that which has been done than there is for its opposite” (AG 101). Thus we see that Leibniz’s notion of logical possibility and his principle of reason are presupposed in both divine and human contexts of action and choice. Leibniz insists that the optimal line (as well as the optimal triangle in the example just above) “would be drawn freely”. He is clearly employing here his ‘principle of reason according to which “everything happens in accordance with the best reason” (AG 101). It seems reasonable to suppose that the use of reason in deciding among various courses of action informs both the predictability and the certainty of the choice, as it is unique and transparent to an all-knowing mind. While according to Leibniz it is certain that a rational agent will draw a straight line, the certainty of the result does not imply that it was logically impossible for the agent to draw a curved line. Whatever the agent does, it does not follow that what he or she did not do was impossible. Rather, according to Leibniz, the agent’s rationality “inclines” the agent to act as reason recommends and as God foreknows.12 The agent’s rationality points to the apparently optimal action without ruling out the others. 6.4 Moral Necessity and Logical Necessity While this example is not taken from the domain of morality, Leibniz’s principle of reason is obviously related to the moral domain, or, more precisely, to the obligation to do the best. In his later writings (notably in

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the Theodicy and the Correspondence with Clarke) Leibniz clearly explicates the obligation of the wise to choose the best with the notion of moral necessity. As Adams clarifies, “‘morally necessary’ has a precise meaning. The morally necessary is what one morally ought to do” (Adams, 1995, 22). While the appeal to moral necessity is frequent in Leibniz’s later writings, the idea of moral necessity is developed much earlier and is clearly rooted in the principle of sufficient reason. An early articulation of this idea is already present in the Elementa juris naturalis (1670-71), where Leibniz writes: “something just [justum] or licit [licitum] is whatever is possible to be done by a good person [vir bonus]”; and “something unjust [injustum] or illicit [illicitum] is whatever is impossible to be done by a good person” (Fifth MS, A 6.1, 465).13 As Murray recently noted, “Although Leibniz’s earliest use of ‘moral necessity’ in an actiontheoretic sense does not occur until 1702, the fundamental features of the view are in place much earlier”. “The metaphysical anti-bruteness”, which Murray holds to be the motivating force behind the notion of moral necessity, is, for Leibniz, the “Principle of Sufficient Reason”.14 In later texts, Leibniz explicitly contrasts the notion of moral necessity with those of logical and metaphysical necessity. He writes: we must also distinguish between a necessity, which takes place because the opposite implies a contradiction; (which necessity is called logical, metaphysical, or mathematical) and a necessity which is moral, whereby, a wise being chooses the best, and every mind follows the strongest inclination (Fifth Letter to Clarke, Alexander (ed.), 1956, p. 56). In the Theodicy Leibniz states that, A very clear recognition of the best determines the will; but it does not necessitate it, properly speaking. One must always distinguish between the necessary and the certain or infallible, as I have already done more than once, and distinguish metaphysical necessity from moral necessity (section 310, p. 313). Leibniz writes that, “moral necessity contains an obligation imposed by reason which is always followed by its effects in the wise. This kind of necessity is happy and desirable, when it is prompted by good reasons to act as one does; but necessity blind and absolute should subvert piety and morality” (Reflections on Hobbes section 3, see also Theodicy 310).

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Leibniz sharply distinguishes between “metaphysical necessity, which leaves no place for any choice, and moral necessity, which obliges the wisest to choose the best” (Theodicy 367). He writes explicitly that moral necessity does not destroy the possibility of the contrary” (GP VI, 386). Rather, as noted above, “moral obligation imposed by reason” presupposes the logical possibility of acting otherwise.15 While the notion of moral necessity pertains primarily to God, it also applies to other rational agents endowed with understanding and will. As Jack Davidson recently observes, “The will has a natural inclination towards the good as a telos, just as the intellect has towards the truth. I believe that Leibniz, from early to late, regards these as necessary (or constitutive) elements of personal, conscious minds, divine and human”.16 Leibniz is explicit about both the similarity and the dissimilarity between the divine and the human mind in the application of the principle of reason. For example, he writes that, “…just as God himself decreed that he would always act only in accordance with true reason of wisdom, so too he created rational creatures in such a way that they act only in accordance with prevailing or inclining reasons, reasons that are true or, in their place, apparent” (Grua 302-6; AG 29). In analogy with the way God chooses the morally best world among equally logically possible worlds and, in analogy with the way God’s understanding conceives of all logically possible worlds and his will inclines to the choice of the best,17 human agents, too, choose from several possible courses of action the one they perceive to be best.18 The major dissimilarity is of course that, while in the divine context these reasons always lead to the best, in the human context, they are often informed by the apparent best.19 Yet in both contexts, the connection between reason and action is not one of logical necessity. While the “best reason” for the agent’s choice may be the cause of the agent’s action, it is not logically necessary that it would; rather, it is morally necessary. Seeskin (1977) articulates this point as follows: “[f]rom the standpoint of logic alone, the will is free to choose anything” (325). “[L]ogic alone can never prove that any reason, no matter how persuasive, will be acted on” (330). “But it is a fact that it [the will] always chooses what the understanding presents as the best possible alternative” (325).20 Although an agent might be able to resist the truth it knows, it does not follow that he will ever do so; rather, according to Leibniz, the agent will act according to the reason that appeals to him the most.21 For Leibniz, pure logic cannot decide between possibilities; rather, logic can fix possibilities according to the principle of contradiction (and the presuppositions I have presented in the first chapter), but deciding between

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logical possibilities involves some moral considerations since it involves excluding some possibilities in favor of others. This is why a distinct modality is required in this context. As noted, the notion of moral necessity is clearly distinct from metaphysical necessity as well as from logical necessity; it applies primarily to moral reasoning of rational agents. In other words, since mere logical possibility (or possibility in itself) does not suffice to decide between alternatives, the principle of sufficient reason and a modality of picking the best are invoked in this context. Note that Leibniz’s employment of the principle of sufficient reason in this context is consistent with his analysis of contingent propositions as propositions whose demonstration (per impossible) requires infinite analysis. Contingent propositions require infinite analysis because their truth also depends on moral considerations, that is, on the principle of sufficient reason and not only on the principle of contradiction. Since contingent truths depend on the free decree of God to create this world – and this is what they are primarily contingent upon – the reason that they cannot be demonstrated is not only technical, i.e., that they cannot be reduced to identities, but also that their demonstration involves some moral considerations which cannot be reduced to purely logical ones. The notion of moral necessity can be also seen as explicating action according to reason in the domain a of logical contingency, that is, the domain of created rational agents. The employment of moral necessity can be put thus: While it is logically possible for a rational agent not to perform an action that seems to be best, the agent has no moral hesitation that that action is the best. 6.5 Final Causes and Moral Laws In his Leibniz on Human Freedom, Parkinson has pointed out that there is a conceptual link between Leibniz’s notion of freedom and his notions of purpose and final causation. He writes: “God, in creating human beings, does not create mechanisms; rather, he creates substances which choose in accordance with final causes” Parkinson 1970, 60). “...[Leibniz] holds that every substance is the source or principle of its actions. To say this is, for Leibniz, to say that it acts purposively, towards a certain end – though it should be added that only some substances (we may call them ‘conscious’ substances) are aware of what their ends are” (Parkinson 1970, 61).22 Thus it is clear that final causes and purposes figure in a rational agent’s considerations of the best course of action. In distinction from other agents, a rational agent may come to know or perceive herself as an agent and as figuring out her ends and purposes.23 As Adams recently noted, “[i]n final causation, as conceived by Leibniz, something is done, or

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occurs, because of the value or apparent value, of an end that is an object of choice or appetition.”24 It is all the more interesting, therefore, that, in his later writings, Leibniz often characterizes acting in accordance with final causes as acting in accordance with moral laws. In his correspondence with Clarke, Leibniz argues that, while bodies are governed by mechanical laws, spirits are governed by moral ones. He writes: “All the natural forces of bodies are subject to mechanical laws, and all the natural powers of spirits are subject to moral laws. The former follow the order of efficient causes, and the latter the order of final causes” (Fifth letter to Clarke, GP VII 419; L 716). It seems clear in this passage that the notion of moral laws applies to individual spirits or agents. The connection between final causes, moral laws and the free actions of spirits is also explicit in the following passage from Leibniz’s Fifth letter to Clarke: … the soul does not disturb the laws of the body, nor the body those of the soul; and …the soul and the body do not only agree together, the one acting freely, according to the rules of final causes, and the other acting mechanically, according to the rules of efficient causes. But this does not derogate from the liberty of our souls; as the author here will have it. For, every agent which acts with choice in accordance with final causes, is free, though it happens to agree with an agent acting only by efficient causes without knowledge or mechanically; because God, foreseeing what the free cause would do, did from the beginning regulate the machine in such manner that it cannot fail to agree with the free cause... (section 94, see also section 124). While this is not the place to discuss the complex relations between final causes and efficient causes in any detail, it seems reasonable to suppose that action in accordance with moral laws is related to the individual agents acting according to their individual rules of action. I already noted that the individuals’ rules of action accord with their ends and purposes. In turn, thanks to God’s foreknowledge and pre-harmonization, acting according to moral laws and purposes is compatible with the order of efficient causes. Murray (1995) argues that, “...the ‘moral law’ consists of the force that compels the will to judge in accordance with what the intellect perceives to be best” (45). This claim presupposes that the notion of a moral law plays a role in the individual law of action. However, it seems to me that Leibniz considers the notion of “force” in this context not primarily in causal terms but in rational ones, that is, as spelling out the individual’s inclination of reason.

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The agent’s program of action may be seen as providing the reasons that inform the agent’s will to choose what seems to her to be the best course of action. As we have seen, Leibniz terms this kind of rational inclination ‘moral necessity’ and distinguishes it from logical and metaphysical necessity.25 6.6 Individual Laws as Prescriptions for Rational Action How is Leibniz’s employment of the principle of reason and of moral necessity related to his view of the individual I presented above? And how can his view of moral necessity be applied to the particular actions and choices of individuals? I already noted that Leibniz defines an individual as having an inherent source of activity and a complete concept. These two aspects are closely related, both historically and conceptually, to the view that an individual has an inner rule providing a complete program for the individual’s activities. Such a “production rule” of the individual’s concept (see chapter 2) functions as a source of the individual’s activities, once the individual is created (see chapter 5). At the same time, as seen in the examples above, it is clear that Leibniz understands some human actions and deliberations in the context of applying the principle of the apparent best or as acting according to what they see as the best course of action. If this is the case, it seems that the production rule of the individual can be seen not merely as the efficient cause of the individual’s actions but also as a prescription according to which rational individuals are to act, in accordance with the principle of the apparent best. From a timeless point of view, the rule may be seen as a description or a specification of the individual's activities (conceived as possible). Yet, in the case of an actual rational agent, it may also function as prescribing the individual’s future activities. The intuition here is that the rule in itself, seen as prescribing a possible course of action, need not have a necessary causal impact on the individual’s activities. As Leibniz wrote: “…although the soul’s present actions are a natural and certain consequence of its preceding state, they are not a necessary consequence. It is rather like the way knowledge of the greatest good makes us choose it, by inclining the soul but not necessitating it.”26 As I suggested in the previous chapter, in itself, the rule of the individual has no causal powers; it simply defines a concept, a possibility – it is not an agent or a real individual. In the context of rational agents, I suggest that the rule can be seen as playing a normative (rather than an exclusively causal) role, that is, the role of pointing to the best course of action for the agent. It thus suggests a way in which the principle of sufficient reason applies to the particular activities of rational individuals.

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In this reading, the individual’s actions, which correspond to these predicates, need not be seen as the unmediated results of the individual’s concept, conceived on the model of either logical deduction or mechanical execution.27 Rather, rational individuals are agents who act according to the reasons that incline them most.28 As Leibniz argues both in the divine and the human contexts, to act rationally according to reasons is not to be logically necessitated by them. The agent’s reasoning need not be seen as an immediate and mechanical procedure. Rather such inclining reasons, specified by the individual’s concept, call for actions that need not necessarily be the results of the agent’s activity, if acting otherwise remains logically possible. Leibniz’s definition of an individual as entailing its source of action and rule of action implies that an agent is not reducible either to a mere mechanism or to a mere concept. Rather, an individual is an active agent. An individual has both a primitive power of action as well as a program of action and for this reason it is not reducible to either one of them. Leibniz’s use of Spinoza’s suggestive phrase, “spiritual or formal automaton” (in the New System of Nature paragraph 15) makes this point clear. For Leibniz, a “spiritual automaton” should not be confused with mechanical automaton.29 As Parkinson clarifies, Leibniz does not think of a soul as a kind of immaterial clockwork; as he puts it (GP VI, 356) ‘the operation of spiritual automata ... is not mechanical’. Rather, the word ‘automaton’ is used in its literal sense of ‘self moving’, the point being that the soul has an internal force which makes it the source of its own actions (Parkinson 1970, 17 n 11). Since the soul is the source of its own actions (i.e., it is spontaneous), the notion of ‘spiritual automaton’ does not eliminate agency; rather, it accentuates it. Likewise, Leibniz’s notion of a rational individual presupposes an agent who is acting for reasons. Yet, the individual’s program of action does not activate itself; rather, a rational agent is to act according to these reasons. Seen in this way, the rule does not necessarily generate the causes for an action; rather, it primarily provides the reasons in the agent’s deliberations. As Sleigh noted, “The principle of sufficient reason requires a reason or cause for each state of affairs that obtains, but there is room within the disjunction – reason or cause – to slip in some version of libertarianism – at any rate, some account of freedom according to which free decisions do not come about in virtue of natural causal necessities, ultimately beyond the control of the

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agent” (1999, 1259-60).30 In the end, the reasons prescribed by the individual’s complete concept indeed constitute the causes of the individual’s activities. Viewing the complete concept in a prescriptive sense allows us to place the individual’s actions and deliberations in the moral context suggested by the application of the principle of sufficient reason in the human context, so that alternative actions remain logically possible. In other words, viewing the individual’s complete concept as a prescription for action helps explaining how an action can be seen as morally necessary but not metaphysically necessary.31 As Leibniz states in the Theodicy: As for the parallel relation of the understanding to the true and that of the will to the good, one must know that a clear and distinct perception of the truth contains with it the affirmation of this truth: thus the understanding is necessitated in that direction. But whatever perception one may have of the good, the effort to act in accordance with the judgment, which in my opinion forms the essence of the will, is distinct from it (section 311, p. 314). Leibniz clearly distinguishes between recognition of the good and acting in accordance with the good. As I already noted, it is one thing to recognize the best course of action and another to act accordingly. Most relevant to this concern is the relation between reason and action which, according to Leibniz, is not metaphysically necessary. Leibniz makes this clear in the continuation of the above passage: “Hence it comes about that our soul has so many means of resisting the truth which it knows, and that the passage from mind to heart is so long. ...Thus the connection between judgment and will is not so necessary as one might think” (section 311, p. 314). 6.7 Intrinsic Predicates and Necessary Predicates Let us now examine whether this interpretation helps accounting for the relation between the predicates entailed in an individual’s complete concept and the individual’s actions to be seen as intrinsic to the individual’s concept but not logically necessary. Let me first observe that, while the connection between the subject of the complete concept and its predicates is a relation between concepts, the relation between the predicates and the individual's actions is not; rather, it is a relation between concepts and the actions of an agent. It goes without saying that concepts and actions belong to different categories. The connection between the actions prescribed by the predicates of the complete concept and the

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agent’s actions depends, among other things, on God’s choice to realize the agent’s program of action as a part of the best world and on the agent’s execution of the program. How does this point bear on Leibniz’s distinction between intrinsic and necessary predicates. Leibniz wrote: "I suspect that Arnauld did not want to grant me this proposition only because he took the connection I am maintaining to be both intrinsic and necessary, whereas I hold it to be intrinsic, but in no way necessary; for now, I have sufficiently explained that it is founded on free decrees and acts" (Remarks on Arnauld’s Letter, May 1686, AG 76). While the predicates corresponding to the individual’s actions belong to its complete concept and in that sense are intrinsic to it, God’s free decrees as well as the individual’s actions are also involved in realizing them. Since the predicates correspond to discrete steps in the prescription, they are intrinsic to it. However, the action indicated by each step does not derive from the prescription alone. If an action depends on the agent’s execution of the instructions, then a step in the individual’s prescription may be seen as intrinsic to it (the individual’s concept) and yet the action it calls for may not be seen as a logically necessary consequence of the concept. For the connection between a predicate and its corresponding action is not deductive or purely logical. Let me examine this point more closely. We know that it is inscribed in Leibniz’s complete concept that he is to travel from Paris to Germany in 1677. According to my suggestion, Leibniz’s complete concept prescribes that he is to travel from Paris to Germany because it is part of his lifeprogram. However, is it logically necessary for Leibniz, the person and agent, to follow the life-program prescribed by his concept? Leibniz clearly thought otherwise: “As if concepts or previsions made things necessary, and as if a free action could not be contained in the concept or perfect view God has of the person to whom it will belong” (LA 17). He goes on to clarify: I do not intend any connection between the subject and the predicate other than that which holds in the most contingent truths, that is, that we can always conceive something in the subject which serves to provide a reason why this predicate or event belongs to it, or why this happened rather than not. But these reasons for contingent truths incline, rather than necessitate. Therefore, it is true that I could fail to go on this trip, but it is certain that I shall go.32

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We may read this fascinating passage as follows: Leibniz’s concept prescribes the reasons according to which it would seem best for him to take the trip to Germany and, in this sense, inclines him to take it. Leibniz’s action, as distinct from the predicate, however, remains contingent, if it is not logically necessary that he will take it. The realization of the concept is something an agent does. Another way to articulate this point is to note the conceptual gap between the concept of an individual and the actions of a real individual.33 Even though a complete concept entails every truth about an individual, concepts and agents belong to different categories.34 The individual’s actions clearly depend on the individual’s program but they need not be seen as necessary consequences of it. Seeing the production rule of the individual in a prescriptive sense makes this point more explicit and intuitive since a prescription is something an agent is not logically necessitated to follow. However, does this intuition hold in the case in which the prescription entails the agent’s very life-program and thus constitutes the individual’s identity? According to Leibniz, God has perfect knowledge of the individual and, therefore, God knows whether Leibniz will or will not take the actions prescribed by the rule. While Leibniz is absolutely clear that God foreknows that he will choose to travel to Germany, he states: ... I am free to take this journey or not, for although it is included in my concept that I shall take it, it is also included therein that I shall take it freely. And there is nothing in me of all that can be conceived in general terms – i.e., in terms of essence, or a species of concept, or an incomplete concept – from which one can infer that I shall take it, whereas from the fact that I am a man, one can conclude that I am capable of thought (LA 52). While Leibniz’s journey is included in his concept, it is up to Leibniz, a rational agent, to decide and to take the journey. This passage makes it clear that a Leibnizian agent is not reducible to its concept. Even if the individual’s concept provides a full program of its future activities, a program does not realize itself; rather, it is the agent who is to realize the program. Leibniz’s two definitions of the individual – as having a primitive source of activity and as having a complete concept specifying the reasons for action – are both essential components of his notion of a created individual. Let me emphasize that the agent and its program of action are not independent of one another. Rather, they should be seen as two complementary and mutually constitutive aspects of a Leibnizian complete individual. By integrating the two definitions of the individual

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mentioned above and by stressing the prescriptive sense of the second definition, a fuller picture of a rational individual emerges. According to the first definition, each individual is inherently active; it is an agent whose spontaneous activity constitutes its being. According to the second definition, each individual has a complete program of its activities. Interpreting the second definition in a prescriptive sense yields an inherent tendency to act according to a comprehensive prescription for action. However comprehensive the prescription may be, the relation between it and the individual’s activities is not purely causal or purely logical. A prescription recommends a course of action for the agent. A rational agent, endowed with understanding and will, perceives various possibilities, “understand the reasons and feel the inclinations” (Theodicy, Observations on Kings, section 16). Thus we see more clearly why the modality of moral necessity is called for in this context. 6.8 Murray on Moral Necessity Indeed Murray (1995) has suggested that moral necessity is a distinct type of modality, which characterizes free acts. However, according to him, free choice springs from the individual’s character, that is, the dispositions one cultivates by moral habits and desires (ibid 94). He argues that the relation between moral dispositions and actions is governed by moral necessity. I agree that the notions of moral laws and moral necessity should be connected through the notion of inclination or moral disposition. However, since Leibniz repeatedly suggests that reasons incline one to action (rather than necessitate it), it seems more adequate to view such inclinations as the reasons for the morally optimal action. Such a connection between reasons and the agent’s inclination to action is evident in passages such as the following: No agent is capable of acting without being predisposed to what the action demands; and the reasons or inclinations derived from good and evil are the dispositions that enable the soul to decide between various courses... (Theodicy, Observations on Kings, section 16). “The dispositions that enable the soul to decide between various courses” are “the reasons or inclinations derived from good and evil.” Thus, Leibniz’s notion of disposition is clearly placed in a moral context where various courses of action seem equally possible but not equally good. However, unlike Murray’s suggestion, the notion of moral disposition need

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not be seen as psychological; rather, it can appeal to the agent’s reasons for action. If the notion of inclination is one of reasons (i.e., reasons to choose the best among the “various courses” of action), then it may be seen as related to the individual’s rational prescription for action.35 In this way the notion of a prescription for action naturally connects the notions of moral law and moral necessity. At the same time, it is worth noting that the prescriptive interpretation I sketched above satisfies the three conditions set out by Murray (1995): 1. The Prevolitional Condition: The subjunctive conditionals of human freedom known by God must have their truth value prior to any free decree of God, i.e., be known prevolitionally. 2. The Sufficient Reason Condition: There must be a sufficient reason which explains why a subjunctive conditional of human freedom has the truth value it does, or, alternatively, why a complete individual concept has the related property instead of its negation. 3. The Spontaneity Condition: This sufficient reason must be such that it allows for the action of the individual to be spontaneous, i.e., it must not consist of a divine predetermination via efficacious concurrence or external causes” (Murray 1995, 84). Since God knows the prescription for action and knows that the agent will heed the prescription, he also knows what would be the activities of the individual (formulated as subjunctive conditionals). This satisfies the first condition. Since the prescription for action provides the reasons for action entailed in the individual's complete concept, the sufficient reason condition is satisfied. Since the sufficient reason has a prescriptive force rather than a direct causal one, it implies that the action of the individual is spontaneous and stems from his or her own rationality. In this way the interpretation I offer above satisfies the three conditions noted above. 6.9 Objections The interpretation presented above faces some difficult problems and objections. Let me begin by a critique of the main idea. I suggested that the distinction between the complete concept of the agent and the agent realizing it helps to make sense of Leibniz’s insistence that it is logically possible for the agent to act otherwise. It may be objected that, whatever

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goes into the agent’s deliberation and decision processes (let alone the result), is already inscribed in the individual’s concept and therefore doesn’t make his actions any less necessary. I would respond that each action an agent performs is spontaneous and need not therefore be viewed as a kind of deduction (more on this point in the next chapter). Even if everything is inscribed in the individual’s concept, the relations between the predicates entailed by the concepts and the agent’s actions are not relations between concepts. However detailed the description of the individual’s activities may be, it cannot make the agent act (either by causal or logical “forces”) because a concept, according to Leibniz does not act; rather, an agent does. This seems to imply that Leibniz rejects weakness of the will and that human agents act according to what seems best to them. But, if so, how can they be said to sin and to be held responsible for their sins? On the one hand, Leibniz argues that God, who knowingly creates sinning individuals is not the author of their sins. (See Sleigh 2005 xxxiii, for the clearest statement on this topic). God permits the creation of sinful individuals because they belong to the best possible world. A creation of another set of individuals would only be worse. Yet God is not the author of sin because (a) these sins are part of the logical possibilities that he conceives in his understanding and (b) because it is the individuals who spontaneously perform them, not God. The same, of course, holds for human virtuous deeds. God does not perform them, humans do. Hence, they are also responsible for what they do – be it morally blameworthy or praiseworthy. It may be objected that the role rationality plays in this picture is redundant. Whether conscious or not, agents would perform the optimal (or rather relatively optimal) action, which is prescribed in their concepts. If the right modality to understand free action according to Leibniz is that an action could be different even if it never will be different, then it is clear that his notion of freedom concerns not only the result but also the way the agent arrives at it. That freedom requires awareness to alternatives is quite intuitive. It would be misguided to say that a falling stone is free only because its falling is contingent. For this reason Leibniz’s notion of freedom requires conscious agency, that is, knowledge that the agent is performing the action and that he is performing it according to his best judgment.36

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6.10

Conclusion

While a Leibnizian individual is defined through its complete concept, it cannot be reduced to it. An individual is also an active agent and a human agent is also endowed with a capacity to reason. This suggests that a complete concept provides the reasons for action and that the individual's active judgment is required for its realization. Accordingly, a rational Leibnzian individual involves a prescription for action, power to act, and the ability to consciously realize the prescription. Thus we see that the notion of possibility (in making sense of logical alternatives) and the notion of agency (in making sense of an individual’s spontaneous action) and the notion of the agent’s rationality (in making sense of the ability to perceive oneself as an agent who can deliberate among alternatives) are all indispensable for Leibniz’s view of freedom. These three aspects of Leibniz’s view of a rational individual correspond to his three requirements for freedom: contingency, spontaneity and intelligence or rationality (Theodicy 288). Let us recall that, for Leibniz, the fundamental ontology of the created world consists of active agents. Although God knows in advance what each rational individual will deem best and how they will act, God himself need not causally intervene in the normal activities of created individuals. God preconceives all possible courses of action and selects those he deems best for actualization. In actualizing these possible individuals, God grants each individual the power to act and a unique prescription for action. It remains for the individuals to realize what they deem best. While they are known by God, both sins and virtuous deeds are performed by created agents, not by God. My aim in this chapter has been to relate Leibniz’s notions of possibility and individuality with those of contingency and rational agency. As we have seen, for Leibniz, the domain of rational agency is understood in terms of moral necessity. In turn, his use of moral necessity can be explicated through a normative (or prescriptive) aspect in the rule that defines each individual as a possibility – a possibility that belongs to the best world. I have suggested that the very rule of action that defines an individual may be also seen as a prescription that a rational agent would realize. While the prescription is constitutive of the individual’s identity, it also requires the agent’s rational execution. First and foremost, I have introduced the prescriptive interpretation of Leibniz’s production rule of the individual as an attempt to account for Leibniz’s insistence that the human individual freedom of action is compatible with its having a complete concept. While I have some doubts whether this interpretation works, I have no doubt that it is worth considering in exploring the Leibnizian labyrinth of human freedom.

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1 GP VI 29; Philosophical Writings, Morris and Parkinson (eds. and trans.),

London, Dent, 1973, 107. See also A 6.1 537. 2 Already in 1668, Leibniz stated that, "a substance is a being that subsists in itself, that is, which has a principle of action within itself" (L, 115). “…omnem substantiam agere, et omne agens substantiam appellari.” "…every substance is active and everything that acts is called substance" (A 6.3 158). 3 Discourse on Metaphysics, articles 8 and 13. See Mercer and Sleigh, “Metaphysics: The Early Period to the Discourse on Metaphysics”, 1994. 4 For Leibniz’s early introduction of per se modalities see Sleigh, 2005 p. xxv. 5 Discourse on Metaphysics 8; AG 40. 6 See Blumenfeld, 1988. 7 As Murray noted, “the issues of freedom and contingency in Leibniz fascinated and frustrated Leibniz’s scholars beyond measure” (Murray, 1995 75). For example, see Lovejoy, The Great Chain of Being 1936 pp. 172-74; Blumenfeld, “Superessentialism, Counterparts and Freedom”, 1982; and “Freedom, Contingency, and Things Possible in Themselves”, 1988. 8 Blumenfeld (1988) in Leibniz: Critical Assessments, 304. For a detailed discussion of this condition, see Frankel “Being Able to do Otherwise”, 1984 pp. 45-59. Hampshire points out that Leibniz’s criterion of freedom (the mere logical possibility of the alternative) does not satisfy our intuitive notion of freedom (The Age of Reason 1956, 167). Parkinson (1995) comments that, “if Leibniz is to produce a successful defense of free will, he must do more than draw a purely logical distinction between two kinds of necessity” (CCL, 220). 9 Commentators have noted two main strategies used by Leibniz to confront this problem, namely, the possible in itself strategy and the infinite analysis strategy. Both strategies and their difficulties are widely discussed in the literature and it is fairly clear that none of them offers an easy way out of the labyrinth of human freedom. For a presentation of these strategies, see Adams, Leibniz: Determinist, Theist, Idealist, 1994, ch. 1. For an illuminating commentary on Adams, see Sleigh's, “Leibniz on Freedom and Necessity”, 1999, 264-65. 10 Leibniz uses this example several times in discussing the question of freedom and contingency both in human and divine contexts. For another clear exposition of this example, see Theodicy 234, also cited and discussed in Savage, 1999, 43. Interestingly, the same sort of examples of are also used in the context of divine agency, as in e.g., Rauzy, 1998, 469; C 534. 11 Note that this example also nicely illustrates Leibniz’s earlier view of inclination as a tendency towards the easier course of action. As he defines it in De affectibus, “An inclination is the easiness of acting.” And “Easiness [facilitas] is what has fewer requisites compared to more similar and equal requisites of something else” (A 6.4 1412).

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12 “In my view it is common to every truth that one can always give a reason for

every non identical proposition; in necessary propositions, that reason necessitates; in contingent propositions, it inclines” (Grua 302; “On Contingency” AG 28, 1686?). For additional references to Leibniz’s use of the phrase ‘incline without necessitating’ see Parkinson 1970 50 n. 35. 13 “Thus, we say that all people want the good and flee the bad, that No-one wants the bad for the sake of the bad. We want what we think good and, conversely, what we think good, we want. But if someone rejects this notion of will, he gives it a meaning other than the one that humans are accustomed to, and probably he will not even be able to say what willing is” (Elementa verae pietatis, sive de amore Dei super omnia (1677–1678) A 6.4, 1360–1361). I Thank Andreas Blank for this reference. 14 “Pre-Leibnizian Moral Necessity”, Leibniz Review 14, 2004, 22. I share this view and argue that this connection goes even deeper in that it also applies to Leibniz’s principle of the individual and its complete concept. 15 Some of the historical background for this view can be traced to Suárez. According to Suárez, “God does not impel his subjects physically “but merely imposes an obligation which is of a moral nature and cannot thus be physically brought about” (De Legibus (1612) Oxford, 1944, I, V; Cited from Wilson 1987, 162). 16 “Leibniz on the Labyrinth of Freedom: Two Early Texts”, Leibniz Review 13, 2003, 25. 17 “The decree of creation is free… the best inclines God, but it does not necessitate him, for his choice does not make impossible what is distinct from the best; it does not bring it about that what God omits implies a contradiction.” (Theodicy 230) 18 “And just as God himself decreed that he would always act only in accordance with true reasons and wisdom, so too he created rational creatures in such a way that they act only in accordance with prevailing or inclining reasons, reasons that are true, or in their place, apparent.” (“On Contingency”, AG 29). This is the context in which Davidson’s (1998) point that “God is the paradigm of freedom and we are only free in so far as we are like him”, or “Insofar as we imitate God, we are free” (ibid 403) seems to be most pertinent. 19 It is arguable that, given a broader context of the best world, the apparent best could not be improved. It is also arguable that Leibniz’s notion of the good is relative to the other possibilities. In fact, the notion of the best reflects this relative sense of the good quite well. 20 « …la nécessite ne doit pas être confondue avec la détermination, car il n’y a pas moins de connexion ou de détermination dans les pensées que dans les mouvements (être déterminée étant toute autre chose qu’être forcé ou poussé avec contrainte). Et si nous ne remarquons pas toujours la raison qui nous nous détermine ou plutôt par laquelle nous nous déterminons, c’est que nous sommes aussi peu capables de nous apercevoir de tout le jeu de notre esprit et de ses

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pensées, le plus souvent imperceptibles et confuses, que nous sommes de démêler toutes les machines que la nature fait jouer dans les corps. Ainsi, si par la nécessite on entendait la détermination certaine de l’homme, qu’une parfaite connaissance de toute les circonstance de ce qui se passé au-dedans et au-dehors de l’homme, pourrait faire prévoir a un esprit parfait, il est sur que les pensées étant aussi déterminées que les mouvements qu’elles représentent, tout acte libre serait nécessaire : mais il faut distinguer le nécessaire du contingent quoique déterminêe » (NE 2.21.13). 21 “I see that there are people who imagine that sometimes we set ourselves for the lesser option, that God sometimes chooses the lesser good, everything considered, and that a person sometimes chooses without grounds and against all his reasons, dispositions and passions, and finally, that we sometimes choose without any reason determining the choice. But I hold this to be false and absurd, because one of the greatest principles of good sense is that nothing ever happens without cause or determining reason. Thus when God chooses, it is by reason of the best, and when a person chooses, it is the option that struck him most” (Letter to Coste, On Human Freedom, GP III 400-4; AG 194). 22 For a diverging view, see J. Hintikka “Was Leibniz’s Deity an Akrates?”, in S. Knuuttila (ed.), Modern Modalities, 1998 pp. 98-101. 23 In her recent book, Phemister also makes this point. She writes, “With selfconsciousness comes the realization that the individual is the acting agent and with this comes responsibility for the effects of its actions” (Phemister, 2005, 246) 24 “Moral Necessity” in Rutherford and Cover (eds.), Leibniz Nature and Freedom, 2005, 184. 25 Davidson (1988) cites the passage from the fifth letter to Clarke and then raises the question of the asymmetry of predictability: Why are the movements of bodies predictable by man while the actions of spirits are only predictable by God. He writes: “By parity of reason [pertaining to mechanical and moral laws], we would think that the actions of spirits are predictable because they are subject to moral laws. While this is the source of such knowledge to God, such laws are inaccessible for the greatest created mind, and the question before us is why.” He goes on to say: “I know of no text where Leibniz unambiguously asks and answers this question... nor of any modern commentator who squarely addresses the issue...” (408). According to the interpretation I propose, it is not difficult to see why God knows all moral laws while humans cannot possess such knowledge. It is because God conceives their prescriptions for actions or moral laws. God himself prescribes, rather than causes, the best course of action for any individual. However, unlike God, the individual may fail to recognize the best course of action (as Davidson (1988) suggests, 409) and even if he doesn’t he may fail to act on the best course of action. 26 Leibniz’s New System and Associated Contemporary Texts, translated and edited by Woolhouse and Francks, Oxford, Oxford University Press, 179.

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27 I discuss this question in more detail in the next chapter. 28 See Adams recent comment that moral necessity is mainly opposed to blind

necessity (“Moral Necessity” in Rutherford and Cover (eds.) Leibniz Nature and Freedom, 2005, 183). 29 In his Comments on Spinoza’s Philosophy (Foucher de Careil, Réfutation inédite de Spinoza par Leibniz, Paris, 1854, pp. 22-70), Leibniz cites Spinoza’s remark in On the Improvement of the Intellect that the ancients “never, so far as I know, conceived of the soul as (as we do here) as acting in accordance with certain laws, like spiritual automata”. Leibniz comments: “The author interprets this as having to do with the soul alone, and not the mind, and holds that the soul acts in accordance with the laws of motion and external causes. Both are wrong, for I say that the soul acts spontaneously and yet as a spiritual automaton, and that this is also true of the mind” (AG 279). 30 In his section on Leibniz in The Cambridge History of Seventeenth-Century Philosophy, 1998, pp. 1259-60. 31 For an interesting discussion of Leibniz’s practical reasoning in contrast to Aristotle’s, see Hintikka 1988. 32 Remarks on Arnauld’s Letter, May 1686, AG 76. 33 Parkinson (1970, 54-55) makes a similar point. 34 Richard Campbell makes a stronger claim. He writes that, “the performing of an action is, for Leibniz, neither logically necessary nor logically contingent; only propositions can be evaluated in this way. It follows that actions are not in the appropriate category to be necessitated by the principle of contradiction” (Truth and Historicity, 1992). 35 I mention this because there is a tendency in the literature on this issue to stress the notion of character and moral therapy (Murray, 1995; Paull, 1992; Seidler, 1985). This interpretation is mainly based on “Necessary and Contingent Truths”. For a discussion of this text, see Sleigh’s “Leibniz on Divine Foreknowledge”, 1994, 547-71. For a criticism of Murray’s reading on the grounds that it violates Leibniz’s commitment to the harmony between mind and body, see Davidson 1998. 36 Curiously, for Spinoza, freedom requires awareness of the necessity and lack of alternative actions. More on this contrast in the next chapter.

Chapter 7 Agency and Necessity 7.1 Introduction We have seen that, in Leibniz, the notions of contingency and agency are interwoven. In addition, we have seen that the notions of rational agency and possibility are crucial for Leibniz’s defense of freedom of action. In contrast, Spinoza sees the notion of agency as compatible with that of logical necessity. According to Spinoza, the unique Substance, God or Nature, is an active being.1 In sharp contrast to Leibniz, for Spinoza, God is a substance whose activity follows necessarily from his nature or essence. Leibniz views God as external to the world and, for him, logical necessity holds in the realm of God’s understanding alone (a realm of pure concepts) and not in the realm of actual agents. As we have seen, Leibniz holds that the predicates of each individual substance are intrinsic to its complete concept but argues that the existence and the activities of individuals are contingent. Spinoza, by contrast, denies mere possibilities altogether (Ethics I p33 but see Ethics II p8). In addition, Spinoza’s doctrine that extension and thought are two attributes of a single substance implies that the realm of thought corresponds to the realm of extension (Ethics II p7s).2 Likewise, he seems to assimilate a logical notion of necessity with a causal notion of necessity, which is captured in his formula causa seu ratio (Ethics I, propositions 11, 16), as pertaining to one and the same reality.3 Spinoza’s claim that God acts by the very necessity of his nature (Ethics I propositions 16, 17 corollary 2) implies (a) that God is necessarily active (as opposed to being passive), and (b) that God’s activity, which follows from his nature, is necessary (as opposed to being contingent). While Spinoza maintains both,4 Leibniz accepts the first and rejects the second. Given the Leibnizian notion of rational activity we have examined above, Spinoza’s notion of a rational being whose activity is necessary deserves some attention. We have seen that, according to Leibniz, the activity of rational agents presupposes contingency or logically possible alternatives. Spinoza, however, holds that the notion of contingency merely attests to human ignorance and delusion regarding the truly necessary course of events (e.g., Ethics I p 29). He famously writes that, “a thing is called 167

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contingent only with regard to a defect in our knowledge” (Ethics I p33 s2). Since Spinoza denies contingency, his metaphysics offers a very interesting context in which the notion of rational agency is separate from the notion of possibility, that is, a context in which agency is strongly related to necessity.5 I believe that the comparison between Leibniz and Spinoza might help to clarify the different ways in which they conceptualize the relations between agency and necessity. In the context of Spinoza, the relation between agency and necessity is characterized by the following assumptions: (a) the primary agent is God; (b) God and Nature are one; and (c) the best model to exemplify God’s activity appears to be a deductive-like relation between concepts and consequences, similar to the one employed in mathematics and geometry.6 Since, for Spinoza, God and Nature are one, the world as a whole is seen as a necessary consequence of God’s active nature – a conclusion that Leibniz struggles to avoid. Spinoza seems to hold that God’s activity can be described in terms of the logical deduction of properties entailed in God’s concept or essence (e.g., Ethics I, Propositions 16, 19). Spinoza also holds that God is the source of power and motion in the world. At the same time, he makes it clear that God’s activity cannot be other than what it is (e.g., Ethics I p. 33). Thus, for Spinoza, the world is a necessary result of God’s activity.7 In other words, the necessary series of events in the world is a result of God’s activity. In light of the Leibnizian relation between concepts and agents we have examined above, the way Spinoza conjoins activity and necessity seems intriguing. If a given property (x) is logically entailed by the idea of God in a similar way as a property is entailed by the concept of a triangle, why would any activity be needed to deduce it? Why, in other words, must God be active in order for x to be a logical consequence of its concept or essence? In what follows I will try to spell out this question in more detail.8 In the first section, I will examine the relation between activity and necessity against the background of Descartes’ mechanistic view of res extensa. In the second section, I will examine the relation between activity and necessity in Spinoza by considering the status of derivation-rules, which are supposed to govern the deduction of properties from an essence. In the third section, I will outline an interpretative approach according to which, for Spinoza, God’s activity is constitutive of his essence, rather than following from it or entailed by it independently of its activity.9 This approach depends on a generative notion of essences and concepts, common to both Spinoza and Leibniz (but much more explicit in Leibniz). I will suggest that the emphasis on generative definitions may make the relation between activity and necessity in Spinoza clearer. I will also

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suggest that Leibniz’s extensive use of generative definitions lends support to the central role the notion of agency plays in his view of substance as well as to the intrinsic relations he conceives between the notion of a possible individual and that of an actual one. 7.2 Descartes as Background for Spinoza and Leibniz According to Descartes’ mechanistic view of the natural world, the domain of extended things (res extensa) should be explained in terms of efficient causality alone, that is, without reference to final causes, purposes, and vital principles. These notions should not figure in a description of nature and must be excluded from its scientific explanation. In the background of Descartes’ view of nature is the exclusion of intrinsic activity from the domain of extended things. For Descartes, internal activity has no place in a mechanical description of nature; nature should be seen as the motion of inert bits of matter described in terms of efficient causality.10 While motion and action are to be described as a chain of efficient causes, their source lies outside the universe, that is, in God. Wartofsky nicely articulated the Cartesian contrast between res extensa and res cogitans as follows: [T]he science of bodies, in their collision and interaction, is a mechanical physics, whose ontology is that of inert matter, whose principle of motion lies outside itself ... But as opposed to the inert and extended property of matter, in which only efficient causes operate, and in which all motion is that of moved movers, the soul or thinking substance has its principle of motion in itself, and is, as soul, fully self-determined, and in this sense has agency, will, and freedom.11 God is the unique source of the activity and motion of extended things. Inert bits of matter, whose motion and collision constitute a complete description of the extended world, have no inherent capacity to act; rather, they are “moved movers” lacking any power and activity. Descartes’ mechanical view of inert matter seems to accord with, if not to imply, a necessary and deterministic conception of nature. If intrinsic activity is excluded from nature, and the laws of motion govern the actual movements of matter, and that is all there is to describe, then necessity seems to be an adequate mode of description. The connection between lack of activity (that is, passivity) and necessity has also surfaced in the correspondence between Leibniz and Clarke. In

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commenting on the difference between the activity of minds and the passivity of bodies, Clarke writes: ...all mere mechanical communications of motion, are not properly action, but mere passiveness, both in the bodies that impel, and that are impelled. Action is the beginning of a motion where there was none before, from a principle of life or activity.12 (110) Thus, ... the true and only question in philosophy concerning liberty, is, whether the immediate physical cause or principle of action be indeed in him whom we call the agent; or whether it be some other reason sufficient, which is the real cause of the action, by operating upon the agent, and making him to be, not indeed an agent, but a mere patient.13 (99) The conceptual connection between agency and liberty, passivity and necessity is brought out clearly in these passages. The connection between passivity and necessity underlies the intuition that I try to formulate: the motion and collision of bits of matter, governed by mere transitive causality, and void of agency, is suitable to a complete and necessary determination via the laws of motion. In outline, this captures Descartes’ reductive program. In Spinoza’s metaphysics, however, the picture of inert extended things cannot be retained. Since Spinoza rejects the Cartesian God in favor of a God or Nature who as an active agent, is the cause of action and motion in the world, the necessary determination of events becomes in effect less obvious. Unlike Descartes, both Spinoza and Leibniz in their description of the natural world attribute inherent activity to substances; they both reject the picture of God as an external source of motion. Indeed, they hold that force and activity are intrinsic to the world and constitute the foundation of its being. They share the view that intrinsic activity is constitutive of real beings or substances. While Leibniz holds that the world consists of infinitely many active substances, Spinoza holds that the world is a unique substance and that it, viz. God or Nature, is inherently active. While Descartes places the source of motion outside the world, Spinoza’s immanent view of God or Nature implies that the cause of motion and activity lies inside the world. I believe that this change in the metaphysical picture has some substantial consequences, especially concerning the relation between agency and necessity.

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A simple-minded approach to the issue of agency in Spinoza would be to argue that Spinoza’s notion of activity is reducible to efficient causality, as in Descartes. However, if this were true, what would be the source of motion in the world? In Descartes’ metaphysics one has recourse to an external source of motion, viz., God, but this is not an option in Spinoza’s metaphysics where the source of motion and power must be intrinsic. While this point is controversial, I think that, for Spinoza, God’s activity cannot be reduced to efficient causality.14 Let me spell out my reasons for holding this position. (1) This position is supported by Spinoza’s firm objection to Descartes’ notion of extended matter, which is entirely inert (see letters 81, 82, 83). As he writes to Tschirnhaus: “from Extension as conceived by Descartes, to wit, an inert mass, it is not only difficult, as you say, but quite impossible to demonstrate the existence of bodies. For matter at rest, as far as it is in itself will continue to be at rest, and will not be set in motion except by a more powerful external cause. For this reason I have not hesitated on previous occasions to affirm that Descartes’ principles of natural things are of no service, not to say quite wrong.“15 For Spinoza, the source of motion must be part of Nature whose very essence is active. (2) This position is also supported by the centrality of notion of conatus, the inherent effort or striving for self-preservation of each individual thing, in Spinoza’s system (Ethics III p. 6). The notion of the conatus suggests that the natural world does not reduce, according to Spinoza, to a mere mechanism of inert matter. As Spinoza made clear in the letter to Tschirnhaus just cited, from such a view of nature, it would be impossible to demonstrate the existence of bodies.16 For Spinoza, particular natural things are not only moved by external ones and transmit the shock they receive; rather, they also actively strive to preserve their unique nature.17 (3) Furthermore, Spinoza’s theory of liberation through consciousness of the causes of the passions, which is indispensable for Spinoza’s ethical theory, is based on attributing degrees of activity (as opposed to degrees of passivity) to individuals. As Hampshire pointed out, the ascription of activity as opposed to passivity is the only positive/negative opposition that Spinoza allows.18 This is made clear in Ethics V proposition 40 where Spinoza directly connects degree of activity to degrees of perfection and reality:

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“The more perfection each thing has, the more it acts and the less it is acted on; and conversely, the more it acts, the more perfect it is”. Demonstration: The more each thing is perfect, the more reality it has (by II Demonstration 6), and consequently, (by III p 3 and p 3s), the more it acts, the less it is acted upon.” (4) In addition, the distinction between Natura naturans and Natura naturata (Ethics I p 29s) brings out the distinction between the purely active aspect of God (the substance and its attributes), seen as a free cause, and the partially passive aspect of God (its modes), which is seen as resulting from God’s active nature.19 For both Leibniz and Spinoza, the activities of a substance are supposed to follow from its essence so that its properties are its logical consequences. While for Spinoza logical consequences must be realized (as they are, in effect, the same activities seen under the attribute of thought), Leibniz believes that the conceptual connections (which are entailed in the individuals’ concepts) are to be realized by created agents and are contingent.20 This gives rise to a major difference between Leibniz and Spinoza: whereas Leibniz holds that the activity of individual substances is not subject to logical necessity (even if it is fully predictable for an omniscient mind), Spinoza holds that God’s activity and all that falls under his infinite intellect is logically necessary (see Ethics I p 33). A really interesting question – though a question I can only begin to answer here – is how these differences are cashed out in their systems. Since Spinoza understands God’s activity on the model of geometrical reasoning, he suggests that God’s activity produces effects in the same way that properties follow from geometrical concepts. The individual modes and all events in the world follow from the essence of God in the same way as the properties of a triangle follow from its concept (or essence).21 In effect, the events in the world are seen as the results of the logical particularization and explication of the essence of God. Given a logically necessary connection between the substance’s essence and its modes (which result from its activity) and the deductive model of this activity, the following question arises: If God acts in a unique way, the way necessitated by his nature, in what sense can the developments of his nature be seen as actions, rather than as mere (passively flowing) consequences of his nature?22 If the logical rules according to which events follow from God’s essence are analogous to the causal laws governing the natural world, as Spinoza seems to suppose (call this the geometric-mechanistic model), then, on this

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model, Spinoza’s notion of activity would seem to be redundant. According to a strictly logical notion of entailment, no activity is required to deduce the consequences of God’s essence, if God’s essence is seen as analogous to a (geometrical) concept. If we consider God’s activity under the attribute of thought, every consequence seems to be already entailed in God’s concept, and if we consider God’s activity under the attribute of extension, everything is supposed to happen mechanically just as in the Cartesian view of nature. Since the purely mechanistic model (the Cartesian model without internal activity) offers a necessary and deterministic outlook of nature, it would seem to be appropriate for describing nature according to Spinoza as well. As we already noted, Spinoza rejects this purely mechanistic model. Furthermore, had Spinoza accepted the geometric/mechanistic model, why would he have introduced the notion of activity in the first place? Why should he have insisted that God actively produces the world?23 In effect, two related questions are at play here: (1) if everything in God or Nature is necessary, as Spinoza claims, what is the role of God’s activity? (2) If God’s nature is to act, as Spinoza presupposes, in what sense are the results of his actions necessarily related to his nature? In other words, how is the notion of God as having a concept that entails all its logical products compatible with the notion of God as an agent or active being? As we have seen in previous chapters, for Leibniz, logically necessary connections hold only at the conceptual level, that is, in the realm of concepts – a realm of truths and possibilities conceived in God’s mind. This is the reason for Leibniz’s reaction in his Comments on Spinoza’s Philosophy, that, “Things that are necessary, and that follow from the infinite nature of God, are eternal truths” (AG 276).24 Famously, Leibniz holds that both analytic and contingent truths are grounded in relations between concepts (or, more precisely, between concepts of subjects and predicates). Yet, as I argued in the previous chapter, according to Leibniz, the activities of existing substances cannot be fully described in terms of concepts alone but must be described also in terms of complete concepts and active agents. As distinct from the notions of essence and possibility, existence and agency go beyond the purely conceptual domain. Thus, in commenting on Spinoza’s supposed deduction of activities from essence, Leibniz points out that there is no “analogy between essences and existing things” (Comments on Spinoza’s Philosophy, AG 278), as Spinoza supposes. Since Spinoza denies possibilities, a real distinction between concepts and agents is not available to him. Hence, the particularization of God’s essence via its individual modes has to be reconciled within the immanent

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framework of a unique being who is seen as an agent and as a concept at the same time. I will now turn to examine the particularization of God’s essence in Spinoza by considering the status of the deductive laws that are supposed to govern the relation between the essence of God (which is presumably reflected in his concept) and its particular logical consequences. 7.3 The Status of Deductive Law Since Spinoza identifies Being and Nature with God’s activity (Ethics I p 16-17; Ethics V p 40), an adequate description of Nature is also a description of God’s activity. Spinoza argues that an adequate description of God’s activity must exclude terms, such as ‘good and bad’, ‘correct and incorrect’, ‘right and wrong’ (Ethics I appendix). He rejects the attribution of normative terms because their use presupposes human judgment and evaluation of nature instead of a description of nature and its causes. Evaluation and judgment assume human standards or ends according to which events can be evaluated (Ethics IV Proposition 73 s). Such evaluation is incompatible with the morally neutral character of God’s necessary activity (Ethics IV Proposition 68 and Letter 19). The evaluation of God’s activity in such terms would make sense only if God’s activity could be different from what it is. Since God’s activity couldn’t be different from what it is, to describe it in normative terms is to merely express a human attitude (deriving from ignorance of the true nature of God) that involves a distortion of its necessary character. It is nevertheless arguable that some normative concepts are pertinent, perhaps even indispensable, for an adequate description of God’s activity. According to Spinoza, God’s thinking produces particular essences by explicating and particularizing his own essence. Spinoza seems to conceive of the explication of God’s essence through a model of deriving all the logical consequences from the essence of God, as certain properties or consequences follow from the essence of a triangle. This is also supported by the geometrical structure of the Ethics, which is supposed to reflect the structure of Nature. Spinoza’s paradigm for modeling God’s rational activity is mathematical or geometrical, so that the consequences of a concept are derived through deductive rules, as properties are said to follow from the concept of a triangle.25 Because it is void of ends and desires, mathematics serves Spinoza as “the norm of truth” (Ethics I appendix). But, can Spinoza’s use of the deductive model to describe God’s activity avoid normative concepts altogether? In the previous chapter I suggested that Leibniz’s notion of complete concepts may also play a normative role

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in the activities of rational agents. Here I will examine whether normative considerations also enter Spinoza’s notion of the particularization of God’s essence. Let us consider the rules according to which certain properties are taken to be the logical consequences of concepts or essences. Since the results of God’s activity are obviously logically valid, it would seem that some basic norms of valid derivation must be supposed. It seems, therefore, that some notion of deductive laws play an indispensable role in the rational explication of the consequences of God’s essence. In seeing reality as the logical explication of the essence of God, Spinoza seems to presuppose some deductive laws of derivation. However, we have seen that Spinoza rules out any use of normative terms. So, shouldn’t his critique of normative concepts apply here, viz., to his own notion of rationality, as well? Let us first observe that the status of the laws of logic is ambiguous. These laws may be taken as describing reality in the way that the Cartesian laws of motion are supposed to describe natural phenomena, or they may be seen as norms that prescribe how rational agents ought to act, and thus to distinguish valid consequences from invalid ones. Now, do the laws of logic describe and predict natural events or do they prescribe the way a rational agent ought to act? Do such rules serve as a guide for God’s rational thinking or do they describe an activity – be it natural or divine – that takes place anyway, and which it makes no sense to describe as either valid or invalid? In short, are the laws governing the explication of God’s essence descriptive or prescriptive? I shall use the term ‘laws’ for the former, and the term ‘rules’ for the latter. Using this terminology, let us ask: is God’s productive activity better described in terms of laws or in terms of rules? I suggested above that, in Leibniz, both normative and descriptive senses play a role. In Leibniz, the descriptive aspect is something like a God’s-eye view of all the would-be activities of a possible individual. The prescriptive aspect presupposes rational agents who apply these rational norms spontaneously as reasons for actions. In the context of Spinoza, the question takes the form of an intriguing dilemma: If the laws of thought merely describe how God necessarily acts, then there seems to be no justification for defining God’s activity as rational (and the results of his activity as valid consequences of his concept). On the other hand, if God’s activity accords with the laws of nature as a falling stone accords with the laws of gravity, then the notion of irrational or invalid consequences seems empty, for there are no standards according to which it could be corrected.26 On the other hand, if the rules of thought are seen as normative, then it becomes conceivable that God could act differently than he does, which Spinoza rules out (e.g., Ethics I 29, 33).

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Although Spinoza identifies God with Nature, he makes it clear that he sees God/Nature as rational activity. God is not simply all natural phenomena taken as a whole.27 Rather, Spinoza’s God is an agent whose rational activity produces the natural world. God is not only natura naturata but also natura naturans. As we noted earlier, Spinoza does not subscribe to a purely mechanical description of the natural world that can be reduced to inert matter in motion or rest. Rather, the natural world is described as motivated by constant active power that is sometimes seen as the source of life and as God’s presence in the world.28 Accordingly, it would seem that God’s productive activity, which particularizes and explicates its own essence, requires some notion of rules for its adequate description. However, as we noted earlier, if the prescriptive model of activity may help in accounting for Leibniz’s notion of contingency, it does not seem compatible with Spinoza’s insistence on the strict necessity of God’s activity. On the contrary, ascription of normative terminology to God’s activity presupposes the possibility of alternative courses of action. Given Spinoza’s denial of such possibilities and his commitment to the logical necessity of God’s activity, the above argument against the application of the normative model seems conclusive. While this point is well known, it refers us back to the other horn of the dilemma. In view of this impasse, let us reconsider our conception of the relations between essences and their logical products in Spinoza. 7.4 Two Models of Logical Production in Spinoza As it turns out, in Spinoza’s writings, we can discern two different models of logical production or, more precisely, two different models of the relations between an essence and its logical consequences. The first model is one of strict logical entailment and it is invoked by the analogy between God’s essence and the concept of a triangle. This analogy suggests a picture of logical entailment in which the concept is given and its consequences are logically and fully determined by its definition. The consequences are, as it were, “already there”, independently of any productive activity. In this model, the concept is fixed and defined and its logical implications follow from it immediately. And, for this very reason, there seems to be no need for activity in this model. This point becomes particularly evident in interpretations of Spinoza that stress the significance of God’s productive activity. For example, Zac writes:

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In the infinite power of God, mathematical necessity and the dynamics of causation are intimately interconnected. The power of God not only internally grounds the being of things, but also their deducibility, which excludes any contingency in their appearance and their mode of existence.29 ...by declaring that God is essentia actuosa, or life, Spinoza ties the idea of productivity to those of immanence and necessity. ...God is pure act and his effects are inseparable from him in exactly the same manner as the properties of a geometrical figure are inseparable from the definition of the figure from which they follow…(158)”. Zac’s statement brings out the connection Spinoza supposes between activity, causation, and deducibility. However, it is precisely the analogy of a geometrical figure and its properties that points to the discrepancy between activity and logical necessity implied in the notion of deducibility. Since no activity is required to deduce the logical consequences of a geometrical figure, how are we to understand the claim that God’s effects are “inseparable from him in exactly the same manner as the properties of a geometrical figure are inseparable from the definition of the figure”? For all the importance Zac rightly ascribes to the notion of activity, once it is explicated in terms of the deductive relations between a figure and its properties, the very notion of activity seem to play no role. If the consequences are entailed in the figure’s definition and thus may be said to be “already there,” what is the role of activity in this model? It seems that, on this model, the role of activity is inessential, not to say redundant. It may be objected that I misperceive the role of activity in this model because I shift from the eternal perspective of logical entailment to a durational one of causality. However, if, for Spinoza, “mathematical necessity and the dynamics of causation are intimately interconnected,” God’s activity, whether considered under the attribute of thought or the attribute of extension, refers to the same reality. In both parallel and necessarily related cases, God’s activity is supposed to be characterized by the same type of necessity. After all, Spinoza’s major contention is that thought and extension are attributes of one and the same substance. God’s activity is the same, whether it is described as a causal unfolding of events or as the logical consequences of his essence. For this reason, it seems to me that there is a strong connection between God’s understanding and God’s essence in Spinoza. Spinoza sees the

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causal aspect of God’s activity and the logical one as parallel descriptions of the same reality and holds that they presuppose an ontological common ground. My point is that, given this supposition, there is a discrepancy between the type of necessity suggested by the standard deductive interpretation and the one suggested by the causal one. This is why I think that another model, that of causal definitions, is pertinent: it suggests that the type of necessity Spinoza assumes is not the one we would normally think of as deductive precisely because the notion of activity is indispensable to it. And, indeed, Spinoza employs such a model of logical production. This model stresses the generative character of the definition of essences. On this model, the very definition of concepts – including the concept of God – requires productive activity. To define a concept on this model is to explain how it is produced. Furthermore, the very nature of a thing is not determined and fixed by a purely abstract definition; rather, a definition is constituted en acte. Likewise, the consequences of a concept are not fixed in advance but rather through its productive activity. Alexander Matheron presented this genetic model of definition by developing Spinoza’s example of a radius turning around its axis and thus producing a sphere (Treatise on the Emendation of the Intellect, 72). In this example, the activity of the turning radius produces a sphere and, at the same time, constitutes its definition. Although Matheron writes primarily in the context of the individual modes, this model clearly applies to the activity of the Substance. He writes: Every individual must present itself under two, complementary and reciprocal aspects: a productive activity (analogous to the radius turning) and the result of this activity (the volume produced by the turning radius). The result is not a different thing than the activity itself: it is simply the structure that it gives itself in its application; in this sense, it is in it, as it is conceived by it. The sphere does not have any reality outside the movement of the radius: as soon as it stops turning, the sphere disappears. In other words, the sphere is an immanent cause of its own structure. ... and this auto-productivity may be considered, by analysis, either as naturing (naturant) or as natured (naturé).30 Matheron remarks that, “the understanding does not fully understand what it constructs, the true definition of a thing must explain the process of its construction” (11). His insightful remark seems to be particularly relevant to the question we are considering. The model suggested by this example is remarkably different from that of logical entailment

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exemplified by the notion of a triangle and its properties presented above. This model stresses the essential, or, more exactly, the constitutive role of activity in Spinoza’s notion of God. God's activities and their results may be seen as two aspects – productive and produced – of one and the same active thing. In this sense, the result of the activity (the sphere in the above example) is not fixed in advance of the actual activity; the concept of the agent is not prior to his actions but rather exists through these actions. This may clarify why activity is so crucial – indeed indispensable – to Spinoza’s view of God or Nature. Since, in Spinoza, there is no room for pure (that is, non-realized) essences or possibilities (as in Leibniz), to have an essence and a concept requires an active agent.31 In turn, this seems to account for Spinoza’s identification of God’s essence with his power (Ethics I 34). As in the case of Leibniz’s view of substance, for Spinoza, too, it is power of activity that is the very essence of a substance. 7.5 Genetic Definitions and Agency in Leibniz Given the significance of genetic definitions in Spinoza, let us now take a closer look at Leibniz’s notion of genetic definitions.32 Leibniz’s notion of genetic definition is very similar to Spinoza’s. Yet the scope of its application, as well as its textual basis, is much wider. For Leibniz, to construct something is first of all to conceive its possibility. For Spinoza, to construct something is at the same time to define its being. As I already observed in chapter 2, Leibniz defines complex concepts and particularly individual concepts through their method of production. For him, an essence or possibility is not identified as a sum of predicates but rather as the rule producing this structure of predicates. Upon creation, the production rule becomes the principle of regulating the development of the substance’s states. Thus, according to Leibniz, a generative or a causal definition entails a principle of construction.33 A causal definition is the formulation of such a principle or law of production. To define an object causally means to specify a principle of generation or a procedural rule on the basis of which an agent can construct itself step by step. In this sense, defining becomes constructing and the possibility of an entity amounts to its constructability.34 Furthermore, a generative definition is exhaustive in the sense that all the properties of the entity can be derived from the law of its construction. Let us consider some examples that testify to Leibniz’s extensive use of generative definitions. Perhaps the simplest example is his definition of

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natural numbers. “Two is one and one, Three is two and one, Four is two and two, and so on.”35 The natural numbers are defined through a procedure that produces them, so that the successive number results from the addition of “one”. The reiterability of this procedure means that it can be carried on without limitation and shows the intelligibility of the series of natural numbers.36 A similar procedure underlies the construction of infinite sequences and series. The characteristic law for each series or sequence should not be regarded as a mere abbreviation or as a place-holder for the infinitely many terms in the series. Rather, the law should be seen as the generating principle of the series, which implies the terms of the series as an ordered progression. Leibniz’s view of the nature of a series may become clearer by comparison with Descartes’ treatment of the continuous progression.37 Whereas Descartes’ aim is to calculate the terms of the progression, to get these terms step by step, one by one into view, Leibniz’s attention is focused on the law producing the series. While the terms of a series are different from each other, they derive from a common law of generation. This explains the connection between all the terms of a series, their unity, and the unique position each term occupies in it. A very interesting application of generative definitions is the infinitesimal calculus. For example, in the case of the “inverse tangents problem” the task is given to find a curve when the law of its change of direction is known, i.e., its first derivative. In this case, the derivative, the differential of the curve, plays the role of its generating principle. The curve in its complete form can be regarded as the end product of its “modus producendi”, the principle and law of its generation. As a recent scholar put this, Leibniz’s operation of differentiation is “a rational technique assisting human beings to discover the hidden law of the generation of curves”.38 The idea of defining geometrical figures through motions (as we have just seen in Spinoza) is present in Leibniz’s early writings39 as well as in one of his very late writings.40 Leibniz also uses generative definitions to define geometrical objects such as straight line, plane, and space as “locus omnium punctorum sui situs unicorum” with respect to a number of points – varying according to the object that is to be constructed.41 While all these examples belong to the realm of mathematics, Leibniz applies the method of generative definition outside mathematics as well. Warm, cold, yellow, green, etc. are confused concepts for us; they cannot be analyzed further because we are not in a position to analyze them into elementary perceptions.42 Here, too, Leibniz’s idea is to specify a procedure of production.43

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In both mathematical and non-mathematical contexts the procedure remains basically the same. The priority of mathematics pertains only to the point of origin. The generative definition seems to originate from the realm of mathematics and then it is applied to the non-mathematical realm. It is significant to observe that in some cases of mathematical concepts, several generative definitions may be given for the same concept. For example, an ellipse can be defined as a cut through a cone, a cut through a cylinder, or, in a plane, through the movement of a thread in relation to two centers. A plurality of generative definitions is possible only for mathematical concepts, which represent abstractions, or “res incompletae”: “in rebus autem completis hoc fieri non posse, et unam adeo substantiam alteri non esse perfecte similem, nec pluribus modis eandam posse generari.”44 For complete or individual concepts, however, a plurality of generative definitions is strictly excluded. As I noted in chapter 2, the precise sense of individual concepts is that they can be produced in exactly one way. For their mode of production provides their principle of individuation. This is why a generative definition is also applicable to individual substance through its rule of production. Let us note that Leibniz’s use of generative definitions presupposes an agent – either the divine agent contemplating all possible concepts, or created agents realizing such possibilities in the world. In some cases, such definitions also presuppose human agents seeking to model and understand the divine understanding in limited ways. Leibniz’s extensive use of generative definitions reveals the deep connection he presupposes between concepts and agents. Thus Spinoza’s view of agency helps us highlight the intrinsic connection between individuality and agency in Leibniz. A generative definition, with all its importance, is not sufficient to define a complete individual. While it may suffice to define individual concepts, Leibnizian individuals are agents for whom primitive activity or force is required as well. The attempt to define individual substances in terms of their production rules or by means of generative definitions alone (suggested already by Gurwitsch, 1974 and more recently by Cover and O’Leary-Hawthorne, 1999) does not allow us to adequately capture Leibniz’s distinction between possible individuals and actual ones. In my view, a mere genetic definition corresponds to a possible being or an individual concept but not to an existing one. 7.6 Conclusion We have seen that, in Spinoza’s case, the notions of agency and necessity are difficult to reconcile with the model of God’s essence that

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entails all its necessary consequences in advance of its productive activity. In the second model, where activity is constitutive of the agent’s essence, these notions are intrinsically related. If the notion of activity is required for Spinoza’s concept of logical production, it would seem that the rules or laws by which events or thoughts are said to result from God’s essence is not fully captured by either normative or descriptive terminology. Rather, God’s activity is constitutive of these rules and cannot be defined in abstraction from them. For Spinoza, God’s activity is not governed by logical rules nor can it be corrected by them; rather, God’s actual activity, described under the attribute of thought or extension, defines these very rules. This is perhaps the deepest expression of Spinoza’s actualism – viz., his denial of any notion of potentiality and possibility. The consequences of the concept of God are inseparable from God's activity in the sense that his activity partly determines what they are. It is not the case that God’s actions follow from an already fixed nature; rather, his very nature is to act and this partly defines what it is. Here I must stress that it is a definition in act, a genetic definition, not one that could be conceived independently of activity, as the deductive analogy seems to suggest. The agent acts by the necessity of his nature in the sense that it is an essential part of God’s nature to act and produce itself. Hence, the results (or consequences) of the activity cannot – and need not – be determined in advance and independently of his activity. Rather, God’s activity is constitutive of its products and its inner laws.45 Interestingly, for Spinoza, God’s activity has no fixed source or predetermined program. It does not follow from something prior to the activity. Rather, the agent and his activity are one. A subject is not prior to what it does; rather, a subject is identified with what it does. This is why the term agent seems so appropriate here. Such activity is necessary, that is, determined but not predetermined, in the sense that there couldn’t be another (but not in the sense that it is a logical deduction of a given concept). In this sense, Spinoza’s view of necessity is the other side of his rejection of possibility. Simply put, if there are no possibilities and there is some activity, then this activity is unique and, in this sense, necessary. It seems to me that Spinoza’s notion of necessity is best seen, in opposition to Leibniz’s, as his ruling out mere possibilities.46 If there are no nonrealized possibilities, there is only actuality. This makes the comparison with Leibniz all the more pertinent and interesting. It points to an intimate connection between the plurality of agents and possibilities in Leibniz and the singularity of the unique agent and the notion of necessity in Spinoza. It also points to a crucial difference in the employment of generative definitions and their relation to agency

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between Spinoza and Leibniz. While in Leibniz there is a production of concepts in God’s understanding, which is logically prior to their realization in the world, in Spinoza there isn’t. The generative definition is not prior to the constitution of the agent and the productive activity is not prior to its results but identical with it. What does the above comparison with Spinoza teach us about Leibniz? In sharp distinction from Descartes, for both Spinoza and Leibniz, the metaphysics of the natural world is grounded in agency, i.e., in the spontaneous activity of individuals. For both Spinoza and Leibniz the activity of agents is constitutive of their very nature – they cannot be understood as mere passive and inert transmitters of motion. Spinoza’s view of the constitutive role activity plays in the particularization of God’s essence clarifies Leibniz’s view of actualization in the following sense: even if Leibniz defines individuals by means of complete concepts, inherent activity (or agency) is required for their being, just as inherent activity underlies God’s being. Without inherent activity, a concept, complete as it may be, remains a pure possibility. This general point regarding the constitutive role of agency is strongly confirmed by the use of genetic definitions. For both Spinoza and Leibniz, an individual is defined through its method of production: the way it is formed or forms itself is essential to its individuality and identity. In Leibniz, however, the notion of the method of production has a dual sense. In the realm of possible things, the method of production serves to define a unique concept through its rule of production; in the realm of actual things, each individual produces itself in the unique way prescribed by its concept. The individual’s inherent spontaneity and its unique rule of production function as necessary requirements for its very definition and being. The intrinsic connection between essence and existence in Spinoza’s view of God points, by way of contrast, to the significance of the distinction in Leibniz. While pure non-realized essences are conceivable in Leibniz, the realization of such an essence is not a mechanical execution of a fixed program; rather, it is a spontaneous production. In contrast to Spinoza, a mere essence for Leibniz is not active. This is why an essence is not a being but only a possibility – more precisely, a possible program of action. To realize such a possibility, the notion of an active substance – a spontaneous agent – is required as well. As we shall see in subsequent chapters, this notion of inherent agency would help us to clarify Leibniz’s enigmatic view of nested individuals as well as the way they differ from aggregates.

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1 Let me clarify that this need not indicate a personal view of God or a view in which Spinoza’s substance is separate from its activity. Whether Spinoza’s God should be described as an agent (noun) or as an activity is a very interesting question that remains in the background of this chapter. Deleuze (1968) has argued that Spinoza’s substance should not be seen as an agent but as power (puissance) and activity. This question certainly merits separate treatment. In any case, God is not an individual in the Spinozistic sense of the little physics after Ethics II p13, where the individual is seen as a mode. As Laerke pointed out to me, calling God an “individual” in a Spinozistic sense runs the danger of taking Spinoza to say that God is nothing but the sum or composition into one individual of all the individuals (or finite modes) in nature, something that would entail the contradictions Bayle imputes to him – i.e., the problem of internal contradiction inside the notion of substance. As we shall see in chapters eight and nine, the problem of the unity of individual substances arises for Leibniz just as well. For both Spinoza and Leibniz the unity of individual substance is not a unity by composition. 2 Ethics II p7; Ethics III p 2 s; and see Yakira (1989 150) for the claim that the relation is better served in terms of equality rather than in terms of correspondence between (presumably) two different things. 3 As Yakira notes, ”[f]rom the point of a view of modal theory, Spinoza’s theory of necessity is an interpretation of modal discourse in terms of causality. Leibniz, on the contrary, attempts to save contingency by clarifying the specifics of logical necessity” (Yakira, 1989, 20). 4 In light of the traditional connection between being and activity, i.e., that no thing can be without being active, the first claim seems to me less problematic. 5 As Yakira suggested, “Leibniz’s critique raises the question of the coherence and solidity of a conception of action [in a metaphysical context] where there is no possibility or choice” (Yakira, 1989, 183). 6 This assumption is not only explicit in the content of the Ethics but also in its form. 7 “Note well that the world is a necessary effect of the nature of God…” (Letter LIV). 8 In this way, I hope to call attention to this tension in Spinoza’s philosophy. I find it curious that most of Spinoza’s commentators (at least those whose writings are known to me) are hardly troubled by this question. They are troubled by the tension between freedom and necessity, regarding which Spinoza has a very clear position. While the question of freedom vs. necessity in Spinoza is widely discussed, the question of agency – which appears to be in more fundamental conflict with the notion of necessity – is hardly dealt with.

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9 As Laerke comments, God’s activity is indeed constitutive of his essence because the attributes, as causa sui, are self-constituting in an active sense of selfcausing (being a radicalization of the Cartesian notion of causa sui). 10 Principes de la Philosophie, second part, art. 23. Note also: “Je dis que [le mouvement] est le transport et non pas la force ou l’action qui transporte, afin de montrer que le mouvement est toujours dans le mobile, et non pas en celui qui meut ; car il me semble qu’on n’a pas coutume de distinguer ces deux choses assez soigneusement”, Principes de la Philosophie, second part, art. 25. 11 “Action and Passion:” in Spinoza: A Collection of Critical Essays, (ed.), Marjorie Grene, 1973, p. 330. 12 Clarke's Fifth Reply, The Leibniz-Clarke Correspondence, (ed.), H. G. Alexander, 1965, p. 110. 13 “There is no similitude between a balance being moved by weights or impulse and a mind moving itself, or acting upon the view of certain motives. The difference is, that the one is entirely passive; which is being subject to absolute necessity: the other not only is acted upon but acts also; which is the essence of liberty.” Clarke's Fifth Reply, The Leibniz-Clarke Correspondence, (ed.), H. G. Alexander, 1965, p. 97. 14 For example, see Gueroult, Spinoza, chapter X; and recently Martin Lin “On Spinoza’s Naturalism”, presented at the APA convention in Cleveland, 2003. 15 Letter 81, Spinoza Complete Works, M. L. Morgan (ed.), S. Shirley (trans.), Indianapolis and Cambridge, Hackett, 2002, 956. For a thorough discussion of Spinoza’s response to Tschirnhaus, see Alexandre Matheron “Physique et ontology chez Spinoza: l’énigmatique réponse à Tschirnhaus”, Cahiers Spinoza, 6, 1991 pp. 83-111. 16 Although Spinoza is not altogether clear, his view certainly has an interesting affinity with Leibniz’s critique of Descartes’ notion of extension (which I discuss in chapter 8). 17 See Moreau 1975, Spinoza, 75. 18 In his “Spinoza’s Idea of Freedom”, reprinted in Hampshire 2005. 19 See Yakira, 1989, 182. 20 Whereas Leibniz distinguishes between conceptual and causal connections, Spinoza holds that everything conceivable realizes itself. That is to say, for Spinoza, conceptual connections (specifically those between a substance’s essence and its properties) must have corresponding causal ones, for they are identical activities whether considered under the attribute of thought or the attribute of extension. 21 “…I think have shown clearly enough (see Proposition 16) that from God’s supreme power, or infinite nature, infinitely many things in infinitely many modes, that is, all things, have necessarily flowed, or always follow, by the same necessity and in the same way as from the nature of a triangle it follows, from

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eternity to eternity, that its three angles are equal to two right angles” (Ethics I 17 s, Curley translation p. 98). In his comments on Spinoza’s Philosophy Leibniz writes: “One cannot prove by any argument that things follow from God as properties follow from the triangle, nor is there any analogy between essences and existing things” (AG 278). 22 See Spinoza’s definition of freedom, Ethics I, definition 7. 23 An obvious answer seems to be that Spinoza needs an internal source of power to generate the chain of causes. However, Spinoza’s God is not a mere source of power; rather, God also acts and produces the world through his actions. 24 Foucher de Careil (ed.), Réfutation inédite de Spinoza par Leibniz, Paris, 1854, pp. 22-70. 25 As we shall see, it is far from obvious that this is the best model for capturing Spinoza’s view. 26 In correspondence, Laerke raised the following objection: “if rational simply means in accordance with what is necessary, as it would for Spinoza, then this doesn’t mean that one cannot talk about invalid consequences – this is what happens when you have an inadequate idea.” However, if by “rational” Spinoza means to describe that which necessarily happens then from a Leibnizian perspective there is no way of justifying it because there is no alternative. If the world for Spinoza is neutral with respect to morality, it would seem to be neutral with respect to rationality as well. 27 Ethics I p16; see also Moreau, Spinoza (1975) p. 63. 28 See “Metaphysical Thoughts, chapter VI; Moreau Spinoza (1975) pp. 74-75. 29 “The Relation Between Life, Conatus, and Virtue in Spinoza’s Philosophy” (157). Citations are from the English translation published in the Graduate Faculty Philosophy Journal, Volume 19, 1, 1996. 30 Matheron, Individu et communaute chez Spinoza, 1968, 12, (my translation). 31 Ethics I p20: “The Essence and the Existence of God are one and the same thing”. 32 In this section, I draw extensively on Gurwitsch, Leibniz. Philosophie des Panlogismus (1974) in his section on Generative Definitions (65-72). While I use Gurwitsch’s survey of generative definitions in Leibniz, I disagree with his panlogical interpretation of an individual as identical to its rule of production. 33 Discourse On Metaphysics, 24 and NE 3.3.5. 34 “… demonstrari talium rerum [of geometrical objects] possibilitatem, quoties ostenditur modus eas generandi vel producendi.” (GP I 213); “… modum producendi explicare, nihil aliud est quam demonstrare rei possibilitatem” (De syntesi et analysi universali, A 6.4 542; GP VII, 295). 35 NE 4.2.1

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36 As I noted in the second chapter, other types of numbers may be defined in this way: negative number as products of subtractions; rational numbers as products of division, etc. 37 See Belaval Leibniz critique de Descartes, 1960, 55. 38 In Leshem, Newton on Mathematics and Spiritual Purity, 2003, 60. 39 To Thomasius, 20/30 April 1669: “Constructiones … figurarum sunt motus” (GP I, 21). 40 “Linea est via puncti. Superficies est via Lineae. Amplum vel Spatium … est via superficiei.” “Via” is characterized as “locus continuus successivus rei mobilis” (Initia rerum mathematicarum metaphysica GM VII, 20 f). 41 Initia rerum mathematicarum metaphysica (GM VII, 21 f). Let us note two other geometrical examples: (1) Leibniz’s proof of the existence of the diameter of a circle, i.e. the proof using a construction (arbitrary continuability of a straight line) by the appeal to the principle of continuity, showing that a straight line drawn through the center of a circle has with the periphery of the latter exactly two points in common (GM V, 195 f). (2) Leibniz’s attempt to prove the possibility of parallel straight lines by means of construction (GM V, 200 ff; NE 3.3.18) as an emendation of Euclid’s definition of parallel straight lines (Euclid, Elements, I, 23) which, according to Leibniz, constitutes only a nominal definition. 42 NE 3.4.4-7. 43 If more evidence is required to see that it is misguided to restrict the method of generative definition to the mathematical realm, consider the following passage from the Protagea, a work devoted to geological questions: “… magnum est ad res noscendas vel unam producendi rationem obtinuisse: quemadmodum geometrae ex uno modo describendi figuram omnes ejus proprietates derivant.” Protagea (Göttingen 1749), 18. A facsimile and partial transcription can be found on the home page of the Protagea project of the Dibner Institute website (http://dibinst.mit.edu/DIBNER/Leibniz/index.html). 44 To de Volder, 6 July 1701, GP II, 225. 45 Such a view of constitutive activity in Spinoza does not imply predetermination since determination is always actual. 46 Some see in Ethics II p8 an affirmation of logical possibility in Spinoza. But I find Gueroult’s (in his Spinoza 1968), comments on this proposition convincing. He writes: “Les essences ont donc une réalité en acte distincte de la réalité en acte de leur existence”(vol. II 101). “Science des possibles qui n’existent pas – et non, comme certains l’entendent, la science des possibles qui n’existerons jamais, car, pour Spinoza, il n’y pas tels possibles” (vol. II 102, note 107).

Chapter 8 Aggregates 8.1 Introduction The focus of this chapter is Leibniz’s notion of aggregates and how they are distinct from true individual substances. Since this distinction turns on the issue of unity, which a true substance possess and an aggregate does not, I begin with some context regarding the traditional connection between being and unity. The Platonic tradition regarded material bodies as changing instantiations of invariant Forms. Since material bodies change, they belong to the realm of becoming, not of Being. In this tradition, the connection between Being and invariance was grounded primarily in conceptual considerations regarding unity. Consider a rock that undergoes erosion. Strictly speaking, the eroded rock is not the same entity as the rock before its erosion. The rock’s erosion disrupts its unity. Since the rock's unity may change, it is not considered a true entity but rather a phenomenon. While such a phenomenon is not a true being, it is not a fiction or a figment of the imagination either. It is phenomenal primarily in the sense that it is changing and therefore it is considered less real.1 The notion of invariant unity served as a criterion of being in this influential tradition and the dictum Leibniz adheres to, “to be is to be one” nicely captures the connection between unity and being that informs Leibniz’s metaphysics. Unlike the Platonic tradition, there is a current tendency to regard changing material bodies as fully real. For example, our current, intuitive notion of reality is strongly connected with our notions of matter and spatio-temporal existence to an extent that a real entity without some spatio-temporal configuration seems hardly conceivable. The status of matter noted above – between having lesser degree of reality and full reality – serves here as a conceptual context to position Leibniz’s notion of material bodies or aggregates. Leibniz’s view of material bodies is, typically, subtle and complex. While Leibniz holds that "to be is to be one",3 he accords material bodies (that are not the bodies of true units) a middle position between true Beings and mere phenomena. He calls such 189

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material bodies "well-founded phenomena" (phenomena bene fundata) and his terminology accurately captures his subtle position. Being subtle, Leibniz’s position lends itself to polarized interpretations: While some commentators have argued that Leibniz’s notion of material bodies is merely ideal, others have argued that, in his middle years, it is fully real. It seems to me that Leibniz’s position lies precisely between these two positions. As Leibniz says, secondary matter is semi-real as well as semi-mental.4 In order to clarify his view, I will try to specify the sense in which a material body or an aggregate is said to be semi-real and the sense in which it is said to be semi-mental.5 My starting point is Leibniz’s use of the traditional criterion of Being noted above – viz., invariant unity – to criticize Descartes’ notion of matter as extension. From this criticism, the details of Leibniz’s position will emerge. I will point out that Leibniz’s view of extension is relational and I will suggest that an adequate interpretation of Leibniz’s view of relations (explored in chapter 3) may shed new light on his notion notion of material bodies as well-founded phenomena. By stressing the ancient sense of the phenomenal (in distinct from the Kantian one) in Leibniz, I will point out that Leibniz’s relational notion of well-founded phenomena can be seen as both mind-dependent and as grounded in reality. My discussion in this chapter (up to section 8.6) is centered on material bodies that are not organic unities, that is, aggregates. Some (but not all) of the points pertain to organic unities, which will occupy the center stage in the next chapter.5 Accordingly, most of my discussion concerns secondary matter (materia secunda) rather than primary matter (materia prima). Hence, the terms ‘matter’ and ‘material body’ usually refer to secondary matter.6 I focus here mainly on Leibniz’s middle years, that is, from 16861698, but refer to some later texts as well.7 8.2 Leibniz’s Relational Notion of Extension As is well known, Descartes held that the created world consists of two types of substances: extended, material things (res extensa) and thinking, non-extended things (res cogitans).8 For Descartes, extension in space is constitutive of material bodies, so that every extended thing is material and every material thing is extended. According to this view, material bodies are spatial realizations of geometrical objects. Fichant puts this point eloquently: “un corps, c’est de l’etendu geomenrique realizée”. 9

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Consequently, for Descartes, material objects may be described in pure geometrical terms. This geometrical notion of extension plays a central role in Descartes’ rejection of the Aristotelian science and enables him to set new standards for describing nature. The notion of extension plays a central role in his mechanistic program, which attempts to reduce all qualitative properties (such as smell, taste and heat), to quantitative/geometrical properties (such as magnitude, shape and number).10 While a description of nature in quantitative terms is considered adequate, any description in qualitative terms is considered inadequate. This implies a vision of the natural world, consisting of inert bits of matter in motion. These bits of matter are void of intrinsic life and activity and their motions and collisions are supposed to explain all natural phenomena. Descartes’ geometrical view of material substances thus serves to eliminate from the description of nature the purpose and activity the Aristotelian science attributed to it. In addition, Descartes holds that the geometrical method and the mechanistic type of description are applicable to all phenomena. Leibniz accepts the geometrical standards set up by the mechanistic program as adequate means of describing extended bodies, but he rejects Descartes’ methodological monism and its sweeping application of mechanistic style explanations. While Leibniz accepts extension as an essential characteristic of material bodies, he argues that the notion of extension provides only a partial description. Leibniz argues that extension is an attribute of matter but not, as Descartes argues, the primary and defining one. Rather, he points out that the notion of extension is incomplete; for it presupposes something which is extended. “Outre l’étendue il faut avoir un sujet, qui soit étendue, c’est a dire une substance a laquelle il appartienne d’être répétée ou continuée. Car l’étendue ne signifie q’une répétition, ou multiplicité continuée de ce qui est répandu…”11 As we can see in this passage, according to Leibniz, extension presupposes a plurality of subjects which, together, form an extended thing.12 Thus, ‘extended’ (in phrases such as ‘extended substance’) turns out to be a relational predicate. ‘Extension’ indicates relations between individual substances whose plurality constitutes the foundation of a material body. Intuitively (but, as we shall see, also somewhat misleadingly), we may think of a rock’s extension as resulting from the relations among its primary constituents. Among Leibniz’s arguments against Descartes, the one from the infinite divisibility of matter is particularly instructive for my purposes.13 This reductio argument is based on Descartes’ assumption that matter is “indefinitely divisible”,14 and attempts to show that it implies absurd

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consequences, namely, that, if so, the reality of extended substances would not be grounded in any entity with invariant unity. The argument may be reconstructed as follows: If material bodies are extended in the Cartesian, geometrical sense, then they are infinitely divisible. This follows from the geometrical properties Descartes attributes to matter. But if a real body were to be divided, as one may try to divide a line in order to reach its ultimate points, the bedrock of reality could be never reached. More precisely, indivisible units whose reality is uniform and unchangeable could be never attained.15 If this were the case, however, there would be nothing substantial, nothing real, nothing unitary and fixed in a material body.16 It would follow that Cartesian extended things are not substances at all, for they do not satisfy the fundamental criterion of invariant unity.17 Leibniz concludes that Descartes’ notion of extended substance is incomplete and must supplemented with ultimate units that ground its reality.18 But what are these units? And is Leibniz’s description of these units compatible with a mechanistic view of nature? In the New System of Nature (GP IV 477-87, 1695), Leibniz calls these units ‘atoms of substance’ or metaphysical points and characterizes them in counterdistinction to physical points (atoms of matter) and mathematical points. He writes: [A]toms of matter are contrary to reason. Furthermore, they are still composed of parts, since the invincible attachment of one part to another (if we can reasonably conceive or assume this) does not eliminate diversity of those parts. There are only atoms of substance, that is, real unities absolutely destitute of parts, which are the sources of action, the first absolute principles of the composition of things and, as it were, the final elements in the analysis of substantial things. We could call them metaphysical points: they have something vital, a kind of perception, and mathematical points are the points of view from which they express the universe… Thus physical points are indivisible only in appearance; mathematical points are exact, but they are merely modalities. Only metaphysical points (constituted by forms or souls) are exact and real, and without them there would be nothing real, since without true unities there would be no multitude. (AG, 142)

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In his Tractatus de Ipsa Natura (GP IV 504-16), Boyle claims that nature simply is the very mechanism of bodies. In response, Leibniz writes: [T]his can, indeed, be approved. But investigating the matter with greater care, we must distinguish the ultimate sources [principia] in this mechanism from that which is derived from them. … [T]he source of the mechanism itself flows not from material principles and mathematical reasons alone, but from a higher and, so to speak, metaphysical source, something that I think will be of use in preventing the mechanical explanation of being extended too far, to the detriment of piety, as if matter can stand by itself and as if mechanism required no intelligence or spiritual substance. (AG, 156-57) For Leibniz, extended bodies have a “metaphysical” and “ultimate” source. The “ultimate source” of a material body is not extended. Rather, the source of an extended body is something metaphysical, consisting of indivisible, non-extended and active units. The picture of matter that begins to emerge differs from both Descartes’ geometrical notion of extension and from Gassendi’s material atomism. According to Leibniz, extended bodies somehow result from a multitude of metaphysical units, which have inherent vitality, power, and perception. The fundamental elements are seen primarily as agents, endowed with power of activity and intrinsic appetite.19 It is noteworthy that, when Leibniz describes the metaphysical source of extension, he uses Aristotelian and qualitative terms. This points to the limits of the mechanistic explanation, “preventing [it] of being extended too far”. According to Leibniz, the mechanical explanation should not be extended to the metaphysical source of the mechanism.20 For the source of the mechanism consists in intrinsic power of activity which cannot be fully captured in quantitative terms. As Garber puts it, “neither size nor speed (nor their product) can represent in a body at time n the ability that that body has at some future time to do work. But since the body really has that ability at time n, there must be something [in] it… beyond its geometrical properties; this is what Leibniz calls force”.21 Thus Leibniz’s criticism of Descartes’ notion of extension leads to the conclusion that an extended body presupposes a plurality of substantial atoms whose reality, in the sense of invariant unity and identity over time, derives from their inherent force and activity.

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8.3 Unity by Aggregation As we have seen, Leibniz’s notion of extension involves two levels: a fundamental level of simple and active substances (prima constitutiva) endowed with primitive force and described in Aristotelian terms; and a derivative level of extended bodies, void of force and activity and described in Cartesian terms. But what is the relation between these levels? 22 As an analogy to illustrate this relation, Leibniz uses the relations between points and a line. In his Comments on Fardella (FC 317-23, 1690), he writes: …one must not infer that the indivisible substance enters into the composition of a body as a part, but rather as an essential, internal requisite; just as one grants that a point is not a part that makes up a line, but rather something of a different sort (heterogeneous) which is, nevertheless, necessarily required for the line to be, and to be understood (AG 103). Leibniz’s analogy of the relation between points and a line is instructive. A point is not a constituent of a line in the same sense that a brick is a part of a wall. While assembling bricks may produce a wall, assembling points does not produce a line. Yet the notion of a line does presuppose a plurality of points. By analogy, indivisible substances are not the parts (or constituents) of an extended body and a material body is not a product of merely assembling individual substances. Yet individual substances are necessary requisites implied by the notion of an extended body.23 There is an infinity of simple substances or creatures in any particle of matter;24 and matter is composed from these, not as from parts, but as from constitutive principles or immediate requisites, just as points enter into the essence of the continuum and yet not as parts.25 Leibniz writes elsewhere that, Accurately speaking, ... matter is not composed of these constitutive unities but results from them, since matter or extended mass is nothing but a phenomenon grounded [fundatum] in things, like a rainbow or a mock sun, and all

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reality belongs only to unities. ... Substantial unities are in fact not parts but foundations of phenomena.26 Two subtle points arise from the passages cited above: (1) Bodies are not composed of a multitude of substances but somehow result from their existence; (2) The foundational level and the derivative level each have a distinct ontological status. While “all reality belongs to the [substantial] unities,” the resulting bodies are seen as phenomena, whose reality is grounded in these unities.27 What hinges on Leibniz’s subtle point that an extended body results from substantial units rather than being composed of them? And does this distinction play a role in seeing extended bodies as phenomenal? Answers to these questions begin to emerge when we notice the logical gap between simple and independent units and extended bodies. Although an extended body is seen as a plurality of individual units, a mere plurality of individual units is not sufficient to form an extended body. However real the substantial units may be, it remains unclear how an extended body is formed of a plurality of such units. After all, each individual unit is selfsufficient, independent, and separate from all others. While a body presupposes a multitude of individual units, the converse does not hold. A plurality of substances does not suffice to constitute a body, since the unity of such a plurality does not come about of itself. The unity of a body, seen as an aggregate of simple units, does not follow from the mere existence of its constituents.28 Leibniz illustrates this point by using several analogies, e.g., the unity of a school of fish as opposed to the unity of the individual fish. While each fish is an organic unity, the school consists of a number of individuals with particular relations among them. The notion of a school presupposes certain relations among its members. The relations between the fish presuppose that the fish are conceived of together (or are unified in the same logical space). Since, for Leibniz, only individual substances exist, their aggregation requires an external act of unification. For this reason, the notion of a school is not directly derivable from the existence of the individual fish. The school is not a direct causal consequence of the existence of the individual fish. The notion of a school requires an additional move, namely, that some mind conceives of them simultaneously as one unit. Likewise, the unity of a flock is not a direct consequence of the existence of its sheep; rather, the notion of a flock requires uniting the sheep together as one whole. This act of unification is indispensable to the constitution of a flock as a group of individual sheep. As Leibniz writes to Arnauld:

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“I think that a block of marble is, perhaps, only like a pile of stones, and thus cannot pass as a single substance, but as assemblage of many. … I hold that a block of marble is not a complete single substance, any more than the water in a pond together with all the fish it contains would be, even if all the water and all the fish were frozen, or any more than a flock of sheep would be, even if these sheep were tied together so that they could only walk in step and so that one could not be touched without all the others crying out. There is as much difference between a substance and such beings and there is between a man and a community, such as a people, an army, a society, or a college; these are moral beings, beings in which there is something imaginary and dependent on the fabrication of our mind” (GP II 73-78; AG 79). As another illustration, (though not of Leibniz) consider the unity of a constellation. The unity of a constellation does not derive from the unity of its isolated stars; rather, a constellation presupposes a unification of isolated stars into one particular group or unit. The move from isolated stars to a constellation requires an act of unification, 29 which requires conceiving the separate elements together. Such an operation unifies the elements into one whole and constitutes them as a group or a single unit. In this way, five separate stars may be seen as the Cassiopeia, which consists of five stars, taken together. Furthermore, the selection of the five specific stars that make up the Cassiopeia among other stars cannot be taken for granted. The act of unification may also involve a selection of a certain subset of elements. To put this in general terms, the unity of a plurality of elements presupposes a logical operation of unifying the elements into one unit: sheep into a flock, fish into a school, soldiers into an army, stars into a constellation, and so forth. These transitions require an act of considering the elements together as a single unit and it is by virtue of such an operation that an ensemble of substantial elements can form one extended body. Since individual substances are (a) the only things that truly exist and (b) causally independent of one another, forming a single unit requires the operation of their aggregation into such a unit. Leibniz clearly distinguishes between aggregates that are formed by virtue of such operations and individual substances whose unity is natural and absolute.30 We can now see that the gap between the foundational

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(metaphysical) level, and the derivative, extended (physical) level is mediated through an operation of aggregation. Assuming that a material body is formed of a plurality of substances, the operation of aggregation is a necessary condition for its unity. Without such an operation, the description of the world would reduce to a single set of substances without distinct material configurations (such as bodies). Thus the unity of extended bodies presupposes a mental/logical31 operation of perceiving relations among individuals. This points to the crucial role that relations play in Leibniz’s view of extended bodies, which I now turn to consider. 8.4 Relations and Extended Bodies As is well known, Leibniz held that every individual is unique. This implies that the relations between individuals are not uniform. As there are no identical individuals, there are no two individuals that have an identical system of relations. Since Leibniz holds that only individuals exist, the relations between individuals also presuppose a simultaneous consideration of several individuals.32 As we have seen in chapter 3, Leibniz’s approach to relations is not purely formal. His view of relations is not syntactical, as in the logic of Frege and Russell. A relation, for Leibniz, is not merely a ntouple; nor is it an entity in itself. Likewise, his view is non- extensional. As Mugnai suggested, Leibnizian relations may be best characterized as consequentia in the medieval tradition.33 For Leibniz, “a relation is that according to which two things are thought of at once” (C 47). “A relation is the concogitabilitas of two things” (C 35) or their simultaneous consideration.34 A simultaneous consideration of two things is typically performed under a certain aspect – namely, “that according to which two things are thought of at once.” For example, the relation between two points may be considered as a straight line, as a distance, or as infinitely many curved lines. Now the result of relating two objects involves some elements that are not found in the relata. The relation ‘3 is smaller than 4’ includes properties that cannot be found in the relata (3, 4), considered separately. A relation presupposes the operation of unification of the relata under a certain aspect. This is why it is impossible to reduce a relation to its constituents (or foundations). At the same time, the resulting relations have different logical and ontological status from the relata. According to Leibniz, the fundaments of a relation are logically and ontologically prior. The relations supervene on and presuppose the individuals. Thus Paris and Helen are ontologically prior to the love between them.35 This relation

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presupposes Paris, Helen, and their simultaneous consideration under a certain aspect. While absolute and independent existence may be ascribed to substances, relations depend, by definition, on their fundaments. In these respects, Leibniz’s analysis of material bodies as founded on simple substances is analogous to his analysis of relations as based on more basic fundaments. Rutherford formulates this connection as follows: Leibniz’s doctrine of relations plays an essential role in determining the nature of aggregative beings. We know that for him relations are merely ideal: they are not themselves created beings but merely “modes of conceiving,” or what a mind imposes upon the world in apprehending the agreement and connections of singular things. It follows that aggregative beings—whose existence is dependent upon relations—can only exist for a mind.… Only to the extent that a plurality of individuals is apprehended by a mind as forming a unitary being is an aggregate determined. Beings through aggregation thus occupy a curious middle ground in Leibniz’s ontology between what is truly real, an unum per se or substance, and what is merely ideal or imaginary. They are at once semirealia and semimentalia. The existence of any aggregate is necessarily mind dependent; yet this does not mean that aggregates are merely mental things. Aggregates are instead “well-founded phenomena”: They are pluralities of individuals, which together determine a single complex being insofar as they are apprehended as having a certain sameness or connection with respect to one another (Rutherford, 1995, 222). Rutherford clearly and accurately describes the role of relations in unifying a plurality of substances into a material body. However, it seems to me that, with respect to the status of relations, his description is inadequate. As I tried to illustrate above, relations for Leibniz are not “merely ideal” or mere “modes of conceiving.”36 Rather, since relations derive from the relata, they are well-founded in the nature of the individuals. While they presuppose a mental act of unification, relations, for Leibniz, have the status of truths. “3 is smaller than 4’ is a relational truth of this kind. Like eternal truths and possibilities, relations, according to Leibniz, do not have a status of entities but a status of thoughts (“second intentions” in scholastic jargon) and mental/logical operations. In the context of God’s understanding and its realm of possibility, such thoughts do not correspond to factual truths (pertaining to the created world) but to relations between concepts and possibilities. The status of relations as mind-dependent does

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not threaten (or even affect) their status as truths. But does this status of truths applicable to relations among created things as well? As we have seen, a mind is required for relating two objects. This mind-dependence, however, does not imply that the resulting relation presents a distorted view of reality. There is nothing distorted in a relation such as ‘3 is smaller than 4’, or as ‘Paris loves Helen’, even if, according to Leibniz, it is (a) mind-dependent and (b) not strictly a real entity. In light of this point, I suggest modifying Rutherford’s formulation by stressing that relations are not ‘merely’ ideal, even if they are minddependent.37 Since ‘extension’ is a relational notion (section 8.2), Leibniz’s view of relations and the logical unification of elements (required for extension) may be linked directly. As I have noted, extension for Leibniz is a predicate binding a plurality of individuals.38 At the same time, the very act of binding, that is, the aggregation of individuals, presupposes an operation of a mind. Leibniz describes this as follows: Our mind notices or conceives some true substances which have certain modes; these modes involve relations to other substances, so the mind takes the occasion to join them together in thought and to make one name account for all these things together (AG 89; GP II 101).39 Suppose that stars are real substances. For an observer, the stars may be related and grouped in various ways, so that different groups or constellations would be formed. In effect, this is what humans have been doing for thousands of years. Likewise, a material body consists of a number of true substances that are unified as one aggregate. But precisely for this reason we may not ascribe to a material body the absolute reality that we may ascribe to its foundational units. Leibniz writes: We can therefore conclude that a mass of matter is not truly a substance, that its unity is only ideal, and that (leaving the understanding aside) it is only an aggregate, a collection, a multitude of an infinity of true substances, a well-founded phenomenon. (GP VII 564; CCL 147 my italics)40 8.5 The Reality of Bodies Well-founded phenomena are distinct from mere phenomena. The logical unification of elements, which is required for an aggregate, does not render a material body a fiction. As Leibniz clarifies,

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In truth, I do not do away with body but reduce [revoco] it to that which is, for I show that corporeal mass ... is not a substance, but a phenomenon resulting from simple substances, which alone have unity and absolute reality. (GP II 275; CCL 152) Well-founded phenomena result from substances that have absolute reality. For this reason, material bodies are not fictions or illusions; rather, they are perceived by a mind and are grounded in true beings (individual substances). While secondary matter presupposes a mental aggregation of substances, it is not itself a substance. To be a substance, secondary matter would require absolute unity, that is, unity that is intrinsic and invariant. However, a material body lacks such unity. Although the unification of simple substances is not absolute or necessarily enduring, it is still based on the network of relations between different individuals. To sharpen this point, consider a school of fish (S) swimming together. Now suppose that one fish leaves the school and joins another school. The unity of S is disrupted, since it depends on the relations among its members. Strictly speaking, S is no longer the same entity. Similarly, a mass of matter without one of its particles is not the same mass of matter. In comparison to the unity of the individual fish or the simple elements of matter, the unity of the school or the unity of the bulk of matter is not guaranteed over time and may be disrupted. Since the unity of a material body is (a) external and (b) subject to change, it cannot be considered a strictly real entity, that is, one that satisfies the criterion of absolute and invariant unity.41 In light of this subtle position, it seems to me that both Garber and Adams have overstated one component of Leibniz’s complex view of material bodies. Garber stressed Leibniz’s claim that material bodies are grounded in the reality of force and concludes that “the world of Leibniz’s physics is not a world of phenomena” (Garber, “Leibniz,” 92).42 Adams stressed Leibniz’s claim that a mind (human or divine) is necessarily involved in unifying simple substances into a mass of matter and concludes that such a body is a mere phenomenon.43 The hybrid status of well-founded phenomena indicates that bodies result from real entities (substances) but presupposes their aggregation into a single group under varying conditions. Thus the notion of well-founded phenomena has its place precisely in between mere phenomena and real substances – a grouping of substances

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that lacks invariant unity. As well-founded phenomena, material bodies presuppose a necessary unification of a subset of simple substances by a mental/logical operation, so that the unity of a body derives from this operation and its reality derives from the reality of the substances. In contrast to some other commentators, I believe that this sort of minddependence does not imply a confused representation of external reality, which is, presumably, mind-independent.44 The mental unification of simple substances produces a partial representation, as it captures a changing state of the substances’ career. Such a state changes as the substances perceived do and as the substance (mind) perceiving does. While such a perspective is necessarily limited, it is not necessarily confused or distorted. Rather, it reflects the traditional opposition between Being and becoming. Mind-dependence does not necessarily render material bodies fictional; rather, they are certain aggregations of substances, seen from a particular point of view and under a particular aspect. According to this approach, normal perception is veridical, even if partial. There is no unique way to unify or aggregate individuals, as there is no unique way to form constellations from a plurality of stars. Only God “sees” everything from an intelligible point of view, which is, of course, not a point of view at all. In observing the natural world, we observe aggregates of individual substances such as rocks, tables and clouds. As aggregates, these bodies have well-defined properties (for example, mass), and they obey the laws of motion and collision. Thus the extent of Leibniz’s phenomenalism does not entail an antirealist view.45 Rather, it is a realistic view according to which active and perceiving substances constitute the metaphysical foundation of reality. The fundamental source of being remains, for Leibniz, force and activity. Leibniz’s variant of realism, however unusual, does not require that the fundamental substances be extended.46 Nor does it require mindindependence. Rather, it requires that the statements of physics pertaining to material bodies as aggregates of substances would be understood as relational. For they always presuppose some relations among the basic substances of the world. Leibniz’s distinction between the fundamental and derivative levels can be now related to their appropriate means of description. According to Leibniz, entities whose unity is changeable (that is, phenomena) are to be investigated by physics and entities whose unity is unchangeable (that is, substances) are to be investigated by metaphysics.47 While physics investigates the domain of well-founded phenomena, metaphysics investigates the domain of substantial entities. This division allows Leibniz to endorse Cartesian terminology in physics and Aristotelian terminology

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in metaphysics. While the Cartesian program for a quantitative description of nature is adequate, its application has to be restricted to the domain of extended bodies, that is, of mass in motion and change.48 While physics is normally restricted to quantitative terms, metaphysics must use qualitative terms in order to describe the realm of active substances.49 As I have tried to show above, the fundamental and derivative levels in Leibniz’s view of extend bodies are intimately related, so that both models of explanation – the Aristotelian and Cartesian – are required for an a full and adequate description of nature. 8.6 Aggregates and Organic Units As we have seen, aggregates, according to Leibniz, are aggregates of substances.50 As Fichant has recently argued in his “Leibniz et les machines de la nature”, starting from the second half of the Correspondence with Arnauld (1687) and explicitly since the New System of Nature (1695), Leibniz makes extensive use of the notion of organic beings, seen as machines of nature, which he identifies with corporeal substances and contrasts with artificial machines and aggregates. Leibniz exemplifies the unity of a corporeal substance with the organic unity of an animal. As we have seen, while an animal has organic unity, a flock of animals does not. Il y a en effet une grande différence entre un animal et un troupeau. C’est pourquoi cette Entéléchie est ou âme, ou quelque chose d’analogue à l’âme, et réalise toujours naturellement un corps organique, qui lui-même, considéré séparément, c’est-àdire l’âme mise à part ou enlevée, n’est pas une unique substance, mais un agrégat de plusieurs, nommément une machine de la nature.51 The following passage clarifies that Leibniz sees a much wider application to this distinction. A suppositum is either an individual substance, which is a complete entity, one in itself, such as God, a mind, the ego; or it is a real phenomenon, such as a body, the world, a rainbow, a woodpile. We conceive the latter on the model of a complete substance, but since body – unless it is animated, or contains

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within it a certain single substance, corresponding to the soul, which they call a substantial form or primary entelechy – is no more one substance than a woodpile; and since again there is no part of it which can be regarded as a unity in itself (since body is actually subdivided, or certainly subdivisible, into parts), it is a consequence that every body will only be a real phenomenon, like a rainbow. Similarly mathematical things, such as space, time, a sphere, an hour, are merely phenomena, which we conceive on the model of substances. And accordingly there is no real substance which is not indivisible one. And indeed, it may be that those things that are divisible and consist in magnitude, such as space, time, and bulk, are not complete beings, but must have something superadded to them, which involves all those things that can be attributed to this space, this time, this bulk . (A 6.4 132; Arthur 265-67) In her La Pensee de la vie chez Leibniz, (1976), Dumas has argued convincingly for two major points: (1) in Leibniz late writings, the terms organism, natural machine and divine machine are more or less synonymous (Dumas, 1976, 128) and they are distinct from artificial machines which fall under the category of aggregates; (2) this distinction can be clarified by attributing an internal source of activity and selfsufficiency to natural machines (Dumas, 1976, 124) while artificial machines and aggregates lack internal source of activity and selfsufficiency. The distinction between artificial and natural machines is, however, a very subtle one. Leibniz says that both are machines within machines, except that, in the case of natural machines, this nested structure goes to infinity. Natural machines are machines in each of their constituents or in the least of their parts (Monadology 64.). It is very curious – as well as initially confusing – that this should be the distinguishing mark between the natural and the artificial – between God’s creation and human fabrication. 52 However nuanced, I will argue in the next chapter that this point is indicative of something deeper: an infinite structure indicates the presence of a rule or a program underlying the structure of and individual. As a possible individual is an infinite structure, which develops to infinity according to its production-rule, perhaps so is an organism with its nested structure. This is the suggestion I will develop in the next chapter. Leibniz illustrates this point with the example of circles within circles (GP II 306). As Dumas points out, it is significant that “Leibniz did not

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give the image (figure) of the emboîtement of circles but the method for constructing them” (Dumas, 1976, 126). This is no accident. Rather, it is typical of Leibniz’s treatment of individuals (see chapters 2 and 7), whose method of production is constitutive of their essence and individuality. In short, this view is consonant with his generative approach to the definition of individuals and will be further developed in the next chapter. Commenting on the difference between finite and infinite schemas, Dumas writes: “[T]he difference is the same as between an infinite and finite figure, between an ideal horloge and a human horloge, as between natural machine and artificial machine: these are two different orders. Consequently, far from having reduced the natural machine to an artificial machine with the aid of the schéma de l’emboîtement, Leibniz has affirmed their absolute irreducibility” (Dumas, 1976, 127). Since each organism is self-sufficient, it realizes its proper end and law (Dumas 129). On the other hand, an aggregate, which is not self-sufficient, is passive and lacks intrinsic finality. For example, a hammer receives its finality and function from the use humans make of it. By contrast, in an organic structure, the finality and function of each constituent are always intrinsic to the structure and are, therefore, natural (rather than artificial). While an aggregate is clearly organized, it is “an organization which lacks self-sufficiency” (Dumas, 130). This implies lack of intrinsic organization in aggregates because the organization does not derive from an internal activity, law and finality. For Leibniz, lack of activity, unity and finality also imply lack of being and life.53 Thus, while the distinction between artificial and natural machines seems to turn on a nuance,54 it is in effect highly consequential.55 Let me try to present, by way of a rough summary, some of these differences: Natural Machines, Organic Units Artificial Machines, Aggregates Are complete individuals.

Are composed of individuals but are not complete individuals. Are intrinsically active and entail Lack intrinsic source of activity and intrinsic force. force. Have no intrinsic end. Have intrinsic end.56 Understood by final causality and Understood by efficient causality belong to metaphysics. and belong to physics.

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Have intrinsic or metaphysical unity. (GP II, 304) Are real beings. Have nested structure to infinity.

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Do not have intrinsic unity but relational or “Arithmetical unity.” (GP II, 304) Are well-founded phenomena. Do not have nested structure to infinity.

Are not composed of parts but of Are composed of parts. constituents that are essentially related to their structure. Cannot decompose Can decompose Have intrinsic source of organization.

Have extrinsic source of organization.

Have intrinsic laws.

Have extrinsic laws.

Are animate.

Are inanimate.

Have internal self-regulation

Have no internal self-regulation.

Have an invariant source of change. Are changing and have no invariant source of change. Are self-sufficient. Have complete concepts.

Are not self-sufficient. Do not have complete concepts.

Dumas claims that, an organism is composed of parts, the ones in correlation with the others, each possessing its own individuality and finality and in concurrence with those of the whole organism. This point, however, must be qualified: An organic unity according to Leibniz, is not composed; rather, it consists of other individuals or organisms. Likewise, an individual cannot be decomposed into its parts. This is why Leibniz’s stresses many times that a true unity, even though it consist of many individuals (see next chapter), does not have parts and cannot be

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decomposed into its parts. Unlike artificial machines, which may decompose into their parts, natural machines cannot be decomposed. Leaving the question of simple substances aside for the moment, the distinction between organisms (or natural machines) and aggregates (or artificial machines) is not only conceptually interesting but also divides Leibniz’s later ontology into two types of things: true Beings and wellfounded phenomena. While the former are organic units possessing substantial unity, the latter are aggregates lacking such unity. On the background of this division, I will consider in the next chapter the nature of Leibnizian individuals. 1 The ancient notion of "phenomenal", which is grounded in the distinction

between the variable and the invariable, should be clearly distinguished from a modern notion of "phenomenal", which is grounded in the opposition between mind-dependence and mind-independence. It seems to me that confusion between these two senses infects the debate over Lebniz's phenomenalism. 2 “I hold this ... as an axiom, what is not truly one is not truly one being either” (Letter to Arnauld, 30 April 1687, AG, 86. See also GP II, 304). 3 “[S]econdary matter results from many monads, together with derivative forces, actions [and] passions, which are only beings through aggregation, and thus semimentalia, like the rainbow, and other well-founded phenomena” (GP II, 306; Rutherford, Leibniz and the Rational Order, 1995, 234). “Beings through aggregation, such as a herd, a pool full of fish, a machine, are only semibeings (semientia), whose reality consists in the union which a mind makes or in an extrinsic denomination or relation” (Hanover, Nieders. Landesbibliothek, LeibnizHandschriften, 4.2.5e.B1.23; cited from Rutherford, 1995, 234). 4 This question has been a source of dispute among recent writers on Leibniz. I am thinking primarily of Garber, “Leibniz and the Foundations of Physics: The Middle Years,” 1985; Adams, Leibniz: Determinist, Theist, Idealist, 1994, Rutherford, "Leibniz's Analysis of Multitude and Phenomena into Unities and Reality,” 1990; “Phenomenalism and the Reality of Body in Leibniz’s Later Philosophy”, 1990; and Leibniz and the Rational Order of Nature 1995; Jolley, “Leibniz and Phenomenalism,” 1986. Roughly speaking, Adams argues that matter is merely phenomenal, and that it results from confused perceptions. Garber argues that, in Leibniz’s early and middle periods, material bodies have the status of fully real substances and Rutherford advocates a middle course, emphasizing the intermediate status of well-founded phenomena. My own position is close to Rutherford’s with the modifications and qualifications that appear below. 5 Since organic unities are extended, my remarks on extension pertain to them as well. However, the unity of an organic unit, such as a fish, is different from the unity of a group of them, such as a school of fish. I will focus on material bodies

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of the second type, that is, bodies of non-organic unities. In traditional terminology, non-organic unity is accidental rather than substantial. Another way to define the scope of this chapter is by reference to Russell’s classification of Leibniz’s different senses of ‘matter’. Russell, A Critical Exposition of the Philosophy of Leibniz, 1992, 76. I focus here on item 4 in Russell’s list, termed by Leibniz as mass, that is, secondary matter whose unity is accidental (unum per accidens). 6 Primary matter is a metaphysical principle of passivity required for a principle of activity in order to form a substance. It is a source of resistance—what Leibniz calls “passive force”. Although this point is controversial, it seems to me that primary matter is not extended. 7 In 1698 Leibniz began to employ the term monad (unit) instead of ‘individual substance’ as designating the true unities that have necessary and absolute reality (or being). Whether this terminological change reflects a more substantial change is not my concern here. 8 Descartes’ position serves here mainly as a background for presenting Leibniz’s. It is presented, therefore, only schematically. 9 Fichant, Science et metaphysique dans Descartes et Leibniz, 1998, 69. 10 “[T]he nature of matter, or body considered in general, consists not in its being something which is hard or heavy or colored, or which affects the senses in any way, but simply in its being something which is extended in length, breadth and depth.” (Principles of Philosophy, part 2, 4, in The Philosophical Writings of Descartes, trans. John Cottingham et al., 1985). 11 See GP IV, 467. “Ceux qui veulent que l’étendue même est une substance, renversent l’ordre des paroles aussi bien que des pensées. Outre l’étendue il faut avoir un sujet, qui soit étendue, c’est a dire une substance a laquelle il appartienne d’être répétée ou continuée. Car l’étendue ne signifie q’une répétition, ou multiplicité continuée de ce qui est répandu, une pluralité, continuité et coexistence des parties; et par conséquent elle ne suffit point pour expliquer la nature même de la substance répandu ou répétée, dont la notion est antérieure a celle de sa répétition.” (FC I 228-30; cited from G. W. Leibniz, System nouveau de la nature, Paris: GFFlammarion, 1994, 39). 12 See Comments on Fardella, proposition 3, FC 317-23; AG 103-05. 13 This is just one of Leibniz’s arguments. I do not intend to present a comprehensive survey of Leibniz’s critique of Descartes here. For another argument see Leibniz’s letter on the question whether the essence of matter consists in extension” (GP II 464-67). 14 Descartes’ “Principles of Philosophy,” part 2, 34, 35. 15 It is noteworthy that Descartes himself uses the divisibility argument to prove the impossibility of material atoms. See Descartes Principles of Philosophy, Part

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2, 20. For a nice presentation of Leibniz’s response to Descartes’ insight regarding indefinite division, see Levey, “Leibniz on Mathematics”, 1998, section 1. 16 “But at least I can say that, if there are no corporeal substances such as I claim, it follows that bodies would only be true phenomena, like the rainbow. For the continuum is not merely divisible to infinity, but every part of matter is actually divided into other parts as different among themselves as the two aforementioned diamonds. And since we can always go in this way, we would never reach anything about which we could say, here is a true being, unless we found animated machines whose soul or substantial form produced a substantial unity independent of the external union arising from contact. And, if there were none, it then follows that, with the exception of man, there is nothing substantial in the visible world” (Letter to Arnauld, GP II 73-78; AG 80). 17 Assuming that “to be is to be one,” this argument contradicts Descartes’ assumption that there are extended substances. Leibniz’s analysis purports to show that the Cartesian expression ‘material substance’ is unintelligible: since ‘substance’ is, by definition, real and ‘matter’ (seen as a mere extension) lacks reality, the expression ‘material substance’ implies something like ‘a real thing [substance] without reality [material]’. 18 “Thus one will never find a body of which one can say that it is truly [or one] substance. It will always be an aggregate of several. Or rather, it will not be a real being, since the parts that compose it are subject to the same difficulty, and since one never arrives at any real being, as beings by aggregation have only as much reality as there is in their components. From this it follows that the substance of a body, if they have one, must be indivisible; whether it is called soul or form does not matter to me” (draft of letter to Arnauld, LA, 72). 19 These are minimal characteristics. As is well known, some substances are also endowed with intelligence and apperception. 20 While the Cartesian terminology is adequate for describing the mechanical aspect of an extended body, it is inadequate to describe its metaphysical source. Even if the motion of bodies can be described in purely quantitative terms, the source of a body’s activity and motion cannot be purely geometrical. For Leibniz, the motion of bits of matter is not primitive notion; rather, it presupposes a metaphysical motive force as its cause. On this basis, Leibniz states that “the foundation of the laws of nature, among other things, provides a notable indication of this. That foundation should not be sought in the conservation of the same quantity of motion, as it has seemed to most, but rather in the fact that it is necessary that the same quantity of active power be preserved, ... that the same quantity of motive action be preserved” (On Nature Itself GP IV 504-16; AG, 157). 21 Garber, “Leibniz and Physics” (1995), in CCL, 287. 22 A number of commentators (Rutherford, “Phenomenalism” (1990), 13-14; Furth, “Monadology” (1967), 188; Garber, “Leibniz and Physics” (1995) in CCL, 284) find this relation obscure. For example, Rutherford writes that, “Material

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things do not form a part of his [Leibniz’s] fundamental ontology. Their existence is to be explained, instead, in terms of the existence of and properties of monads alone. Yet how exactly such an explanation might work remains one of the most difficult problems in the interpretation of Leibniz’s philosophy” (Rutherford, 1995, 219). 23 See letter to Volder, June 1704, GP II, 248-53; AG, 178-89. 24 “Each portion of matter can be conceived as a garden full of plants, and as a pond full of fish. But each branch of a plant, each limb of an animal, each drop of its humors, is still another such garden or pond. Thus there is nothing fallow, sterile, or dead in the universe, no chaos and no confusion except in appearance, almost like it looks in a pond at a distance, where we might see the confused and, so to speak, teeming motion of the fish in the pond, without discerning the fish themselves.” (Monadology, 67, 69, AG, 222) 25 FC, 324; cited from Rutherford, “Leibniz’s Analysis,” 1990, 544. 26 GP II, 268; L 536; CCL, 145. 27 “Everyone agrees that matter has parts, and consequently that it is a multitude of many substances, as would be a herd of sheep. But since every multitude presupposes true unities, it is obvious that these unities cannot be material, otherwise they would still be multitudes and not at all true and pure unities, such as are necessary finally in order to make a multitude. Thus, the unities are in fact substances in their own right, which are neither divisible nor consequently perishable... And it is this simple substance, this unity of substance or monad, which is called soul... These unities truly constitute substances and each unity uniquely makes a single substance; the rest are only beings through aggregation, and collections or multitudes.” (GP VII, 552-53; Rutherford, 1995, 220). 28 In addition, homogeneity considerations between the parts and the whole play a role in Leibniz’s arguments why individual substances can’t, strictly speaking, be “parts” of a body. Here is an example from a letter to De Volder: “But my unities, that is, my simple substances, are not diffused…, nor do they constitute a homogeneous whole, for the homogeneity of matter is brought about only through an abstraction of the mind, when it is considered as being only passive and therefore incomplete.” (AG 183) I thank Brandon Look for drawing my attention to this point as well as to this passage. 29 In fact, this point holds for any plurality. Even the move from one to two in mathematics is far from trivial, according to Leibniz. See Grosholz and Yakira, Leibniz’s Science of the Rational, 1998, chapter 3. 30 For this distinction, see the last section in this chapter. Against this background, it is easier to understand Leibniz's motivation for developing his later accounts of unity in or organic units or corporeal substances, such as the dominant monad, the notion of an organism, and the substantial bond.

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31 I call it a mental/logical operation because, for Leibniz, there is a close relation between them, especially with respect to God’s mind. I should stress, though, that this intimate connection does not involve a psychologistic notion of logic. As we have seen in chapter 1, Leibniz’s views of logic and possibility presuppose the intelligible activity of God, that is, the thought of all possible concepts and their interrelations in God’s mind. The relations between created substances that constitute material bodies are perceived by God’s mind. This supposition is in the background of Leibniz’s approach to relations, in general, and to material bodies, in particular. Rutherford formulates this points as follows: “The role played by God in this scheme is critical. …assuming the existence of certain monads, and assuming the presence of a mind capable of apprehending those monads in relation to each other, there will be determined, as a result, some aggregative being. If we accept, as Leibniz does, that the divine mind knows all the states of monads at every instant, then aggregates must result, given the existence of individual monads.” (Rutherford, 1995, 223). 32 Since I discussed Leibniz’s view of relations in chapters 3, my account here is very brief. 33 For details, see Mugnai, Leibniz’s Theory of Relations, 1992. 34 “A relation is an accident which is in several subjects and is only a result or supervenes with no change made on their part if several things are thought at once; it is concogitabilitas” (C 74). 35 This ontological priority is related to Leibniz’s supposition that the simple is prior to the complex since the complex is produced by a combination of simples. Similar reasoning holds for relations: since a relation is constituted by a mental unification of two elements (relata), the elements precede the relation. 36 Adams holds a similar position concerning the status of relations. “For extension, as defined here, consists in a relation among substances repeated, and Leibniz held that relations depends on perceivers who apprehend them ... Writing to De Volder in 1704 or 1705, Leibniz explicitly connects the relational character of extension with its being something intrinsically ideal (res per se idealis)” (Adams, 1995, 234). 37 This leads Rutherford, whose general approach I accept, to argue that Leibniz reduces material bodies to the substances on which they are founded (Rutherford, 1995, 219, 225-6). However, as we have seen, a relation entails elements that are not entailed in the relata and, therefore, it is impossible to reduce relational predicates to non-relational (monadic) ones. Russell accused Leibniz of attempting such a reduction. A number of commentators have shown convincingly that this accusation is unjust. See, for example, Ishiguro, Leibniz’s Philosophy of Logic and Language, 1972; Mates, The Philosophy of Leibniz, 1986; Mugnai,

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Leibniz’s Theory of Relations 1992. A similar misunderstanding lead some of Leibniz’s scholars (e.g., Adams, Garber, and Rutherford) to contrast a material body as we perceive it and the way such a body exists in itself. Since the act of aggregation constitutes a material body, speaking of a material body as it exists in itself seems to be misleading. This use of Kantian terminology leads us to believe that mind-dependence undermines a veridical perception of reality. However, claims about “entities” whose unity depends on a mind (such as aggregates) are not necessarily fallacious. As we have seen above, this is precisely the status of mathematical (and eternal) truths. Relational statements (in Physics as well as in Mathematics) may be true even if they are not about entities in the strict sense of the word. In contrast, relational statements are about the relations between these entities. While these relations presuppose a mind, this mind-dependence does not distort the preexisting reality of the relata. Rather, it constitutes relational which are not independent of such mental unification. 38 In a letter to de Volder GP II 169; AG, 171. 39 This passage continues as follows: “This is useful for reasoning, but we must not let ourselves be misled into making substances or true beings of them; this is suitable only for those who stop at appearances, or for those who make realities out of all the abstractions of the mind”. 40 Note that it is the unity rather than the reality or being that is merely ideal. Adams infers that the being of an aggregate is also merely ideal. He writes: “Leibniz’s claim is that aggregates have their unity, and therefore their being, only in the mind, and that is even true of aggregates of real things” (Adams, 1994, 246). But such conclusion does not follow. It only follows that such an aggregate is not a true being but a phenomenon. It is, however, a well-founded phenomenon whose being is not necessarily in the mind; rather, its being is grounded in the substances aggregated. 41 Leibniz does allow, however, a less restricted notion of identity over time. A substance may undergo a change of properties and remain the same substance. This is the case as the principle of change, activity, and unity remains one and the same. In the case of substances, this principle is intrinsic. In contrast, the principle of unity of aggregates is external and may change over time. 42 To be more precise, even Garber overstates both aspects: on the one hand, he argues that “Leibniz’s physics is firmly grounded in reality, the world of Leibniz’s physics is not a world of phenomena” (Garber, 1985, 92). On the other hand, he writes that “phenomenal aggregates .... belong to the apparent” (CCL, 297; Garber, 1985, 90). 43 Adams writes that “aggregates of substances are merely appearances” (Adams, 1994, 240) and “...extended things as such are merely phenomena (because merely aggregates)” (Adams, 1994, 237; see also 234). “The mature Leibniz is motivated largely by worries about the unity of bodies… The unity of a body comes to it by an external denomination, namely, by relation to a mind that perceives relationships among the things that are aggregated. Since Leibniz

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adhered to the scholastic maxim that ‘being’ and ‘one’ are equivalent (GP II, 304), he inferred that aggregates that have their unity only in the mind also have their being in the mind (Adams, 1994 245-6).” 44 “So if (as I claim) the aggregation of substances to form aggregates depends on (apparent) spatial properties of bodies, that will tend to infect the aggregates with mind-dependence, and diminish their reality. But that is no objection to my interpretation of Leibniz. It is part of my interpretation, providing one of the reasons for the phenomenality of corporeal aggregates” (Adams, 1994, 255). 45 See GP, VII, 468. 46 On this point, I side with Adams’ critique of Garber. The issue of how realistic Leibniz was does not depend on his commitment to the reality of primary matter. Rather, as Adams notes, “what [Leibniz] regarded as essential to realism about bodies is belief in the reality of forces, especially of the active forces that he identified with substantial forms. For Leibniz, it is on the concept of form, not of matter, that realism in physics principally depends” (Adams, 1994, 339). 47 Leibniz founded Dynamics as a science that investigates force in quantitative terms. This science occupies a middle position between physics and metaphysics: while its object (force) is primarily metaphysical, its methods are physical (that is, quantitative). 48 Garber holds that Leibniz employs two kinds of explanation: a scholastic which is stated in terms of forms; and a mechanistic, which is stated in terms of shape, size, and motion. He argues that these are alternative explanations of the same phenomena: “[S]ince these living creatures are corporeal substances, unities of matter and form, everything can be explained as the schoolmen do. But at the very same time, everything in nature can be explained mechanically, even the voluntary motions of creatures like us. In this way, Leibniz quite self-consciously reconciles the philosophy of the schools with the most radically mechanistic philosophy of the moderns; both are correct and the two pictures will always agree with one another” (Garber 1995, in CCL, 331). However, I think that the two kinds of explanation Leibniz employs (scholastic and mechanistic) correspond to two different explanandums: when the metaphysical realm of true beings is considered, the Aristotelian model is to be preferred; when the physical level of extended bodies and masses is considered, the mechanistic model is to be preferred. 49 As noted, Leibniz’s science of Dynamics, which treats forces in quantitative terms, is a conspicuous exception to this division. 50 « Dans les corps je distingue la substance corporelle de la matière, et je distingue la matière première de la seconde. La matière seconde est un agrégé ou composé de plusieurs substances corporelles, comme un troupeau est composé de

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plusieurs animaux. Mais chaque animal et chaque plante aussi est une substance corporelle, ayant en soi le principe de l’unité, qui fait que c’est véritablement une substance et non pas un agrégé » (GP III, 260). 51 “ […] multum enim interest verbi gratia inter animal et gregem. Adeoque haec Entelechia vel anima est, vel quiddam Animae analogum, et semper corpus aliquod organicum naturaliter actuat, quod ipsum separatim sumtum, seposita scilicet seu semota anima, non una substantia est, sed plurium aggregatum, verbo, machina naturae” (GP IV, 395-396, 1702). 52 “….the whole of nature is, so to speak, the workmanship of God, indeed, so much so that any natural machine you may choose consists of a completely infinite number of organs (which is the true and insufficiently appreciated distinction between the natural and the artificial), and therefore requires infinite wisdom and power of the author and ruler” (On Nature Itself, GP IV 504; AG 156). 53 “I thus restrict corporeal or composite substances to living things alone, or to organic machines of nature. All the rest are for me mere aggregates of substances, which I call substantiata; and an aggregate only constitutes an unum per accidens” (GP II 520). 54 “In truth, every organism is a mechanism, but more excellent and more divine” (Dutens II 2, 136; cited from Dumas, 1976, 132). 55 For a very informative and illuminating exposition of the history of the distinction between machines and natural machines, see Fichant 2003, “Leibniz et les machines de la nature”. 56 Regarding the distinction between aggregate and natural machines, see Dutens. II, 2, p. 144 and Dumas, 1976, 129.

Chapter 9

Nested Individuals 9.1

Introduction

Having focused on Leibniz’s notion of aggregates and the way they differ from substances and organic beings in the previous chapter, I now turn to examine Leibniz’s notion of individual substances and organic beings more closely. According to Leibniz, everything in the world – whether organic or inorganic – consists of individual substances and their properties. Each of these individuals is causally self-sufficient and unique being whose identity remains unchanged over time. The causal selfsufficiency of individual substances implies that they are causally independent of one another. At the same time, individual substances are not independent in the sense that their activities, which are prescribed by their concepts, harmonize with one another. Given this picture, I focus in this chapter on a particularly intriguing feature in Leibniz’s notion of individuality. For Leibniz, individuals not only contain other individuals as the body of an animal may contain worms or germs but also typically consist of other individuals who are organized in a hierarchical structure and are nested one within another to infinity.1 I term this interesting and controversial feature ‘nested individuality’ and I will try to clarify what the notion of ‘nested individuality’ might imply in the context of Leibniz’s metaphysics.2 Tension arises between this feature of Leibniz’s individuals and some of his suppositions noted above. This tension pertains to the very definition of Leibniz’s notion of substance: is it simple or composed, is it one or many? Leibniz’s equivocations on these issues are notorious and have puzzled scholars in recent years (see e.g., Robinet 1987, Adams 1994). Cover and O’Leary-Hawthorne (1999) go as far as considering the expression “corporeal substance” as “a misleading shorthand for ‘simple substances related thus and so’” (54). Look has very aptly formulated this “deep problem” in questioning “the very possibility of composite substance within the Leibnizian monadology” (in Lodge 2004, 258). He concluded his study of the Des Bosses correspondence as follows: “In the end, study of the Leibniz-Des Bosses correspondence 215

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leads to the inescapable conclusion that Leibniz, despite his sanguine claims in his best known works, cannot give us a consistent and convincing account of the unity and reality of composite substance” (in Lodge 2004, 259). My formulation of the question here in terms of nested individuality is an attempt to address this very difficult and important problem. Versions of Leibniz’s notion of nested individuality appear in his earlier writings3, but they develop and mature in his later writings, especially following the New System of Nature (1695) in which the notion of a natural machine is introduced.4 The main features of his view of nestedness are articulated in the following passages: “I define an organism or a natural machine, as a machine each of whose parts is a machine, and consequently the subtlety of its artifice extends to infinity, nothing being so small as to be neglected, whereas the parts of our artificial machines are not machines. This is the essential difference between nature and art, which our moderns have not considered sufficiently” (letter to Lady Masham (1704), GP III 356).5 ...Thus we see that each living body has a dominant entelechy, which in the animal is the soul; but the limbs of this living body are full of other living beings, plants, animals, each of which also has its entelechy or its dominant soul (Monadology, 70, cited from AG). According to a widely accepted interpretation, Leibniz’s notion of nestedness applies to bodies at the physical level but not to individual substances at the metaphysical level.6 According to Duchesneau, the notion of nestedness is mechanistic,7 so that it is to be applied to bodies or machines which are not individual substances. In what follows, I will suggest that there is also a metaphysical notion of nestedness which is not primarily mechanistic but which does not reject a mechanistic description at the level of bodies and well-founded phenomena. I will suggest that we find in Leibniz a metaphysical notion of nestedness, which pertains to the relations of activation and domination in the sense of functionally organizing less active constituents of the same organism. This sense of nestedness is best captured in metaphysical terms and applies to the relations between individual substances.

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It is well known that, for Leibniz, a mechanical account of nature (in terms of shock, impact, and efficient causation among bodies) need not exclude a metaphysical account in terms of final causes, activation and domination. Thus, while, I do not reject the mechanistic account, I would like to stress that Leibniz’s notion of nestedness is not fully captured in mechanistic terms alone.8 It is important to keep in mind that Leibniz’s notion of nestedness does not apply to any physical body or to any machine but only to organic bodies and/or natural machines. This is especially significant in light of the fact that Leibniz identifies natural machines with corporeal substances that are true units, as distinct from artificial machines. As Fichant has recently made clear, “Ce n’est donc pas n’importe quel corps qui peut être reconnu comme substance corporelle. Seuls valent pour des substances corporelles les animaux dont le corps organique — machine de la nature — est actualisé ou réalisé par une âme ou, mieux, par l’entéléchie primitive de la substance simple qui en est la monade dominante.” (“Leibniz et les machines de la nature“, 2003)9 This view differs from the view that the nesting relation holds only at the level of bodies, aggregates or phenomena and can be fully captured in mechanistic terms. At the same time, I should make clear that the texts are not conclusive on this point and, as scholars such as Robinet and Catherine Wilson have argued, it is likely that Leibniz is working with more than one model of substance in his later philosophy. Keeping this in mind, I formulate a model of nested individuals which seems to be consistent with the texts and which I find philosophically fascinating. Whether it was in fact Leibniz’s view or not, I cannot make out on the basis of the textual evidence. The argument I offer in this chapteris meant as a reconstruction of what might have been Leibniz’s metaphysical view of nested individuals. 9.2

Leibniz’s Model of Nested Individuality

In accordance with Leibniz’s commitment to the intrinsic connection of being and unity, the structured ensemble of nested individuals must have substantial unity or else it would not differ from mere

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aggregates.10 This implies that an ensemble of nested individuals must be united as one single substance, as Leibniz states in a letter to De Volder (GP II 248-53): Although I said that a substance, even though corporeal, contains an infinity of machines, at the same time, I think that we must add that a substance constitutes one machine composed of them, and furthermore, that it is activated by one entelechy, without which there would be no principle of true unity in it (AG 175, my italics).11 The source of true unity requires that a corporeal substance, which contains an infinity of machines, would be activated by one entelechy or one source of action.12 As opposed to artificial machines, natural machines consist of infinitely many such machines. Unlike aggregates, they form a single unit that possesses true unity by virtue of its unique source of activity. The very distinction between artificial machines and natural machines (GP III 356) suggests that Leibniz sees an intrinsic connection between possessing a natural, organic unity and possessing a nested structure to infinity. Non-organic machines do not have a nested structure that develops to infinity. We might say that they have a different sort of nested structure in the sense that each of their constituents has a nested structure. For this reason, the question of how such a structure of infinitely many natural machines is considered by Leibniz to be a single unit, as distinct from aggregates, cannot be ignored.13 Yet the question of unity has to be considered in light of the restraints noted above, namely, the causal independence as well as the conceptual relations among all individual substances. At first it seems that these restraints render Leibniz’s notion of nestedness even more puzzling. Though all nested individuals are causally independent of one another, they are all supposed to form one organic unit such as a fish or a human. In the passage cited above, Leibniz suggests that the unity of a composed substance derives from its single source of activity, i.e., its dominant entelechy. A single and dominating entelechy is said to activate and unify the whole hierarchy of causally independent individuals nested within it. Look has recently stated this point in relation to the question of corporeal substance as follows:

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“The dominant monad makes the animal into one machine by serving as the ‘nerve center’, so to speak, of all the primitive active forces of the subordinate monads. In Leibniz’s philosophy, of course, the primitive active force is associated with the substantial form and provides the source of activity of a substance. And, on the view I am suggesting here, the dominant monad will, insofar as it unifies the primitive active forces of its subordinates, become the source of the activity of a composite substance” (in Lodge 2004, 247). Since Leibniz accounts for the notion of unity in terms of activity, another question arises: what could be meant by such activity in a Leibnizian world characterized by causal independence? I will suggest that this sort of activity should be understood primarily in terms of the functional organization of the nested individuals that constitute the organic body of an individual. I will also suggest that this organizing activity might be on Leibniz’s mind when he speaks of the domination of one monad or entelechy over those subordinated to it. Organization and domination can be understood primarily in terms of functional hierarchy between nested individuals, which also helps to account for the differences between individual organic substances and inorganic aggregates. Let me now present Leibniz’s model of nested individuality in some more detail. This model includes (at least) the following suppositions: 1. An individual substance is a union of an active entelechy (or substantial form) which animates and organizes matter (GP II 248-53; AG 174-78).14 2. An individual substance requires true unity – both of form and matter and of all its constituents. This is directly related to Leibniz’s fundamental commitment to the connection between unity and being.15 3. Organic, complete living beings such as humans, animals and plants are among Leibniz’s paradigmatic examples of substantial unities16 and are conceptually distinct from aggregates, such as lakes, flocks and armies which lack substantial unity.17 4. While they are the paradigmatic examples of substantial unity, animals and plants are seen as individual substances that include other such animals (or organic unities) nested within them.18

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5. The animals nested within an individual substance are themselves complete individuals which have a similar nested structure; they are not mere “parts of the substance but are immediately required for it”.19 6. The structure of nested individual substances involves a hierarchy of dominating and dominated substances, which is not accidental but rather typifies the nature of living individuals. 7. Such a structure of nested individuals is one by virtue of the activity of a single and dominant entelechy.20 Taken together, these commitments suggest a fascinating model of individuality and of the organic world. As Ishiguro notes, “... at every level there are organisms with unity, and we can still proceed another level down, ad infinitum. It is a claim about the chain of dominant or unitygiving substances at every level. It is this stratified structure, the successive embedding of organisms within each organism that is insightful.” 21 It is no less insightful, though perhaps less perspicuous, that the unity of all these nested organisms is grounded in a certain notion of activity. To see this point, I would like to examine the sort of unity and nestedness this model of individuality presupposes. In considering the unity of various components, we are inclined to think of material parts being held together as one cohesive spatio-temporal unit. As distinct from the aggregate model, in which unity is relational and external, we tend to seek something that will hold all the constituents together.22 However compelling this picture may be, it is quite clear that it is not the kind of substantial unity Leibniz has in mind. He clearly states that the substances contained in an animal are not parts of the substance but are rather required components of the necessary structure of a composite substance. As we have seen in the passages cited above, the unity of a corporeal substance is a unity that relates to single entelechy animating and organizing the organic body it dominates. Since the organic body of a corporeal substance consists of the individual substances nested within it, this structure seems to imply a hierarchy of activating and activated individuals, nested one within the other. If the unity in question is not that of cohesiveness of parts but rather one of activation and organization, then Leibniz’s stratified model of individuals requires the domination of an entelechy over the whole organic body and the activation of subordinate entelechies at every level. By definition, each substance has such a structure. As Leibniz writes:

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Each monad, together with a particular body, makes up a living substance. Thus, there is not only life everywhere, joined to limbs or organs, but there are also infinite degrees of life in the monads, some dominating more or less over others. (Principles of Nature and Grace, Based on Reason, section 4, AG 208) What I call a complete monad or individual substance [substantia singularis] is not so much the soul as it is the animal itself, or something analogous to it, endowed with a soul or form and organic body (Letter to Bernoulli 20/30 September 1698, GM III 54-42; AG 167-68).23 Let us now examine some implications of this model. Leibniz’s model of corporeal substance as a stratified structure of infinitely many substances signals a radical break from the traditional formula of “one body, one substance”. While Leibniz’s model seems to be in tension with some deeply rooted (both historically and philosophically) suppositions about individuality, it is strongly related to views of emboîtement endorsed by theorists such as Malebranche and illustrated by the microscope-based observations of Leeuwenhoek and Malpighi.24 Yet, I will suggest that Leibniz’s employment of ‘nested’ does not only mean being literally and physically within another individual but also being activated and functionally organized by another dominating individual. For Leibniz, as for Aristotle, individual substances are hylomorphic units characterized by an inherent entelechy or principle of activity (the form) determining a principle of passivity (the matter). At the same time, Leibniz holds that each component of an organism, while included in its organic body and subordinated to the dominant entelechy of its substance, has its own entelechy (Monadology, 70). Thus, for Leibniz, as distinct from Aristotle, an entelechy does not activate merely passive matter but in some sense the many other entelechies nested within it as well. The idea that an entelechy activates another entelechy seems initially surprising in the Leibnizian context since the other entelechies, beings sources of activity, need not be activated from without. Entelechies have their own active force and act spontaneously. Furthermore, a constituent of an organism and the organism in which it is nested are not only compatible with one another but are also required for their very individuality. For example, an organ is not an accidental part of a human being; rather, it is a

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required constituent in the strong sense that it, and only it, completes the individuality of a certain human. Unlike some parasitic worms or viruses that can exist without a certain individual (and the individual without them), in the Leibnizian model we are considering, the nested structure is constitutive of individuals.25 The hierarchical structure indicates that individuals are partly characterized through their place in the hierarchy of individuals. Since the nested hierarchy is not accidental but rather essential to the individuality of each individual, the relations each one has with the others are constitutive of it. This implies that the very individuality and uniqueness of a substance are partly determined through its place in the structure constituted by other individuals.26 This is what the term ‘nested individuals’ is meant to bring out. Given the structure of nested individuals, the question I raise here is more nuanced than the one generally considered, namely, that an individual substance consists of many individuals. Instead, I emphasize the fact that an individual substance has an inherent nested structure which is constitutive of every individual within it. Taking into account the inherent and constitutive nested structure of individuals may seem to make the picture even more complex and puzzling but this way of presenting the question may open the way for a better understanding of Leibniz’s notion of unity in this context. By presenting the question in this way, I stress the consequential role played by the nested and hierarchical structure (in addition to the mere plurality of substances) in the unity of organic beings.27 9.3 The Organic Body of a Nested Individual If Leibniz believes in a notion of unity constituted by activity and organization, what are the implications for his notion of the organic body? We have seen that an organic body, together with the (dominating) entelechy or monad, constitutes a living substance. The question of the nature of corporeal substance has been at the center of debate among Leibniz scholars for some time. Roughly put, the debate revolves around the question of whether Leibniz was an idealist or a realist. The debate is complicated by a variety of issues and nuances which I shall ignore here. What I wish to point out is that the idea that nested individuals make up the organic body of a living substance suggests a way of reconciling these two seemingly incompatible views. In fact, Phemister has recently suggested an ingenious way of reconciling these views in “Leibniz and the Elements of Compound

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Bodies”, (BJHP, 7 (1) 1999: 57-78). She writes that, “Leibniz considered bodies to be rather more than the results of the aggregation of unextended and indivisible monads: that he regarded them also as aggregates of corporeal substances. Corporeal substances are living creatures, having both a soul (or something similar) and an extended organic body” (57). This conciliatory view is consistent with the model of nested individuality presented above in which the organic body of a nested individual consists, in effect, of the other individuals nested in it. As Phemister clarified, the Aristotelian concept of the union of active form and receptive matter remains intact: A soul or a substantial form which is an entelechy is not a potentially disembodied being. Its very essence is tied to the organic body it animates and with which it forms one unit. The entelechy cannot fulfill its function as the actualizer and lifeforce of the body if there is not matter for it to shape and inform. So tied is the entelechy to the real existence of the body that Leibniz frequently stresses that ‘entelechies are never found without organs’ (to J. Bernoulli, 13/23 Jan. 1699, GM III 565; AG 171) and that ‘no entelechy ever lacks an organic body’ (to De Volder, 20 June, 1703, GP II 251; AG 176) which it naturally activates. (74-75) Yet the organic body is no longer seen as some mere passive extended matter which receives its form from the active substantial form; rather, it has a structure similar to that of the dominating individual, except that it is activated and dominated by an entelechy of a higher order. At the same time, the dominant entelechy also activates the entelechies that form its own organic body. Phemister characterizes three (possible) types of monads: Type (1): a soul or soul-like immaterial entity; Type (2): a soul or substantial form (also described as an entelechy or primitive active force); and Type (3): a corporeal substance (72). Using the above definitions, she summarizes her position as follows: I have argued that prime matter is modified as extended through the creation of other substances which are ‘placed next to one another’. These further created monadic units, themselves also of type (2) monads, are subordinate to the first. Of course, with the prime matter of these subordinate monads, the same process is repeated on this lower level. These, then, together with their own

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organic bodies, are the corporeal substances which are aggregated as the body belonging to the initial, or dominant, type (2) monad. Since every entelechy-monad has prime matter and its prime matter is modified in the way described, Leibniz is able to claim that every monad has a spatially extended, organic body which belongs to it in such a way as together to form a new unity, namely, a new corporeal substance or monad of type (3). (Phemister 77) It seems clear that Phemister’s position is consistent with the model of nested individuals presented above. However, Phemister’s proposal is not equally applicable in the case of bodies which are essentially aggregates (such as rocks) and the organic bodies of living or true substances. This distinction is subtle but it is clear and fundamental for Leibniz. Both aggregates and organic bodies are extended, but in different ways. In the case of organic bodies, the advantage of the nested individuals model is that it does not view the body of a living substance as a mere aggregate; rather, the organic body consists of other individuals that essentially belong to it and have a definite place in its hierarchy. A possible source of confusion lies in the fact that aggregates of nonliving things are also aggregates of corporeal substances. However, aggregates do not have the structure of nested individuals ad infinitum which typifies living substances or natural machines. The unity of aggregates is both external (involving a mind perceiving relation) and may vary overtime. By contrast, in a living substance, every constituent, which is itself an individual, is constitutive of the individual within which it is nested. Yet, as Phemister points out, not every individual found within the body of another need be a constituent of it. In correspondence with Clarke, Leibniz distinguishes the matter that truly belongs to the substance from matter that is present, but extraneous to it. As we shall see in the next section, this point speaks in favor of my reconstruction of nestedness for it implies that an individual may be in another (in the physical sense) but not nested in it, if it is not an essential constituent of the other individual. Thus, a worm may be physically in me without being metaphysically nested in me (for the worm’s activity may not be functionally organized by my substantial form). My emphasis on the nested structure of living substances may also help to explain the modification of prime matter into extended matter through a plurality of substances which are ‘placed next to one another’ (77). As pointed out earlier, the substances in organic unities are not just ‘placed next to one another’ or aggregated, but also possess an internal structure to

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infinity as well as unity. This accounts for the distinction between bodies of mere aggregates and the organic bodies of individuals. While Phemister’s view adequately characterizes aggregates, the notion of nestedness is required in the case of living things in order to account for their organic body. The body of individual substances is best described in terms of the structure of dominated individuals nested within it. In the nested individuality model, the organic body is not entirely passive; rather, it is less active (or more passive) than the entelechy that dominates and activates it, and it is more active than the entelechies nested in it.28 Thus activity and passivity becomes a matter of degree, corresponding to the entelechy’s place in the hierarchy. 9.4 Models of Nestedness We have seen that the organic body of an individual substance can be viewed as a stratified structure governed by dominating substances and ‘populated’ by dominated ones. It is time to more carefully examine this notion of nestedness. Given the terms ‘nested in’ or ‘emboité dans’, we tend to think primarily of spatial nestedness as analogous to the way a set of Russian babushkas fit together. In fact, Leibniz himself invites this interpretation when he uses the imagery of Harlequin. Let me call this the physical model of nestedness. For x to be nested in y in this model, spatial relations must exist between them such that x is smaller than y and is spatially within y. In this model, the relation of ‘nested in’ is clearly asymmetrical. A different model of nestedness can be suggested by stressing a logical interpretation of the nested relation. For x to be nested in y in this model, x must be logically entailed by y. In this model, spatial relations need not play any role. A variant of this model would stress semantic implications rather than strictly deductive relations. For example, we could say that the notion of a street is semantically included in the notion of a town, houses in that of a street, walls in that of a house, etc. The question whether this relation is symmetrical is not easy to decide. It seems to depend on the examples we consider. For example, while it is arguable that the notion of a street implies that of a town, it is clear that the notion of houses does not imply that of a street. For Leibniz, the relation between organism and its organ clearly works both ways. In addition, we should consider the expression and representation model, which is clearly present in Leibniz’s texts.29 A version of this model has been articulated by Duchesneau as follows:

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“The organic bodies are presented as machines of nature, developed to infinity; but these bodies form composed substances only to the extent that they imply a monad of which they constitute the expression in the order of phenomena. Certainly, the dominant monad of an animal envelopes in its expression the specific expressions of many other monads.” While it is clear that the expression relation plays an important role in Leibniz’s notion of corporeal substance, it is too weak for my purposes. While I do not deny that nested individuals express or represent one another, the expression relation is not sufficient to account for the unity of nested individuals. Relations of expression hold between the constituents of aggregates as well as between those of individuals. Similarly, I do not deny that the model of physical nestedness plays a role. Rather, I argue that these models do not fully capture the notion of nestedness in the metaphysical context of living individuals. Evidently, the claim that ‘one individual is in another’ may have several interpretations. I would like to emphasize a metaphysical meaning of nestedness that involves degrees of activity versus passivity, corresponding to the functional hierarchy and organization typical of living beings. In this model, the degree of activity (and domination) corresponds to the place and functional role in the hierarchy. We can illustrate this point as follows: A substance (S’) is nested in another (S) if it is activated (or dominated) by it, that is, if it is functionally organized by it. Perhaps a better way to put it would be that S’ is nested in S if its activity plays a role in (or if it contributes a function to) S’s program of action. I suggest that this is the primary sense in which S’ is said to be nested in S and S’ is a constituent or requirement of S. Since a substance is defined by having its own source of activity, S’ is also active in the sense that it will activate another substance, call it S’’, nested within it. In its turn, S’’ will activate S’’’ which will activate S’’’’ and so on to infinity.30 There is a sense in which this relation is symmetrical and a sense in which it is not. The relation between S and S’ (S is a nesting individual and S’ is a nested individual) is symmetrical in so far as they are mutually required for the individuation of one another. But, in so far as S is activating and S’ (in the sense of including S’ in its program of action), the relation between them is asymmetrical. If S’ is nested in S, then S is nesting S’, but S’ is not nesting S. For there is an hierarchical structure here, starting from the one dominating individual and going down to less and less dominating ones.

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9.5 Activation as Domination and Functional Organization This point brings us back to Leibniz’s (non-causal) notion of activity. Let us recall a constraint on the conclusion we reached above, namely that each dominating substance activates all the other individuals which constitute its organic body. If Leibnizian individuals are causally independent of one another, the notion of activation has to be explained in non-causal terms (that is, at least not in terms of efficient causation). This point should clearly apply to the domination/subordination relation. I believe that a key concept in understanding this notion of activation is functional organization. The notion of functional organization is nicely exemplified in organisms, which would partly explain why Leibniz often refers to organic units as the paradigmatic examples of true beings or individual substances (e.g., GP VI 543). Let me then try to clarify Leibniz’s sense of nestedness by reflecting on why, according to him, living beings are the paradigmatic examples of individual substances and why the nested structure, ad infinitum, is the distinguishing feature of natural machines, which are considered to be true substances, from artificial ones which, like aggregates, are not considered to be true substances. Animals and plants vividly exemplify a functional hierarchy, which is particularly evident in the Aristotelian notion of final causality ascribed to their activities and endorsed by Leibniz. It is also consistent with Aristotle’s notion of a hierarchy of ends. For example, an acorn develops into a mature oak through the activation of matter by its entelechy in accordance with the acorn’s final form. In such organic examples, the various functions of the constituents comprising the animal or plant may be seen as serving the telos and executing its natural development. In turn, the telos of an individual can be viewed as a program of action consisting of numerous sub-programs of action. All the sub-structures that make up an oak tree – branches, leaves, cells, subcellular constituents, etc. – are organized by a single program and directed towards a single end, which gives the tree its unity. At the same time, each constituent is fully organized (and in turn organizes its sub-structures) towards the fulfillment of its function. A leaf is a unit whose function is to produce sugar which provides energy for the tree’s growth. The leaf itself may be seen as a fully organized unit whose constituents are organized and activated in order to perform their functions (e.g., one of chlorophyll’s functions is to provide color) and thereby to contribute to the function of the leaf. In turn, their constituents, such as cells, are themselves entirely

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organized towards performing their function in the overall program of the leaf, which in turn is organized towards performing its function in the program of the oak. This model of a functional hierarchy with a complete individual’s program informing an unending series of constituents exemplifies Leibniz’s notion of nested structure. In this description of the oak tree, the primary sense of nestedness is functional and it cannot be fully captured in material/physical terms, which is why it is applicable to the domain of the living and adequately described in metaphysical terms. The idea of a stratified structure of organisms is intrinsically connected to another feature of Leibniz’s notion of individuality (discussed in Nachtomy 1998). The inherent hierarchy of nested individuals is ordered by degrees of complexity that correspond to varying levels of activity and individuality. Although individuals are nested, and hence dominated by other individuals, they are nevertheless complete individuals, rather than mere parts of individuals. The notion of level of individuality does not imply that a certain individual is more or less of an individual. The question of whether x is an individual or not is decided by considering whether x has its own source of activity (which is also its source of unity and identity over time) as well as a complete concept. The notion of ‘levels of individuality’ indicates that an individual may be more or less active and, correspondingly, more or less passive (that is, more or less dominating in the hierarchy). In other words, the degree of activity corresponds to the place the individual occupies in the hierarchy of nested individuals, which may also correspond to degrees of domination and perfection. Since an individual is defined by means of an inner source of activity, it can be nested within a more active individual (i.e., dominated by such an individual) without eliminating its own individuality, unity, and identity. In turn, it may also dominate other individuals nested within it. Thus the notion of levels of individuality is to be primarily understood in terms of degrees of activity (or domination and organization) as opposed to degrees of passivity. Note that the expression “degrees of activity” is only shorthand for the relative proportions of activity and passivity or the relation between active and passive forces. The essential role of activity in individuals in general, and that of a program of action in particular, is compatible with this interpretation of nestedness. The notion of activation as functional organization helps us seeing why Leibniz held that the structure of nested individuals, which is based on activity, proceeds to infinity. Furthermore, we can also see why Leibniz thinks that artificial machines, being devoid of internal activity, do not also possess a nested structure.

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A nested individual is a unique and complete being whose unique “place” plays a constitutive role in the program of the nesting individual. It is in the nesting individual but not necessarily in the physical sense. There is a metaphysical sense of nestedness, which has to do with functional relations rather than with physical and efficient causal ones. The interpretation of nestedness I suggest here is opposed to the attempt to describe Leibniz’s notion of nestedness in purely mechanistic terms. According to this interpretation, there is an intrinsic relation between nestedness to infinity and the other characteristics of Leibnizian individuals such as being, unity, indestructibility and life.31 Let us not forget that, according to Leibniz, it is the nested structure to infinity that distinguishes natural machines from artificial ones, which is strongly related to the infinite nature of the complete concept of an individual. 9.6 Conclusion Let us briefly return to our first question, namely, the unity of nested individuals. Following a remark by Ishiguro, I have suggested that the unity of an ensemble of nested individuals is the result of a uniting activity. This uniting activity is the organizing activity of the constituents in a functional and teleological order, so that the activity of each constituent contributes to the end of the dominating entelechy. It is primarily the single end of the dominating entelechy that unifies the structure of nested individuals, not causal influence between them (which, as we know, Leibniz denies). A significant sense of nestedness therefore is the functional organization of an individual whose constituents play an active and constitutive role in realizing the nesting individual’s end. I have suggested that the unity-giving notion of activation corresponds to Leibniz’s famous, if little investigated, notion of domination.32 I have tried to illustrate the following claims in this chapter: (1) An individual substance has a nested structure. (2) The unity of such a structure is seen through its single (dominating) source of activity. (3) Both the notion of nestedness and that of unity can be understood according to the metaphysical model of active functional organization in addition to the physical model as well as the other models noted in section 3.33 (4) The relevant notions of activation and domination are interpreted in terms of functional organization, which is explicitly related to the notion of final causation. (5) The notion of organizing and uniting activity is closely related to the notions of being and life, such that aggregates and mere possibilities are neither alive nor fully exist. This is consistent with the

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essential role Leibniz ascribes both to passivity and to activity. Possibilities are organized but are not active while aggregates are not organized according to a single internal principle and therefore are not internally united. Thus, aggregates are considered to be well-founded phenomena since they are not essentially one. This chapter has been at attempt to address a formidable difficulty in Leibniz’s metaphysics: on the one hand, a substance is said to be one and indivisible; on the other, it is said to consists of infinitely many other substances. I have attempted to sketch a picture in which a hierarchy of functionally organized individual substances is one in the sense that it is united through a single end and program. This picture, however, can only serve as a preliminary sketch of Leibniz’s notion of nested individuality. Whether this picture can be substantiated, made more precise, and reconciled with other texts, remains of course to be decided by future research.

1 Since the distinction applies to the substance rather than the substance’s body, it is supported by the homogeneity principle that the parts must be similar to the whole. I thank Pauline Phemister for this point. 2 This feature is curious but not at all strange in its historical context. Spinoza, for example, apparently entertains a very similar view with the qualification that he admits only one individual substance. For the historical background of this notion in relation to life, see Duchesneau, Les models du vivant de Descartes á Leibniz (where the chapter on Malpighi is especially pertinent); Pyle, Malebranche, chapter 7; Catherine Wilson, The Invisible World chapter 4. 3 In his Paris Notes, Leibniz writes: “any part of matter, however small, contains an infinity of creatures, i.e., a world” (A 6.3 478-79; SR 33). For Leibniz’s early views on this point, see Beeley, “Mathematics and Nature in Leibniz’s Early Philosophy”, (1999) and Mercer (2001), chapter 7. Mercer argues “that during the winter of 1670-71 Leibniz invented panorganism, according to which the passive principle in a corporeal substance is constituted of a vast collection of corporeal substances, each of which is itself a corporeal substance whose passive principle is so constituted, and so in infinitum” (Mercer, 2001, p. 256). The main point in this formulation, which was later modified, has to do with the word ‘collection’. Thus, in the model of the nested individual, the passive principle or the body of a corporeal substance is not a collection but an organized structure of corporeal substances which are both organized by the substance in which they are nested and which organize the corporeal substances nested in them. In this way, passivity becomes also a matter of degree, depending on the individual’s place in the hierarchy.

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4 “We must then know that the machines of nature have a truly infinite number of organs, and are so well supplied and so resistant to all accidents that it is impossible to destroy them. A natural machine still remains a machine in its least parts, and moreover, it always remains the same machine that it has been, being merely transformed through the different enfoldings it undergoes, sometimes extended, sometimes compressed and concentrated, as it were, when it is thought to have perished” (GP IV 482; AG 142). For some later texts on the notion of nestedness, see: GP VI 543-44; L 589; GP III 340, 356, 565; GP VI 539; L 586. In his correspondence with Fardella we find this passage: “So in a fish pond there are many fishes and the liquid in each fish is, in turn, a certain kind of fish pond which contains, as it were, other fishes or animals of their own kinds, and so on to infinity” (AG 105). Note that here we still do not find the full thesis of a nested structure to infinity but only that each substance involves the infinity of others. For a very textually informed and illuminating presentation of the genealogy of Leibniz’s thought about natural machines, see Fichant “Leibniz et les machines de la nature”, 2003. 5 “Je définis l’Organisme, ou la Machine naturelle, que c’est une machine dont chaque partie est machine, et par conséquent que la subtilité de son artifice va à l’infini, rien n’étant assez petit pour être négligé, au lieu que les parties de nos machines artificielles ne sont point des machines” (Letter to Lady Masham (1704), GP III 356). 6 See Justin Smith (1999) and Dissertation, Colombia University (2000). 7 See also Duchesneau (1998) Les models du vivant 326- 329, 339-343 and La physiologie des Lumières 76-78. As evidence, Duchesneau cites (among others) the following passages: “Et nihil aliud organismus viventium est quam divinior mechanismus in ifinitum subtilitate procedens” (C 16, cited from Duchesneau 1998, 339), Leibniz’s fifth letter to Clarke, sections 115 and116; GP VII 417-18. 8 I thank Justin Smith for clarifying this point. 9 “Je ne compte pour substances corporelles que les machines de la nature qui ont des âmes ou quelque chose d’analogique; autrement il n’y aura point de vraie unité” (Letter to Jaquelot, 1703, GP III 457). 10 “..since I am truly a single indivisible substance, unresolvable into any others, the permanent and constant subject of my actions and passions, it is necessary that there be a persisting individual substance over and above the organic body.” (Comments on Fardella, AG 104). 11 See also GP II 252; GP VII 502 and C 13-14. It seems clear here that what is activated by a single entelechy must itself be a single substance and not a mere single body or a machine. Let me also quote Dumas who writes: “A Leibnizian organism is first of all irreducible to Cartesian mechanism (Dumas 1976, 131). “

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12 As Brandon Look recently noted, “Insofar as I am an animal, or an individual corporeal substance, it is clear that I am unified by the action of my dominant monad, which, it seems, will be equivalent to my mind or soul” (“Leibniz Correspondence with Des Bosses”, in Lodge (ed.) 2004, 241). 13 Ishiguro argues that the notion of organic unity is primitive and immediate and in this sense need not be accounted for (Proceedings of the VII Leibniz International Congress, September, 2001). This may very well be the way that Leibniz viewed it. However, we would still need to see why he takes such a position. In a recent article, Levey has considered the matter in the context of the Leibniz-Arnauld correspondence as follows: “If, on the other hand, his view is that substances are not composite beings but instead are to be identified with their incorporeal souls, then no explanation of the true unity of the composite is necessary, since there is no composite with true unity to be explained, and Leibniz’s silence on this point is precisely what we should expect” (“On Unity: Leibniz-Arnauld Revisited”, in Philosophical Topics Vol 31, Nos 1 & 2, 269). 14 For a substantiation of this claim, see Mercer and Sleigh (1994) and Mercer (2001). While Leibniz’s notion of form is Aristotelian, his notion of matter is, as I discuss in section 3, more complex. One obvious difference is that matter, according to Leibniz, is not entirely passive. 15 See Letter 17 to Arnauld, December 8th, 1686. 16 Leibniz’s paradigmatic examples include, of course, God, the I, the Ego and the Soul, but I think he makes it clear enough that the entities denoted by these expressions are seen as the dominating, active aspects of organic beings and not detached or disembodied. As an example, see Theodicy §124. 17 “je ne veux pas à la vérité qu’un morceau de pierre soit luy même une substance corporelle animée ou douée d’un principe d’unité et de vie; mais bien qu’il y en par tout de telles là dedans, et qu’il n’y a aucune pièce de la matière, ou il n’y ait ou animal ou plante, ou quelque autre corps organique vivant, quoyque que nous n’en connoissions que les plantes et les animaux. De sorte que une masse de matière n’est pas proprement ce que j’appelle une substance corporelle, mais un amas et un résultat (aggregatum) d’une infinité de telles substances” (GP VI 550). See also Letter to Arnauld, (AG 80) ; GP VI 553-54: “animals are never formed out of non-organic mass”; and Wilson’s “De Ipsa Natura”, 1987, 169. 18 E.g., “…the machines of nature being machines to the least of their parts are indestructible, due to the envelopment of a small machine in a larger one, to infinity” (GP VI 543); Monadology 67-70 cited above. “I hold that it is enough for the machine of things to have been constructed with such wisdom that, through its very development, those very wonders come to pass, chiefly (as I believe) by means of organisms unfolding themselves through some predetermined plan” (On Nature Itself, AG 156). “My view is that every

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substance whatsoever is a kingdom within kingdom, but one in precise harmony [conspirans] with anything else”. (Comments on Spinoza’s Philosophy AG 280, ca 1706) 19 “If you take mass (massa) to be an aggregate containing many substances, you can, however, conceive in it one substance that is preeminent, that is, one substance animate by a primary entelechy. Furthermore, along with the entelechy, I don’t put anything into the monad or the complete simple substance, but the primitive passive force, a force corresponding to [relatus ad] the whole mass [massa] of the organic body. The remaining subordinate monads placed in the organs don’t constitute a part of the substance, but yet they are immediately required for it, and they come together with the primary monad in a corporeal substance, that is, in an animal or plant. Therefore I distinguish: (1) the primitive entelechy or soul; (2) the matter, namely, the primary matter or primitive passive force; (3) the monad made up of these two things;(4) the Mass [massa] or secondary matter; and (5) the animal, that is, the corporeal substance, which the dominating monad makes into one machine” (Letter to de Volder, AG 177, my italics). 20 “it seems probable that animals ... and similarly plants ... are not composed of body alone, but also of soul, by which the animal or plant, the single indivisible substance, the permanent subject of its actions, is controlled” (Notes on some comments by M. A. Fardella, AG 104). 21 “Unity Without Simplicity”, (1998) 550. 22 We may be inclined to think for example of the model of a molecule in which the atoms are bound together by covalent relations. 23 As Adams has stressed, there are other passages in which appetite and perception figure as the essential features of simple substances, e.g., “there is nothing in things except simple substances, and in them perceptions and appetites” (GP II, 270). While I cannot argue for this here, I think that Leibniz’s notion of a simple substance may not be incompatible with its having a nested structure. The crucial sense of simplicity here seems to be that of indivisibility. And it is clear that the structure of nested individuals is meant to be one and indivisible. 24 It seems to me that what Pyle says of Malebranche can also be said of Leibniz: “Experimental biology (Leeuwenhoek’s microorganisms, Malpighi’s chicks, Swammerdam’s butterflies) are used to illustrate the theory [of emboîtement] rather than to confirm it” (Malebranche, (2003) 172). 25 As Ishiguro recently put it: “if x is a constituent of body y, then it is necessarily a constituent of y”, The Proceedings of the VII Leibniz International Congress, Poser, et al. (eds.), 2001, 540. 26 This view has an interesting corollary to Leibniz’s notion of individuation through the complete concept of an individual. To be complete, the concept of an individual must include relations to other concepts.

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27 The structure of nested individuals to infinity fits with the definition of possible individuals through their rules of production and the essential role the order of predicates within a structure plays in their individuality (see chapter 2). 28 In commenting on this, Phemister remarks: I think that the existence of the organic body comes about through the completion of the dominant monad (as entelechy and primary matter and that together with this, the monad and organic body comprise the corporeal substance. I see the mere aggregate as an aggregate of corporeal substances but with no overall dominant force – so I do agree that there is a distinction between the organic body (that has an dominant entelechy) and a mere aggregate that does not, but I still regard the organic body as an aggregate (just not as a mere aggregate). 29 E.g., GP II, 251. See also (Adams 1994) 285-91. 30 Phemister pointed out (in correspondence) that, “there has to be a sense in which the active force of the dominant entelechy is matched by or is even identical with the combined active forces of the subordinate entelechies. Thus, if the dominant entelechy is taken as being a force ‘1’, the subordinate ones in the body will have to collectively add up to ‘1’, e.g., as 1/2 + 1/4 + 1/8 + 1/16 + … ad infinitum, or something similar”. 31 Leibniz makes such explicit connections in GP VI 543. 32 In a recent work, “On Monadic Domination in Leibniz’s Metaphysics” (2002), Look has investigated the notion of domination and suggested several criteria for characterizing the domination/subordination relations. In a different work, he succinctly summarized his position: “…I believe that there are several distinct criteria that must be met in order to say that one monad dominates some group of monads: first, the dominant monad must bear an ordered and regular relation to those that occur in its body; second, it must bear some kind of quasi-causal role in the functioning of the monads that constitute the entire composite substance; third, it must be more perfect than the other monads, that is, it must have clearer perceptions than the others and contain the ‘reasons’ for what happens in the other monads” (Proceedings of VII Leibniz International Congress, 738). If we can interpret the quasi-causal role in the functioning of the monads as final causation (appropriated by Leibniz for the domain of substances), and hence as consistent with the other criterion that explains what happens in the dominated monad, then Look’s criteria are consistent with the model of nested individuals outlined above. 33 In my view, Leibniz’s notion of simplicity (as well as that of indivisibility) can also be understood in terms of activity rather than extension. Thus, a substance is indivisible and simple because it is active, and since its activity

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derives from one source, it cannot conceptually be divided or broken down. This view has a surprising consequence, namely that simple substances may contain others and therefore the distinction between simple and composite substances need not be seen as mutually exclusive. In other words, if the notion of simplicity is grounded in activity, a substance may be seen as both simple and composite. This may shed some new light on what is usually taken as an exclusive classification of substances as either simple or complex in texts such as the opening paragraphs of the Monadology and The Principles of Nature and Grace.

Chapter 10 Possibility and Individuality 10.1 Introduction In this chapter I take up the question discussed in the previous one, namely, how according to Leibniz an ensemble of nested individuals is seen as a single and simple substance. To this central question, I add two others: (1) To what extent is Leibniz’s definition of an individual through its production rule, which functions as the substantial form of a created individual, compatible with the nested structure of a living organism; and (2) how is Leibniz’s notion of nested individuals compatible with the noncompositional unity of an individual substance? The non-compositional view of substance seems to be a direct consequence of Leibniz’s commitment to the unity and simplicity (i.e., the indivisibility) of an individual substance. My objective in this chapter is to show that Leibniz’s notion of a possible individual, as I presented it in the first part of this work, is compatible with the nested structure of actual individuals that I presented in the previous chapter. My suggestion is that the definition of a possible individual by means of its law of production sheds light on the nature of Leibnizian individuals: on the one hand, individuals are seen as nesting other individuals as essential constituents; on the other, they are seen as single and simple entities. I will try to show that the related notions of law of action and program of action are such that they may include other laws and other programs as essential proper constituents. At the same time, since a law of action is essentially one and an indivisible unit, in this sense, it may also considered to be simple.1 This, I believe, is one of the most significant senses in which a Leibnizian substance is said to be simple. Put succinctly, my suggestion is that the notions of a law of production and that of a program of action, which serve to define possible individuals, also have an inherent nested structure, as well as inherent unity and simplicity. While this may seem surprising, some intrinsic connection between possible individuals and actual ones is, of course, to be expected. While Leibniz’s notion of possible individuals as well as that of actual (nested) individuals is very intricate, the relation between the possible and the actual should in my view remain straightforward. 237

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The questions noted above and my suggestions will be clarified in view of the lack of substantial unity and a nested structure in aggregates (chapter 8). As we have seen in the previous chapter, this distinction is subtle and yet very consequential. While aggregates also contain real organic beings or individuals (such as fish, sheep or humans), they are not considered by Leibniz to be true units or individuals. According to Leibniz, all real beings are organic, at least in the sense of being active units. However, unlike organic units, such as a fish or a human being, Leibniz does not consider aggregates (such as a school of fish or an army) to be individuals precisely because the ensemble of real constituents, which make up an aggregate, does not have real or substantial unity. For this reason, aggregates and artificial machines also lack life and are considered to be inorganic and inanimate. In addition, the distinction between artificial machines and natural machines turns on the nested structure to infinity of the latter. This subtle distinction provides a crucial clue to explain why organic units are Leibniz’s prime examples of individual substance. Unlike aggregates, individuals are governed and produced by a law of production that generates their nested structure to infinity. In the previous chapter I argued that the key concept in Leibniz’s notion of the unity of nested individuals is internal and functional organization. We have also seen that organisms and aggregates are organized in significantly different ways. While organisms are intrinsically organized through a single source of unity and finality, aggregates are externally organized so that their end and unity is external to them. We have also seen that the notion of internal organization may account for the relations of domination and subordination, which hold between the individuals nested in an organism. The notion of functional organization informs the hierarchy of a nested structure in the sense explained in the previous chapter and is consistent with the non-causal relations between Leibnizian individuals. The notion of active entelechy presupposes the notion of a rule of action. A rule of action prescribes a course of action of an actual individual corresponding to the way a possible individual is defined in God’s understanding (see chapter 5). In this manner, the notion of functional organization is related to the definition of possible individuals in terms of their rules of production – a rule prescribing a unique program of action corresponding to their end. Since the notion of functional organization plays a central role in uniting the ensemble of nested individuals, let us see to what extent this notion of organization is present (at least implicitly) at the level of possibility. More generally, let us examine to what extent

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Leibniz’s notion of nested individuals prefigures in his notion of possible ones. 10.2 The Production Rule of the Individual and its Nested Structure Given Leibniz’s doctrine of a complete concept and our understanding of possible individuals in terms of complete concepts, it seems clear that there is a close connection between possible individuals and actual ones. If every truth about an individual is derivable from its concept, then there is some conceptual connection between possible individuals (seen as complete concepts) and their actualized counterparts. Furthermore, since Leibniz views the predicates of complete concepts as corresponding to the actions of individuals (e.g., Julius Caesar crossing the Rubicon corresponds to that predicate in his complete concept), it seems natural to think of the order of the individual’s actions as entailed by the individual’s concept as well. And indeed, as I emphasized in chapter 2, the notion of order plays a significant role in Leibniz’s notion of the individuating principle of any individual. With this point in mind, I would like to suggest that Leibniz’s notion of nested individuals in the sense of functional organization explained above is consistent with, if not implied by, his notion of possible individuals. If this is the case, Leibniz’s notion of possible individuals can shed light on his notion of the nested structure of actual individuals and especially on their unity.2 Before I turn to developing this suggestion, I would like to address an objection that immediately comes to mind. If functional organization is one of the defining features of living organisms, shouldn’t it be absent from the definition of possible individuals? After all, possible individuals are not active and certainly not living things. Yet let us not forget that organization is only one of the defining features of an organism. Since, according to Leibniz, actual individuals are defined through both a complete concept and an intrinsic source of activity, possible individuals are organized structures (expressed in their complete concepts) that lack activity and life. This view is consistent with Leibniz’s view of actualization I presented in chapter 5 and it is this line of argument that I develop below. Let me observe that, at the conceptual level of pure possibility, the notion of organization is atemporal. Given the atemporal and conceptual aspect of organization (typical of possible individuals), and given (a) that an individual (as distinct from an aggregate) has a complete concept, and (b) that a complete concept of an individual is grounded in a unifying rule of action, and (c) that actual individuals are living organisms with a nested

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structure in which the rule functions as the substantial form, it seems that the complete concept of an individual has to express the other individuals nested in it. And, indeed, this point immediately calls to mind Leibniz’s doctrine of expression, according to which (DM 9, GP I 383-84) each individual expresses the whole universe, that is, all the other individuals that make up the same world.3 As Fichant puts it: “Expression is defined (in a general way) as a rule-governed correspondence between disjoint series, [each] defined by an invariant law”.4 It is in this sense that “[e]ach possible individual includes (enferme) in its notion the laws of its world”. Of course, given the results of chapter 4, in which we have seen that concepts of individuals and possible worlds are mutually constitutive, this is the view we would expect. However, while the doctrine of expression plays an important role, it is too weak for my purposes here. The reason for its weakness is this: Since the expression relation holds between all individuals, it is not in itself sufficient to distinguish between nested individuals and the individuals found in aggregates. In other words, since the relation of expression holds between all the laws of individuals, it is not sufficient in itself to account for the distinct relations between nested individuals, whose programs of action are not just inter-related but also intra-related.5 It might be argued that the difference is a matter of degree and I will address this point after considering whether the use of relations may suffice to clarify the question of unity in Leibniz’s notion of nested individuals. Following Rutherford (1994), Look has recently suggested that God’s knowledge of relations could account for the reality of composite substance. He writes, “The reason that scientia visionis is important is that it seems to be a method by which Leibniz argues that the relations between monads can be reified, and the reification of the relations between monads will serve to guarantee the reality of composite substance” (in Lodge, 2004, 255). I have already stressed that relations play an essential role in the very constitution of complete concepts of individuals and that the relations of organization and domination are not causal ones but rather functional and conceptual. This point clearly implies that conceptual relations hold at the level of possibility. Since this view coheres with Leibniz’s view of relations and the constitutive role they play in completing individuality, one might attempt to address the problem of unity by suggesting that the hierarchy of nested individuals is already represented in God’s understanding, where all relations among possible individuals are conceived. If, as I suggested in chapter 4, relations contribute to the very individuality of substances, perhaps relations could also account for the individuals’ unity.

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While this suggestion goes a long way in the right direction, it, too, is not sufficient. The main difficulty that remains is that, like the notion of expression, it applies equally well to aggregates and to individual substances. For this reason, it is not sufficient to distinguish between the intrinsic unity of nested individuals and the extrinsic unity of aggregates. As we have seen, according to Leibniz, the relations among the fish making up a school can also be derived from their concepts. Indeed, this is precisely the reason why Leibniz sees aggregates as well-founded phenomena rather than as true substances. As I argued in chapter 8, due to their relational notion of unity, armies and schools of fish cannot be considered as fully real or, what amounts to the same thing, as full individual substances. It may be suggested that the distinction is one of degree so that some individuals are more strongly related to others or that they express the others more clearly. However, if that were the case, the very distinction between substances and aggregates would become one of degree as well. And this is at odds with the texts. As far as I know, Leibniz never says that a fish is more a substance than the school. Rather, he says very clearly that a fish as well as the Ego are complete substances and that a school and an army are not. If relations are not sufficient to distinguish between individuals and aggregates, then they are not sufficient to account for the substantial unity of nested individuals. In the context of nested individuals, something stronger than expression and relations has to play a role. As distinct from aggregates, a nested structure is an intrinsic feature of individuals. As I argued in the previous chapter, I interpret the relation of ‘nested in’ in terms of activity and, in particular, in terms of functionally organizing activity. This activity gives an ensemble of individuals its unity by organizing each of them according to their proper function within the program of the individual. The organizing activity unifies all constituents by directing and orchestrating the activities of all the nested individuals within the framework of a single end. In this way, the nested individuals play a role in the program of the individual in which they are nested. The individuals are united under a single program of action which is directed towards a certain end, and in this sense is dominating the functions and sub-functions of each constituent. We have also seen that a possible individual can be partly defined through the rule that generates a unique and infinite structure of predicates in God’s mind. I argued that such a rule could be seen as a program of action whose actualization realizes the individual’s end. In other words, the course of action prescribed by the program satisfies the individual’s end.

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Once a substance is created, the production rule functions as its substantial form, i.e., it provides the substance with reasons and causes to act according to its end (see chapter 5). In this way, the rule provides the source of unity, identity and individuality, both in the context of possibility and in the context of actuality. Having considered the doctrines of expression and relations, let us now consider whether the rule generating a possible individual in God’s understanding can complement the missing requirement for the unity of nested individuals. As I already noted, an intrinsic relation between the definition of a possible individual and the program of action that constitutes its actual counterpart is to be expected. An actual individual is an actualization of a possible program of action. In the realm of possibilities, the production rule forms an individual concept by combining, ordering, and unifying the predicates into unique (and infinite) structure. If, as I suggested above, the most significant sense of nestedness is that of functional organization, rather than nestedness in the sense of material inclusion or physical emboîtment, then the production rule of the individual seems to be a promising candidate. 10.3 Some Illustrations As a way of illustrating the role of the production rule as a complement to expression and relations, let us consider a production rule of a fractal. In this case, we can see clearly that a mathematical rule produces a structure which has similar sub-structures nested in it to infinity. The rule of production generates the structure and unifies all the different substructures into one whole. Furthermore, the relations between the production rule of the fractal, considered as a whole, and the sub-rules that form its constituents are not merely causal relations but also conceptual ones. The relations of domination and organization that we have identified in the context of Leibniz’s notion of nested individuals may be understood by analogy to the relations between the whole structure and the substructures nested in a fractal. In this way, a full hierarchy of domination and subordination can be exemplified in a fractal-like structure developing ad infinitum. While obviously anachronistic, the analogy merits further development. In this analogy, we can also see the rule of production as prescribing (and as constituting) the individual’s program of action for its entire development, including, of course, its future and past states. In addition, such a program directs the individual’s activities towards a certain end. In this example, the finality is given by the very development of the fractal form through the execution of the program. The development of a fractal’s

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form, however, is infinite, just as the development of Leibnizian individuals is. A fractal-like structure is infinite in a dual sense: it is infinite both in the development of its constituents, each of which is also infinite, and in the development of its whole structure. In addition, the whole structure consists of precisely the structures nested within. Since the constituents make up the whole structure, by executing their own programs of action they contribute to its program (and thus also to its end). This corresponds to the relations of functional organization between the program and its sub-programs. Such relations correspond to the functional hierarchy of organization and domination we have observed in the Leibnizian notion of organic units. Let us now consider whether the dominating rule of production can be said to entail the reasons (in addition to the causes) for the dominated and nested sub-structures in the hierarchical structure (of sub-structures within structures) noted above. Given that the production rule of the whole fractal structure entails its final form, it may be said that, by virtue of assigning the nested sub-rules their role in the whole structure, the dominating rule provides the reasons and instructions for the constituents to ‘act’ accordingly. In other words, the rule may be seen as both producing and prescribing the instructions for the sub-programs that are essential components in its own overall development. In this respect, too, I find the notion of a production rule to be useful in clarifying the peculiar nature of Leibnizian individuals. Whether we think of the production rule as generating a mathematical series or as a fractallike structure or as an algorithm prescribing a program of action, its nested elements are constitutive of the whole. This is the case because a rule may have sub-rules and an algorithm may have sub-algorithms as essential components. Likewise, a program of action may have sub-programs that contribute to its proper execution. In addition, the concept of end, especially as exemplified in the Aristotelian sense of living beings, may include many sub-functions that contribute to the realization of an entity’s nature or essence. If the individual’s production rule can be seen as prescribing the end of an individual and thereby as prescribing the reasons for the sub-functions of the constituents nested within, then it seems adequate for accounting for the unity of nested individuals. Let us consider more closely the notion of an algorithm as another illustration of this point. As we have already seen in chapters 5 and 6, we might think of an algorithm as a prescription or program of action. This fits with the Leibnizian definition of actual individuals as possessing primitive power of activity conjoined with their unique program of action. It also fits with the notion of final cause and with Leibniz’s notion of

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preestablished harmony, which requires that all possible programs of action be considered in God’s mind ‘before’ creating the best subset of individuals.6 I have described the combinatorial operations in God’s mind as being reflexive and reiterative. A question that becomes pertinent now is whether the notion of a production-rule, when viewed as an algorithm that orders and unifies predicates into a unique structure, may also be seen as integrating other algorithms within itself, and as being constituted by its sub-algorithms. Here, too, there is an interesting point of analogy between Leibniz’s notion of nested individuality and the combinatorial activity in God’s mind that gives rise to the concepts of individuals. Given the reiterative and reflexive character of the combinatorial operations, it seems that, once concepts of individuals are formed, they may become nested (or embedded) in more comprehensive production rules and structures. When an individual concept (seen as a consistent and unique structure of predicates) is formed, it may be integrated into another individual concept, and thus become nested within its individual concept. Thus the nested structure of individuals may be generated in God’s mind. In addition, this point has to be seen in conjunction with the close connection between complexity and individuality presented in chapter 2. Let us recall that the very complexity of the structures resulting from these operations plays a role in their individuality, so that the more complex a structure, the more particular it is. This idea clearly applies to the notion of nested individuals as well. In addition, the notion of order – and especially the direction from the simple to the complex – is consistent with the notion of an algorithm whose reiterative operations produce a nested structure of sub-algorithms (and they, the sub-algorithms) within a larger algorithm. Thus it seems that Leibniz’s notion of a nested structure as characteristic of individuals fits well with his view of possible individuals. 10.4 Composition, Non-composition and Simplicity While I find the above suggestion attractive, I wish to consider some objections. A substantial point of dissimilarity seems to obtain between the formation of possible individuals in God’s mind and Leibniz’s notion of actual, nested individuals. The combinatorial activity I described in the second chapter starts from simple conceptual constituents and constructs more complex structures through reiterative operations. In other words, the combinatorial activity in God’s mind is compositional and goes from the simple to the complex. However, in the case of Leibnizian organic unities, we do not have such a compositional order. More precisely, we do not have a compositional order at all; rather, organic beings are complete

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beings and in this sense are simple, non-compositional units.7 As the opening paragraphs to the Modadology and Principles of Nature and Grace make clear, Leibniz refers explicitly to both simple and composed substances. While I am not certain how to adequately account for this, I think that it is safe to suppose that Leibniz’s assumption regarding the nature of substance, namely, that a substance is necessarily one, is never given up.8 In fact, to adequately respond to this question requires a clarification of Leibniz’s notion of simplicity – a task that goes beyond the scope of this work. Yet, I would like to sketch one way to go. It is clear that Leibniz’s notion of simplicity is strongly related to his notion of indivisibility (as the opening paragraphs of the Monadology and Principles of Nature and Grace make explicit). This point is also made very clear in the New System of Nature. It seems to me that Leibniz’s notion of indivisibility should be seen in the context of the unity of activity rather than in the context of material indivisibility.9 However, if this is the adequate notion of simplicity, it only seems to indicate a deeper dissimilarity between the domain of possible things and that of actual things. Leibnizian organic units are, in principle, not composed of parts; and for this very reason, they cannot be decomposed. “…no entity that is truly one [ens vere unum] is composed of parts. Every substance is indivisible and whatever has parts is not an entity but only a phenomenon”.10 It is clearly in this sense of indivisibility that substances are considered to be simple . 11 While Leibnizian individual substances do not decompose, they do have a nested structure. We have already seen that Leibniz’s notion of a nested structure is not to be understood in terms of the composition of parts. Although consisting of infinitely many other individuals, an individual is said to be simple and indivisible. Since its constituents are not parts but essential constituents or requisites, it cannot decompose; nor can it be composed (GP VI 544). In this sense, the model of composition does not belong to the description of organic units. Leibniz consistently emphasized that the notion of unity is fundamental and constitutive of substances. As I noted, it is in this sense, namely that substances are indivisible units, that they are also simple.12 This is a subtle and difficult point: An individual entails infinitely many other individuals as its proper constituents; yet, it is considered to be a simple and indivisible unit. Perhaps the difficulty can be lessened when we realize that the simplicity and unity in question is not that of material parts being held together but one of activity deriving from a single law of action. In response to the question “what is the simple according to Leibniz?” Becco has written: “It is the internal law of the substance by which it

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tends to its perfection” (Becco 1975, 116). This notion of simplicity and unity is compatible with a law of activity generating an infinite structure. Let me emphasize that the unity in question is not that of material parts which are held together by some physical force rather, it is a unity deriving from a dominating program of action whose identity and finality would be disrupted if any of its constituents were different. A Leibnizian substance is primarily identified through its form or its organizing principle and its active force. In turn, such a principle is primarily identified with the substance’s program of action. A program of action cannot decompose or become divided without changing its identity and individuality. As I have pointed out, a program of action can include subprograms of action – in fact, infinitely many sub-programs, which are in a sense distinct programs in their own rights too. Thus we see that the rule of action can be seen as integrating and hence reconciling the notions of infinity and simplicity. This can be seen as another reason why Leibniz does not identify the principle of individuation not merely with a structure of predicates (let alone a set) but also with its rule of production. A program of action can be seen as a rule-governed composition of elements and may entail infinitely many sub-programs. While such a program (analogous to a complex concept) can be analyzed down to its constituents, it cannot be decomposed. If a program were to decompose or to be broken down, the program would lose its identity (in other words, the ‘it’ would no longer refer to the original program). Think again of our fractal example or of a function entailing other functions, or of Leibniz’s favorite example of an infinite series of numbers. These are all examples of a law underlying an individual substance. In all these examples, the whole can be analyzed but it cannot be decomposed into parts without disrupting its proper unity and identity. These considerations regarding compositionality and simplicity lead to important insights. The definition of an individual by means of its rule of production and power of action points to an adequate sense of applying these terms to Leibnizian substances. Leibniz’s notions of composition (presented in chapter 2) and nestedness (presented in chapter 9) and his notion of simplicity need not be taken in a physical-spatial sense or in a formal one. Rather, both the simplicity and the non-compositionality of individuals derive from a common source: the unity of activity – a unity that derives from the indivisibility of the agent as well as from the indivisibility of its program of action.

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10.5 Conclusion As we have seen above, approaching Leibniz’s metaphysics from the vantage point of his view of possibility yields some interesting insights. In particular, the conclusion reached in chapter 2, namely that possible individuals are to be defined genetically by means of the law producing unique structures of predicates in God’s mind has proved to be quite useful. I observed that such a rule may be seen as a law-like program of action. As we have seen in chapters 8 and 9, the notion of an individual, as defined by an internal program of action, can help in distinguishing individuals and aggregates, as well as to account for the nested structure of individuals. In conclusion, let me summarize several interesting implications of using the notion of an internal program to define an individual as a living substance or as an organic unit. Since the notion of a program may include infinitely many sub-programs, each of which is itself a program on its own right, it is consistent with the nested structure to infinity, which, according to Leibniz, typifies living beings or organisms. In this way, the program functionally organizes the constituents of an organism. Since the program functionally organizes the constituents of an organism, it may be seen as its source of unity and identity over time. While a program may be analyzed into its constituents, it remains indivisible; it is essentially one due to its end, and any division would disrupt its identity and unity. It is also in this sense of indivisibility that an individual can be considered by Leibniz to be simple. The notion of a program is required for the internal regulation typical of living things as distinct from machines and it helps to reconcile mechanism and finalism, efficient causes and final ones, as it encompasses both the source of the activity and its end. Given Leibniz’s distinction between organisms and aggregates, the notion of a program may be used to distinguish between living and non-living things. While an organism is definable through its unique program of action, an aggregate lacks such an intrinsic and unique program. Therefore, an aggregate also lacks unity and identity over time. While a program for action is a mere possibility, when given power of action, it may be seen as informing the development of an organism.

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1 As I will point out later, this point is similar to the conclusion Becco has reached in the fourth chapter of her study Du simple selon Leibniz, Paris, Vrin, 1975, namely, that “the simple is the internal law of a substance (116).” 2 Let me point out that the methodology of comparing Leibniz’s notion of possible things with that of actual ones may be more general, so that it may be useful to investigate other questions in Leibniz’s metaphysics as well. 3 As Leibniz’s response to Arnauld makes clear, he holds that, from the concept of Adam the concepts of all humankind can be derived. 4 “Leibniz et l’universel”, in Science et metaphysique, 133. 5 I thank Mark Bickhard for suggesting this terminology in this context. 6 It is worth noting that the notion of an algorithm as a program of action is also useful in explaining the connections between possibles and actuals in contemporary biological terms. See Jacob La logique du vivant, 1970. 7 This point is clearly related to the inverse priority of parts and wholes in the context of real beings as distinct from mathematical beings. For example, Leibniz says: "There cannot be a most rapid motion or a greatest number. For number is something discrete, where the whole is not prior to its parts, but conversely” (A 6.3 520; SR 79, my italics). 8 It is important to keep in mind here that scholars such as Robinet and Wilson have argued that Leibniz is working with various models of composite substance, not one. As Look and Rutherford put this recently (in correspondence), the extension of ‘simple’ in Leibniz seems to be inconsistent. 9 This intuition is nicely brought out in one of Leibniz’s early dictums in his Paris Notes, namely that, “Whatever acts, cannot be destroyed, as long as it acts”. 10 Cited from Brown 2000, The Leibniz Review 10, 41. 11 This point is rightly emphasized by Cover and O’Leary-Hawthorne (1999). 12 “The parts are not always more simple than the whole, although they are always less than the whole” (1715, GP III 583). Leibniz’s example here is that the unit is simpler than its fractions. This example clearly shows that Leibniz’s notion is related to basic unity. The unity of a whole number is presupposed in its division.

Conclusion

I started this book by presenting Leibniz’s early presuppositions about the notion of possibility. I have shown that, from very early in his career, Leibniz was working with a rich and original approach to possibility, which is embedded in metaphysical and theological contexts. I also noted that Leibniz’s preoccupation with the notion of possibility was partly motivated by moral and theological concerns and that it serves him as major resource in his effort to provide an alternative to a naturalized and necessiterian world view expressed in the philosophy of Spinoza. I developed Leibniz’s approach to possibility in some detail, arguing that it includes the following commitments: Possibilities are situated in a conceptual realm understood as consistent thoughts in God’s understanding. Consistent thoughts are explicated in terms of complex concepts, whereas complex concepts consist of self-consistent simpler elements. Leibniz presupposes logical simples, indefinable and unanalyzable, which he identifies with God’s simple attributes or forms. At the same time, Leibniz views God as an active mind whose primary activity is thinking and self-reflection. God’s reflections on his simple attributes are seen as mental combinations of his simple forms that produce complex forms. Likewise, God’s reflective operations are iterative, so that he reflects upon his reflections. God thinks the combinations among his simple forms and more complex concepts arise in his mind. In addition, God combines the simple forms in a natural order – from the simple to the complex – and, in this sense, Leibniz’s system of possibility is both recursive and yields infinite concepts. Taken together, these presuppositions characterize Leibniz’s approach to possibility and provided the point of departure in this work. I have argued that Leibniz’s view of possibility is closely linked to his projects of the universal language and the real characterstica, which can be seen as a human effort to model and comprehend the realm of divine ideas and concepts by means of symbols. In turn, the compositional structure of concepts and possibilities clarifies Leibniz’s view of representation and symbolization in terms of one-to-one correspondence between the components of a concept and the components of the symbol representing it, as well as between their methods of production. Leibniz’s view of 249

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possibility also clarifies that the construction of various notation systems rather than a unique universal language is the adequate realization of his grand project. In turn, a variety of notation systems play a role not only in representing concepts but also in enabling our acquisition of new concepts that facilitate the discovery of new knowledge. Human knowledge requires language and notation as means of partially representing and improving our insights into the realm of pure concepts in God’s mind as well as into its realization in the created world. I have also pointed out that Leibniz’s notion of truth as the inherence of a predicate term in the subject term is motivated by his views about concepts and possibilities. If possibility is understood as self-consistency among terms (so that it pertains to concepts rather than to things), and if concepts are formed by a unique combination of constituents, it is natural to understand predication, as well as the nature of propositions, (along its traditional form) as an ascription of a predicate term to the subject term. Such an ascription yields a true proposition just in case the predicate term is included in – i.e., is one the predicates making up – the concept of the subject; and it yields a false proposition in case it is not included therein. On this basis, I attempted to provide an account of Leibniz’s original notion of an individual concept that, roughly speaking, corresponds to his notion of a possible individual. Such a concept has been often identified with the individual’s complete concept. I have argued that there is an important distinction between a basic or thin individual concept and a complete concept of an individual. Given that God’s understanding is the proper locus of concepts and possibilities, I first addressed the question of how such an individual concept is formed in God’s mind. I have argued for a three fold thesis concerning the formation of ‘thin’ individual concepts in God’s understanding: (1) Leibniz sees an internal connection between composing simple concepts into complex ones and the individuation of concepts, so that the complexity of concepts contributes to their uniqueness and individuality. (2) An individual concept should not to be identified as a set of predicates but rather as a unique structure of predicates, in which the order of predicates plays an essential role. (3) An individual concept should not to be identified merely with a unique structure of predicates but also with the combinatorial rule that generates such a unique structure of predicates in God’s understanding. Such a combinatorial rule orders and unifies various forms in a unique way. The production rule is considered as the principle of individuation and an individual concept is thus given a generative definition. If Leibniz defines a possible world as consisting of compossible set of individuals, the notion of a world involves the notion of relations between individuals. Investigating the notion of a possible world and that of

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relations has yielded some surprising results. It turns out that the notions of complete individual concept and that of a possible world are mutually constitutive. In other words, the notion of an individual concept is completed or becomes fully individuated within the context of a world. Complete individuation requires that the relations among all possible individuals would be considered. This view makes it clear that the insightful idea that worlds logically precede individuals captures only one side of the story. I have argued that relations are indispensable for completing the very individuation of complete concepts. At the same time, I pointed out that Leibniz’s view of relations implies that they presuppose some non-relational foundation, in which the relata are grounded. This view complements the notion of the production rule as the principle of individuation in the sense that the production rule constitutes the basis (or non-relational predicates) for individuation. Complete individuation requires considering the relations between the various production rules or the basic individual concepts. In light this intrinsic connection between possible individuals and possible worlds, I suggested that Leibniz’s notion of actualization is best understood as the realization of possible rules or programs of actions. By comparing Leibniz’s notions of possible and actual individuals, I arrived at the conclusion that what a possible individual lacks to become actual is primitive power of activity or primitive force. The divine act of rendering the chosen set of possible programs of action active (and thus actual) is called creation. The unnatural moment of creation constitutes individual substances as inherently active agents. The rest of natural phenomena, aggregates, extension, motion, space, and time are explained by reference to these fundamental active units of being – i.e., units of active force. In other words, God only needs to actualize – i.e., give force of action – the basic individual rules of action and the rest emerges as a result of the relations between them. This accords with the fundamental role Leibniz ascribes to units of force and the derivative (or relational) character that he ascribes to extension, space, and time. Against the background of Leibniz’s view of actualization as the creation of individual agents, I approached the labyrinth of human freedom. This Leibnizian labyrinth is a familiar one: if each individual is defined and individuated by a complete program of action, such that each one of its predicates is constitutive of the individual’s identity, how can Leibniz insist that the individual’s actions are contingent and that rational agents may act freely? My approach to this question turns of two facets: (1) Leibniz’s notion of a program of action that defines each individual can also be interpreted prescriptively (rather than only causally), that is, as

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prescribing the reasons for the individual’s course of action; (2) the notion of agency and especially rational agency stresses that an agent acts spontaneously, not as a mechanism which is causally determined or as if the actions are deductive consequences of the individual’s concept; rather, a rational agent is acting for reasons, according to the principle of the apparent best. In this sense, the relation between the predicates of an individual’s complete concept and his actions can be characterized not as one of logical necessity, such that there is no alternative action, but as one of moral necessity, such that the agent opts for the alternative that seems best from his unique (and necessarily limited) perspective. In this sense, for Leibniz, the notions of rational agency and contingency (the denial of logical necessity) are intrinsically related. By contrast, for Spinoza, the notion of rational agency is intrinsically related to that of necessity. In order to shed some light on both Leibniz and Spinoza’s views, I have attempted in chapter 7 a detailed comparison of their views on agency and necessity. I pointed out that, for both, generative definitions play a fundamental role and that its employment by Spinoza could make the relation between activity and necessity clearer. I also suggested that Leibniz’s extensive use of generative definitions lends support to the central role agency plays in his view of individual substance as well as in the intrinsic relation he conceives between the notion of a possible individual and that of an actual one. In chapter 8 we have seen that Leibniz’s distinction between aggregates, which he sees as well founded phenomena, and individual substances, which he sees as true beings, turns on the intrinsic connection between Being and unity. A true being such as a soul is a true unity but an aggregate, which is composed of many individuals, is not. I attempted to clarify the subtle status of aggregates as semi-real and semi mental against this supposition. The unity of aggregates, to the extent that they have one, is relational, i.e., it derives from a mind perceiving the relations between them. At the same time, my main objective has been to examine the unity of Leibnizian true beings in light of this contrast. If Leibniz’s considers an aggregate of many substances as lacking true unity, what makes him consider an organic unity, which also consists of many individuals, to be a true unity? This is the main question I addressed in the third part of the book. I have argued that Leibniz’s notion of an actual individual implies a nested structure of infinitely many individuals, hierarchically and functionally organized, which he regards as essentially one. I suggested that Leibniz’s notion of nested individuality helps clarifying the type of unity he has in mind – a unity of functional organization that derives from the individual program of action. Such a program of action is already defined as a possibility in God’s

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understanding. The notion of a program may be seen, on the one hand, as essentially one and, on the other, as nesting (and consisting of) infinitely many sub-programs. In this sense, Leibniz’s view of possible individuals is shown to be intrinsically and, I think, illuminatingly related to his view of actual ones.

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Index Change (law of), 126, 129 Combinatoire, 35, 59, 80 Comparison, 1, 58, 63, 107, 131, 182, 200 Compossibility, 4, 23, 91, 93, 105 Concepts individual, 64–71 complete, 131, 239–240 Contingency, 157, 167–168, 252 Contradiction, 16–17, 31, 55, 134 Creation, 5, 54, 72, 88, 111, 123, 133, 179

Abstraction, 59, 113, 114, 181, 181, 182, 209, 211 Accident, 90, 101, 132, 133, 204, 210, 221 Action, 126–128, 130, 145, 154–156 Activity (active principle) combinatorial, 9, 34–40, 54–64, 69 intelligible, 57–58 divine, 12–16, 24–27, 69, 133–135 Actual, 123, 124–129, 131–132, 133–139 Actualist theory of possibility, 17, 19, 20, 32 Actualization, 51, 123, 131–133 Agency, 145, 167, 179–181 Agent, individual, 124, 153, 251 Aggregates, 189, 202–206 Aggregation, 194–197 Algorithm, 8, 40, 70, 94, 243 Analysis, 32, 66, 113–114 Animals, 65, 95, 219, 220, 227 Arbitrariness (arbitrary, 55, 76 Aristotelianism, 15, 18, 32, 45, 65, 125, 130–131, 191, 193, 194, 201–202, 212, 223, 227, 232, 243 Attribute simple, 22–23 of God, 22–24

Definition real; 33, 48 causal, 28, 178, 179 Dependence conceptual, 85, 97 Determinism, 70, 131, 165, 169, 173, 198, 221 Divisibility and indivisibility, 130, 237, 245–247 Domination, 227–229 Entelechy, 222–223 Entity, 51–52, 202 Essences as possibilities, 18, 136, 137, 173, 179 eternal, 3 immutable, 3 Eternity, 18, 186 Existence and possibility, 15, 18, 134, 137, 173 Expression, relation, 226, 240 Extension, 190–193, 199

Being and becoming, 12, 201 Calculus, 40, 59, 65, 180 Causes, and reasons, 152–154 265

266

Index

Force, 132 Forms absolute, 23, 80 simple, 22–24, 54–58 substantial, 129, 223, 237 combinations of, 54, 61, 69, 94 Geometry, 60, 80, 168 God attributes of, 22–24, 55 freedom, 145, 160 intellect of, 32 mind of, 3, 19, 124, 134, 136 will of, 14 Harmony, 26, 85, 244 Hylemorphism, 130, 131, 221, 227 Ideas in God’s mind, 19, 36, 37, 39 Idealism, 7, 222 Inconsistency, 19, 20 Inclination, of reason, 148–149 Indestructibility, 130, 229 Individual actual, 5, 52, 126, 133, 148, 238, 239, 251, 252 substance, 107, 108, 116, 125, 215, 222 concept, 64–69 possible, 241–242, 244, 251 Individuation, 116–119 Infinite being, 25 complexity, 37, 38 series, 70, 87, 130, 246 Knowledge complete, 40–42 Divine, 166, 240

Language natural, 77 combinatorial, 34 Law of the series, 70, 180 individual, 154–156 Life, principle of, 170 Logical notion of possibility; 21, 52 space, 97, 109 Machine artificial, 202–204, 218, 228–229 natural, 203–204, 216–217, 218, 224, 229, 238 of nature, 202–203, 216, 226 Matter primary (prime matter), 130, 190 secondary, 199, 200 Mechanism, 54, 67, 152, 155, 171, 193 Metaphysics, 87, 91, 123–124, 146 Microscope, 221 Mind, 4, 12, 17, 24, 25, 36, 37, 38, 63, 116, 148, 202, 239 Modes, 3, 27, 40, 58, 128, 148, 172, 173, 178, 198–199 Modifications, 131 Monads dominant, 219, 226 Nature, 167 Natural machine, 203–204, 216–217, 218, 224, 229, 238 Naturalism, 10

Index

Necessity, logical, 149–152 metaphysical, 145, 150, 151, 152, 154 moral, 159–160 Negation, 23, 55, 64 Nested individuals, 215, 218–222 structure, 239–242 Nominalism, 90–94 Notation, 38–40, 43 Number primary, 30 infinite, 58–59, 69, 71 Omniscience, 13, 19, 23, 25, 63, 94, 97, 172 Ontological status, 4, 34, 61, 86, 93, 195, 197 Order natural, 27–29 Organic body, 222–225 unity, 1, 195, 202, 218, 252 function, 227–229 Organism, 237–239 Parts, 209 Passivity, 130–131 Perception clear and distinct, 156 confused, 206 Perfection, 22, 23, 28, 134, 136, 137, 139, 171, 172, 228, 246 Perfections of God simple, 23 positive, 23 Phenomena well founded, 7, 190, 198–201, 217, 230, 241, 252 mere, 7, 189, 199, 200 Phenomenalism, 201

267

Physics, 132, 200–202 Points, 28 Possibility as non-contradiction, 11, 19 as intelligibility, 17, 24 as what is understood clearly and distinctly, 16, 18 and Principle of Contradiction, 11, 31, 134, 137, 151, 152 and striving towards existence, 134, 136, 137 and real definition, 33 Potentiality, 15, 32, 182 Predication, 32–34 Principle of activity, 85, 170, 221 of unity, 211 Priority conceptual, 27, 97, 105, 106, 107 natural, 27 Production Rule, 69–71, 239–242 Program of action; 2, 5, 73, 124, 129, 145, 154, 155, 157, 158, 183, 226, 227, 228, 237, 238, 241, 242, 243, 246 Propositions, 30, 32, 33, 40, 43, 57, 58, 65, 90, 93, 109, 146, 152, 157, 168, 171 Reflection, 24, 27 Relational predicates, 89–91, 93, 97, 100–103, 108, 110, 113–117, 131 unity, 220, 241 Relations causal, 85, 238, 242 conceptual, 25, 91, 218, 240 Realism, 201, 206, 212 Reality, 199

268

Index

Reasons and causes, 242 inclining without necessitating, 151, 154, 155, 164 sufficient, 11, 107, 134–137, 150, 152, 154–156, 160 Representation, 32 Requirements, 129, 132, 149, 162, 183, 226, 242 Rule of action, 5, 70, 129, 133, 145, 155, 162, 238–239, 246 Scholasticism, 51, 52, 65, 66, 116, 118, 126, 212 Science, 31, 49, 56, 59, 169, 191, 212 Semi-mental beings, 190 Simplicity of substances, 130, 237 Spontaneity, 125, 128, 160, 162, 183 Striving possibles, 2, 107, 133–137, 139 Structure of predicates, 2, 3, 5, 8, 53, 71, 94, 99, 131, 179, 241, 244, 246, 250 Subjects, 54, 126

Substance, 124, 126 Sufficient Reason, 11, 107, 134–137, 150, 152, 154–156, 160 Truths eternal, 14, 114, 173, 198, 211 of reason and of fact, 15 Unit, 202, 204 Unity relational, 220, 241 of aggregates, 211, 224, 241, 252 of nested individuals, 2, 226, 229, 238, 241–243 Universals, 34, 39, 41–42, 66, 69 World actual, 51, 106, 107, 112, 135, 136, 142 best possible, 133, 137, 161 possible, 1, 4–5, 11, 23, 51, 58, 85–86, 88–91, 105–113, 123, 127, 134–137, 139, 142, 151, 240, 250–251