The Science of the Individual: Leibniz's Ontology of Individual Substance (Topoi Library, 6) 1402032595, 9781402032592

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The Science of the Individual:

The Science of the Individual: Leibniz's Ontology of Individual Substance Stefano Di Bella

THE SCIENCE OF THE INDIVIDUAL: LEIBNIZ’S ONTOLOGY OF INDIVIDUAL SUBSTANCE

TOPOI LIBRARY VOLUME 6 V

Managing Editor: Ermanno Bencivenga, University of California, Irvine, U.S.A. Editorial Board: Daniel Berthold-Bond, Bard College, Annandale-on-Hudson, U.S.A. William James Earle, Baruch College, City University of New York, New York, U.S.A. W Ann Ferguson, University of Massachusetts, Amherst, U.S.A. David Lloyd, Scripps College, Claremont, U.S.A.

Topoi Library is sponsored by the Department of Philosophy and the School of Humanities T at the University of California, Irvine

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THE SCIENCE OF THE INDIVIDUAL: LEIBNIZ’S ONTOLOGY OF INDIVIDUAL SUBSTANCE

by STEFANO DI BELLA Scuola Normale Superiore, Pisa, Italy

A C.I.P. Catalogue record for this book is available from the Library of Congress.

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978-1-4020-3259-2 (HB) Springer Dordrecht, Berlin, Heidelberg, New York 978-1-4020-3260-8 (e-book) Springer Dordrecht, Berlin, Heidelberg, New York 1-4020-3259-5 (HB) Springer Dordrecht, Berlin, Heidelberg, New York 1-4020-3260-9 (e-book) Springer Dordrecht, Berlin, Heidelberg, New York

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“There is no face . . . whose contour does not form part of a geometric curve and cannot be drawn in one stroke by a certain regular movement.” ((Discours de métaphysique, § 6, A VI.4, 1538).

“But never can we reach by way of analysis the most universal laws [of our world], nor the most exhaustive rational explanation of singular things. Necessarily, indeed, this knowledge is reserved to God alone.” ((De natura veritatis, contingentiae et indifferentiae, A VI.4, 1518)

Contents Acknowledgments

xi

Introduction. Individual Substance in the Discourse Metaphysics: Some Problems

1

Part I. The Genesis of a Complete Being Section 1. Individuals and Concepts at the Origins of Leibniz’s Project

23

Chapter 1. A World of Individuals: Particularist Ontology 23 r Chapter 2. AW World of Concepts: Combinatorial Science and the Individual 33 r Chapter 3. Abstraction and Predication: At the Boundary of Concepts and Things 44

Section 2. Origo Rerum ex Formis The (Onto-)logical Construction of a World from Conceptual Atomism to Individual Substance

55

Chapter 1. “Mira res, aliud esse subjectum quam formas seu attributa” 55 r 1.1 A Rediscovery of Subject 55 r 1.2 Attributes: The Clash of Paradigms 61 r Chapter 2. Modes and Requisites: The Genesis of Finite Things 72 r 2.1 Modes 72 r 2.2 Conditions, Causes and Reasons 77 r Chapter 3. Ens Completum: The Emergence of Complete Being 88

Section 3. Series Rerum The Causal-Temporal Structure of Things: Model Metaphysics and Philosophy of Mind Chapter 1. De affectibus: From the Dynamics of Passions to the Series of Substance States 99 r Chapter 2. Subject of Action 111 r Chapter 3. Subject and Time: The Birth of a Continuant 117

99

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CONTENTS

Interlude. On Truth

129

Chapter 1. The Double Root of Truth 131 r Chapter 2. Fundamentum V Veritatis 137 r Chapter 3. Conceptual Containment 144

Part II. A Logico-Ontological Framework for Substances Section 4. Categories (1). Concepts, Things and the Reform of the Category Table

155

0 Introduction to the Category Tables 155 r Chapter 1. Varietas V . Identity for Concepts and Things: The General Framework 161 r 1.1 Substitution and Concept Identity 161 r 1.2 Sameness and Change: The Phenomenological Approach 169 r 1.3 Discernibility and Categorization: Identity for Abstract Objects 173 r Chapter 2. Concepts, Things and the Grammar of Substance 179 r 2.1 Things and Terms 179 r 2.2 The Grammar of Substance: From Abstract Terms to Complete Being 184

Section 5. Complete Concept and Substance The New Alliance of Concept and Thing

197

Chapter 1. Complete Concepts 197 r Chapter 2. Conceptual Individuation: Complete Concept and the Identity of Indiscernibles 206 r 2.1 The “Paradoxes” of IdInd 206 r 2.2 Individuals as Infimae Species 214 r Chapter 3. Conceptual Individuation: Complete Concept and Transtemporal Identity 218 r 3.1 A Concept Involving Change 218 r 3.2 Concept, Essence and the Subject of Change 226 r Post-Script. Twenty Years Later: De Volder (and Others) Facing Individual Concept 235

Section 6. Categories (2). The Theory of Conditions in the Categorial Framework

239

Chapter 1. Consequentiae. A Theory of Causal Temporal Order 239 r Chapter 2. Conditions and Inherence: An Ontology for Predication 248

Part III. Notio Completa. Complete Concept and Individual History Section 7. The Debate on DM 13: Some Leading Ideas

265

Chapter 1. Complete Concepts in God and/or in Themselves 266 r Chapter 2. Compactness 274 r Chapter 3. Completeness 285

Section 8. Scientia Dei. Individual Concepts in God’s Mind Chapter 1. Truthmakers for the Future: Complete Concepts and Future Contingents 301 r Chapter 2. Conditional Truths and Possible Decrees 309

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CONTENTS

Section 9. Law, Concept and World The Nomological and Relational Structure of Complete Concepts

ix

325

Chapter 1. Laws, Worlds and Concepts 325 r Chapter 2. Conceptual Holism. The Individual and His/Her World 338

Post-Script 1. Individual Concepts and the Infinitary Solution

353

Post-Script 2. Individual Concepts and Leibniz’s Metaphysics of History

359

Substances, Concepts and Individual Essences. Some Concluding Remarks

365

Chapter 1. Complete Beings and their Concepts 366 r Chapter 2. A New Essentialism 373 r Chapter 3. Analogies for a Strange Concept: Complete Concepts, Dynamics and Philosophy of Mind 381 r Chapter 4. Building Complete Concepts: Substance- and Concept Structure 384 r Chapter 5. The Quasi-Science of Individuals 391

Bibliography

393

Index of Names

405

Index of Leibniz Texts Cited

409

Acknowledgments I wish to thank here the many persons I have met during my research on Leibniz, my interest on this topic having begun about twenty years ago. Heinrich Schepers has been an extremely generous and helpful host during my stays at the Leibniz-Forschungsstelle of the University of M¨u¨ nster, and he introduced me to the secrets of Leibniz’s manuscripts. Needless to say, we owe him the masterly edition of volume A VI.4 of Academy edition, embracing the decisive years for the working out of Leibniz’s mature metaphysics, and including a lot of earlier unpublished drafts I comment on in my work. Massimo Mugnai guided me in the work for my doctoral thesis on Leibniz, a seed for this book, and is up to now a constant presence accompanying my Leibnizian interests. I have discussed this work with him at different stages of elaboration. I received also precious comments on my manuscript from Robert M. Adams and Nicholas Jolley. I am the only one responsible, of course, for any flaws in my work. Besides this, I profited from some discussions on these and other Leibnizian topics with Fabrizio Mondadori, Daniel Garber, Michel Fichant, Francesco Piro and Enrico Pasini. My bibliography should bear witness to my intellectual debt to other scholars who have written stimulating contributions to this topic in recent years. I had also the opportunity of presenting and discussing some parts of this work in conferences and seminars at the Scuola Normale in Pisa and at the universities of Padua, Irvine and Edinburgh. I am grateful to all participants to these discussions, in particular—besides some Leibniz-scholars I have already mentioned—Ermanno Bencivenga, Nicholas White, Theodore Scaltsas, Kit Fine, Massimiliano Carrara. During my visits to Germany, I also gained from the kind help of Herbert Breger at the Leibniz Archiv in Hanover and from some stimulating contacts with Hans Poser and Martin Schneider. I wish also to thank the people of the Leibniz-Forschungsstelle in M¨u¨ nster, especially Gerhard Biller and Herma Kliege-Biller, for their friendly readiness to help an Italian guest. Above all, I remember with gratitude the late Albert Heinekamp, who received me as a

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ACKNOWLEDGMENTS

young student and favored with his trust and passion my first steps in Leibniz’s scholarship. The Italian CNR supported a stay in Germany in 1998 for research on Leibniz’s manuscripts. Other stays have been supported by the Scuola Normale Superiore. For this research, I have also benefited from financial support from the fund SNS-03. I am grateful to Remo Bodei and the late Vittorio Sainati for having accompanied my first interests in Leibniz; to Claudio Cesa and Tullio Gregory for having always encouraged my research, and to Ermanno Bencivenga for giving me the opportunity and encouraging me to write this book. Last but not least, my parents Ines and Gianvalerio have encouraged me to take up a life of study. My wife Roberta and my children Maria, Anna and Giovanni have shared, in the last years, the consequences of my engagement in this inquiry and in the working of this book. I am grateful to them all also for this. Pisa, September 2004

S.D.B

Introduction Individual Substance in the Discourse Metaphysics: Some Problems Return to Individual: Leibniz’s ‘Remake’ of Categories 5 During the cold winter of 1686, while working as a supervisor of Hartz mines, the thirty-nine year old G.W. Leibniz wrote the draft of a short brilliant treatise on metaphysics.1 Then he sent it, through the Catholic Prince Hessen-Rheinfels, to Antoine Arnauld, the prominent theologian of the Jansenist movement. As is well known, Arnauld reacted badly. His vehement disapproval was excited especially by section 13 of the draft, where Leibniz flatly asserted the ‘inclusion’ of the whole history of a human individual in his/her concept (‘notion’). From this reaction stems one of the most exciting intellectual exchanges of the seventeenth century.2 Moreover, the debate about Leibniz’s real intentions has not ceased even today. The ‘fatalistic’ consequences that terrified Arnauld in section 13 were only the corollary of a thesis put forward in section 8, the very heart of the draft. I wish to briefly expound this well-known text, in order to introduce the problems from which this research starts. First of all, a few words are in order about the position of DM 8 within the general architecture of the Discourse. 1

2

See Discours de metaphysique ´ , A VI.4, 1529–1588 (GP IV 427–463). As is well known, Leibniz never sent to Arnauld the complete Discourse. I am strongly inclined to think that the redaction of some articles of the Discourse we actually possess—I think especially of the intensively discussed DM 13—actually follows f the discussion with Arnauld. For the related correspondence with Arnauld, see GP II 1–138. A critical edition of the correspondence is available, Briefwechsel Leibniz-Arnauld, ed. by R. Finster, Hamburg, Meiner 1997. For a valuable and thorough analysis of the Leibniz-Arnauld correspondence, see R. C. Sleigh, Leibniz and Arnauld: A Commentary on Their Correspondence, New Haven, Yale Univ. Press, 1990.

2

INTRODUCTION

God’s plan in creating our world, hence the theme of perfection, divine and cosmic, is the true basso continuo underpinning the whole of this metaphysical baroque symphony. God’s perfection is the opening theme in sections 1–4. From the theory of divine perfection flows the cosmological sketch of sections 5–7 concerning world perfection. Here the first occurrence of the topic of miracle is located, that will be a leitmotiv in the Discourse. The discussion of the particular-general pair, applied to divine will, reveals the close confrontation with the greatest philosophical theodicy of the moment, the ‘Cartesian’ system of Father Nicholas Malebranche. We should remember that Leibniz’s interlocutor, Antoine Arnauld, was involved in a harsh controversy with Malebranche on these themes. The opening of DM 8 alludes, indeed, to a controversial issue of Malebranchian philosophy: “It is rather difficult to distinguish God’s actions from a creature’s ones . . . ”3 Now, it was one of the central theses not only of Malebranche, but of the whole Occasionalist movement, that God only acts, i.e. God is the only efficient cause, of both physical and mental modifications. The belief in the activity of ‘secondary causes’ is stigmatized as the “most dangerous mistake of ancient philosophy” in Malebranche’s Recherche de la v´e´ rit´e.4 Leibniz does not settle the question of whether the thesis, or its opposite, according to which God does limit Himself ‘to conserving’ the force of created substances, is right. Instead of analyzing the notion of ‘action’, he shifts the focus of attention onto its subject, substance: “Now, since actions and passions belong properly to individual substances (actiones sunt suppositorum), it should be first explained, what to be such a substance means.”5 Under the apparently neutral appeal w to the Scholastic dictum, Leibniz seems to solve the dilemma in favor of the second alternative. In any case, a first shift has led us from the concept of action to that of substance. The problem now is to define the latter, i.e. we are firstly concerned with the ‘intensional’ question of spelling out the notion of substance, better of ‘individual substance’ (the two are evidently held to be synonyms), which has to be carefully distinguished from the ‘extensional’ one of establishing which things in the world, and how many, are to be considered as substances. The first characterization Leibniz gives of ‘individual substance’ is: the subject, to which all predicates or attributes are referred, without itself being referred to any other. This definition is still inadequate according to him, however. It is in fact merely a ‘nominal’ definition. In the terminology Leibniz had elaborated in earlier years, the label is reserved for a description which, 3 4 5

A VI.4, 1539–1540 (GP IV 432). Recherche de la v´e´ rit´e, book VI, part II, ch. III. A VI.4 1540 (GP IV 432).

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though correct and capable, as a matter of fact, of picking out an object by a ‘clear’ idea, does not exhibit, nevertheless, the possibility of its definiendum, as is the case with a ‘real’ definition. Anyway, the burden of definition is transferred from substance to predication. Already in putting forward this nominal definition as something that goes without saying, Leibniz makes a first decisive choice. Literally understood, his definition is far from original, being nothing but a revival of the oldest definition of substance, such as was advanced in Aristotle’s logical work, precisely in chapter 5 of the Categories. Maybe we can appreciate Leibniz’s move better if we consider it against the background of the philosophy of his time. Far from being a Scholastic relic, in fact, the topic of substance lay at the core of the most innovative contemporary philosophies. They never emphasized, however, its ‘individual’ character. Despite their severe criticism of the ‘universals’ of the School, substance was thought of as something general, deprived of individual qualities: be it Hobbes’s corporeal substance, or Descartes’ mind and body. Coming back to the Categories model, on the contrary, Leibniz achieves a double result with the same move. Firstly, he places the individual again at the center of the ontological scene; secondly, he replaces the inspection of mental contents with logical-linguistic analysis. Aristotle was not very concerned with the use-mention distinction in his treatise, and he left ambiguous enough for his commentators in the following centuries, whether he was speaking about words, meanings or things. At first sight, this feature is shared to a large extent by DM 8. Anyway, in Categories 5 primary substance was introduced precisely as the ‘ultimate subject’. More exactly, it was qualified as that which is not said of a subject, nor is in a subject. The pair of ‘being said of ’ and ‘being in’ was handled accurately in chapter 2 of Aristotle’s treatise. Roughly speaking, the first relation (a ‘predication’, in the proper sense) connects an essential feature to a subject; typically, it predicates of an individual the species or genus to which it belongs: in the technical language of the Categories, a ‘secondary w substance’, i.e. what we would call a ‘sortal’ such as ‘man’ or ‘horse’. The other relation, instead, connects a non-essential characteristic, or accident, to a subject, and is labeled as ‘inherence’. Aristotle’s elusive characterization is largely negative. To be in a subject, or to inhere, means “to exist within something else, without being a part of it, and being unable to exist separately from it.”6 Hobbes, as we shall see, still had great difficulty in his De Corpore in providing a precise definition for Aristotle’s intended notions of inherence and accident. Now, this is precisely what Leibniz aims to do, passing from the ‘nominal’ definition to a more adequate one, or in proper Leibnizian terms, 6

Categories, ch.2.

4

INTRODUCTION

to the ‘real’ one: “We should consider what it means to be truly attributed to some subject.”7 Once again, a seemingly innocent move conceals two strategic advances. Firstly, as a matter of fact Aristotle’s distinction is simply left out in the Leibnizian account. His ‘being attributed to’—which is expressed, a few lines below, as ‘being in’—simply cumulates, without further discussion, the two relations accurately distinguished in the ancient Categories. How such a shifting is performed so carelessly is perhaps a bit less surprising, if we observe that almost no reader, neither Arnauld nor later twentieth-century interpreters, noted it. For everyone, it is something quite in order, exactly as it was for Leibniz. Clearly, something should have happened in the tradition, between Aristotle and Leibniz, which decidedly determines the understanding of predication. I shall try to understand this in what follows, and great attention will be paid to the influence of the Nominalistic tradition. Here I would only remark, that the disappearing of the distinction of Categories 2 is accompanied by the disappearing of the whole topic of ‘secondary substances’, which occupied the main part of Categories 5. Secondly, if the relation resulting from blurring together the two Aristotelian ancestors derives its name from inherence, its description matches more with the ancient idea of ‘predication’, or ‘being said of’. Moreover, the problem passes into the definition of true predication, hence ultimately of true proposition. So we come to the decisive shift from inherence to truth. “Otherwise, I Do Not Know What Truth Is”: Conceptual Containment as an Alleged Truism At this point, Leibniz introduces what he himself later will present to Arnauld as the very heart of the matter, and the decisive argument against all objections. I allude to the so-called “containment theory of truth.” One of the clearest formulations of the theory is to be found in a text, known as First T Truths , which w Louis Couturat, the pioneering discoverer of Leibniz’s logic, emphasized as the true key to the understanding of the Discourse metaphysics. As is well known, indeed, according to the French scholar, all of Leibnizian metaphysics logically depends on the containment theory. From this perspecT became, at the beginning of last century a classic supporttive, the First Truths ing document for the ‘logicist’ interpretation. Although the Academy edition has shifted Couturat’s cherished text to some years later,8 and despite some 7 8

A VI 1540 (GP IV 432). The text was first published by Couturat under the famous heading Primae veritates. Editing and commenting it, he expoused his interpretation of Leibniz’s metaphysics. See L. Couturat, Sur la metaphysique ´ de Leibniz, in Revue de m´e´ taphysique et de morale 10 (1902); reprinted

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relevant differences of perspective, the parallelism of the two writings is nevertheless striking. The First T Truths opens directly with the problem of the classification of truths. After discussing the dichotomy between primary and derivative truths, the former coinciding with formal identities, and the latter being reducible to the former through substitution, Leibniz is in a position to state the containment principle as a common rule of truth embracing both fields: The predicate or consequent always is in the subject or antecedent, and here the general nature of truth lies, as Aristotle himself noted, I mean in the connection between the terms of a proposition . . . and this holds for every affirmative truth, universal or singular, necessary or contingent.9

From this principle many consequences are drawn, which largely correspond to the ‘corollaries’ that DM 9 derives from the concept of complete notion. Now, a wholly ‘analytical’ theory of truth is likely to sound astonishing to our post-Kantian ears. Leibniz, however, can present it to Arnauld as the straightforward consequence of some self-evident, if not commonsense, principles expressing our elementary intuitions about truth. Moreover, he often reinforces his claim by invoking, this time explicitly, the authority of the greatest metaphysician of common sense: “as Aristotle himself noted.” Attributing the seminal idea of the containment theory to Aristotle is usual in the Leibnizian accounts of it. Leibniz’s alleged Aristotelian genealogy alludes to the relation of “belonging to” (hyparchein h ) of the syllogistic theory. This assimilation is made possible by the simplification of the predication theory with respect to the Categories model. Moreover, Leibniz’s definition gives a decidedly intensional reading of containment. But if the view of the individual as the basic building block of the ontological construction was actually an Aristotelian one, the same could hardly be said for this idea of truth. The account of truth prevailing within the Aristotelian tradition, in fact, was in terms of correspondence between a proposition and the world. On the contrary, in Leibniz’s theory, verifying a proposition seems to be a task one could perform looking simply into a concept, without caring about its attaching to the world. However this may be, Arnauld declared he was impressed by Leibniz’s argument. The true import of Arnauld’s admission, however, is far from clear. I strongly suspect that it concealed an extremely weak reading of the analytical theory, having the effect of making it devoid of ontological value, as we

9

in G.H. Frankfurt, Leibniz: A Collection of Critical Essays, Garden City, N.Y., Doubleday Anchor, 1972. It has been edited in the Academy edition under the title Principia logicometaphysica (A VI.4, 1643–1649) and attributed on material grounds (watermarks) to the period of Italian travel (1689), hence after the correspondence with Arnauld. A VI.4, 1644 (C 518–519).

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INTRODUCTION

shall see later. A major task of interpretation will be, therefore, to clarify the content and motivations of Leibniz’s theory of truth, whose exact meaning is far from established and surely cannot be justified simply by relying on any well-known tradition.10 In any event, three centuries after Arnauld’s, and one century after Couturat’s reading, and whether one takes seriously the ‘analytical’ claim (as Couturat did), or not (as, I think, Arnauld finally did), the problem is still open. How could Leibniz believe to draw such weighty metaphysical consequences from such abstract logical principles? He seems guilty of blurring together two different levels, or, if we prefer, material and formal speech. This, no matter whether the ‘deduction’ goes from logic to ontology, as Couturat and Russell held, or the opposite way, or better there is no univocal deduction, but an unbreakable whole of logical-metaphysical intuitions, as almost all later historians, reacting to ‘logicist’ interpretation, ended up holding. Nevertheless, I shall try to show that Leibniz’s move from the logical to the ontological level is far less uncritical than interpreters ever suspected. Notio Completa and Ens Completum: Concept and Object We are now, in our reading of DM 8, at the crucial juncture. From the containment theory, in fact, Leibniz draws his answer to the substance problem: This being premised, we can say it is the nature of an individual substance or complete being to have a concept so complete that it is sufficient to make us understand and deduce from it all the predicates of the subject to which the concept is attributed. An accident, on the other hand, is a being whose concept does not include everything that can be attributed to the subject to which the concept is attributed. Thus the quality of king which belonged to Alexander the Great, if we abstract it from the subject, w is not determined enough to define an individual, for it does not include the other qualities of the same subject or everything which the concept of this prince includes. God, on the contrary, in seeing the individual notion or ‘haecceity’ of Alexander, sees in it at the same time the basis and the reason for all the predicates which can truly be affirmed of him—for example, that he will conquer Darius and Porus . . . .11 10

11

The historically and theorically eccentric character of Leibniz’s theory of truth has been stressed in E.M. Curley, Der Ursprung der Leibnizschen Wahrheitstheorie, Studia leibn., 20/2 (1988), 161–174; and R.M. Adams, Predication, Truth and Transworld Identity in Leibniz, in J. Bogen, E. McGuire (eds.), How Things Are, Dordrecht-Boston, Reidel, 1985, 235–283. Now see the wide reconstruction of J.B. Rauzy, Leibniz et la v´e´ rit´e, Paris, PUF 2001. A VI.4, 1540–41 (GP IV 433, L 307–308).

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“This being premised”: that is, if we admit that the containment theory provides the required ‘real definition’, or adequate understanding of predication. Then, it is easy to construct the concept of individual substance, by applying the containment criterion to true singular propositions. But what is the precise structure of the highly brachylogical argument? An attentive reading of this decisive passage dispels the suspicion of an unnoticed coincidence or, worse, of a sheer confusion, between object and concept. ‘Individual substance’ clearly is an ontological item i.e. something belonging to the furniture of the world, on a par with its correlate, ‘accident’ or ‘quality’. I wish to emphasize the fact that the adjective ‘complete’ makes its first appearance in DM 8 just as an attribute of this substance (‘complete being’) and not of the concept. Confronted with substance, accident is considered implicitly as an ‘incomplete being’, whatever this might mean (presumably, we can render it as ‘abstract’, which has to be cleared up, anyway). a Both substance and accident, then, have their ‘notions’, or conceptual counterparts. The containment principle, however it should be understood, holds precisely on this level, or between these concepts. But what exactly about the ‘subject’ the concept is attributed to? As the context unmistakably shows, the possession of a complete concept is meant to work as a condition both necessary and sufficient for being an individual substance, or a complete being. Now, according to the general rule of truth, the containment of all predicate concepts within the appropriate subject concept happens to be verified for all truths, whatever concept they concern. Therefore, this feature could hardly be seen as a distinguishing one for individual substances, i.e. as a condition sufficient to circumscribe these ontologically basic items.12 As Leibniz says in a letter to Hessen-Rheinfels: “Can one deny that every thing (whether genus, species or individual) has a complete concept, according to which God, who conceives of everything perfectly, conceives of it, that is to w say a concept which contains or includes everything that can be said of the thing . . . ?”13 In other words, the universality of the rule of truth establishes containment also for specific concepts: but then, if ‘subject’ were to be simply read as a logical subject, also properties such as ‘being a king’, or abstract beings such as ‘triangle’, when figuring in the subject position, would satisfy our requirement and they would claim to have complete concepts, or to be complete beings, in blatant contrast to the general tenor of DM 8. A note in a draft of the letter of July 1686 to Arnauld, however, draws an accurate distinction between the two types of ‘completeness’. The technicality of the 12

13

This point has been made in D. Rutherford, T Truth, Predication and the Complete Concept of an Individual Substance, in Leibniz: Questions de Logique, Studia Leibnitiana Sonderheft 15, Steiner, Stuttgart 1988, 130–144. GP II 131, Mason 73.

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INTRODUCTION

remark is attested by the fact that it is written in Latin: “a full concept [notio plena] includes all the predicates of the thing e.g., of heat; a complete concept [completa] all the predicates of the subject, e.g. of this hot thing [hujus calidi]. In the case of individual substance they do coincide.”14 It is the only explicit echo, in the Arnauld correspondence, of the great deal of linguistic ontological reflections Leibniz devoted to the problem of abstractness. What is important now to remark, is the distinction between ‘full’ and ‘complete’: where the former qualifies the predicative completeness of an abstract subw ject, while the latter is reserved for the predicative completeness of the true subject. This ‘subject’, therefore, should be intended as an ontological item, the ultimately underlying being the concepts of both substance and accident are attributed to and which they express partially, in the case of the accident concept, or totally, in the case of the substance concept. All this amounts to saying that the ontological idea of ‘subject’ and the related completeness is presupposed by the construction of the complete concept. In the dense phrases of DM 8 we can divine the meeting point of two trains of thought which develop, in a relatively parallel way, though mutually interacting. On one hand, the growth of the ontological idea of the ‘complete being’ (ens completum), playing the role of the metaphysical subject of predication; on the other, the construction of the ‘complete concept’ (notio completa), working as a logical subject of proposition, on the ground of the containment theory of truth. Of this interpretative hypothesis, my research will offer a sort of historical confirmation, if not a quasi-genetic verification. Thus, the first part of my book will try to explore precisely the development of the ontological idea of ‘complete being’. We should bear in mind that Leibniz’s reflection on the relationship between thing and concept takes place in a period shaped by the deepest conflicts between competing ontological and epistemological paradigms: in a word, a period of deep transformations in the way of thinking the relations among things, ideas and words. Maybe the man to whom the Discourse is addressed, the ‘great Arnauld’, is the best symbol of these changes. Forty years earlier, Arnauld had a great discussion with Ren´e Descartes about the very nature of a ‘complete substance.’15 Descartes defended the possibility of inferring a real distinction between two substances from a conceptual one, i.e. from the fact that I can conceive the notion A without B, and vice versa. This possibility lies at the core of his capital ‘proof’ of the mind-body distinction, and is a typical 14 15

GP II 49 note. See F Fourth Objections and Replies, On the nature of mind, AT A VII 197–203; 219–227. For a comparison of the Arnauld-Descartes and the Arnauld-Leibniz discussions from the viewpoint of the argumentative strategies employed, see S. Di Bella, Completeness and Essentialism: Two Seventeenth-Century Debates, in T Topoi 2000/2, pp. 123–136.

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move of the new ‘way of ideas’, according to which we have access to things only through the analysis of our mental contents (‘ideas’). To this argument, Arnauld objected that we are not assured that our notion of A is complete, instead of being cut off from a richer one. In other words, we are not assured that it includes all the predicates of A. In Arnauld’s counterexamples, Descartes’ argument was reduced to a fallacious ‘inference from ignorance’, blurring an epistemic logic for a logic of truth. In his reply, Descartes distinguished this sense C1 of completeness from a sense C2. A concept is C1-complete, iff it comprehends all the predicates of the related object; it is C2-complete, iff we are assured that it is not obtained through an act of abstraction. Descartes reserved the term “complete” for the latter—the only relevant one, according to him, for the question of real distinction—while calling a C1 concept “adequate”. For Descartes, only C1 is struck by Arnauld’s objection. Human beings are indeed unable to exclude the divine ‘overdetermination’ of the concepts they possess, hence to be assured of their predicative completeness. On the contrary, the fact that a concept possesses C2—a necessary and sufficient condition for real distinction—falls within the scope of evident human knowledge. Compare now this discussion of Arnauld with his 1686 one with Leibniz on DM 13. Notional completeness is now invoked, not to decide about the mind/body distinction, but about the nature of individual substance and its relation with accidental properties. The overturning of Arnauld’s stance strikes the eye. Against Leibniz, he will defend precisely the view of completeness that Descartes had argued for against him in 1640. For his own part, Leibniz claims the C1 requisite for the true concept of an individual substance. His revaluation of C1-completeness does not mean, however, a return to the preCartesian priority of ‘things’ versus ‘ideas’, but is rather the result of a new approach to things (substances) through the medium of logic and language. The discussion about singular proposition and individual concept shows, how Leibniz’s new science of concepts tries to capture ‘things’ in a manner more adequate than the Cartesian ‘way of ideas’. Knowing the Individual as Such: Haecceity, and Other Scholastic Tools Focusing attention on individual substance Leibniz, as I have said, looks back to Aristotle. On the contrary, insofar as he puts the individual concept at the very heart of metaphysical knowledge, he makes a move which deeply subverts the Aristotelian scheme. Though being the basic building-block of the ontological fabric, in fact, the individual as such was practically excluded from the Aristotelian science, which dealt with essences located at the specific level. Leibniz’s conceptualizing of individual seems to break down the old taboo expressed by the dictum: ‘Individuum est ineffabile’.

10

INTRODUCTION

True, already within the Aristotelian tradition, Scholastic thought, especially since the later Middle Ages, had brought the problems of individuality to the center both of epistemology and ontology. So, in the theories of knowledge of Ockham and Scotus, we have a direct grasp on individual. At the same time, we find in this tradition a great concern for the problem of individuation. More exactly, in the case of nominalistically minded authors like Ockham, the epistemological option for the direct intuition of the individual is accompanied by the refusal of properly posing the ontological problem of the ‘principle of individuation’. Within a conceptual scheme, where we have a direct epistemic access to individuals and only to them, and all there is, is individual, there is no point in asking what makes something an individual; rather, the main problem to be faced is the need to explain how we can get some universal concept. On the contrary, for more generous ontologies, including both individual and universal items, the problem arises. One of the most sophisticated theories of individuation had been worked out by Duns Scotus. In order to determine (‘contract’) the ‘common nature’ to individuality, Scotus, as is well known, introduces a new ontological element, which he labels ‘haecceity’. Leibniz alludes precisely to this famous, but also highly controversial, conceptual tool, in order to illustrate his ‘individual concept’ in DM 8: “God, seeing Alexander’s individual concept or haecceity . . . ”. The hint is the more intriguing, as Leibniz had the opportunity of dealing expressly with the Scotistic concept in his first writing, the dissertation De principio individui. But the point is, that he spent there most of his forces just to reject the notion of haecceity as unintelligible. Consistently, Leibniz’s own solution, according to which the individual is individuated through its whole being (tota sua entitate), was very close, both from an historical and conceptual point of view, to the nominalistic idea that an individual thing is such immediately, or by itself. In the Preface to Nizolius of some years later, Leibniz takes ‘haecceity’ as an example of the obscure Scholastic language he wants to criticize in that work.16 Hence, we cannot help asking whether the reference of DM 8 marks some effective revaluation of Scotus’s technical concept, or rather the term is used in the generic sense of ‘principle of individuation’, to cover something quite different. At the time of the Discourse, Leibniz is actually rehabilitating some Scholastic concepts, but he rethinks them in an original way. A proper revaluation of Scotus’s idea is quite unlikely. Anyway, the choice of a term, especially at this strategic juncture, surely is not by chance. What it seems to suggest to 16

“ . . . certain alchemists . . . had sounder and clearer insight into the nature of things than did any philosophaster sitting behind closed doors, bent exclusively over his haecceitates or his hoccitates.” (GP IV 143; L 124). In the same text, Leibniz also criticizes the linguistic form ‘haecceitas’, and suggests ‘hoccitas’ as more suitable: “The Hoccitas will be the reason why something is said to be ‘this’. . . or the quality of this, insofar as it is a ‘this’.” (GP IV 141).

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the reader is the idea that the individuating concept is not a mere sum (or set) of predicates, but a principle of deduction, i.e. something which gives to its owner (God, at least) a key to the intelligibility of the individual. Whereas a complete concept intended as the sum of the individual’s characteristics might rather recall the ‘tota entitate’ of the nominalistically minded youthful solution. For now, I limit myself to remarking that the question about the real sense of the haecceity reference has opened up another question, concerning the internal structure of individual concept. Is it simply a maximal set of predicates, or does it work as a principle of deduction, somehow transcending them? On the whole, Leibniz is willing to use some Scholastic terms or statements, putting them in a schematic manner, a bit as if they were slogans, apt for expressing some of his own theses in a concise and suggestive manner. This is the case not only with haecceity, but also with a perhaps more exotic piece of the Scholastic way of thinking, i.e. the Thomistic doctrine concerning the individuation of angels. Here also we have, at least at first sight, a contrast with the strategy pursued in the dissertation of 1663. Aquinas’s solutions were left aside there, precisely because they did not offer a unitary account for individuation, holding both for material and immaterial beings. Now, in the Discourse Leibniz advances an absolutely general account, but he is eager to consider it just as the generalization of the solution Aquinas reserved for immaterial beings. All this is stated in section 9, to express the first corollary of the complete concept thesis, which is nothing but the famous ‘principle of the identity of indiscernibles’. From now on, Leibniz’s most famous thesis about identity will be usually accompanied by the ritual reference to Aquinas’s angels. Treating the individual ‘as the infima species’ becomes Leibniz’s characteristic mode of signifying the deep shift which I indicated as ‘conceptualizing the individual’. Once again, reflecting on Leibniz’s use of Scholastic references could help us to grasp his real intention. In whatever manner we conceive its content, surely the label of ‘haecceity’ indicates that the complete concept is intended by Leibniz to play the role of a principle of individuation. As such, it provides the ultimate ground for the identity assertions concerning individual substances, as the corollary of the identity of indiscernibles has shown. Substance as a ‘Power of Contraries’ and Leibniz’s Theses about Identity The first claim about identity which is implied by the complete concept doctrine is the well-known identity of indiscernibles (IdInd) of DM 9. The converse of it, i.e. a very austere thesis of indiscernibility of identicals (IndId), is stated in the following discussion with Arnauld. At the heart of the

12

INTRODUCTION

discussion about DM 13, Arnauld challenges Leibniz’s idea of the completeness of the individual concept, by arguing that we may conceive counterfactual claims concerning one and the same individual. Hence, no predicate expressing them is included in his/her individual concept. Leibniz’s reply is that such counterfactuals do not reflect the truth of things: If in the life of some person . . . or even of the universe as a whole, some event were to occur in a different way than it actually does, there would still be nothing to prevent us from saying that this would be another person or another possible universe which God has chosen. And it would in that case be truly another individual.17

Now, what is the ground for this astonishing thesis? As I have said, it is based on the completeness requirement and containment theory of truth. It is worth noting that this deduction is closely connected, in Leibniz’s exposition, with that of transtemporal identity: There must . . . also be a reason a priori . . . which justifies us in saying that it is I who was in Paris and that it is also I and not someone else who am now in Germany and that consequently the concept of myself must combine or include these different conditions.18

Leibniz is willing to endorse the transtemporal identity of substance as a continuant underlying the phenomenon of change while rejecting, instead, the possibility of counterfactual identity. The asymmetric linkage between the two theses is a highly intriguing fact, both for the comparison with the Aristotelian model and for the question of the internal consistency of Leibniz’s theory. As regards the first point, one of the two theses takes up again some important features of that traditional model, while the other severely challenges it. In order to see this, let us look briefly again at Categories 5. The last part of the chapter indicates as the most characterizing feature of substance that of being “a power of contraries”, i.e. something which is capable of sustaining contradictory predication. A substance, indeed, is now white and then not-white, while remaining one and the same. Reference is made to the all-pervading w phenomenon of change. This makes clear that Aristotelian substance at its very origins is the ontological correlate of a weakening of the indiscernibility requirement. The most important feature of substance in Categories 5, in fact, corresponds to the well-known restriction of the ‘principle of contradiction’, as it was formulated by Aristotle himself: “a thing a cannot be B and not-B at 17 18

GP II 53 (L 335). Ibidem.

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the same time and in the same respect.” ““At the same time”: but it can be B and not-B at different times, and this is precisely what Categories 5 emphasizes. “In the same respect”: a modal difference could be meant. A thing a is actually B and possibly not-B. Before going further, let me point out that the other half of the so-called ‘Leibniz’s Law’, i.e. the identity of indiscernibles, was also not suitable to work as an identity condition for Aristotelian substances. In the Aristotelian corpus we find at least an explicit denial of the principle ((Metaphysics Z 15), which is all the more significant, insofar as the Stagirite argues there against w the possibility of obtaining the knowledge of an individual through a complete description in general terms, hence through conceptual means. As one could easily expect, therefore, Leibniz’s theses about non-temporal identity (IdInd and IndId) show his neat distancing from the Aristotelian substance model, implied by his ‘conceptualization’ of individual. On the other hand, by the same move Leibniz intends to provide a better basis for the this time truly Aristotelian idea of transtemporal sameness. The asymmetry does not fail to provoke some pressure on the cluster of Leibniz’s theses. The foundation invoked for transtemporal identity, far from supporting the denial of counterfactual identity, could rather reinforce the latter. As some interpreters have observed, in fact, if the properties included in the complete concept are time-indexed, what prevents us from indexing them also to possible worlds? Or, in terms of the ‘Leibniz’s Law’: if we can qualify it by indexing properties to time, why cannot we do the same with worlds? This move seems more available to Leibniz, insofar as he is commonly held as the father of the picture of possible worlds, and his whole discussion with Arnauld about alternative stories is placed in this framework. The point is, however, that Leibniz’s individuals are unequivocally worldbound, as the quotation above has shown. This fact puts us at the center of the most passionate discussions in recent Leibniz literature. But before turning to this, let me briefly recall another ‘paradox’ of DM 9, which has deserved a lot of attention in the literature, and has some important bearing on the identity theses and the view of substance. ‘Connexion des choses’ and Russell’s Internal Relations From the complete concept theory, DM 9 draws the consequence that an individual substance ‘mirrors’ its whole world, through the circumstance that all its properties, hence also the relational ones, are grounded within its concept. It is well known that Russell considered the alleged reduction of relational predicates the most serious flaw within Leibniz’s theory. When he wrote about Leibniz, he was interested in fighting idealistic monism of the

14

INTRODUCTION

British variety; and the Leibnizian view on relations appeared to him as a standard example of that ‘doctrine of internal relations’ which would cause the monistic collapse. Under this heading is meant a thesis which considers the relations an individual holds with other individuals (ultimately, with the whole of its world) as something which constitutes its self-same identity. From this perspective, Leibniz’s ‘mirroring thesis’ seems to represent a further powerful ground for the thesis of world-bound individuals (WBI), although it should be clear that the problem of counterfactual identity, and its denial, are conceivable also if one abstracts from the question of relational predicates. As regards the other ‘paradox’ on identity, notice that Leibniz seems to have professed a very strong version of the IdInd, affirming that any two individuals are internally distinguishable: and this, via the fact that relational properties are founded on monadic ones (in ontological jargon: on intrinsic accidents in the category of quality). As a matter of fact, the reference to the world context, and to the ‘mirroring thesis’ strikes the eye in the documents of the Arnauld correspondence: the marble block of Geneva, imagined in a counterfactual situation, is said to be numerically different for the imperceptible changes caused in it through the ‘connection of things’. Notice that this connection of things has to be taken in the strongest sense. Leibniz, in fact, does not limit himself to stating that every relational property should have an ‘intrinsic’ foundation. He goes further saying that a change in the relation must somehow affect all related terms. On the contrary, it was commonly accepted in the Aristotelian categorial framework that a relation can change also if one of the related terms does not change. In challenging this principle, Leibniz commits himself, once again, to the abandonment of an intuitive framework for individuals. The paradoxical aspect here is that Leibniz’s strange thesis about changing relations, though presenting itself within an ontological reductionist framework, is more in tune with an extremely ‘realist’ account of relations and ultimately with their irreducibility.19 Once again, this puzzling fact poses the problem of the relation among individual, concept and truth. Superessentialism without Essence? During the last decades, an intensive debate has developed about Leibniz’s denial of counterfactual identity, obviously under the influence of present-day discussions concerning the philosophical interpretation of possible worlds

19

This has been remarked by M. Mugnai, Leibniz’s Theory of Relations, Steiner, Stuttgart, 1992, ch. III, 49–55.

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semantics. ‘Superessentialism’ is the label coined20 to designate the view where, if an individual thing were to lack (better, if he had lacked) one of its w properties, it simply would not have existed. And this amounts to saying that no counterfactual sentence could be literally interpreted, or in modal terms, that no individual could have different properties than the ones it actually possesses; in the language of possible worlds, finally, that it does exist in no more than one possible world. From this perspective, the contingency of a statement about an individual would reside only in the fact that the statement turns out to be false in all other worlds, in which that individual does not exist; hence, the ‘root of contingency’ would be only the possible non-existence of the individual. A further corollary to this view would be Leibniz’s commitment to a sort of counterpart-theory ante litteram, as it would be documented by his talk about “possible Adams” in the Arnauld correspondence (and about “possible Sextuses” in the final tale of the later Theodicy). This complex of ideas has been variously challenged by several critics, especially insofar as it seems to commit Leibniz precisely to the undesired modal consequences he wanted to avoid in the correspondence. A textual datum should be firstly granted: as a matter of fact, and regardless of terminological questions, Leibniz effectively endorsed the rather astonishing doctrine dubbed above as ‘superessentialism’—i.e., he maintained the denial of counterfactual identity (or, if we prefer, of trans-world identity). The hard work, however, is to understand why he endorsed it, and what the precise import of this doctrine was. A first circumstance that should forewarn us is the fact that Leibniz, surprisingly enough, puts forward the denial of counterfactual identity while he is striving to dispel the allegedly fatalistic implications of the complete concept doctrine feared by Arnauld. Hence, he seems to hold the denial of trans-world identity (TWI) for being relatively independent from, or in any case innocuous to, his defence of contingency. Moreover, while striving to 20

By F. Mondadori in Reference, Essentialism, and Modality in Leibniz’s Metaphysics, Studia Leibnitiana, 5, 1973, 74–101; Idem, Leibniz and the Doctrine of Inter-World Identity, Studia Leibnitiana 7, 1975, 22–57. The framework for the issue had been traced in the seminal papers of B. Mates Leibniz on Possibile Worlds, in van Rootselar and Staal (eds.), Logic, methodology and philosophy of science, vol. 3, 1968, 507–529, and Idem, Individuals and Modality in the Philosophy of Leibniz, in Studia Leibnitiana 4, 1972, 81–118. Mates has given his most complete contribution to this topic in his classic The Philosophy of Leibniz: Metaphysics and Language, New Y York-Oxford, Oxford Un. Press, 1986. Other important stages in the superessentialism debate have been marked by Sleigh’s ‘super-intrinsicalness’ thesis in his Leibniz and Arnauld, and the reconstruction of the logic and metaphysics of counterfactual non-identity in R.M. Adams, Leibniz. Determinist, Theist, Idealist, New YorkY Oxford, Oxford Un. Press, 1994, ch.3–4 (53–108). More recently, see J.A. Cover, J.O’LearyHawthorne, Substance and Individuation in Leibniz, Cambridge, Cambridge Univ. Press, 1999. On all this more below in my Concluding Remarks.

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INTRODUCTION

counter Arnauld’s charge of ‘fatalism’, he insists on his strange theory of truth. Finally and most surprisingly, the sharp-minded polemical Arnauld does not seem to fear any dangerous modal implication from the denial of TWI and ultimately surrenders to the argument drawn from the truth theory. I find all this a very puzzling story. Scholars have correctly stressed that the denial of counterfactual identity— differently from what Leibniz himself said—cannot be logically derived from the conceptual containment theory alone.21 None of the supporters of the ‘superessentialist’ reading properly thinks that the denial of TWI can be deduced simply from complete concept, or from its foundation in the conceptual containment theory of truth. For Fabrizio Mondadori himself, for instance, this is only half the story. According to him, in fact, superessentialism stems from the following premises taken together: (1) the individual concept defines the individual, insofar as it corresponds to the individual essence, or haecceity; (2) the individual concept is complete. Premise (2) is drawn, in its turn, from (3) the containment theory of truth, insofar as it is applied to singular sentences.22 Let us forget, for the moment, that the application of (3) is likely to presuppose, as I have advised above, an ontological idea of what has to be counted as the subject of a singular proposition, and concentrate rather on (1). Mondadori is eager to specify that the defining role of complete concept does not descend from a merely epistemological problem of individuation; that is, it does not come (simply) from the problem of identifying an individual among the infinite number of actual and possible ones. A metaphysical interpretation of the role of complete concept is required, where it represents an ‘individual essence’. I think that this is quite right, but I also think that further inquiry is needed to explain what this postulate means. The substantial issue in the so-called superessentialism debate bears precisely on the understanding of this point. In order to grasp the problem at stake, I would briefly refer to another distinguished scholar, Benson Mates. He shares with Mondadori the conviction of Leibniz’s commitment to a ‘world bound individuals view’, and the related modal consequences. He seems more perplexed, however, with regard to the Leibnizian reasons for this commitment, and he himself formulates the objection I recalled above of the ‘world indexed concept’. The true difference of approach of the two interpreters in spite of their largely common reading and conclusions lies in the fact that Mates seems to have trouble in making a clear sense of assumption (1). In his reading, rather, the only conjecturable motivation for Leibniz’s embracing of the WBI thesis assumes an unmistakable 21

22

Adams has shown this clearly in Predication, Truth and Transworld Identity in Leibniz, trying to give an account of the missing link. My historico-ontological reconstruction will come to confirm some main points of this account. See Mondadori, Leibniz and the Doctrine of Inter-World Identity.

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Quinean flavor. According to Mates’s conjecture, Leibniz’s decisive ground for denying TWI could have been the acknowledged impossibility, in view of his principle of continuity of forms, of drawing any intelligible boundary line between the properties of a thing which are, or are not, essential to it.23 I am not interested here in evaluating the merits of Mates’s proposal. In any case, it draws our attention to a fact which risks being unnoticed, maybe because it is somehow masked by the suggestive label of ‘super-essentialism’. I mean, a thesis which effaces the venerable distinction between a privileged subset of properties and a halo of accidental ones could also have some ‘antiessentialist’ grounds. Surprising as it might be, a kindred train of thought should not be excluded right from the start from the ones available to Leibniz. As regards the notion of necessity, his interpretation of it in terms of what we would consider a linguistic necessity, grounded on meaning, is universally known. And from an ontological point of wiew, Leibniz’s scholarship in the last decades has shown the influence exerted on him by nominalistic concerns and ideas. Once again, the problem goes back to the way of thinking of the relationship between an object and a concept. If this relationship is thought of as sufficiently loose, it is difficult to give a truly ‘essentialistic’ sense to Leibniz’s ‘superessentialism’. The same point, or a very similar one, can be grasped from a slightly different perspective. Consider the relationship between the complete concept and transtemporal identity, and the way it was understood in Russell’s book. Differently from Couturat, Russell largely underestimates, at least at the time of writing his book, the ‘analyticity’ seemingly implied by Leibniz’s theory of truth. Therefore he can read Leibniz’s example of the inclusion of a future journey in his concept as amounting to “[a] the assertion of permanent substances; . . . [b] the obvious fact that every proposition about the future is already determined as true or false . . . ”24 Now, a complete notion conceived in this way, i.e. as a set of predicates which is extrinsically stuck to an individual, could hardly explain the denial of counterfactual identity and make a metaphysically relevant sense of ‘superessentialist’ talk. The alleged analyticity, or inclusion of predicates in the concept, would be left with no de re import. Substantialism without Substrata? Qualities and Bundles So far, the difficulty in making sense of the metaphysical import of complete concept seems to amount to the difficulty in making sense of the 23 24

See Mates, Individuals and Modality in the Philosophy of Leibniz. B. Russell, A Critical Exposition of the Philosophy of Leibniz, 2nd ed., London, Allen & Unwin, 1937, p. 19.

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INTRODUCTION

connection between the individual and its factual history on one hand, and their conceptual description on the other. Well, one could suspect that the reason for Leibniz’s ‘paradoxes’ is just the following: far from presupposing a divorce between the logical (conceptual) and the metaphysical subject, his theses about identity would reflect precisely the irrelevance of one of the terms, that is the ontological subject as opposed to concept; or the substance as opposed to the bundle of qualities. The possibility of attributing such a reductionist attitude to Leibniz has been sharply envisaged in Russell’s seminal monography. Though acknowledging that the historical Leibniz was obviously far from professing such an attitude—in many occasions he presented his metaphysics as centered around the notion of substance25 —Russell held that a ‘bundle theory’ of substance would have been the only coherent ontological counterpart of the complete concept doctrine. Pursuing decidedly this track, Robert Yost did not refrain from attributing a kindred bundle theory to the historical Leibniz himself.26 For his own part, Strawson in his Individuals27 argued that the Leibnizian individuation via complete concepts can be made coherent only at the price of assimilating an individual to the corresponding concept. Leibniz’s individuating conditions, in fact, would match well with an ontology of concepts, not of particulars. In this sense, Leibniz’s monadology would represent the most extreme attempt at giving an ontological framework in purely general terms (something analogous to Quine’s attempts to parse away singular terms), and it would be open to the criticism Kant moved in his Amphiboly to the possibility of a purely conceptual individuation. For these interpretations, the identity of indiscernibles works as a crucial test. Exactly as, in present-day discussions, a bundle theory stands or falls with the necessity of that principle, so the possibility of ascribing to Leibniz such a reductionist trend is bound to the answer one gives to the question, whether he regards his famous principle as one holding in all possible worlds, or as a contingent one, dependent on God’s will. Beside commitment to the necessity of the IdInd, another objection which is usually raised to bundle theories (or, on the semantic level, to descriptivist theories of proper names) relies just on the unpalatable consequence that all true statements about an individual would result in being analytic truths. But this is precisely the thesis Leibniz seems to be willing to endorse and from which my questioning stemmed. Also the IndId, therefore, could be seen as a clue alluding to an underpinning bundle theoretical approach. 25

26

27

Not only in 1686, notice. Think of his defence of the philosophical fruitfulness of substance against Locke’s criticism of the ‘bare substratum’, in NE II ch. 23. See R. Yost, Leibniz and Philosophical Analysis, Univ. of California Publ. In Philosophy, Berkeley and Los Angeles, 1954. P.F. Strawson, Individuals, London, Methuen, 1957, ch. IV, Monads.

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My general hypothesis is that Leibniz, on the contrary, was well aware of the need to draw an accurate distinction between the individual and the related concept, or the bundle of its properties, and he was eager to maintain it within his ‘logical’ substance theory. Some interpreters have stressed, in recent years, the need to distinguish conceptual containment from ontological predication in Leibniz.28 I will try to show the parallel development of these two dimensions of predication and truth, which are not blurred nor detached by Leibniz. To understand their connection correctly, we need to grasp his original way of reconciling concept and thing. Finally, we need to explain his final commitment to a ‘conceptual’ individuation of substances, despite this attention to the thing-concept distinction. The implicit adherence to a qualitativist ontology could also work as a motivation for embracing a Lewisian-style theory of individuation. The primacy of quality, which amounts to the absolute submission of numerical identity to indiscernibility, can be applied also to the transtemporal case; in Lewis’s words: “this [counterfactual] sameness is no more a literal identity than the sameness between you today and you tomorrow.”29 In present-day debates, the acceptance of TWI from the modal viewpoint mainly corresponds to a traditional view of temporal persistence, while the counterpart theoretical approach matches well with the substitution of the traditional ‘continuant’ by a construction built from temporal parts. Leibniz’s asymmetric handling of counterfactual and transtemporal identity seems to imply a corresponding stance at the level of ontological options, insofar as it would match well with a rather traditional view of continuant on one hand, and with a qualitativist approach to modal individuation on the other. Things are more complicated, however. The passages where Leibniz seems to share a reductionist (if we prefer, a constructivist) attitude to substance, or at least to seriously contemplate its possibility, are to be found precisely within the context of analyses of transtemporal identity and change, indeed. On the other hand, we could also find passages where, from the modal point of view, Leibniz envisages the construction of possible worlds through counterfactual variations of the actual one. True, one might suppose that this approach reflects only the point of view of our finite knowledge. In any case, the ontology 28

29

I am thinking in particular to H. Burkhardt, Skizze der Leibnizschen Theorie der Pr¨a¨ dikation, in Theoria cum Praxi. Akten des III. Int. Leibniz-Kongr., Stuttgart, Steiner 1980, vol. 3, 89–93; K. Clatterbaugh, Leibniz’s Theory of Individual Accidents, Stuttgart, Steiner, 1973; M. Mugnai, Leibniz’s Theory of Relations, Stuttgart, Steiner, 1992. For the tension between the two dimensions, see also C.D. Broad, Leibniz’s Predicate-in-Notion Principle and some of its alleged consequences, in Theoria 1949, 54–70. D. Lewis, Counterpart Theory and Quantified Modal Logic, Journal of philosophy 65, 1968, p. 115.

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INTRODUCTION

implied by the complete concept view and related theses about identity should be not taken too much for granted. Leibniz seems to move, rather, on the boundary between two alternative and internally coherent clusters of interrelated ontological intuitions. Anyway, both a qualitativist ontology and a theory of subject intended as a ‘bare substratum’ or ‘bare particular’ are bound to the impossibility to provide an adequate basis for de re modal claims. Aristotelian essentialism, on the contrary, provides such a basis at the cost of holding that the world is built of individuals-with-properties, and some properties are on a quite different ontological level from others, insofar as they identify what the individual is. But this was precisely the work done in the Categories model by sortals or ‘second substances’ and by the first way of predication i.e. the relation of being-said-of as distinguished from that of ‘being-in’: that is, by these elements in the Categories account that have been left out in the Leibnizian reshaping. Thus, it remains uncertain whether Leibniz’s indisputable profession of ‘superessentialism’ is to be intended as an extreme strengthening of the essentialist claim, or rather as a consequence of its weakening. The risk of anachronism always lurking in this type of consideration, and Leibniz’s anxiety of connecting his ideas to the most traditional ones, should not obscure, in my opinion, how much his attempt at rethinking substance was really unprejudiced and problematic. What has been evoked so far is sufficient to confirm how Leibniz is an exceptional fellow-traveller for people engaged in the substance debate in the analytical tradition. But this, and the questions raised about his commitment to an essentialist substance theory, can be appreciated and, respectively, answered only in the historical background of an age when such problems were radically debated. The search for a new theory of substance, putting the old Aristotelian idea on a new basis, has to be understood in the background of the giants’ paradigm battle I have alluded to above, that is to say, nothing less than a deep rethinking of the conceptual framework governing the relationship of things, concepts and language. This is the story I will try and tell in the following pages.

Part I The Genesis of a Complete Being

Section 1 Individuals and Concepts at the Origins of Leibniz’s Project Chapter 1. A World of Individuals: Particularist Ontology The first writings of the young Leibniz—the two dissertations De Principio Individui (1663) and De Arte Combinatoria (1666)—emblematically represent, at the very beginning of his career, two constantly present though apparently divergent trains of thought, which are both deeply entrenched in his mind: on the one hand, the imperative of being faithful to concrete things, hence of acknowledging only individuals as the true constituents of the world; on the other, the project of a conceptual analysis aimed at isolating the ultimate elements of our knowledge, in order to reconstruct the systematic building of science and reality. In this section, I try to point out some aspects of these seminal intuitions and to show how the problem of the individual subject emerges at the boundary between particularist ontology and universal conceptual analysis.1 1

This double inspiration was happily expressed by the title of D. Mahnke’s work Leibnizens Synthese von Individualmetaphysik und Universalmathematik, Halle 1923. I will reconstruct the development of Leibniz’s ideas under a particular perspective—the working out of the ontology of complete being. For a wider genetical study on Leibniz’s metaphysics see now— after the pioneering work of Willy Kabitz, Die Philosophie des jungen Leibniz, Heidelberg 1909, and the valuable works of Francesco Piro, V Varietas identitate compensata. Studio sulla fformazione della metafisica di Leibniz, Napoli: Bibliopolis 1990, and Catherine Wilson, Leibniz’s metaphysics: A Historical and Comparative Study, Princeton: Princeton Univ. Pr., 1989—the book of Christia Mercer, Leibniz’s metaphysics. Its Origins and Development, Cambridge Un. Pr, 2001.

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The Particularist Claim: Nominalistic Heritage and the Search for Concrete Things His 1670 preface to the new edition of the Italian humanist Nizolius’s work De veris pricipiis gives Leibniz, among other things, the occasion for a critical assessment of nominalism, a doctrine which Nizolius was explicitly committed to. Leibniz firstly sketches a concise historical survey, reconstructing the constant leading thread of a nominalistic attitude through its different stages: first and foremost the medieval one, which culminates in William Ockham, and represents, in Leibniz’s view, the greatest achievement W of Scholastic thought; then the Renaissance, represented by Nizolius himself, when nominalistic weapons are applied to dispel the conceptual framework of w the same Scholastic tradition. Finally, all pioneers of seventeenth-century new science and philosophy are seen as inclined to nominalism, which matches well with their scientific purposes. The prominent exponent of the third stage is Thomas Hobbes, who is labeled and criticized as ‘ultra-nominalist’, however, for the conventionalist drift of his nominalism. The common content underlying such different philosophical styles is reduced by Leibniz to a principle of ontological parsimony: Nominalists are those who are committed to the existence of singular substances only, taking all the rest for mere names; hence, they do away with the alleged reality of any abstract or universal item.2

The core thesis of ‘nominalism’ is identified here with a decided ‘Particularist Claim’: all that exists (or can exist) is particular. In a particularist ontology, there is no room for universal or abstract items, which are to be accounted for as ways of speaking (names), or at most ways of thinking (concepts) about particulars. If we were to make explicit what the intension of ‘particular’ is, I suspect that two ideas would prevail, coming from the traditional understanding of ‘singular substance’ in the line of Aristotle’s Categories and of our intuitions about ordinary objects: (a) the incapacity of having many instances, which marks their distance from universals; (b) the attitude of existing separately from whatever else, which marks their opposition to abstract items. Now, this ontological core of nominalistic attitude—as distinguished from conventionalist developments, and leaving aside the further problem of the linguistic vs. conceptualist interpretation of universal and abstract terms—is highly praised by Leibniz, as being in tune with his aim of achieving a reform of science and philosophy. What is more: the stages of his brief historical 2

Dissertatio Praeliminaris, A VI.2, 427 (GP IV 15).

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survey could be read as a way of rethinking his own intellectual development, retracing a unitary inspiration through apparently divergent influences and styles of thought. On one hand, ‘humanistic’ and ‘scientific’ nominalism are at the center of the selfsame Preface, through the reception and critical assessment of Nizolius’s and Hobbes’s theses; on the other, the influence of the oldest stage of the same tradition can be traced back to Leibniz’s Scholastic dissertation of 1663. I will make some remarks about the presence of the ‘Particularist Thesis’ in this first writing of Leibniz. “Tota sua entitate”: Individualism without Individuation? Leibniz’s juvenile thesis on the principle of individuation could hardly be neglected, obviously, by anyone who is interested in understanding his mature ideas about individuals; at the same time, one should be a bit cautious in evaluating a seventeen-year old undergraduate’s exercise (how precocious he surely was!). I think, indeed, that the Scholastic arguments of the Disputatio are taken sometimes too seriously at their face value by interpreters. The point I want to make is not one of immaturity, however. Also the fact that Leibniz’s handling of some problems is, from the point of view of the Scholastic debate, roughly oversimplified, points in my opinion in another direction. I cannot enter here into the intricacies of Leibniz’s discussion and its possible sources. I limit myself to drawing attention to the wider context, so far rather neglected, which is constituted by his teacher Jakob Thomasius’s Preface and by the w Corollaries Leibniz himself draws from his own thesis. As he was accustomed to, Thomasius presents us an historical outline of the problem of individuation. The first aspect I wish to emphasize is his general assessment of the question discussed—one of the most debated in late Scholastic thought—as “more subtle than necessary”. In this perspective, the thesis defended by his pupil—an individual is individuated by its whole entity (‘tota entitate’)—is praised as “the simplest and truest” precisely because it gets rid of the problem.3 On the whole, the dispute is likely to be meant by him almost as an exercise of deconstruction of the Scholastic framework 3

See J. Thomasius, Origo controversiae de principio individuationis (Preface to the Disputatio), A VI.1, 5–8. For a study on Leibniz’s Disputatio, see L. McCullough, Leibniz on Individuals and Individuation. The Persistence of Premodern Ideas in Modern Philosophy, Dordrecht-Boston-London, Kluwer, 1996. McCullough emphasizes the relevance of the Disputatio for Leibniz’s mature theses much more than I am ready to do. For a more sober evaluation, see R. Ariew, Leibniz’s Metaphysical Disputation on the Principle of Individuation: A Scholastic Exercise. In Nihil sine ratione. Akten des VII Leibniz-Kongr. Berlin 2001, 33–40. See also T. Hoffmann “Individuation bei Johannes Duns Scoto und Gottfried Wilhelm Leibniz. Medioevo. Rivista di storia della filosofia medievale, 24 (1998), 31–87.

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from within, that is by using the conceptual tools and methods offered by the Scholastic tradition itself, in particular in its nominalist variety. From the historical point of view, indeed, Leibniz’s solution—literally, the same that is endorsed in the most important available treatise on individuation, Suarez’s Fifth Metaphysical Disputation—is explicitly connected by Thomasius with F the nominalistic approach. Hence, it is meant to be equivalent to the intuition that every individual is such by itself (a seipso individuatur). The point is a straightforward one: within the frame of a particularist ontology, the problem of the so-called ‘principle of individuation’ does not really arise. This question, on the contrary, urges for a ‘realist’ ontology which allows for universal items like properties or essences, and goes on further to construe individuals from them. If we accept only particulars in the furniture of world, however, there is no point in asking about what makes them particular. From this perspective, it is the universal aspect of thought and language, if anything, which stands in need of an explanation. Endorsing the ‘tota entitate’ solution in this vein can rightly be considered—and, as a matter of fact, seems to be considered by Thomasius—as a way of answering the disputed question about a ‘principle of individuation’ simply by dissolving it.4 This reading is confirmed by the choice of authorities in Leibniz’s Disputatio, which w provides a seminal suggestion for the philosophical genealogy we find seven years later in the Preface to Nizolius, i.e. in a frankly anti-Scholastic text. In Suarez also, notice, we find the Particularist Claim in one of its classic formulations: “it must be said that all things that are actual beings or that exist or can exist immediately, are singular and individual.”5 Suarez, however, is far from drawing (or, at least, from emphasizing) the related radical consequences for the individuation problem. Also the different order of exposition could be linked to this different attitude. In Suarez’s F Fifth Disputatio, the section (I) devoted to the extension of individuality—hence to the establishing of the Particularist Claim—is followed by a long and decisive section (II) concerning its intension: what being an individual means, and what being an individual does add to the features which are common to many. In this context the great Scotistic, nominalistic and Thomistic models are discussed. 4

5

This is why a Scotistic-inclined author like Fonseca warned that the thesis of the nominalists was not a possible answer to the individuation problem, but rather a preliminary obstacle to be removed to simply pose the relevant question. Suarez, Disp. Met. V V, sec. 1 § 4, transl. G. Gracia, Suarez on Individuation, Ithaca, Cornell Univ. Press, 1982, p. 32. For the relationship with Suarez of Leibniz’s Disputatio see J.F. Courtine, Le principe d’individuation chez Suarez et chez Leibniz, in A. Heinekamp (ed.), Leibniz et la Renaissance, W Wiesbaden, Steiner, 1983, 174–184; I. Angelelli, The Scholastic Background of Modern Philosophy: Entitas and Individuation in Leibniz, in J. Gracia, Individuation in Scholasticism, 535–42.

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Only thereafter (sections III–VI), Suarez occupies himself with the ‘real’ (or ‘physical’) problem of the ‘principle of individuation’ (that is, of the cause of individuality) which constitutes, instead, the whole subject of Leibniz’s discussion. This might simply be a thematic restriction, actually presupposing Suarez’s partition. The shifting of the discussion of Scotus’s position, however, is an interesting clue. According to Scotus, the intelligibility of the individual requires that one is able to distinguish within it two aspects: common nature on one hand, i.e. what is common to other individuals belonging to the same species, individual w difference on the other, which constitutes precisely its individuality. The latter is the famous ‘thisness’ or haecceity (haecceitas). The individuating role of thisness, however, can be understood only within the whole of Scotus’s ontology, which is labeled in Leibniz’s Disputatio as an extremely realistic one. This ontology, in fact, admits within one and the same concrete thing a lot of entities, the so-called formalities (f (formalitates), which are separable only in thought, while being nevertheless different prior to the mind’s act. Common nature and haecceity are just two examples of formalities. In order to hold this ontology, Scotus elaborates the conceptual tool of ‘formal distinction’, an intermediate one between real distinction and ‘distinction of reason’—the former holding between two separable things, or real constituents of a thing, and the latter between items which are distinguished only by an act of the mind. Now, Scotus’s haecceity was discussed by Suarez entirely within the context of his section (II). Although Suarez rejects formal distinction and translates it into a conceptual one (a distinctio rationis), he does admit, on this conceptual level, some ‘metaphysical’ composition from common elements and individual difference. In this way, he saves the core of Scotus’s intention as something belonging to the data of the individuation problem; and, though endorsing the main ontological theses of nominalists, he parts company with them because he does not consider that problem as an ultimately senseless one. Leibniz devotes some important sections of his discussion to a sharp criticism of formal distinction. While concentrating on the ‘physical’ or ‘real’ problem of individuation, he shifts to it the handling of Scotus’s position. This is discussed and refuted as a particular answer to the individuation problem, whose plausibility is entirely defeated together with the ontology of formal disw tinction: “If we do not concede a formal distinction, haecceity is destroyed. But the former is the case,”6 he insists. The haecceity solution is rejected 6

For Leibniz’s criticism to haecceity, see Disp. De Princ. Ind., §§ 16–25, A VI.1, 15–18 (GP IV 23–26). For an analysis of Ockham’s criticism to Scotus’s theory of distinctions, see M. McCord Adams, Ockham on Identity and Distinction, Franciscan Studies, 36, 1976, 5-74.

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precisely as the most sophisticated attempt at attributing individuation to a component, hence to a part—be t it a purely conceptual one—instead of to the whole of individual being. A final remark on this: the later occurrence of “haecceity” in the Discourse could be read, on the contrary, as an echo of the general (neutral, so to speak) usage of the term for which Suarez’s discussion paved the way, and which Leibniz left aside in his youthful work. I am thinking of “haecceity” intended as the conceptual constituent of individuality, which could even coincide, in reality, with the whole being. To sum up: in the 1663 Disputatio, some elements of the Suarezian model are displaced in tune with Thomasius’s deflationary interest, so that the fundamental ontological option for particularism is freed from Suarez’s ecleptycal concessions to the worries and exigences of a realistic point of view. Matter, Angels and Haecceity: At the Origins of Leibniz’s Topoi on Individuation In his introductory historical reconstruction, Thomasius rather surprisingly locates the origins of the question of individuation within an ontological scenario which is determined by the Greek idea of a material principle coeternal to God, all other things being a mixture of matter and pure form. According to Leibniz’s teacher, the Thomistic thesis of individuation through matter, locating itself in that progeny, is unsatisfactory, especially from the point of view of a ‘Christian philosophy’; not counting the drawback of being a solution just limited to material substances. Interestingly enough, also the related idea that all immaterial beings are specifically different—that is, the complementary Thomistic view, which the mature Leibniz often refers to with approval and extends to all individuals—is severely criticized by Thomasius. Among other things, it would be the origin of a controversial opinion (here attributed to Scotus), where also human souls are specifically distinct one from another. Needless to say, Thomasius’s reconstruction is far from being historically tenable; nevertheless, it has enormous interest for the better understanding of some schemes and suggestions which surely acted on the development of Leibniz’s thought. In my introduction, I have called attention on the references to Scotus’s haecceity on one hand, and to Aquinas’s angelic individuation on the other, that are to be found in the Discourse. Rather than supporting the idea of a proper influence of those historical sources, they are all the more interesting as symbols of highly idealized conceptual alternatives; and Thomasius’s usage of these historical materials surely constitutes an important source behind Leibniz’s later references. In the 1663 disputation, one can guess a sort of division of labor between teacher and student: whereas Thomasius’s criticism concentrates itself on

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the Aristotelian-Thomistic individuation through matter, Leibniz’s discussion leaves aside this solution, precisely on the ground that it is not a general one, and devotes most effort to the criticism of Scotistic haecceity. Once again, the suggestions coming from Thomasius’s historical sketch further determine Leibniz’s use (and distortion) of the Suarezian framework. Suarez’s complex architecture gradually shifted from material substances to a general, all-embracing solution, fitting for all finite beings. In Leibniz, instead, the claim for a general solution is posed directly from the start, in order to exclude the consideration of individuation through matter. What about the side of Thomistic doctrine concerning immaterial beings? Suarez aimed at showing that this opinion finally coincided with a particular case of his tota entitate solution. At the same time, his understanding of the doctrine was significantly different from the original one of Aquinas. For the latter, the doctrine concerning angels depends on the idea that matter is the principle of individuation. Accordingly, the essence of immaterial beings is not, properly speaking, their principle of individuation, because we have not here any individuation at all. Suarez on the contrary shows how the entity of immaterial beings works precisely as an individuation principle. The subsuming of the ‘special’ theory of immaterial individuation under the ‘tota entitate’ rule is made possible here by the extension to immaterial beings of the Particularist Claim. That is to say, angelic essence, insofar as it is something real—apt to exist, and actually existing—is individual. At the same time, also in this case it is possible to distinguish conceptually essence as such from its individuality. For his own part, Leibniz in the Discourse will present his own theory of complete concept as a generalization of the Thomistic doctrine of angels. What is worth noting, however, is that he appeals precisely not to the Suarezian reading, but rather to the original Thomistic sense: individuals are treated as Aquinas’s angels, just because they are to be considered as ‘species infimae’. The difference of attitude from Suarez on this point strikes the eye, if one considers how Suarez keeps numerical diversity distinct from discernibility: for him, immaterial substances “are said to be distinguished by themselves, not because they are not similar, but because one is not from itself the other; for similarity does not exclude distinction.”7 Leibniz, on the contrary, will employ the Thomistic reference to illustrate his own IdInd. I leave these remarks open: like the former ones, they confirm the complex relationship of continuity/discontinuity between the first Leibnizian account concerning individuals, with their presumed Scholastic models, and the mature one.

7

Suarez, Disp. Met. V, sec. VI, § 18, Gracia 136.

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“Essentiae rerum sunt sicut numeri” So far, I have used Thomasius’s Preface to test the deep insights of Leibniz’s Disputatio. Now, w I wish briefly to focus my attention on some of its Corollaries. The modern reader is likely to be puzzled by a set of theses which at first sight do not seem to have any immediate link with the subject of disputation. In effect, we should not think of ‘corollaries’ in the technical sense of deductive consequences. Nevertheless, I am persuaded that the main thesis defended in the disputation and these theses (or many of them) form a sufficiently organic w whole. The first two corollaries are concerned with material beings: I) Matter possesses for its own part an ‘entitative act’ (a technical expression for the ffact of having being); II) It is far from unlikely that matter and quantity are really one and the same.8 What kind of connection could we guess between these theses and the Disputatio ontology? I put forward a conjectural line of reasoning, starting from the defeat of realistic ontology which is confirmed by the whole Disputatio. Although Leibniz’s general discussion does carefully abstract from the distinction of material/immaterial substance, one can divine some repercussions on the matter-form composite. The Particularist Claim implies that the only real unity is the individual one: every real constituent of being is individual through and through, and there is in reality no room for any kind of diminished unity. Now, in the tradition of Aristotelian hylemorphism, form was the element which gave to the composite, and to matter itself, their ‘actuality’, conferring both unity and being on them. But this amounts to saying that the constituents of substance, like matter and form, are somehow re-identified by belonging to substance itself. If one insists, however, that every real element must have its individual and determinate unity, such a view becomes problematic, insofar as matter will have its being and unity from itself. Note that corollaries I and II echo those developments in Scholastic concepts which made room, beyond the hylemorphic view, for matter as it came to be considered by the science of the ‘moderns’. The alternative to the holistic view above cannot help being a ‘combinatorial’ view, where the whole is the sum of its parts: therefore, the identity of a complex substance will be wholly defined by its constituents. The ‘tota entitate’ solution of Leibniz’s Disputatio, then, would work as a general rule, posing two types of constraints on individuation theses: a) as concerns a complex substance, we get its individuation through the sum of its constituents; b) as concerns each single constituent, or a non-complex substance, they are self-individuated. It is in relation to case (a), I believe, that we have to 8

See Disp. De Princ. Ind., Corollaria, A VI.1, 18 (GP IV 26).

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understand the at first sight rather mysterious Corollary III: “The essences of things are similar to numbers.”9 We are faced here with a traditional maxim, whose canonical source lies in the Metaphysics, Book 8, where Aristotle draws w the comparison between essences (and related definitions) and numbers. As Aquinas explains in his commentary, numbers, for any as small addition or subtraction, do change their species . . . Accordingly, essences and definitions for whatever variation (addition or subtraction) do change specifically.10

Though being complex, essence works as something indivisible, insofar as every addition or subtraction destroys its identity, replacing it with another essence. The comparison is closely bound also to the thesis about the specific distinction of immaterial substances: a difference pertaining to forms determines a change in specific essence; this is why, angels (as pure forms) are similar to numbers as regards their diversity.11 It is worth noting that the comparison used Platonic elements, going back to the theories of Ideas-Numbers. This remote Platonic root could explain the fortune of the dictum also among Renaissance and seventeenth-century authors interested in Pythagorean-style metaphysics, like Mersenne. The underlying idea—a variation on the ‘great chain of being’—is that of a combinatorial rule for the production of beings, which determines a series or ordered hierarchy of essences. When opening w up his path through the Scholastic forest, Leibniz is already under the influence of such suggestions. In any case, the combinatorial idea expressed by the dictum works as a principle of mereological essentialism; where this label designates the doctrine, according to which each part of a whole is necessary for its identification. Once again, however, the exact metaphysical import of this form of essentialism depends on which sort of constituents are admitted. So, we should not hasten to read here a sort of individuation through qualities, in a word a discernibility claim. Again, the tradition reserved the number comparison for essences lying at the specific level. The fact that it is stated at 9

10 11

“Essentiae rerum sunt sicut numeri”, ibidem. For the contrast between a combinatorial and a holistic view of substance, see T. Scaltsas, Substances and Universals in Aristotle’s Metaphysics, Ithaca-London, Cornell Univ. Pr., 1994. Aquinas, In Metaph. § 1723, ed. Marietti 472. As Aquinas puts it: “as concerns beings which are separated from matter, they cannot be distinguished except according to their species. Different species, however, are constituted according to different grades; hence they are similar to numbers, whose species are diversified through the addition and subtraction of unity.”, Quaest. Disp. De Anima, art. 3. In another passage, Aquinas insists on the fact that species possess an order per se, contrary to individuals. See Quaest. de Spirit. Creat., art. 8.

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the end of a discussion devoted to individuals might incline to the idea that Leibniz has, instead, individual essences in mind. The matter, however, is far from being crystal clear. It is also far from clear whether accidents are taken into account, which will be a crucial point for Leibniz’s later ‘superessentialism’. The field of disputation is expressly limited to the individuation of substances; only the last point takes into account the problem of accidents, in the context of an argument against haecceity. From haecceity—Leibniz argues in a very compressed manner—one cannot explain the production of individual accidents, whereas the ‘tota entitate’ solution does the job, “because there are dispow sitions of matter to form.”12 The suggestion is rather cryptic; the talk about some “dispositions to form” alludes to the intensive debate about the genesis of form, hence to other intra-Scholastic conceptual developments which put under pressure the hylemorphic scheme. In his F Fifth Disputation, Suarez devoted no less than two sections to the topic of individual accidents. He rejected the traditional thesis which attributed their individuation to the substance they belong to. Accidents, like everything else, are individuated through themselves. On the contrary, Leibniz’s brief remark seems to suggest some close dependence of individual accidents on the constituents of the individual substance. A Suarezian Way to Superessentialism? If we wish to indulge in the slightly risky exercise of looking for some trace of this Scholastic framework—or, more precisely, for some trace of Suarezian influence—in Leibniz’s mature philosophy, perhaps we should look in a rather different direction than the simple proposition of the ‘tota entitate’ claim. One of the opinions refuted by Leibniz in the Disputatio identified the principle of individuation with the existence of the thing. Leibniz’s criticism divides into two parts: a) if existence differs only conceptually from essence, then the opinion falls into the ‘tota entitate’ solution, because essence turns out to be the principle of individuation; b) hence, the opinion has a full sense only if we admit a real distinction between essence and existence. But this is not the case, and Leibniz’s argument concentrates on proving it. We find the same dichotomy in Section V of Suarez’s text, which is also devoted to the existence solution. In dealing with the alternative (b), however, Suarez does not attack its premise (the essence/existence distinction), but he concedes it, for the sake of discussion, and goes further to argue against the existence solution. This is his first argument: 12

Disp. De Princ. Ind., § 26, A VI.1, 18 (GP IV 26).

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First . . . because essence rremaining within the realm of essence is made individual, and the specific essence is contracted and determined in it . . . The major is evident, because specific, that is, essential differences accrue to the species by a necessary connection, according to which propositions in which essential predicates are predicated are said to be perpetually true; and so (likewise), its individual difference accrues to the individual. Hence, it is as necessary for Peter to be this man, as to be a man, and it is as necessary for Peter to be placed under man, as it is for man to be under animal. Therefore, this contraction and subordination is not caused by actual existence, which comes contingently to the fully constituted and individuated essence.13

In order to show that a thing is already fully individuated at the level of essence, that is of its possible being, Suarez exploits a modal feature of essential attribution, i.e. its perpetual and necessary character. And he does not hesitate to consider individual features as essential in this sense, as specific and generic features are. Contingency affects only the existence of the (necessarily) fully determinate individual essence. In the 1663 Disputatio there is no trace of a Leibnizian reception of this line of thought. Objectively, however, it has much more to do with Leibniz’s later theses about individual concept than the tota entitate thesis.

Chapter 2. A World of Concepts: Combinatorial Science and the Individual Conceptual Atomism: The Combinatorial Claim and the Search for the Simple “Consider that almost all that exists or can be conceived of is composed of parts, the latter being real or at least conceptual . . .”14 : the far-reaching applications of the mathematical doctrine of combinations in the De arte combinatoria (from now: DAC) open with a straightforward statement of the historically recurrent ‘myth of analysis’. Some pages later, the imperative of analysis will find its limit, which is also the completion it needs in order to accomplish its epistemological task: that there are simple elements, this 13 14

Suarez, Disp. Met. V, sec. 5 § 3, Gracia 114. DAC, Usus of Problems I and II, A VI.1, 177 (GP IV 44).

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is a fundamental requirement of the whole combinatorial project.15 If the Particularist Claim considered the world as an aggregate of individuals, and engaged us in the search for concrete elements, the Combinatorial Claim—a powerful postulate of analytical intelligibility—urges us to look for the simple. Leibniz seems to be committed to a version of logical, or better of conceptual atomism, working as a regulative idea for his inquiry. This is the background for his dream of an ideal language, where the descriptive part of the alphabet should correspond to the set of simple terms, often called the “alphabet of human thoughts” (alphabetum cogitationum humanarum). He never gave up his search for the “catalogue of first notions”: moreover, he vigorously took up this attempt in correspondence with every successive phase of intensive logical production. The question I would like to raise here is, whether and how the metaphysical assumptions of this conceptual atomism do harmonize with the particularist ontology evoked above. From an historical point of view, one is left with the apparent contrast between the two inspirations: nominalistic tradition on one hand, and a Lullistic-Pythagorean mathesis of essences on the other, which could be well expressed by the dictum “essentiae rerum sunt sicut numeri.”16 This contrast, however, is to a large extent only apparent: far from constituting two objectively divergent, or at best merely juxtaposed directions, the ‘conceptual-combinatorial’ and the ‘particularist’ approaches are in Leibniz’s mind, from the very beginning, the two mutually integrating sides of an entire project—although they are still in need of more satisfying integration. We will be able to understand this, if we abandon the idea that these aspects are the merely passive legacy of Lullistic metaphysics or, respectively, Scholastic training. On the contrary, these suggestions and styles of thought are consciously used by the young Leibniz, already in his early dissertations, for sketching a research project which somehow strives—with all its archaic traits—at locating itself within the area of the ‘modern’ renewal of philosophy. Thus, Leibniz in the DAC, while acknowledging his historical debt to Lullistic ideas, is willing to distance himself from the inadequate conceptual analyses to be found in that tradition.17 Just at this point, where 15

16

17

“Our analysis runs as follows: given a term, it will be resolved into its formal parts, i.e. it will be substituted by its definition; parts, then, will be in their turn resolved into their own parts, i.e. the terms of the definitions will be substituted by their respective definitions, and so on, until simple parts or indefinable terms are reached.” DAC § 64, A VI.1 194–195 (GP IV 64–65). For this historical background of Leibniz’s combinatorial project, see Paolo Rossi, The Twisted Roots of Leibniz’s Characteristica, in The Leibniz Renaissance. Firenze: Olschky, T 1989, 271–289. DAC § 60, A VI.1, 193 (GP IV 63).

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he is programmatically introducing his own version of combinatorics, he relies on Hobbes’s dictum about thought conceived of as a calculus. Now, the theory of the De Corpore—whose influence on the DAC is not confined to that suggestion—is really an outstanding example of how the model of an analytical-synthetic universal science of concepts could well coexist with the Particularist Claim. The comparison with it will be useful to understand the Leibnizian framework for concepts and things in the period 1666–1670. “Foecundus in abstrahendo”. From the Porphyrian Tree to the Alphabet of Differences As a matter of fact, the logical, ontological and epistemological theory of the De Corpore is a complex and stratified whole, where different and even contrasting strands of thought are brilliantly pursued without always finding a satisfying synthesis. In particular, the vindication of a rigorous nominalism, taking universals as mere words, is accompanied by strong conceptualist motifs. In any case, Hobbes is well aware that the universal science of (concepts and/or) names is superimposed in a highly problematic manner on a basic physicalist ontology of particular bodies. Now, I do not think that Leibniz for his own part, when sketching his mathesis of concepts, does profess some wholly uncritical Platonism. Rather both philosphers, endorsing an ontology w of individuals, are faced with the abstraction problem, the classic one for particularist theorists; and both try to solve it in a different manner than Scholastic tradition does. Some remarks from the DAC support the view that Leibniz is consciously operating at an abstract level, and eager to avoid conceptual reification; and this worry seems to retain some echo of Hobbes’s lesson. This is the case with the concise ontological foundation of mathesis opening the DAC: Metaphysics . . . deals with being and with the affections of being as well. Just as the affections of a natural body are not themselves bodies, however, so the affections of a being are not beings.18

Talking about the “body’s affections” is likely to be a hidden reference to T Hobbes’s ontology. Of course, his crude physicalist language (corpus) is translated into the more abstract one of a general ontology (ens). Treating names of accidents as names of things (bodies) is one of the most dangerous categorial 18

A VI.1, 170 (GP IV 35; L 76). Also the following sketchy categorial scheme reflects the worries of an anti-realist ontology: “Clearly neither Quality nor Quantity nor Relations are Beings. . . ” (ibidem).

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mistakes Hobbes denounces in his theory of semantic fallacies. Again, in the DAC we find a favorable reference to this analysis: From the complexions which are possible, Hobbes holds that only homogeneous terms can combine together. If this is the case, and it really is—given that also common philosophy holds that abstract and concrete terms, accident and substance, primary and secondary notions are incorrectly predicated reciprocally—then it will be very useful to the art of inventing propositions, that is to say to the choice of useful combinations among the multitude of things.19

In order to fully appreciate this point, we should briefly consider the impact of the combinatorial approach on the traditional categorial order. According to one of Leibniz’s autobiographical remarks, the first stimulus toward the combinatorial project was given him by the desire to extend the traditional table of categories. In this perspective, the search for simple terms is the search for the most general ‘‘predicamenta’. Starting from the class of simple concepts, then, each class of complex concepts is determined by the grade of complexity of its members, or by the number of simple concepts within each of them. This hierarchy of complexity, however, seems to ignore any difference of types of entities: all concepts are homogeneous, and their relations are simply of inclusion. The approval for Hobbes’s distinction of semantic types contrasts with this levelling of terms, showing Leibniz’s interest in making room for a categorial articulation within the combinatorial constitution of concepts. At the same time, he observes that “among primitive terms we count not only (terms of) things, but also of modes or relations.”20 Besides connecting different types of entities (such as accidents and substances) with the relation of ‘being-in’, the traditional categorial doctrine ordered the entities belonging to each type according to the relation of ‘beingsaid-of’. In the tradition stemming from the commentaries on Aristotle’s Categories, the last order was commonly identified with the figure of the “Porphyrian Tree”. According to this well-known model, concepts are hierarchically ordered, within each category, from the highest genus to the lowest species, passing through the intermediate ones. Descending the tree, concepts increase their content, while having less extension. Traditionally, conceptual 19

20

DAC § 16, A VI.1, 178 (GP IV 46). For Hobbes’s thesis, see De Corpore, Chapter 5, OL I 51–52. DAC § 66, A VI.1, 195 (GP IV 65). Later, within the example of first geometrical concepts, Leibniz notes: “Because here we do not start from the absolutely first terms, we need to introduce some signs, in order to signify the grammatical cases of words and other connections necessary to discourse.”, DAC § 87, A VI.1, 199-200 (GP IV 70).

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trees were held to reflect the ontological structure of reality, articulated in the essences of natural kinds. During the great paradigm struggle of the seventeenth century, however, these classifications—though commonly used in logic and generally in learning—were closely questioned for their ontological and epistemological value. Also on this, Hobbes’s criticism was one of the most radical. In the final paragraphs of the chapter On Names of De Corpore, he takes care to notice that such classifications of names are not to be taken too seriously.21 In the DAC, the combinatorial doctrine is applied to the traditional problem of the classification of concepts, the so-called ‘division’. We are asked here to find all lower species moving down within a given genus and using a fixed set of conceptual differences; or to find the intermediate species moving up from a given set of ultimate ones. Now, our mind is indeed so prolific in abstracting, that whichever things be given, surely it is able to find a genus, that is a concept which is common to them and only to them.22

This explains—he continues—“the enormous variety of subalternate genera”, causing in its turn the fact that different authors, confronting the common task of constructing the tables of divisions, . . . actually follow quite different ways, ending up nevertheless with the same lowest species.23

The ‘enormous variety’ of the possible classifications of things involves a sort of conceptual relativity, with the effect of troubling the Porphyrian order. This is threatened also by another, apparently harmless shift. In the context of the combinatorial construction of concepts, genus g and differentia are perfectly interchangeable: ‘animal’ can be considered a differentia of ‘rational’, as well as ‘rational’ a differentia of ‘animal’. Practically, this amounts to saying that genera are differences, and their combination does not follow a linear and univocal subordination, such as was represented by the Porphyrian hierarchies.24 21

22 23 24

“Nobody should think, that the schemes above are exhibited by me as the true and certain ordering of names; such an order cannot indeed be established except through a perfectly developed philosophy.” (OL I 25). A true categorial scheme, hence, is not a senseless one, but it needs the achievement of natural philosophy. DAC § 53, A VI.1, 192 (GP IV 61). Ibidem. For this explosion of the Porphyrian order, see Eco: “what we used to consider genera and species are only names which label groupings of differences; . . . the tree can be

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Thus, the combinatorial division no longer prospects a tree, but rather an alphabet of differences. Also this idea that knowing things means knowing their differences was shared both by Platonic-Lullistic and empiricistically minded authors, such as, respectively, Bisterfeld or Gassendi. A first objective constraint shows itself, however. Using differences interchangeably, we can obtain a lot of intermediate species, along different lines of increasing complexion (or division), but we are left in the end with the same set of lowest species. The new hierarchy, therefore, is wholly relativized, except for its basis of infimae species and for the opposite extreme of simple concepts. Also the selection of the intermediate species, however, is not a wholly arbitrary combinatorial game, but it hooks onto reality: Even if our mind does not find the common genus, God or angels will know it; therefore a foundation f of all these abstractions will pre-exist.25

To sum up: a) our concepts are the result of an act of abstraction of our mind, which obeys, however, some objective constraint (Leibniz uses the vocabulary w of ‘finding’); hence, b) even if we do not grasp any similarity between things, conceptualization can be performed by some other mind, or by God himself; c) the act of God is anything but arbitrary, having an ontological correlate in things. A Leibnizian note to Nizolius indicates his debt to Hobbes for the notion of abstraction.26 The reference to God’s mind, instead, is a move that— while not being available to Hobbes—was open to theistic nominalists. Thus, w Leibniz shifts onto divine ideas the epistemological burden which realists attributed to universals within things. Remember Corollary IV of the 1663 Disputatio, according to which “essences are eternal only in God”. Point (c) alludes to the Scholastic concept of ‘‘fundamentum in re’, according to which every conceptual distinction or likeness, ontologically weakened as it w may be, nevertheless has to be grounded, at risk of resulting fully devoid of sense, on some ontological basis within the thing itself. This constraint on explanation, notice, was commonly accepted also by authors who held an anti-realistic point of view. The language of ‘fundatum ‘ in re’ is, as such, still largely neutral with respect to the realism/nominalism opposition. So, the ‘foundation’ of universal items could simply allude to the fact of resemblance between the particulars themselves, without further relying on the presence in them of a common element.

25 26

always reorganized according to different hierarchical relations among the differences,” L’antiporfirio, in P.A. P Rovatti-G. Vattimo (eds.), Il pensiero debole, Milan: Feltrinelli 1983, 68-69. A VI.1, 192 (GP IV 61). “Hobbes has thaught that ‘to abstract’, taken in a good sense, means nothing but to consider one thing, without considering another one.” Notes to Nizolius, A VI.2, 464.

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At the Root of Porphyrian Tree: Individuals as the Ultimate Species? The basis of logical division, though deeply rearranged in the combinatorial game, is always constituted by the ‘infimae species’. In the tradition of the Isagoge, the expression indicates the lowest position in the hierarchy of predicables: the ‘species specialissimae’ are the endpoint of classificatory activity. Another Greek expression for these species—‘
toma ε dh’—claims atomicity for them: not, of course, as real indivisibility, nor as conceptual simplicity, but in the sense that they cannot be further divided into more determined sub-species. Below, there are individuals; the latter, however, remain outside the system of ‘universals’, i.e. of collecting and classifying concepts. On the other hand, individuals are, according to the Categories, the basic blocks of ontological building. But what do we find, then, at the root of the Porphyrian tree? Some uncertainty lurks in the tradition. Porphyry himself, after stopping the logical descent before reaching individuals, went further to treat the individual in the section devoted to species. At the time of Leibniz, among Schoolmen the debate was still alive about the legitimacy of treating ‘individual’ as a sixth ‘predicable’. In any case, this consideration of individual was seen as a ‘logical’ one, properly bearing on the concept of individual. This was the ‘logical meaning’ of ‘individual’ that Leibniz excluded at the start of his Disputatio, in order to concentrate his attention on the real individual as considered by metaphysics. In this ‘logical’ meaning, the individual has a place (to be sure, as a limiting case) within the system of concepts. How is this logical place circumscribed in the tradition? The Isagoge offers a double answer: the (logical) individual is a) what is able to be predicated of a thing only—i.e. of itself; b) what further pursues the determination of the thing beyond the specific level, by giving of it a uniquely definite description: “Socrates”, “this white man”, and “this one approaching”, for example the son of Sophroniscus, if Socrates were his only son, are held to be individuals . . . They are called individuals because each of them is composed of a collection of properties which can never be the same for another; for the properties of Socrates could not be the same for any other particular man.27 27

In the original statement of Isagoge the ‘logical’ and ‘metaphysical’ sense were not clearly distinguished, of course. It has been rightly observed that in this context the acception of ‘individual’ seems to be a logical one. See J. Gracia, Introduction to the Problem of Individuation in the Early Middle Ages, ch. 1, Munich: Philosophia Verlag,1987.

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The Porphyrian text is highly suggestive for a modern reader, because it approaches the theme of individuality through considering indexical devices and definite descriptions. A Leibnizian scholar can be impressed by this kind of discernibility statement, though expressed in a rather ambiguous form: it is not at all clear whether the identifying force is given by all the properties taken together, or by one or more of them being uniquely exemplified. Traditionally, the definite character of description was associated with some predicates belonging to certain standard loci: place, time and so on. In any case, the theme of identifying description—where the epistemological dimension is stressed— seems to be bound to the Porphyrian-Boethian tradition of Isagoge, hence to the ‘logical’ approach to individual within the theory of predicables; on the contrary, it was conspicuously absent from the metaphysical individuation problem, as handled in the Disputatio. Now, an anti-realistic reading of the system of predicables, doing without ‘second substances’, i.e. genera and species, exactly as it deprived the metaphysical individuation problem of sense, tends also to disqualify the intermediate grades of that ‘logical’ framework, and to level them out on individuals. The young Leibniz was well acquainted with a kindred attempt—if not when he wrote the DAC, a few years later. I am thinking of Nizolius’s resolute claim that individuals themselves are the infimae species. Nizolius’s attitude to the whole Scholastic theory of predicables is, as usual for him, harshly negative. w In the background, there is his nominalistically minded destruction of the ontological role of ‘second substances’, reduced to collecting linguistic devices. In this context, Nizolius launches his vigorous attack against the lower limitation of Porphyry’s tree. According to him, ‘genus’ is every concept which is further specifiable, whereas the name of ‘species’ in its strict (logical) sense should be reserved for fully determined concepts, that do not have inferiors.28 It is worth noting that the denial of multiplicity below these true lowest species entails the denial of the notion of a purely numerical distinction, which is felt as meaningless.29 Leibniz limits himself to observing that Nizolius’s opinion about lowest species is shared by some authors, Gassendi being the best known among them. Given that he annotates accurately his points of disagreement from 28

29

“The label of ‘species specialissima’ does not belong to the species of man or horse, but to singular men and singular horses, as well as to individuals of the other species, this distinction only being granted: ‘man,’ ‘horse’ and kindred items are intrinsical, essential and divisible species; ‘Trojan,’ ‘Thebanus,’ ‘ancient,’ ‘modern’ and so on, are extrinsic and accidental species, and divisible as well; individuals, finally, are indivisible and specialissimae species. . .” Nizolius, De veriis principiis et vera ratione philosophandi contra pseudophilosophos, Roma, Bocca 1956. Book I, ch. 5, 59–68. Book II, ch. 2, 140. ““All which differs, differs specifically or generically . . . hence all individuals differ specifically and not numerically.” De veris principiis, B. II, ch.2, 144.

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Nizolius, should we think that in this case he endorses the opinion of the Italian humanist, which is literally in tune with some of his own later statements? Perhaps, the combinatorial approach might lead him in this direction, the individuating description being the culminating point of the complexion of differences. Or, by contrast, could we guess that Thomasius’s old hostility against the idea of specific differences among individuals still operates behind his cautious attitude? In my opinion, a key for understanding Leibniz’s reluctance to accept Nizolius’s suggestion lies, rather, in his different evaluation of the epistemological significance of individuals. Beyond the Limits of Combinatorics: Singular Proposition The distance between the real basis of the Porphyrian tree (the individual substances) and the logical one (the species infimae) covered a more puzzling tension within the Aristotelian view. Individuals, indeed, are the basis of Aristotle’s ontology, while being somehow excluded from his epistemology. In the Isagoge, renouncing to descend below ultimate species is coherent with the prohibition of making science of individuals as such.30 In an anti-realistic reading, such tension threatens to become intolerable. Rejecting real universals, the plausible ontological correlate for universal knowledge, one is left with the alternative of giving up science itself, or of deeply modifying the model of scientific enterprise. Nizolius resolutely took the second alternative: according to him, science does not concern universals, but is directly about individuals.31 Needless to say, his sharp vindication of the individual’s role as lowest species matches well with this overthrow of the Aristotelian prohibition, and with the desire to fill the gap between particularist ontology and epistemology. On the contrary, the particularist Hobbes is persuaded of the universal and necessary status of scientific knowledge, and of the possibility of having this, though rejecting realistic ontology and allowing himself only the resources of an austere nominalism. One of Leibniz’s main aims in discussing Nizolius is to take a position on this epistemological contrast. He stands unequivocally on the side of Hobbes, though refusing the latter’s main strategy, i.e. conventionalism. Already in the DAC—where the construction of complex concepts starting from simpler ones provides the ‘matter’ for propositions—he ranges himself under the Aristotelian-Hobbesian view of the universality of scientific knowledge, when 30

31

“Individuals, which are below the lowest species,are infinite. It is for this reason that Plato . . . says to leave the infinite individuals alone, for there can be no science.” Isagoge, On Species, transl. Warren 1975, 39-40 (modified). I say ‘directly,’ because Nizolius vehemently criticizes every abstraction procedure; for him, the object of universal consideration is nothing but the collective set (or mereological sum?) of individuals.

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discussing singular propositions. Sections 83–84 sound like a rude awakening from the pure logical dream of universal combinatorics—or at least as the emergence of an unsurpassable limit. They are worth quoting at length: One should bear in mind that this combinatory art (ars complicatoria) is wholly applied to theorems, i.e. to the propositions which belong to eternal truths, that is to say, which do not depend on God’s free will, but on His nature. All singular propositions, indeed, like the historical ones— for instance, Augustus was emperor of Rome—or the observations—i.e., general propositions whose truth is not grounded on essence, but on existence—are true almost by chance, or for God’s will; for instance: all grown-up Europeans have knowledge of God. Of these propositions, there is no demonstration, but only induction . . . To this kind of observation belong all particular propositions which are not converse or subalternate of universal ones. Hence it is clear, why it is said that singular propositions do not have demonstration, and why the very profound Aristotle posed the loci of arguments in Topics T ,w where propositions are contingent and proofs are probable, whereas there is only one locus for demonstration: definition. When something is predicated of something else, without being deduced from the intimate nature of the latter—for instance, that Christ was born in Bethlehem—nobody will rely on definitions; history, on the contrary, will provide matter and occasions for remembering.32

Singular propositions do not belong to the field of demonstrative knowledge, and not just insofar as they have individual subjects: one class of general propositions—the empirical ones—is excluded as well. Terminology and criteria for this partition reveal a double source. At first, again, Hobbes’s model, who, at the very beginning of the De Corpore, draws a sharp distinction w between scientific knowledge—consisting in the system of deductive knowledge, or of ‘theorems’—and the ‘historical’ (i.e., empirical, or factual) one. As concerns the inner characterization of the two types of knowledge, and their modal status, reference is made to the Scholastic framework of a ‘divine epistemology’, i.e. to the doctrine about God’s knowledge and its different objects. For the time being, it is enough to stress that ‘historical’ truths cannot be drawn from definitions,33 because there are properly no definitions of individuals as such. Singular propositions lie outside the scope of the ‘complicatory art’, indeed, because their subject lies, in its turn, outside it: the individual’s concept cannot be constructed through the ‘complication’ of general traits. Thus, the Porphyrian tradition did not provide us with a definition, but at most 32 33

DAC §§ 83–84, A VI.1, 199 (GP IV 69–70). Leibniz’s metaphor alludes to the ontological depth of the thing itself: “drawn from the entrails of a thing.”

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with a description of the individual, relying on circumstances which are already individual: the standard examples, remember, used indexical devices or definite descriptions containing other proper names (‘son of Sophroniscus’). Given this, the move of § 84 seems reasonable, where (echoing some of Bisterfeld’s suggestions)34 the treatment of the singular proposition is shifted from conceptual combinatorics to the study of the ‘relations of being with being’. The logical space of individual, then, is not circumscribed by the combinatorial framework of conceptual differences, but by the factual one of contingent relations. The study of these relations will give us the new Topics T , suitable for arguing about facts involving individuals. The exclusion of the concept of the individual from combinatorial construction could help understanding that (and why) Leibniz would not be sympathetic to Nizolius’s proposal to treat the individual as the lowest species. On the other hand, it is quite clear that the exclusion of the singular proposition from the domain of combinatorial science is by no means determined by some privileged logical role it would play, as is the case in modern logic. On the contrary, the singular proposition continues to be handled, in the most traditional way, a simply as a limiting case of those quantified categorical propositions that constitute the main subject matter of Aristotelian logic and the test for the combinatorial account of truth. In the section of the DAC dedicated to syllogistic theory, indeed, Leibniz devotes § 24 to defend the current assimilation of the singular proposition to the universal one. Now, this simple fact seems to be in blatant contrast with the exclusion, in § 83, of the self-same singular proposition from the combinatorial theory. I think that this is not the case; on the contrary, I will show that the treatment of singular proposition within the syllogistic theory confirms that exclusion. Once acquainted with a singular proposition like “Socrates is the son of Sophroniscus”, we can use it well in a syllogism and take it, from the point of view of quantity, as a universal one. But it can hardly be considered a definition, and has not been constructed by merely combinatorial means. In order to show the equivalence of singular and universal proposition, Leibniz avails himself of a particular kind of logical paraphrase, which he borrows from a logician of his time: The proposition: “Socrates is the son of Sophroniscus”, if it is paraphrased according to the analysis of Johannes Raue, will read as: “Whoever is Socrates, this is son of Sophroniscus.”35 34

35

For the reference to Bisterfeld, see DAC § 85, A VI.1, 199 (GP IV 70). On Bisterfeld, see Mugnai, Der Begriff der Harmonie als metaphysische Grundlage der Logik und Kombinatorik bei Johann Heinrich Bisterfeld und Leibniz, Studia Leibnitiana 5/1, 1973, 43–73. DAC § 24, A VI.1, 182–83 (GP IV 50–51).

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Through the paraphrase, the universal quantifier is introduced into the proposition. But this was not the main innovation of Raue’s approach. To better evaluate the significance of Leibniz’s move, we should turn to a short work of two years later, which relies precisely on this place of the DAC and presents Raue’s analysis as the decisive logical tool for solving some far-reaching problems.

Chapter 3. Abstraction and Predication: At the Boundary of Concepts and Things A Piece of Trinitarian Logic: Predication and Distinctions So far, I have considered side by side, within Leibniz’s youthful philosophical projects, the framework of a particularist ontology on one hand, and the combinatorial system of concepts on the other. The phenomenon of predication determines a space where the two perspectives have to meet, maybe also to mix with one another. Two years after the DAC, Leibniz engages himself in a rational defense of Trinitarian dogmas against the attacks of a Socinian author, J. Wissowatij. The T title of Leibniz’s theological writing announces that the orthodox view will be vindicated through the aid of some “new logical discoveries,” and reference is explicitly made to the DAC.36 The logical weapon invoked is nothing but the analysis of predication inspired by Raue. The theological connection should be hardly surprising. Not only predication, but almost all topics I am dealing with in this research—identity, individuality, substance, relation—had been intensively developed from their Aristotelian or Neo-Platonic origins, during many centuries of Scholastic reflexion, for the sake of articulating the Trinitarian doctrine. Also Scotus’s theory of formal distinction was directed, T among other things, to spell out the relation of identity and distinction within the Trinitarian God. Wissowatij’s objections, on the contrary, are formulated from the viewpoint of a rigorous assertion of the principle of indiscernibility of identicals. So, for instance, if not all attributes of the Father are predicable of the Son—or, if ‘Son’ and ‘Father’ are not mutually substitutable in all contexts without loss of truth—then it seems to be impossible to claim that they are a unique substance. 36

Defensio Trinitatis contra Wissowatium, A VI.1, 518–530 (GP IV 111–125). On Leibniz and Trinitarian dogma, see M.R. Antognazza, Trinit` T T ta e incarnazione. Il rapporto tra filosofia e teologia rivelata nel pensiero di Leibniz, Milan 1999.

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Let me briefly consider the analysis of predication Leibniz relies on to answer most objections. According to Raue, ordinary propositions conceal their true logical form. In his paraphrase, both subject and predicate terms reveal an inner predicative structure: subject S becomes ‘is-qui est-S’ and predicate P ‘is-qui est-P’. The true copula of the proposition turns out to be the tie connecting these two complex elements, that is the third and most important ‘est’: ‘(is-qui est-S) est (is-qui est-P)’. The family air with Fregean analysis is intriguing. Both subject term and predicate term, in fact, are shifted to a predicative position (though they continue to be distinguished as ‘subject’ and ‘predicate’), and attributed to a ‘third common item’, which plays a role comparable to that of variables in modern quantified logic. Angelelli—to whom we owe most information about Raue37 —points out, however, that the w logical value of the principal copula is likely to be intended by Raue more as an identity relation between the two pronominal occurrences, than as a class-inclusion. Bearing all this in mind, I come to Leibniz’s use of this logical machinery. He is eager to reserve Raue’s treatment only for one type of universal proposition: I put forward in general, that the copulae in the premises of syllogisms are commonly not conceived of correctly. Propositions per se and per accidens should be distinguished, however. So, we simply say correctly: “Every man is rational”, but we do not say correctly: “Every man is white”, also if this turned out to be true, because whiteness does not w pertain immediately to humanity. Rather one should say: “whoever is a man, he is white”. Similarly, one should not say: “every musician is white”, but “whoever is a musician, he is white.”38 w

Leibniz is trying to capture the difference between a universal proposition which holds on purely conceptual grounds and one which, as a matter of fact, w happens to be true—exactly as was the case with the accidental generalizations of DAC § 83. Raue’s ‘deep’ analysis—in itself, neutral to the distinction—is taken to be appropriate to express the second type of proposition, presumably because it makes clear that we are not concerned with a purely conceptual (or intensional) relationship. If this reading is correct, the DAC application of the same analysis to singular proposition comes out to confirm, contrary to appearances, the assimilation of the latter to the universal accidental one, which DAC § 83 excluded from the scope of combinatorics. Leibniz, therefore, w feels the need of two different theories of predication and proposition: an intensional one on one hand, which is perfectly adequate for concepts (termini) 37

38

See I. Angelelli, On Johannes Raue’s Logic, in I. Marchlewitz-A. Heinekamp, Leibniz’s Auseinandersetzung mit Vorg¨ gangern und Zeitgenossen, Stuttgart 1990, 104–109. g¨ A VI.1, 520, note (GP IV 118).

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and their combinatorial treatment; and an extensional one on the other, which takes into account the reference to individuals.39 With regard to the theological use of Raue’s tool in the replies to Wissowatij, W I want to stress only the general line and some interesting applications. I have said that the Socinian objections mainly emphasized the violations to the Indiscernibility of Identicals. Now, the new analysis of predication allows Leibniz to call attention to what we would call a referential use of terms (or descriptions); in this way, some inferences are blocked, which would hold only for intensions. In this context we find—to my knowledge, for the first time— Leibniz’s example of ‘triangle’ and ‘trilateral’, which will often occur in the semantic reflections of his mature thinking.40 In another reply, Leibniz goes on to affirm that even disparate notions—that is, concepts having nothing in common—can be referred to the selfsame thing. The underlying idea is to neutralize contradictory predication by reduplicative devices, where the different intensional aspects receive a mereological interpretation.41 Now, the strategy of conceding robust intensional distinctions within extensional identity recalls Scotus’s ‘formalistic’ approach. Terminology apart, the need of a fundamentum in re seems to be more marked than in the notes to Nizolius: “One cannot say, that God is so strictly one, that within Him could not be found any really separate item (i.e., separate before the mind’s operation).”42 Every approach to predication, which intends to save 39

40

41

42

See on this the analysis of G. Nuchelmans, JJudgment and Proposition. From Descartes to Kant. North-Holland, 1983: ch. 11, 214–232. Here, he construes a blatantly fallacious syllogism, working as a counterexample to an objection based, as usual, on the alleged failure of substitutivity: “Every Trilateral has as its immediate abstract Trilinearity; Triangle has not as its immediate abstract Trilinearity (it has rather Triangularity as its immediate abstract; and if Triangularity were immediately the same as Trilinearity, then also ‘angleness’ and ‘lineness’ would be the same, being what remains once threeness is left aside. But angleness and lineness are not indeed the w same, because two lines can also be without an angle, e.g. parallels). Therefore, the Triangle is not the Trilateral, which is absurd.” And now Leibniz’s solution, by an application of Raue’s analysis: “the major premise has to be formulated in the following way:‘All that is trilinear has as its immediate abstract trilinearity’. But the major premise so formulated should be denied. The Triangle indeed is nothing but the Trilateral, but nevertheless it has not Trilinearity as its immediate concept.”A VI.1, 522, note (GP IV 120). “I plainly deny, that disparate terms cannot be predicated either of each other, or of a third thing; provided that we observe what I said about the copula . . . it can happen, that one says correctly: something which is iron (for a part), is wood (for a part); something which is soul (for a part), is body (for a part).” A VI.1, 523, note (GP IV 121). This real distinction is labeled as a ‘formal’ one, reduced in its turn to one of ‘ratio r ratiocinata’: “Being formally distinct, their difference will be one of ‘ratio r ratiocinata’; but this difference will have a foundation in the thing, hence within God there will be three really distinct foundations.” A VI.1, 526 (GP IV 123).

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its foundation in reality—ultimately, to save the mirroring of reality in our language—is faced with Scotus’s shadow. At the same time, however, Leibniz’s conceptualism remains hostile to realistic commitments. The general semantic consequence he immediately draws from his example of triangle/trilateral is interesting in this respect: If we apply this principle, we can abstain from all the boring rules of Schoolmen about suppositio.43

The theory of suppositio was used by Ockham and his followers as a powerful tool in order to explain the different semantic values of terms, without being committed to realistic assumptions. Leibniz’s example (“‘Animal is a genus’ is not a universal proposition: that which is animal is not a genus, indeed”) shows that the theory becomes superfluous precisely because one of its leading ideas—I mean, the fundamental value of the suppositio personalis (i.e., of the use of words to pick up concrete particulars)—is, so to speak, already incorporated in the new canonical analysis of proposition. Accordingly, abstract reference, or second intentions (“Animal” in ‘Animal is a genus’) are automatically set aside as non-canonical or derivative ways of speaking. What could appear, at first sight, as an implicit revaluation of Scotistic themes—or at least, as the emphasizing of realistic elements within a conceptualist position—is still tied to an anti-realistic reading of predication. Using Raue’s analysis, Leibniz aims at substituting both the realistic move of giving referential value to abstract terms, and the opposite nominalistic strategy of distinguishing the semantic value of a term in different contexts. Instead of them, we have the introduction of a systematic distinction between the thing on one part and the concepts on the other. But in order to fully appreciate the significance of this move, we have to reconsider the whole problem of predication, as it was consigned to Leibniz by the ontological tradition and its reformers.44 The Breakdown of the Ontological Square and the Nominalistic Account of Proposition In a standard realistic reading of predication, the substance or thing is designated by the subject term, and some ‘predicative entity’ by the predicate term. This ontological account was modeled on the ‘predication square’ from chapter 2 of Aristotle’s Categories, constructed around the two relations of 43 44

A VI.1, 522 (GP IV 120). For the early-modern Scholastic background, see L. Hickman, Modern Theories of Higher Level Predicates, Munich: Philosophia, 1980.

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‘being-said-of’ and ‘being-in’, which determined the particular/universal and substance/accident pairs and their crossing: (1) Universal Substance said of a subject not in a subject man, animal (3) Particular Substance not said of a subject not in a subject Socrates

(2) Universal Accident said of a subject inhering in a subject white, color (4) Particular Accident not said of a subject inhering in a subject this white

The main point of nominalistic critique was to deny that any real item corresponds to places (1) and (2) of the scheme. As a consequence, nominalists were bound to give an account of predication which does not avail itself of these ‘predicated things’—hence to sharply distinguish logico-linguistic predication from any ontological relation. In medieval nominalism, predication turned out to be a relation holding among signs (the ‘terms’ of Ockhamistic tradition, embracing both concepts and names). The link with reality was granted by the semantic relation which each of these signs entertains with individuals in the world. This relation, in its turn, was fundamentally that of suppositio (‘to stand for’), whose basic canonical form was ‘personal supposition’: in modern jargon, the denotative relation between a term and concrete individual things. It is important to note that this type of suppositio was common both to subject- and predicate terms. This reading allowed accounting for the relation between language and reality, without making any reference to those fictitious ‘predicative entities’ which had been wiped out by the criticism to realistic ontology. The related account for the truth conditions of a proposition has been dubbed as ‘identity theory’ or ‘two-name theory’. Although these labels are surely reductive for Ockham’s well-developed extensional semantics, they seem indeed to fit for Hobbes’s much less sophisticated account in chapter III of the De Corpore (I call it ‘account A’).45 In this view, by uttering “A is B”, a speaker is committed to the truth of the following sentence: (i) “ ‘A’ A and ‘B’ are two names which stand for the same thing(s).” The copula is interpreted as a relation of coreferentiality holding between two names, which 45

EW I.3.2. Analogously at OL I 27. Hobbes (like Nizolius and then Leibniz himself) has practically lost the contact with the tradition of suppositio. See on this H. Weidemann, “Scholasticorum taediosa circa suppositiones praecepta.” Leibniz und die Problematik der ffur Geschichte der Philosophie, 73 (1991), 243– Suppositionstheorie Ockhams, in Archiv f¨ 260.

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denote the same item(s). Subject term and predicate term are handled on a par, their semantic difference being completely effaced. Hobbes gives also a formulation in terms of ‘containment’: (i’) “ the name ‘A’ is contained in the name ‘B’,” which strikingly recalls Leibniz’s later ‘containment theory’: “The first name is usually called subject, or antecedent, or contained; whereas the latter is called predicate, or consequent, or container.”46 Differently from Leibniz, however, Hobbes’s containment (of subject within the predicate) has to be understood in an extensional sense: (i”) “the things which ‘A’ stands for are included among the things which ‘B’ stands for.” In the following, however, an unmistakable intensional reading of containment is put forward, when Hobbes deals with necessary propositions. w In any case, that extensional account of predication would be in agreement with the claims of an austere nominalistic ontology, allowing itself only concrete particular things as extra-linguistic items, to which the expressions of language refer. We should be cautious, however, in connecting univocally a certain semantic analysis with a determinate ontology. To give the truth conditions for sentences in the language of the identity theory—i.e., to say that a sentence is true iff subject and predicate terms stand for the same things—is not peculiar to the nominalistic approach. For instance, the Thomistic tradition (professing a moderate realism) adopted the same formula, only emphasizing that the terms are identical insofar as the thing concerned is the same (or as concerns the ‘praedicatio ‘ materialis’), whereas they differ insofar as the way a of conceiving is concerned.47 This implies rejecting the restriction of the canonical signification relation to denotation and making room for a semantic distinction between the roles of subject- and predicate terms. Conversely, the latter distinction is to be found also in Hobbes, the nominalist, as I will show in the following. From r Predication Theory to Linguistic Therapy: Hobbes, Leibniz and Abstract Terms In that same chapter III of the De Corpore, we find a slightly different perspective on predication (I label it ‘account B’), which can be seen as a complementary one to that of the so-called ‘identity theory’. This line of thought is pursued in the context of a reflection on the third element of proposition—the copula—and on the related topic of abstract reference. I dwell on this analysis, because it will turn out to be a cornerstone for Leibniz’s own handling of 46 47

OL I 27. See J. Trentman, Predication and Universals in Vincent Ferrer’s Logic, Franciscan Studies, 28, 1968, 47-62.

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predication. Hobbes transfers the handling of abstract terms from the chapter on names to the chapter on proposition, because they depend on the former operation of compounding concrete names through predication to form sentences. More precisely, they owe their origin to the copula ‘est’48 : ‘whiteness’, w ‘justice’, or ‘humanity’ are equivalent to ‘to be white’, ‘to be just’, or ‘to be human.’ On the whole, this account is tied to the conceptualist strand of his philosophy of logic: “Abstract names denote the cause of the corresponding concrete name, and not directly the thing.”49 Hobbes, on one hand, concedes an autonomous semantic role to abstract terms of the F-ness form—according to their stated equivalence with the ‘to-be-F’ forms—distinguishing them from the corresponding concrete nouns; on the other, he is keen, by this very fact, to deny them a properly referential function: they do not ‘name’ anything, but rather they signify a way of being. He is well aware that these linguistic items encourage the undue reification of fictitious entities, typical of bad metaphysics.50 This, however, is only a misleading drift in the correct use of a valuable linguistic device. Abstract terms in their substantival form are required, precisely in order to achieve the ideal of thought as calculus: that is to say, to isolate the aspects of things our scientific activity is interested in, and to manipulate them within the computatio.51 It is now time to move to Leibniz’s reception of this theory of abstract terms, in his Preface to Nizolius. The Preface conforms to a cultural strategy, one of whose central moves is the reform of philosophical style, assuming ordinary language as the clarity standard. So, ontological realism is now dispelled also through linguistic analysis. What is worth noting is that Leibniz professes an even more radical reductionist attitude than his Hobbesian model. The epistemological value of abstract talk, which Hobbes acknowledged, is explicitly denied; Leibniz admits its usage only in ordinary, loose language, as an economical expressive device, but he systematically prefers the adjectival form (calidus) to the substantival one (calor), the latter being in his opinion 48

49 50

51

“. . . because if there were no sentence, from whose copula they arise, there would be no abstract name”, OL I 29. OL I 29. “The abuse of abstract terms consists in this: seeing that it is possible to consider the increasing and diminishing of some accidents, without considering the related subjects or bodies . . . some people speak of accidents as if they could be separated from all bodies.”, OL I 30. “The positive use of abstract terms consists in the fact that without them we are simply unable to reason, that is to compute the properties of bodies. Assume that we want to add, divide, subtract color, light, or velocity: if we were to add or multiply them by using their concrete names, saying that the colored or the warm, or the bright, or the moved is double, we would not duplicate the properties, but the bodies themselves, which are warm, or bright or moved . . . ” , OL I 29–30.

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unnecessary and misleading. From this perspective, Hobbes figures, with a slightly curious effect, as a supporter of abstractions: If . . . anyone wants to give a perfect exposition of the elements of philosophy, he must abstain from abstract terms almost entirely. I do recall that the penetrating Hobbes ascribes some usefulness to abstract terms, by the argument that it is one thing, for example, to double some hot object, quite another to double heat. But this duplication of heat can itself be expressed in concrete terms, for if I say that the same thing has been made twice as hot, or that the effect by which the heat is measured is double, everyone will understand that it was not the hot thing but the heat that was doubled.52

Inherence The semantic analysis of abstract reference—more or less eliminativist as it may be—does not exhaust the ontological problem of predication. Hobbes’s account (B) prolongs itself, through the causal-explanatory value of abstract terms, into the problem of the real basis of the activity of conceptualizing: The causes of names . . . are the same as the causes of our concepts, that is to say some power or action of the conceived thing, or some modes of things, as some people usually say, or accidents.53

I have talked above about an ‘austere nominalistic ontology’ which would provide the basis for a purely extensional account of predication, grounded on the semantic primacy of denotation. This was an oversimplification, however: Ockham himself admitted, besides things, also qualities in his ontological inventory. Accordingly, his semantics made room for a relation of connotation: terms like ‘white’ have the double semantic function of denoting white things and connoting qualities. These are individual accidents, standing in relation of ‘inherence’ with respect to individual substance. This ontological relation should not be mistaken for the semantic one of predication. Nevertheless, 52

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A VI.2, 417 (GP IV 147; L 126 modified). Such a radical semantic devaluation of abstracta is coherent with Leibniz’s apparent interest in Hobbes’s criticism of the copula est: “It should be remarked, what Thomas Hobbes acutely as usually observed: for those people—such as many Eastern nations are—which usually omit of expressing the verb ‘to be’, the most part of Scholastic philosophy cannot absolutely (or at most very difficult) be expressed; while those people being nevertheless no less than other apt to philosophizing, and their languages being rich and developed in what concerns the expression of real knowledge,” A VI.2, 415 (GP IV 145). OL I 29.

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the inherence of individual accidents works as the ‘fundamentum ‘ in re’ of predication. Hobbes is very puzzled by accidents. His tentative definition oscillates between a phenomenistic reading (mode of appearing) and a more robust one, pointing to the ‘fundamentum ‘ in re’ of an appearence: practically, to the corresponding dispositional fact in the thing.54 Even in this respect, Leibniz seems to be more austere: the phenomenistic reading of accident is clearly privileged in the Preface, going together with the subsumption of the accident under the categorial heading of ‘Relation’: Concrete things are really things; abstractions are not things but modes of things. But modes are usually nothing but the relations of a thing to the understanding, or phenomenal capacities.55

It is also worth noting that in the same text Leibniz denounces the terminology of ‘inherence’ as a case of undue usage of metaphorical language in philosophy.56 Anyway: Hobbes and Leibniz (exactly as the other seventeenth-century ‘reformers’ of philosophy) prefer to speak of ‘mode’, rather than ‘accident’, and this reflects their purpose of weakening the ontological autonomy of ‘real’ accident with respect to the thing. Hobbes’s inquiry about accidents concludes in chapter 8 of the De Corpore with a physicalist reinterpretation of the substance-accident pair, where the role of ‘substance’ is filled by ‘body’. His perplexity about the ontological status of accident redoubles in the trouble he runs into in his attempt to define the relation of “being-in”. This attempt will be further pursued by Leibniz. In the Aristotelian definition of inesse, in Categories 2—“the accident is within the subject not as a part, but in such a way, that it can be subtracted without the loss of subject”—Hobbes emphasizes the need to distinguish the inesse relation from the part-whole one. This is in agreement with his wish to deny a real distinction within the thing; but it makes the task very hard of providing a physicalist reinterpretation for the inesse. The job seems to go better with the subject: the body is the ‘suppositum’ we are ultimately talking about in our predication acts. This relies not so much on the semantic tradition of suppositio, as rather on the idea of suppositum as a substratum opposed to properties (think of ‘material’ predication in the Thomistic tradition); and also on the new phenomenistic sense of an entity we are not directly acquainted with, but we infer by reason. Anyway, in this physicalist translation the subject 54

55 56

“a mode of the body, according to which it is conceived of; which amounts to saying, a power of body through which it impresses a concept of itself on our mind.”, OL I 91. Diss. Prael. to Nizolius’s edition, A VI.2, 417 (GP IV 147; L 126). See Ibidem.

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turns out to be matter. The correlate of this is the practical demolition of the whole essentialistic framework: something unheard of even in the nominalistic w tradition. This hidden collapse of essentialistic ontology has a semantic trace I go on to consider now. The Substantive/Adjective Distinction and the Oblivion of Essence While Hobbes insists on the concrete/abstract pair, Nizolius privileges the grammatical distinctions of substantive/adjective and proper/common noun, to draw out the ontological articulation of things and ways of being— practically, to reinterpret the predication square, saving its ‘particularist’ side. Thus, the substantive/adjective distinction would reflect that of thing (substance) and quality.57 In the case of Hobbes, instead, the neglecting of the substantive/adjective distinction is apparent in the fact that he handles absolutely on a par ‘being white’ and ‘being a man’, both expressing transient ways of being of the body;58 nor does Hobbes apply to ‘white’ the tool of connotative signification, as Ockham did. This implies the loss of a central intuition of Aristotelian essentialism, according to which some items (roughly speaking, our ‘sortals’ for natural kinds) are attributed to the privileged ousia-category, insofar as they are apt to answer the ‘what is?’ question; whereas items in the category of quality answer the ‘how is?’ question. Leibniz’s attitude on this point is not quite clear. In one of his remarks to Nizolius, he already puts forward the idea which will lead him, in the later papers about characteristica verbalis, to judge the substantive/adjective distinction as philosophically irrelevant. According to him, every adjectival form can be easily turned into a substantival one, because at a deep level they are semantically equivalent. Simply, the substantive implies (‘subintelligit’) the term ‘Ens’ or ‘res’, which in the case of the adjective should be supplied in order to get a substantive.59 The terminology of ‘subintellectio’ seems to be his version of the idea of ‘connotation.’ It is interesting to note, however, that its application has been overturned with respect to the Ockhamistic tradition. No more the ‘form’, in fact, but the thing is said to be ‘connotated,’ i.e. indir rectly referred to. This also could have to do with the modern phenomenistic 57

58 59

Obviously, only particular substances and qualities are admitted, while the corresponding common nouns are meant to designate collective wholes of them. See M. Nizolius, De veriis principiis etc., Book I, ch. 5, 59–68. De Corpore 8, §§ 20–23, OL I 103–105. See Notes to Nizolius, A VI.2, 449. Also the interchangeability of genus and differentia I discussed above, obviously, concurs to this demolition of essence. In the Porphyrian model difference was distinguished from genus because the former is predicated in quid, the latter in quale.

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approach, for which our epistemic access to things is no longer a direct and unproblematic one: we are directly acquainted with properties, from which we can infer an underlying subject.60 Anyway, Leibniz justifies a semantic levelling of terms of the type Hobbes had already put into practice. He does not assume, of course, the physicalist equivalence of the ontological subject of predication with body or matter. Rather, his ‘ens’ as ‘the primitive substantive’ plays a role very similar to the ‘X’ to which both subject- and predicate terms were attributed in the Raue-style analysis of predication. To sum up: Leibniz is led from the Hobbesian account (B), through the usage of Raue’s ideas, to sketch a rather original theory of predication. Contrary to the purely extensional approach of the so-called identity theory, the semantic difference of subject and predicate terms is acknowledged. This difference, however, has somehow been moved away from the terms which constitute proposition. Both subject- and predicate terms, in fact, are semantically equated in a new way, both being just (predicative) terms (i.e. concepts). The crucial difference occurs between these terms taken together, on one hand, and the ontological subject, or ‘thing’, on the other. This is why Leibniz will be able to develop an intensional theory of proposition and truth entirely on the conceptual level, while maintaining, on another level, the ontological dimension of inherence. 60

Remember that for Hobbes, in contrast with Ockham (and Nizolius too!) the fundamental semantic relation holds between word and concept, and no longer between word and thing. This shift surely depends on epistemological grounds (connected with the ‘annihilatory hypothesis’), hence on a change in the conception of what we are directly acquainted with. h Also on this, Leibniz stays on the same side of Hobbes and not of earlier nominalism.

Section 2 Origo Rerum ex Formis The (Onto-)logical Construction of a World from Conceptual Atomism to Individual Substance

Chapter 1. “Mira res, aliud esse subjectum quam formas seu attributa” 1.1. A Rediscovery of Subject The Subject-Forms Asymmetry During the last year of Leibniz’s stay in Paris, many scattered remarks tend to organize themselves, in the so-called P Paris Notes, into the first outline of a philosophical synthesis. Within this context we come across the attempt to identify a set of primitive notions, called ‘simple forms’, which should provide a sort of unified conceptual background both for physics and metaphysics.1 Quite differently from its twentieth-century counterparts, Leibniz’s dreamt-of “logical Aufbau” is, of course, a frankly metaphysical one.2 I would even say ultra-metaphysical, if we consider that it aims at reconstructing the possibility not only of a world, but also, and above all, of God himself. In this enterprise, the problem of predication again comes to the fore. This is especially clear in a text of April 1676, whose title is On Forms, or the Attributes of God: 1 2

For a comprehensive introduction to this series of texts, see Parkinson, Introduction to SR. For an interesting comparison with present-day ‘logical construction of the world,’ see R. Y Leibniz and Philosophical Analysis; more recently, M. Schneider, W Yost, Weltkonstitution durch ¨ logische Analyse. Kritische Uberlegungen zu Leibniz und Carnap, Studia Leibnitiana 1995, 67–84.

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It is a wonderful fact that a subject is different from forms or attributes. This is necessary, because nothing can be said about forms on account of their simplicity; therefore there would be no proposition unless forms were united to a subject. Thought is not duration, but that which thinks is something that endures. And this is the difference between substance and forms. One must see if it is right to say that thought endures, changes, exists; that one motion is greater than another; that there is some ratio of number itself, and of ratio. An attribute of God is any simple form.3

The subject-forms distinction appears here as the object of a true rediscovery. This seems to conflict with the image of a thinker who would be, on one hand, historically dependent on the old substance-property distinction and, on the other, logically bound to efface it. The text could also be puzzling from the viewpoint of the historical reconstruction I have traced so far. Leibniz seems to accept here the viewpoint of a realistic ontology of qualities, for which the main problem is no longer that of abstraction, but the opposite one: how to get a concrete particular, starting from abstract and (presumably) universal items, such as qualities are.4 Should we think that Leibniz’s combinatorial approach leaves aside the ontological precautions of his earlier writings, to reveal a frank Platonic commitment? Terminology itself—talking no longer about terms, but about ‘forms’—could reinforce this suspicion. A somewhat closer look into Leibniz’s ‘forms’ is needed. To say first: a Platonic echo is not to be excluded, insofar as the revaluation of Platonic views is well documented in the P Paris Notes. Leibniz’s forms, however, are not to be looked for in some metaphysical heaven. Rather, they are to be found by exploring the contents of our mind.5 As a matter of fact, Leibniz’s search for simple forms, despite his criticism of Descartes,6 moves within the coordinates of the latter’s project, as this was expressed in his unfinished and unpublished epistemological treatise Rules for the Direction of Mind. At the very heart of that project, we find a theory of ‘simple natures’: each of them being the simple object of an act of intellectual acquaintance, able to be conceived per se. K Keeping in mind the parallelism of the approaches, it is hardly surprising that Leibniz sketches an inventory of forms which—being, 3

4

5

6

A VI. 3, 514 (SR 69). See on this topic Werner Schneiders, “Deus Subjectum. Zur Entwicklung der leibnizschen Metaphysik.” In Leibniz a` Paris. St. Leibn. Suppl. 18 (1978), 20–31. Actually Leibniz’s doubtful final expressions and his comparison to number should warn us that he is aware of the abstract character of these qualities, and of the related problems. “We perceive many things in our mind, such as thinking or perceiving, perceiving oneself, perceiving oneself to be the same, perceiving pleasure and pain, perceiving time or duration.”, On the Origin of Things from Forms, A AVI.3, 518 (SR 75). “Descartes did not carry his analysis to what is most profound, i.e. to primary forms; that is, he did not start from God”, On Truths, Mind, God and the Universe, A VI.3, 508 (SR 57).

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like Descartes’, far from complete—is strongly reminiscent of the latter’s first notions: Thought, Self, Extension, Existence, Duration and so on. The fact that in many places Thought and Extension appear side by side is significant, given that later on Leibniz will sharply criticize the claim that Extension is a primitive notion.7 “On Account of their Simplicity”: Descartes’ and Socrates’ Dreams What is the trouble about predication one is faced with, when working with simple forms? Our text clearly indicates it: “nothing can be said of forms on account of their simplicity; therefore there would be no true proposition unless forms were united to a subject.” The feature of forms which prevents the possibility of talking about them is their logical simplicity—or their atomicity. The way out of the aporia is the adoption of a kind of ontological asymmetry:8 forms are referred to a ‘subject’, the latter being an entity belonging to a quite different ontological type, i.e. not being itself a form. Thus, they are shifted from the role of conceptual atoms to that of ‘attributes’ (“forms or attributes.”) It is worth comparing the passage on predication of On Forms with one of the possibility proofs Leibniz drafted six months later for the improving of the ontological argument on the occasion of his meeting with Spinoza. In A Most Perfect Being Exists,9 the argument runs as follows: (1) Simple forms are undefinable or unanalyzable; (2) every demonstration of a universal proposition is achieved through the analysis of its subject; (3) hence, no universal proposition can be demonstrated of an unanalyzable term (for 2); (4) therefore, only (universal) undemonstrable propositions can be true of unanalyzable terms (for 3); 7

8

9

On Forms presents also a distinction into ‘common’ and mutually excluding forms, parallel to Descartes’ one into ‘special real’ (extension and thought) and ‘common real natures’, like existence or duration: “Extension and thought are certain more special forms. For existence, duration, and so forth are common forms; duration belongs both to that which thinks and to that which is extended. But it is extraordinary that one form should be more special than another. So forms differ in this: that some are more or less relative.”, AVI.3, 513 (SR 69). A similar idea can be found in Plato’s Sophist—a t text of a group which influences Leibniz’s reflection in this period, as we shall see. I take this expression in the sense of the substance-properties (subject-predicate) ‘asymmetry’ studied by Strawson. A VI.3, 575–76 (SR 97).

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(5) but only identical propositions are universal, undemonstrable, true propositions; (6) therefore, universal true propositions having simple forms as their subjects can only be identical (for 1, 4, 5), if true; (7) now, the proposition (P) “A and B cannot be together in the same subject”—where A and B are supposed to stand for some simple forms—if true, surely is a universal necessary proposition; (8) but (P) cannot be demonstrated (for 4); (9) nor can (P) be an identical proposition; (10) hence, (P) cannot be true (for 6, 7, 8, 9); (11) therefore, the opposite of (P) is true: (P’) “for any simple forms A and B, they can be in the same subject”, i.e. they are mutually compatible; (12) hence, all simple forms are compatible, i.e. (12’) a being having all forms (perfections), or a most perfect being is possible. The same feature of forms—conceptual atomicity—which in the April note determined the aporia of predication, in the November proof, on the contrary, becomes the key for solving the compatibility problem. At the same time, this positive use of atomicity/impredicability in steps (7–12) is likely to impress the reader negatively. What about the possibility—one could ask—that in the same framework we try to prove directly the affirmative proposition (P’): “For any simple forms A and B, they can be in the same subject”? For the same reason invoked in (7–9), it will be impossible to prove (P’), hence its opposite will be true. Therefore, the compatibility argument would be liable to a rather obvious retort. Be that as it may, I turn to the “impredicability argument” of steps 1–6, already suggested in a compressed manner in the April text, leaving open, for the time being, the perplexity raised by its use in the wider compatibility proof. The double assumption (2, 5) ruling it is an epistemological one, stating that truths are either demonstrations or identities, and demonstrations are analytic. Clearly enough, this dichotomy holds for universal (or necessary) truths, the only ones which are considered here: we could say, for conceptual truths. This view can be traced back to Leibniz’s reception of the Hobbesian model of science as a chain of definitions. A comparison with Descartes’ simple natures might help here. Descartes’ inaugural dream was the revelation of the framework of simple natures as a series of evidence atoms. Far from being conceptually unrelated items, however, Cartesian natures are bound to enter into a plurality of deductive chains. The well-known ideal of demonstration as a “continuous chain” of intuitions is based precisely on this fact. Descartes insists on the “synthetic” P nature of the link, whose necessity appears to be a semantic one. The Paris

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Notes show Leibniz as engaged in an intensive critical reflection on our cognitive resources. Descartes’ intuitionism does not attract the young thinker ffascinated by formal reasoning and influenced by Hobbes’s lesson. According to him, demonstration is not a chain of intuitions but of definitions: that is to say, a procedure where at each step the definiens is substituted for the definiendum, until an explicit identity is reached. This characterization is given in syntactic terms and aims at providing “mechanical” criteria for checking the validity of a proof. A more pronounced commitment to a form of logical atomism seems to be the natural counterpart to this alternative epistemological development of the theory of first notions: if forms are deprived of any internal complexity or, so to speak, of any reciprocal conceptual need, then an intuitive synthetic linkage among them fails to be a plausible candidate for explaining our deductive reasoning, and this has to be accounted for in terms of substitution. This account of demonstration, however, applies only to complex ideas and not to simple forms themselves. Consider now Leibniz’s brief note to steps (2–3): “Plato noted this [i.e., the impredicability of simple forms] in the Theaetetus w when speaking about ‘elements.’”10 Let me see whether it can shed some light on his train of thought. Bear in mind that in 1676 he was working on the translation of the Theaetetus and Phaedo. Several clues point to the fact that the study of Plato’s middle dialogues is deeply intertwined with his own reflection on the problem of predication. And this is in no way by chance: those dialogues show, among other things, the laborious working out of a theory of predication, moving from an ontology of Forms (better: from the first and paradigmatic ontology of Forms). No doubt, Leibniz’s Theaetetus quotation alludes to the so-called “Socrates’ dream.” The interest of the reference grows, as soon as we realize that the fascinating story Socrates goes on to tell is nothing but the seminal intuition lying behind any combinatorial theory of language and reality. In the margin of his Theaetetus translation, in fact, Leibniz annotates with approval: “This is a very important intuition, provided it is understood correctly.”11 According to this view, reality is composed of a set of “primary elements.” Considered in themselves, they “have no account,” but “each of them can only be named,” whereas “just as the things themselves are woven together, so their names, woven together, come to be an account.”12 It hardly needs to be recalled, how Wittgenstein took this Theaetetus passage as a classic expression for some basic assumptions of logical atomism. Of course, it is tremendously difficult to identify what sort of “simples” Plato had in mind, when sketching 10 11 12

A VI.3, 575 (SR 97). A VI.3, 309 note. See Theaetetus, 201d-202d, transl. J. Mc Dowell, Oxford 1973, 94–95.

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the “dream view,” nor is the task much easier in the case of Wittgenstein. But this does not matter so much—nor does it matter for Leibniz—insofar as the general problem of “talking about simples” is concerned. For Leibniz also, a combinatorial theory in Theaetetus style, to whose basic tenets he is prepared to subscribe, leads to the conclusion that no truth (except identities of the form A = A) can be stated about simple elements. But, then, he is left in a situation which strongly recalls Plato’s aporia: he has an explanation of what to make a true statement or to give a proof concerning complex ideas means; but this model cannot account for any statement directly concerning first elements. Little reflection is needed to realize that also the first type of statement is struck by the aporia. While in Socrates’ dream there was apparently no perplexity about the possibility of ‘weaving’ together simples and their respective names to get complex objects which can be accounted for and talked about, according to On Forms, instead, “no proposition could be true, if forms were not united with a subject.” Assuming complex ideas means, indeed, that we should have previously been able to combine the simple ones; the impredicability claim, however, makes it very difficult to conceive this. Plato elsewhere realized the impossibility of giving an account of discourse as a mere concatenation of “names.” A major discovery of the Sophist is, indeed, that discourse can arise only weaving together items of different semantic types (a “noun” and a “verb”). This awareness is not excluded by Leibniz’s consideration; his “forms being united with the subject,” however, points in a slightly different direction: the forms that are combined belong to the same ontological and semantic type and are opposed as a whole to the “subject.” Rather than a semantic dualism in Sophist style, he suggests an idea of hypocheimenon h as the metaphysical partaker of Forms, as in the Phaedo or Tymaeus T . As a matter of fact, some echoes of these suggestions can be found in the P Paris Notes, as we shall see. Moreover, the 1676 ontological subject, approached moving from a qualitativist ontology, prolongs the role of the “ens” in the Raue style analysis, that was conceived of from the point of view of a particularist ontology. The trouble with complex ideas is especially urgent for Leibniz, if we bear in mind that in the same period he is led—as one can exemplarly see in the drafts on the ontological argument—to systematically question the possibility of the complex ideas we conceive of. We are not sure that a complex idea is possible, until we have a proof of its being non-contradictory. If, however, we cannot state anything about simple forms, how can we frame a proof of their compatibility? Russell made this point, when raising, against Leibniz’s analytical theory, the need to give a synthetic explanation for the (in)compatibility of simple elements: that is, something of the kind Cartesian simple natures showed. Leibniz on the contrary, relying on atomicity, would be left with the

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quite unsatisfactory argument of the impossibility of proving incompatibility analytically, which could be easily turned against him. I suspect that something in Leibniz’s train of thought has got missed by this criticism. I have said that the combination problem cannot be solved at the level of forms; this means that a direct proof of compatibility using only the logical and conceptual relations of forms is excluded right from the start. This is why one has to shift to the ontological subject. Only once this subject is given, compatibility becomes conceivable—and by the same move, notice, incompatibility too; earlier, forms are simply wholly unrelated. The drafts on the ontological argument, therefore, do already presuppose the ‘wonderful’ discovery. Atomicity, then, plays a role only in excluding the hypothetical threat coming from conceptual oppositions, this way just at the level of forms. To sum up: completing the well-known (indirect) analytical proof of compatibility with the (mainly unobserved) reality of subject, gives us a possible explanation for the striking asymmetry in Leibniz’s application of the atomicity argument. Ontological dualism would provide Leibniz with that synthetic element that was requested by Russell. This synthesis, however, would place itself (contrary to Descartes’ view on the links among natures) on a different level from that of conceptual contents, leaving intact, on the latter, the analytical approach.

1.2. Attributes: The Clash of Paradigms The Subject of Infinite Attributes The theme of Subject-Forms ontological asymmetry is not at all an isolated one within the context of the P Paris Notes. On the contrary, it is the key idea around which Leibniz (a) goes on sketching a metaphysics of the divine Subject; (b) puts forward a reinterpretation of Spinoza’s substance of infinite attributes; (c) lays the basis for a radical rethinking of the whole substance ontology of the “moderns.” Concerning point (a): God is the subject of all absolute simple forms . . . etc. So there are already in God these two: that which is one in all forms, and essence, or a collection of forms. That is to say, God, who is one and the same, is absolutely ubiquitous, or omnipresent; he is absolutely enduring, i.e. eternal; he is absolutely active, i.e. omnipotent . . . 13

The suggestion has an unmistakable Neo-Platonic flavor, with the contrast between the One and the plurality of Forms. Reading the subject-forms 13

On the Origins of Things from Forms, A VI.3, 519–520 (SR 79).

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distinction through this One-Many polarity warns us against hastily identifying the metaphysical subject which is opposed to Forms with a kind of bare substratum. Rather, the dimension of subject provides the ineffable element of simplicity which is required beyond the plurality of forms/attributes. The idea of substratum is far from absent, however. The metaphysical appreciation of Extension here goes beyond the acknowledgment of its autonomy, to rejoin its theological promotion in contemporary Neo-Platonism and Spinozism: absolute Extension is handled as a divine attribute. Now, this “Immensity” actually plays the role of a kind of substratum, from whose modification finite things originate: Things are not produced by the mere combination of forms in God, but along with a subject also. The subject itself, or God, together with his ubiquity, gives the immeasurable, and this immeasurable combined with other subjects brings it about that all possible modes, or things, follow in it. The various results of forms, combined with a subject, bring it about that particulars result.14

The chora of the seminal Tymaeus T view comes to mind. We pass here from the construction of absolute Subject to that of finite particular things, so that the subject-forms asymmetry presents itself as a quite general ontological structure. Taking Apart Ethics I: Mono-Attribute Substances and T Spinoza’s Identity of Indiscernibles Coming now to points (b) and (c), we have to consider that also within the projects for a radical philosophical reform, the notion of substance maintained a central role. Some privileged first notions (in the language of the De Summa r rerum , some “Forms”) are promoted by the reformers to the rank of substances, in order to provide the ontological basis for a unified science. This is the case with Hobbes’s ‘body’ and Descartes’ extended and thinking things. Leibniz also, after giving up old hylemorphism, accepts that conceptual framework, only trying to complete the Hobbesian philosophy of body through a new philosophy of mind. His own rediscovery of the significance of the subject-forms distinction, however, will lead him to question this approach to substance. His awareness of this grows through confrontation with his 1676 the Hague host B. Spinoza, who held God to be the unique Substance and considered the two ‘modern’ substances of matter and mind just as His (better, ‘Its’) ‘attributes’. 14

On Simple Forms, A VI.3, 523 (SR 85).

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The terminology itself of ‘attributes’ is openly connected with a venerable theological tradition on one hand, and with Spinoza’s heterodox reinterpretation of it on the other. For theologians, the classic problem with attributes was that of reconciling their plurality with divine simplicity. Spinoza also is ffaced with similar difficulties, which were intensively debated within the small circle of his disciples; and some echoes of these discussions came to Leibniz since 1675 through his friend Tschirnhaus. Leibniz devotes considerable attention to these problems, when he can finally read the text of the Ethics, presumably two years after leaving Paris (1678). Commenting on the definitions of substance and attribute of part I, he aims at breaking the equivalence of conceptual (‘being conceived per se’) and ontological selfcontainment (being in se).15 Considering, then, Spinoza’s definition 6, of God as the whole of infinite attributes, he stresses the need for a possibility proof; in practice, of proving that (a) there are many attributes that are conceived per se; (b) all can co-exist in the same subject. The reader will immediately recognize here a major concern of his own 1676 metaphysics of forms. Unfortunately, the following remark—echoing the classic theological puzzles about divine attributes—seems to affect even his own construction of God’s idea from simple forms: Furthermore, it can be doubted whether the same simple essence can be expressed through many different attributes. There are in fact many definitions of composite things, but only one of a simple thing, and its essence can be expressed, it seems, only in one way.16

In order to understand what is at stake here, we have to consider his immediately preceding criticism to Ethics I 2–5. It is worth having an overall view of Spinoza’s strategy in this first piece of the Ethics—where he provisionally works, notice, with an idea of substance as constituted from one attribute only. His first important aim is to establish (P7) the equivalence of “substance” and “causa sui.” The decisive step is to prove that (P6) a substance cannot be produced by a different one. Proposition 6 is, in its turn, argued for in the following way: (P2) two substances having different attributes have nothing in common; (P3) hence, they cannot cause one another. But (P4) two substances can be distinguished only by having different attributes; hence, (P5) they cannot share any attribute. Joining (P2–P3) with (P4–P5), we obtain (P6). It is easy to see that two propositions (P2 and P4) about the diversity of subtances play a decisive role in this strategy. P4 seems to be the Spinozistic version of 15 16

See his criticism to the definitions of substance and attribute in A VI.4, 1765 (GP I 139). A VI.4, 1766 (GP I 140).

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a principle—the Identity of Indiscernibles—cherished by rationalist thinkers in general, but especially associated with Leibniz. Leibniz, however, does individuate a counterexample to (P2): (1*) let A, B, be two substances that are only partially (dis)similar, e.g. let A be constituted by the attributes c, d and B by the attributes d, f. It is easy to see that, unless one is able to exclude the possibility of (1*), (P 2) fails to be a general principle; hence, P5—that is, the exclusion of any shared attributes among substances—does not follow from P4, the latter alone excluding at most the possibility of two substances sharing all their attributes. Spinoza, therefore, is bound to furnish a proof of (P*): “there cannot be two only partially dissimilar substances”—and this seems a hard job to do. Now, Leibniz suggests an argument that might have led Spinoza to the (implicit) acceptance of (P*).17 The argument works, however, only at the high price of simply excluding the possibility of many per se conceived attributes of the same substance.Thus, the exclusion of the ‘partial community view’ implies a collapse into the one-attribute substance. To avoid this conclusion, the assumption that should be abandoned is not the per se conceivability of forms/attributes, but (E*) the idea that an attribute does express the whole essence of its subject: I . . . wonder why he [Spinoza] takes here the word “nature” and the word “attribute” as equivalent, unless he means by “attribute” that which contains the whole nature. If this is assumed, I do not see how there can be many attributes of the same substance which are conceived through themselves.18

Far from contrasting Spinoza’s Def. 6, Leibniz challenges, whether he is aware of this or not, the former’s residual dependence on Descartes. Assumption (E*), in fact—that blocks the passage to the many-attributes substances, let alone to that of infinite attributes—is the heritage of Descartes’ essentialism, centered around the theory of ‘principal attribute.’ Already in On Forms, in connection with his ‘wonderful’ discovery, Leibniz observes, presumably alluding to Spinoza’s view: The attributes of God are infinite, but none of them involves the whole essence of God, for the essence of God consists in the fact that He is the subject of all compatible attributes.19 17 18 19

A VI.4, 1767 (GP I 141). A VI.4, 1768 (GP I 142). A VI.3, 514 (SR 69).

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The divine subject, we know, does not coincide with the sum of all simple forms, let alone with one of them. So, the one-many polarity implied by ontological asymmetry becomes the key for rethinking Spinoza’s substance of infinite attributes. P4–P5 could be considered as the Spinozian form of the Identity of Indiscernibles (from now: IdInd). According to (P4), “two or more distinct things do distinguish each from another either for their different substantial attributes or for their affections”: that is to say, numerical difference is conceptually dependent on discernibility, i.e. on some difference of properties. Leibniz accepts this thesis as one enjoying quasi-axiomatic clarity, the ultimate reason of his acceptance being a kind of epistemic constraint: “Conceivable things necessarily can be known, hence can also be distinguished, through their attributes or affections.”20 Things become more complex as concerns P5—literally the closest to the classic formulations of IdInd: “In the nature of things there cannot be two or more substances of the same nature, or attribute.” Leibniz raises two questions: [a] it is not clear, what he means by “in the nature of things”. Does he understand: in the whole of existing things, or in the region of ideas or possible essences? (b) It is also not clear, whether he means that there are not many essences sharing a common nature; or that there are not many individuals sharing the same essence.21

The first question is one interpreters have raised against Leibniz’s IdInd itself; in more familiar words: is IdInd a law for all possible worlds, or only for the best one? It is interesting to see him urging the same alternative to Spinoza; but unfortunately, he does not suggest any answer. The second alternative opposes two readings, connected respectively to the level of essences and to that of individuals. Essences are likely to be bundles of forms, whereas individuals are instances of the essences themselves. So far, Leibniz has developed his discussion at the former level; from this perspective, P5 would amount to the Spinozian denial of the ‘partial community view’ I have already discussed. Alternatively, it could amount to the inconceivability of a numerical distinction within the same essence. It is worth noting that Leibniz quotes with approval Spinoza’s P8—where the numerical uniqueness of an essence considered per se is affirmed—and its Scholion, according to which the number of the individuals of a given kind cannot be accounted w for through their common essence alone, but always requires some external 20 21

A VI.4, 1768 (GP I 142). Ibidem.

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cause to be explained. This does not mean, however, that individuals differ only numerically, or are not discernible by the properties they exemplify. I think that the distinction between ‘attributes’ and ‘affections’ becomes relevant here. Individuals are to be distinguished not through attributes, i.e. through simple forms as such (in this sense, they all partake of the same conceptual material, which originally constitutes God’s essence), but through affections— that is to say, through forms insofar as they are variously limited and modified. There is a shift of ontological levels from the combinatorics of pure forms to their particularization, often neglected by interpreters. To understand this, we should take into account Leibniz’s reception and transformation of the Spinozian ontology of modes. Before this, however, I wish to show how the technical discussion about attributes—in particular, about their claim of being identical with substance—contains the seed for a powerful criticism to some leading ontological ideas of the age. Mind, Body and the Semantic Objection Consider the example Leibniz puts forward in On Forms: “Thought is not duration, but that which thinks is something that endures.” In Descartes’ jargon, a special real nature (Thought) is connected with a common real one (Duration), common natures (or forms) being suitable to combine with any other. But what would happen if we substituted the “duration-enduring thing” pair with “extension-extended thing”? We would obtain the objection against Descartes’ mind/body distinction raised in Hobbes’s De Corpore, w when dealing with abstract reference: Hence come the crass mistakes of some metaphysicians: so from the fact that one could consider thought without considering body, they claim to conclude that there is no need of the thinking body.22

And in his well-known Objections to Descartes’ Meditations, he challenged the inference from “I think”, or “I am a thinking thing” to “I am Thought”: exactly—he said ironically—as one would infer from “I am ambulating” to “I am ambulation.” For Hobbes, Descartes’ metaphysics of mind would be the product of a categorial mistake, that can be dispelled through linguistic analysis; hence, we could speak of a “semantic objection”. Now, could Leibniz’s remark admit this application? One is inclined to deny this, in view of his well-known anti-materialist concerns and of his Paris Notes, to Descartes’ treatment of Thought apparent closeness, in the P 22

OL I 30.

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and Extension. If this is the case, Leibniz would limit the predicative ‘weaving together’ of forms to the “common” ones. This is not the case, however. We need only reconsider step (9) of A Most Perfect Being Exists, stating that proposition (P) “A and B cannot be in the same subject” cannot be an identical one. Now, he explicitly suggests interpreting ‘A’ and ‘B’ as “Thought” and “Extension”, respectively: “for to say that thought is not extension is very different from saying that they cannot exist in the same subject.”23 And this is nothing but an explicit denial of the heart of Descartes’ proof for the mind/body distinction. Descartes, in fact, used the heterogeneity of the notions of thought and extension as the decisive premise for inferring the real distinction of their objects, i.e. their being the notions of two quite different things. Leibniz, on the contrary, already in his Trinitarian writing against Wissovatij emphasized that even “disparate terms”—i.e. wholly heterogeneous concepts or properties—can coexist in the same subject. The subject of the P Paris Notes, just insofar as distinct from “forms”, clearly continues to do this job. Moreover, this feature is crucial for the role it has to play in the compatibility proof. If notional diversity—in the sense that A and B can be distinctly conceived of independently one from another—were a sufficient condition for real distinction, i.e. for recognizing two distinct subjects, then the compatibility argument would simply fail. So, Leibniz’s “ontological asymmetry” directly works against the Cartesian mind-body metaphysical dualism: that is to say, a quite general distinction between two ontological types blocks the distinction between two regions of being. For Descartes, the meaning of the abstract terms ‘extension’, or ‘thought’, wholly captures the descriptive content, or essence, of their subjects. Hobbes himself, notice, basically accepted this logic as concerns body (except for the usage of abstract talk), while denouncing it in the case of thought. Leibniz, on the contrary, rejects it on both accounts. Interestingly enough, he will use against this logic the semantic objection stemming from Hobbes, but chiefly in a quite anti-Hobbesian sense. He will apply it, in fact, not so much to the Cogitatio—hence, as Hobbes did, to challenge the autonomy of the thinking thing—as to the Extensio, hence to challenge the autonomy of body. I will make a brief excursion into his later years to show this. If Extension in the P Paris Notes is still handled as a simple form in pure Cartesian style, a few years later its demolition will begin. Among other arguments (Leibniz’s physical discoveries, above all), it is possible to trace a criticism which points precisely to the abstract character of the notion, in order to deny its claim to capture substance. Perhaps, the clearest example of this line of thought is to be found in the late Conversation of Philaretes and 23

A VI.3, 575 (SR 97).

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Ariste (1715), where Ariste alias Malebranche puts forward a reformulation of the substance definition as “concrete independent.” If being concrete is the mark of substance, however, extension fails to pass the test; nor can its typically Cartesian identification with its concrete counterpart be taken for granted: One cannot concede to you that “the extended” and “extension” are one and the same thing. There is no example in created beings of the identity of the abstract and the concrete . . . extension is nothing but an abstraction and demands something which is extended. It needs a subject; it is something relative to this subject, like duration.24

Moreover: while the Cartesian approach is eager to stress that the descriptive content of a subject is wholly expressed by its attribute, Philaretes alias Leibniz does make the attribute dependent on the subject not only for its ontological basis, but also for its conceivability: “Extension presupposes also something prior to it within the subject. It implies some quality, or attribute, or nature in the subject, which extends or expands . . .”25 As is well known, Leibniz will usually try to identify this positive expanded quality with antitypy. Be that as it may, the criticism about the abstract status of extension rejoins here the slightly different one concerning analyzability. From r Knowing to Being: Cartesian Distinctions The charge of categorial mistake—specifically, of blurring abstract and concrete terms—makes us realize that we are faced with a clash of competing ontological paradigms, that is to say of different intuitions about what it means to be a thing, and how to identify things. This is far from surprising, from authors who put forward projects of radical philosophical reform. The case of Cartesian extension, indeed, was only a piece of a general ontological program, where the central role played by the so-called “principal attributes” Extension and Thought reflected a methodical foundational strategy. We can find it in the Descartes-Arnauld discussion I have evoked in my introductory chapter. Descartes’ argument for real distinction was a paradigmatic case of inference from knowing (grasping the ideas of mind and body as entirely distinct 24 25

GP VI 583. GP VI 584.

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one from another) to being (affirming the real distinction of their objects). To defend, against Arnauld, the completeness of the notions involved, he introduced, remember, the distinction of two senses of ‘complete concept’: (CC1) the concept C is a C1-complete concept of the object a iff C includes all the properties that belong to a; (CC2) the concept C is a C2-complete concept of the object a iff C suffices to make clear that a can exist per se, and therefore is not the product of an act of abstraction of ours. The latter is the only relevant one for claiming a real distinction, i.e. substantiality. To characterize CC2 Descartes shifts from the language of ideas to that of being: a complete concept is what captures a complete being; in so doing, he seems to be open to blatant circularity. This is not the case, however: rather, we are facing the bedrock intuition lying at the core of his substance metaphysics; that is, the intuition of what does count as a thing, or a substance. Moreover, this intuition is accompanied by a “quasi-transcendental” justification, insofar as our ontological assertions are seen as determined by the cognitive means we have at disposal for our access to being. Accordingly, a ‘complete thing’ is “a substance clothed in the forms or attributes from which I am able to acknowledge that it is a substance.”26 We are not, indeed, w directly acquainted with substances, but they are inferred starting from some “forms” we directly grasp and which exhibit autonomous conceivability on one hand, while still being in need of a subject of inherence, on the other. The ontology of the Principia establishes the scholastic outcome of this “way of ideas,” distributing all notions into the three basic ontological categories— substance, attribute, mode—which Leibniz finds defined at the beginning of Spinoza’s Ethics. The counterpart of this ontological framework is the elaboration of a new and simplified theory of distinctions, which codifies the operations of the underlying epistemic strategy. We can draw the following scheme: epistemic procedure exclusion abstraction one-sided dependence

type of distinction real of reason modal

ontological category substance attribute mode

A modal distinction is drawn, fundamentally, between two ideal contents A and B, if the first is thought of as independent, whereas the latter needs the former in order to be conceived of: a particular thought (or type of thought) with respect to the thinking thing, or a particular shape or motion (or the 26

AT VII 222.

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general idea of shape and motion) with respect to corporeal substance. As concerns the distinction of reason, finally, it occurs between two contents A and B which cannot be distinctly conceived of without one another; it is a kind of bilateral dependence, that marks the relationship between a substance and its inseparable attributes, or among attributes themselves. The most significant case is that of the principal attribute (thought or extension), which is held to constitute the whole essence of a substance.27 Its outstanding role is rooted in the fact that grasping it is the only way we come to recognize the existence of the substance/subject. In this way, Descartes founds a new essentialism, which is no longer modeled, like the old Aristotelian one, on natural kinds grouping ordinary biological objects, but rather on the intuition of mathematical essences, or of pure thought as it discloses itself in the experience of self-knowledge. Now, each form of essentialism is accompanied by an intuition concerning de re necessity. While ancient essentialism was inspired by natural necessity, Cartesian essentialism considers only the necessity which is typical of purely conceptual connections—let us leave open the difficult question of what this necessity consists in. The basic ontological relations are accounted for in terms of conceptual dependence-independence. Finally, all this provides a new interpretation of predication. More precisely: while disregarding the linguistic aspect of predication, the Cartesian model offers a direct analysis of the underlying ontological fact of inherence, which would be captured by modal dependence. I have dwelt on this, because Leibniz’s own understanding of ontological completeness—and hence, the new brand of essentialism he will put forward—is worked out, to a large extent, as an alternative to this framework, which he becomes for the first time critically aware of just on the occasion of w his discussion of Spinoza’s ontology. Forty Years Later: Leibniz and de Volder on Attributes F Leibniz will directly criticize the Cartesian ontological program in his later discussion with a Cartesian scientist, the Dutch physicist Burcher de Volder. The seminal topic of the correspondence is Leibniz’s discoveries in the field of dynamics. De Volder’s most urgent objections are not directed as much against Leibniz’s physics, but against the passage from physical description to the metaphysical interpretation of force. His problem takes the form of a request to prove that substance is essentially active, and this leads to discussing 27

“Thought and extension can be considered as constituting the nature of thinking and corporeal substance, respectively; therefore they should be conceived of as being nothing but thinking and extended substances themselves . . . .”, AT VIII 30–31.

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its definition. When De Volder’s identification of substance with its principal attribute becomes explicit,28 Leibniz sharply disagrees: I do not at all approve of the doctrine of attributes which people are formulating today; as if one simple absolute predicate, which they call an attribute, constituted a substance. Nor do I find any entirely absolute predicates in concepts, that is, any which do not involve connections with other predicates. Certainly thought and extension, which are commonly proposed as examples, are far from being such attributes . . . And, unless the predicate is taken concretely [in concreto], it is not the same as the subject; so the mind coincides with the thinker indeed (though not formally), but not with thought. For it is a property of the subject to involve future and past thoughts, in addition to present ones.29

This remark is highly interesting in a threefold respect: firstly, it makes the divorce explicit between the attributes we know and talk about on one hand, and simple forms on the other. This does not mean that forms per se are given up, or that the construction of God starting from them is no longer valid; only, the abstract attributes we deal with in our conceptual knowledge are to be accurately distinguished from simple forms. Cogitatio, notice, is on a par with extension in this respect. Secondly, “the predicate is not the same as its subject, unless it is taken in concreto.” Faced with the Cartesian approach, Leibniz makes this eidetic essentialism react with the Hobbesian-style appeal to concrete things through language. So, a linguistic remark is used to challenge the autonomous conceivability of the attribute within the horizon of the ‘way of ideas’. The remark—analogous to that made to Extension in the Conversation—this time is applied to Thought. The abstract character of the latter, however, is not imputed to its isolation from extension (as in Hobbes’s and Arnauld’s objections to Descartes), but rather to its failure to give an account of the inner richness of its modes. This criticism is close to de Volder’s concern about the genesis of modes within one and the same attribute, and also to the aspect of completeness discussed in the 1686 Leibniz-Arnauld debate. Finally, the subject-properties distinction (or the concrete-abstract one, on the semantic level) is connected with the temporal dimension of a changing subject. The problem of the genesis of modes goes back to Leibniz’s 1676 metaphysics of forms and its confrontation with Spinoza, to which I now return. 28

29

“Given my substance definition, . . . every perfection [in the absolute sense of simple forms] denotes a different substance”, and: “Although we conceive of substances through attributes or properties, I do not think that we could say that attributes inhere in substances, but rather they are substances.”, de Volder to Leibniz, letter XXI, GP II 242. Leibniz to de Volder, Letter XXV, GP II 249 (L 528 modified).

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Chapter 2. Modes and Requisites: The Genesis of Finite Things 2.1. Modes Reinterpreting Spinoza’s Modes Descartes’ and Spinoza’s attributes were quite different from the universal properties of Schoolmen. Each of them was a real being, the all-embracing totality of a certain ‘nature’, from which finite modes are cut off. This is the case with Extension, conceived of as a simple all-pervasive form, if not as a divine attribute. The P Paris Notes are still influenced by a kindred view, be this already tied to Spinozian suggestions, or rather to Neo-Platonic ideas. Also in this transitory phase, however, the relation of modification which finite things entertain with divine attributes has to be carefully disw tinguished from that of inherence, or of part-to-whole. Leibniz seems to be willing to establish between forms in God and forms in finite things a relation which is closer to traditional ‘eminence’, though being expressed in a new w language: There is in matter, as there is in space, something eternal and indivisible, which seems to have been understood by those who believed that God w himself is the matter of things. But this is not said correctly, for God does not form a part of things; instead, he is their principle.30

The two leading ways of thinking of the subject-forms distinction in God— according to the substratum idea, or the one-many dialectic—are also employed to explain the genesis of modes: “It is sufficiently clear . . . that the immeasurable is not an interval, nor is it a place, nor is it mutable. Its modification occurs without any change in it, but with the addition of something else, namely bulk or mass . . . .”31 This addition is identified with the intervention of matter. The production of modes, however, cannot be explained within the boundaries of a single attribute. The subject-forms asymmetry, breaking the limits of mono-attribute essentialism, allows this important step. In On Forms,

30 31

A VI.3, 392 (SR 45). A VI.3, 519 (SR 79).

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remember, Leibniz warned that no single attribute expresses the whole essence of God, which embraces all forms. Because of this, any property or affection of God involves his whole essence; thus, that God has produced something that is perceived by us, however small it may be, involves the whole nature of God, since it involves the whole series of things of that sort. But an infinite series results only from infinite attributes. But when all other things are related to any attribute, there result modifications in that attribute; hence it comes about that the same essence of God is expressed in any genus of the world in its totality, and so God manifests himself in infinitely many ways.32

Bear in mind that Leibniz’s friend Tschirnhaus in the same period urges Spinoza to clarify the topic of the infinite attributes of Substance. According to Leibniz, we can explain the genesis of modes by admitting some kind of mutual reference among different attributes—although neither a causal relation, nor a mixing of different essences has to be assumed. This solution could be inspired, too, by a Spinozian idea, that of ‘parallelism’ among the series of modes of different attributes. We would look in vain for more conceptual precision in this type of draft, but one should be clear about this: the ‘mode’— in practice, a label for a finite thing—is something which is not marked by conceptual simplicity but, on the contrary, by infinite notional complexity. This implementation of the Spinozian doctrine of mode goes in the direction of an overturning of Cartesian ontology, with its primacy of attributes. The following step to be taken will be the frank acknowledgment of the abstract nature of the attribute, as we have seen in the later discussions on extension. Per-aliudr concipi and In-alio-esse: the Monistic Threat In Descartes’ and Spinoza’s ontologies, the relation of modification was defined through one-sided conceptual dependence and captured the traditional one of inherence. As is well known, Spinoza’s handling of finite things as modes of the unique substance amounts to stating their being in the latter. Leibniz himself admits some equivalence of conceptual and ontological dependence in the case of mode: The correct way of considering the matter is that forms are conceived through themselves; subjects, and the fact that they are subjects, are conceived through forms. But that whose modification depends on the 32

A VI.3, 514 (SR 69–71).

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attributes of another, in which all its requisites are contained, is conceived through another. That is, it cannot be perfectly understood unless the other is understood. Those things are connected of which the one cannot be understood without the other.33

We come across the language of requisita r here, whose general intuitive sense is that of “conditions”. I will study this new causal dimension in the next chapter; for now, I will deal with a related aporia concerning the notions of essence and modes. Analysis into the existence conditions of finite things should in the end arrive at the same set of simple forms which constitutes the essence of God. Should we conclude, then, that the essence of all things is the same, and coincides with God himself? This is precisely what the 1676 draft That a Perfect Being is Possible does argue; more interestingly for us, it connects this move to the Cartesian doctrine of distinctions: It can easily be demonstrated that all things are distinguished, not as substances (radically) but as modes. This can be demonstrated from the fact that, of those things which are radically distinct, one can be perfectly understood without another; that is, all the requisites of the one can be perfectly understood without all the requisites of the other being understood. But in the case of things, this is not so; for since the ultimate reason of things is unique, and contains by itself the aggregate of all requisites of all things, it is evident that the requisites of all things are the same. So also is their essence, given that an essence is the aggregate of all primary requisites. Therefore the essence of all things is the same, and things differ only modally, just as a town seen from a high point differs from the town seen from a plain. If only those things are really different which can be separated or which one can be perfectly understood without the other, it follows that no thing really differs from another, but all things are one, just as Plato argues in the Parmenides P .34

The reference to Plato deserves to be taken seriously, given the attention Leibniz gives in this period to his theory of forms. More immediately, one 33 34

A VI.3, 514–515 (SR 71). That a Perfect Being is Possible, A VI.3, 573 (SR 93–95). See on this text W. Janke, Das ontologische Argument in der Fr¨u¨ hzeit des Leibnizschen Denkens, Kantstudien 54, 1963, 259–287; for a discussion of the monistic threat, R. Adams, Leibniz, ch. 4.3: Is Leibniz’s Conception of God Spinozistic?, 123–134, and M. Kulstad, Did Leibniz Incline Towards Monistic Pantheism in 1676?, in Leibniz und Europa. Akten des VI. Int. Leibniz-Kongr., Hanover 1994, 424–428; Idem, Leibniz’s Early Argument that All Things Are One in Relation to Descartes’ Notions of Real and Modal Distinction, in Nihil sine Ratione. Akten des VII. Int. Leibniz-Kongr., Berlin 2001.

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thinks of Spinoza; so that the ontology of forms seems to run directly into a monistic collapse. The impression can only be reinforced, because Leibniz advises us few lines later about the difference between a ‘popular philosophy’ and a more esoteric one, containing heterodox conclusions which would not be commonly acceptable. Surely, he has never been so close to Spinoza’s views. Nevertheless, the sense of this ‘proof’ is not easy to be univocally established. First, the import of the terminology of “being radically r distinguished”35 is not clear to me. Is it simply a synonym for “really” or “substantially”; or rather is it a kind of qualification, imposing a further stronger requirement on ‘simple’ substantial distinction? This could recall Descartes’ double definition of substance, which was already intended to avoid the consequences Spinoza later drew: in the first and strict sense, God alone is a substance, being the only self-conceived and causally independent thing. Moreover, Leibniz’s reflection on Cartesian epistemic criteria for distinction is to a large extent a critical one. Considering the hypothetical form of his argument: “if only those things are really different . . . ”, one might suspect that Leibniz is simply testing their application. What is important to realize, however, is that the problem is not merely derived from Spinoza’s or Descartes’ views, but is closely connected with the possibility of a combinatorial metaphysics like his own, where we ultimately dispose of the same conceptual material—simple forms—to ‘build up’ both God and the world. So, how can we distinguish the two? How can we distinguish things one from another? In order to cope with the combinatorial “monism of essence”, Leibniz relies basically on two great metaphors: the arithmetical one of the analysis into prime factors, and the optical one of the “point of view”. Two Metaphors The prime number comparison appears in several passages of the Paris P Notes, and also in the notes on Spinoza: 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 × 2, 6 = 4 + 2, etc. Nor may one doubt that the one expression differs from the other, for in one way we think of the number 3 or the number 2 expressly, and in another way we do not; but it is certain that the number 3 is not thought of by someone who thinks of six units at the same time. It would be thought of, if the person were 35

“Radically” has been added by Leibniz.

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to impose a limit after three had been thought. Much less does someone who thinks of six units at the same time think of multiplication. So just as these properties differ from each other and from essence, so do things differ from each other and from God. I use the word “thing” readily, for we are accustomed to say “God is a being”, but we are not accustomed to say “God is a thing.”36

In the Theaetetus ‘Dream’, Socrates put forward the selfsame example of number six, in discussing his aporia about knowledge: how could we know the whole, according to the Combinatorial Claim, if elements are in themselves unknowable and the whole is made up of their sum? The young Theaetetus tried to avoid the aporia, suggesting that the whole is something different from the sum of its parts; Socrates, however, argued that everything that has parts is necessarily identical with their sum: [Socr.] “And what about this: is a sum at all different from all the things? For instance, when we say ‘one, two, three, four, five, six’, or ‘twice three, or three times two, or four plus two’, or three plus two plus one’, are we talking about the same thing in all these cases, or something different?” [Theaet.] “The same thing” [Socr.] “Namely six?” [Theaet.] “Yes.”37

Leibniz draws from Plato’s example an opposite moral. Though embracing the Combinatorial Claim, he lays emphasis on the differences among the many ways of expressing the whole. Analogously, the simile of the town seen from different perspectives could easily appear as a merely epistemical way of distinguishing. Bear in mind, however, that also in the mature monadology all monads do express the selfsame intelligible content, the only differences among them reducing to their different points of view. The type of distinction captured by the similes, therefore, surely is a ‘merely modal one’, but this does not necessarily support the idea of a part-whole or inherence relationship between finite beings and the infinite one, nor does it amount to a denial of the distinction itself. The difficulty is this: at the end of 1676, Leibniz still does not have a clear concept of substance, or ‘being in itself’, or ‘subjecthood’, which is able to be applied to finite particular things and to be characterized w independently from epistemic conceivability relationships. 36

37

A VI.3, 518–519 (SR 77). See also On Truths, the Mind, God, and the Universe: “Just as the number 3 is one thing, and 1,1,1, is another—for 3 is 1 + 1 + 1, and to this extent the form of the number 3 is different from all its parts—in the same way creatures differ from God, who is all things [omnia]. Creatures are some things [quaedam].”, A VI.3, 512 (SR 67). Plato,Theaetetus, 204b10-c5, transl. J. Mc Dowell, Oxford 1973, 98.

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2.2. Conditions, Causes and Reasons From r Forms to Requisites: Absolute Subject as Causa Sui In That a Perfect Being is Possible, the maximal set of simple forms is enough to ensure its self-position into existence. In order to do this, they are transformed—after playing the role of attributes, and then of perfections, in spelling the construction of divine Subject—into a set of ‘requisites’. In this way, a the absolute Subject is promoted to the rank of causa sui. The core of the proof runs as follows: (1) The most perfect being, in order to be able to exist, must have a reason for its existence; (1’) this reason will be a se or ab alio; (2) but it cannot be ab alio, because the most perfect being contains all requisites; (3) hence, either the most perfect being will be a se, or it will be simply impossible (for 1, 1’, 2); (4) but we have proved that the most perfect being is possible; (5) hence, it is a se, i.e. it does necessarily exist. On the other hand, the quest for requisites, when applied to finite things, leads to the opposite situation: On Existence—another text of the same group— shows how internal requisites are not enough to explain the existence of such a thing. Hence, one is committed to look for its existence conditions beyond its boundaries, and ultimately in God, who plays the role of the “last reason of things.”38 In both arguments, the core assumption is the assimilation of the intelligibility conditions (constituting the essence of a thing) to the proper causal ones (constituting the reason for its existence). ‘Forms’ and ‘requisites’ express two different ways of considering the same factors: “requisites seem to indicate a relation to existence, attributes to essence.”39 The forms/requisites ambivalence in the 1676 drafts conceals, however, some serious logical and metaphysical problems. As concerns the promotion of divine essence to causa sui, steps (3–4) of the argument above seem to incur a confusion between the causal sense of possibility and the logical one. On the other hand, the conclusion concerning finite things—taken together with the identification of the ‘sum of requisites’ (or ‘last reason’) with the ‘essence’—exposed the whole metaphysics of requisites/ forms, in the last part of That a Perfect Being itself, to the danger of monistic collapse I have dealt with in the preceding chapter. To better understand the ambivalence, I need to briefly explore the origin of the Leibnizian notion of ‘requisite’.

38

39

A VI.3, 587 (SR 111–113). R. Adams devotes attention to the early metaphysics of requisita r in his Leibniz, ch. 4.1, 115–123. That a Perfect Being is Possible, A VI.3, 573 (SR 95).

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Theory of Conditions: A Logic for Determinism The language of requisites Leibniz uses in the seventies can be brought back to two main sources. First, we have his interest in a ‘logic of conditions’ in the juridical context of his youthful dissertations On Conditions—written shortly after the DAC—that can be seen as a significant sketch of a propositional logic.40 Conditional connections, in fact, hold there among propositions, or better among their truth values. Anyway, the ‘if. . . then’ connective is likely to be interpreted as an implication stronger than a material one. This formal inquiry provides Leibniz with some ideas he will later apply to spell out his analysis of determination. The main inspiration, however, has to be probably found, once again, in the De Corpore. For Hobbes like for Aristotle, science is causal knowledge. Hobbes the mechanist, however, tends to reduce the plurality of Aristotelian causes to the efficient one (the cause of motion), and to conceive of our world as a causal chain ruled by inflexible determinism. In Chapter 9 of his philosophia prima, the cause/effect pair is introduced from the basic notion of action: a body is said to act, when it brings about a change in another body. This familiar situation is analyzed into a set of causal factors, for which a precise ontological interpretation is offered: they belong to the category of accidents, that is to say they are properties or states of the relevant bodies. Whereas conditionship, in Leibniz’s studies for a juridical logic, connected propositions and truth values, here it connects things and properties. The basic notion for the logical working of this conceptual setting is just that of requisite (requisitum r ), which is defined as a necessary condition.41 The whole sum of these (necessary) conditions works as a sufficient condition and is what properly deserves the name of ‘cause’.42 From such a perfect cause the effect 40

41

42

See Disputatio Juridica de Conditionibus, Prima et Posterior, A VI.1, 127–150. On this, see H. Schepers, Leibniz’ Disputationen ‘De Conditionibus’: Ansatze ¨ zu einer juristischen Aussagenlogik, in Akten des II. Intern. Leibniz-Kongresses, Bd. 4, Stuttgart 1975, 1–17. For the wide range of meanings of the Leibnizian “requisitum r ”, see S. Di Bella, Il ‘Requisitum’ leibniziano come ‘pars’ e come ‘ratio’: tra inerenza e causalit` ta, in Lexicon Philosophicum. Quaderni di terminologia filosofica e storia delle idee del Lessico Intellettuale Europeo, 5, Ateneo, Roma 1991, 129–152. On the historical genesis and the relevance for Leibniz’s metaphysics of the theory of requisites, see now the important study of Francesco Piro, Spontaneit` ta e ragion a sufficiente. Determinismo e filosofia dell’azione in Leibniz. Roma: Edizioni di storia e letteratura, 2002. “The accident of both the agent and the patient, without which the effect cannot be brought about, is called ‘the cause sine qua non’ and ‘hypothetically necessary’; and is also called the requisite for the effect being produced.” OL I 107. “The cause simply considered, or the entire cause, is the set of all accidents of all agents and of the patient, a set such that if all its elements are given, the effect cannot help being produced; and if only one of them is missing, the effect cannot be produced.” Ibidem.

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does certainly follow: otherwise, it would not be a sufficient cause. All this amounts to frankly recognizing that every sufficient cause necessarily brings about its corresponding effect.43 I call this Hobbesian thesis (TH1). Leibniz’s first inquiries into the ‘principle of reason’ in the seventies are framed in this conceptual vocabulary. In the Confessio philosophi and De Summa Rerum we find the notion of ‘requisitum r ’ as a necessary condition for the existence of something else. “The whole sum of requisites” (“aggregatum g omnium requisitorum”) becomes his standard definition for “ratio r ”or “causa”. Moreover, he is entirely ready to accept the deterministic logic of Hobbes’s theory. When assuming this definition of cause, indeed, he is committing himself to the Hobbesian (TH1). From r Formal Causes to Causal Definitions In the Aristotelian paradigm for causality (the well-known ‘theory of four causes’) the central role was played by the formal cause, that is by the essence of the object of inquiry, that furnished the real ground of all properties on one hand, and the principle of our demonstrative knowledge on the other. The ‘new science’ of the seventeenth century radically challenges the role of essences (especially if intended as ‘substantial forms’), putting in their place efficient causes only. The latter are conceived of, in their turn, according to the two models for the new science of motion: mechanical impact and geometric deduction, so that geometry tends to work as a kind of ‘basic science’. The De Corpore chapter on scientific methodology—after pointing out that the alleged “formal cause” is nothing but an efficient one having regard to our cognition—offers some interesting hints towards a causal reinterpretation of the notion of essence, or nature of a thing. Reading the ancient definition of science as “scire per causas” through the primacy of efficient causality, Hobbes puts forward a view of science as an inquiry into the production of things, carried out by an analytic-synthetic procedure, i.e. by resolving our experience into its first conceptual elements and then reconstructing phenomena thereon. The background is the conceptualist strand of his theory. The resulting notions are, indeed, conceptual (not physical) parts with respect to the concrete items of our experience—the latter being, according to a traditional distinction, ‘first for us’, i.e. prior in the order of knowledge, while the former are ‘prior by nature’.44 Anyway, the synthetic constitution of more 43

44

“ “And, if we define a ‘necessary cause’ as the one which, supposing that it is given, the effect cannot help being produced, then one can derive also that every effect that is produced, is produced by a necessary cause.” OL I 109. “As parts, I do not mean here the parts of the thing itself, but the parts of its nature: so, as ‘parts’ of man I do not mean the head, arms, and so on, but rather figure, quantity, sense,

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complex concepts is interpreted as a causal operation. This view on concept constitution is reflected in the theory of definition, where causal or genetic definitions come in the foreground, instead of the traditional ones by genus and differentia, that were still privileged in the conventionalist account: “The names of the things that are known to have a cause must contain in their definition this cause or way of generation: so, we define the circle as the figure that arises by rotating a straight line on the plane, and so on.”45 The Leibnizian writings related to Nizolius’s edition bear witness to his reception of the ‘modern’ interpretation of causality. Leibniz attacks Suarez’s definition of causation as “influere existentiam”: according to him, an example of undue usage of a metaphoric language in philosophy. The conciliatory letter to Thomasius does not diverge from the leading ideas of ‘mechanist philosophy’, insofar as the Aristotelian types of causes are all reduced to motion as the efficient one. The suggestion of the geometric model is also present. Already in the letter, Leibniz refers to geometric constructions to stress the causal character of geometric knowledge.46 More interestingly, at least from the end of his Paris stay, he relies on the topic of “real definition”, in order to cope with Hobbes’s conventionalist challenge. Such a definition is not a matter of convention, not because it is anchored to existence, but insofar as its possibility is granted. Now, the best way of assuring possibility is to provide a possible way of producing the object defined. Conceptual Involvement and Causal Dependence: A Criticism to Spinoza’s Causal Axiom Bearing in mind that the ontological argument is the cradle of the Leibnizian topic of real definition, it is easy to understand that it is also a favorite terrain for the new contamination of essence and causality, as is the case in the 1676 metaphysics of conditions. But this raises also some tensions, as we have seen. In the period after the Hague meeting, Leibniz seems to be sensitive to

45 46

reason and so on, i.e. the accidents that taken together constitute the man’s whole nature, and not its mass.” OL I 60. Hobbes, the nominalist, does not hesitate to qualify the basic items grasped through analysis not only as ‘simple concepts’, but frankly as ‘universal’, even as ‘most universal’ (universalissima): “As concerns universal notions, as they are included in the nature of singular things, they should be drawn from within through analysis by reason . . .” OL I 61. OL I 72. “[mathematics] does demonstrate from causes. For it demonstrates figures from motion; from the motion of a point a line arises, from the motion of a line a surface, from the motion of a surface a body. The rectangle is generated by the motion of one straight line along another, the circle by the motion of a straight line along an unmoved point, etc. . . . ”, A VI. 2, 439 (GP IV 169; L 98).

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these problems, and tries to modify his metaphysics of conditions in order to escape them. As concerns the monistic collapse of finite things into the First Cause, I have already pointed out his attempts to distinguish the unique set of absolute forms from the many sets of particularized forms. As concerns the causa sui, he will be eager to stress the difference between logical implication and causal production in some remarks in the early Hanoverian years.47 All this leads him to criticize the attempt to interpret causal dependence as a conceptual one. In That a Perfect Being the ontological dependence relation of ‘having some (none) of its requisites outside itself’ was accompanied by its epistemic translation into the Cartesian language of ‘being conceived per aliud (per se)’. As I have hinted above, this equivalence seems to hold also for Leibniz; nor does this seem to be confined to the 1676 episode. Let me consider, however, a Leibnizian remark on the proposition 25 of Ethics I, echoing the topic of the divine production of essences: “God is the efficient cause not only of the existence of things but of their essence as well. Otherwise the essence of things could be conceived without God, by Axiom 4.” Leibniz questions precisely this foundation on a causal axiom: But this proof carries no weight. For even admitting that the essence of things cannot be conceived without God . . . it would not follow that God is the cause of their essence. For the fourth axiom does not say that “the cause of a thing is that without which it cannot be conceived” (This would be false, for a circle cannot be conceived without a center, or a line without a point, yet the center is not the cause of the circle, nor the point of the line). The fourth axiom says merely that “the knowledge of the effect involves the knowledge of the cause”, which is something far different. Nor is this axiom convertible—not to mention the fact that to involve something is one thing and to be inconceivable without it is another. The knowledge of the parabola involves the knowledge of its focus, yet the parabola can be conceived without it.48 47

48

See the note Causa sui, A VI.4, 1372, and the distinction between ‘causa’ and ‘ratio r ’ in the Elementa verae pietatis, A VI.4, 1360. On this, S. Di Bella, Die Kritik des Begriffs ‘causa sui’ in den Leibnizschen Anmerkungen zu Spinoza’s Ethica, in Leibniz: Tradition und Aktualit¨t t , Akten des V. Intern. Leibniz-Kongresses, Hannover 1988, 52–56; Idem, t¨ “Nihil esse sine ratione, sed non quidem nihil esse sine causa”. Conceptual involvement and causal dependence in Leibniz, in Nihil sine ratione. Akten des VII. Internationalen Leibniz-Kongresses, Hannover 2001, pp. 297–304. A VI.4, 1774 (GP I 147). Observe that Axiom 4 is the ground of Spinoza’s well-known ‘parallelism’ between the ‘series of things’ and that of ‘ideas’. On the causa/ratio pair in Leibniz, see B. Mates, Leibniz and the Phaedo, Akten des II Int. Leibniz-Kongr. Studia leibn. Suppl. 12(1973). Wiesbaden: Steiner, 135–148; M. Bobro and K. Clatterbaugh,

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It is possible to distinguish several strands within this objection. A first one concerns the adequacy of our intuitions about conceptual dependence. This is the point Leibniz wants to stress, in my opinion, in the last lines of his remark, when emphasizing the difference between ‘A being not conceivable without B’ and ‘A involving B’. In his example, we can grasp a geometric figure (the parabola), though ignoring a property which is actually implied by its notion. The epistemic “to be able or not to be able to conceive without” is too subjective for establishing the logical or ontological dependence expressed by ‘involvere’. The remark ranges itself within his general struggle against Cartesian intuitionism and its subjectivistic drift. The core of Leibniz’s criticism is not this, however. Though being cleansed of subjectivistic accents, in ffact, the relation of ‘involvere’ is not able to capture the meaning of causality. According to Leibniz, the alleged proof of proposition 25 fails because Axiom 4 is ‘not convertible’. Spinoza’s axiom reads: “The knowledge of the effect depends on the knowledge of the cause and the former involves the latter”, and is nothing but the epistemological translation of the ontological Axiom 3, which states the reciprocal implication of cause and effect. Leibniz does not intend at all to question the possibility of concluding from the knowledge of the cause to the knowledge of the effect, and conversely (which is a part of the deterministic program). What he means to exclude is the inference from the simple holding of some (not further specified) conceptual involvement to the obtaining of causal relation. Beyond the Geometric Model: From Construction to Individual Genesis As a counterexample to the equivalence of conceptual and causal dependence, Leibniz presents a case of geometric construction: though being involved in the notion of a line, the point is not its cause. In so doing, he seems to distance himself from an ideal of rational explanation he has subscribed to, where geometric construction is the privileged paradigm. Considering some w texts of the early Hanoverian years on the topic of genetic definition, we can divine the growing difficulty of the geometric model in capturing dynamic connections. This awareness has to be linked up with Leibniz’s reflection on the ontological and epistemological status of abstract beings, such as mathematical objects. Unpacking the Monad: Leibniz’s Theory of Causality, in The Monist, 1996, 408–25; S. Di Bella, Leibniz on Causation: Efficiency, Explanation and Conceptual Dependence, in Quaestio 2/ 2002, 23–59, pp. 23–59; and now the comprehensive reconstruction by V. Carraud, Causa sive ratio. La raison de la cause de Suarez a` Leibniz, Paris: PUF, 2002, ch. V, 391–506.

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Already in quoting from Spinoza the classic example of the definition of circle, Leibniz notes that several constructions are often possible for the same geometric object, “although one is the simplest of all.”49 The De Synthesi et Analysi, then—a text of the early eighties, that presents us with one of the most detailed accounts of the topic of real definitions—introduces a new distinction between constitution and generation g . The former expresses a possible way of production (for instance, one of several possible ways of construing an ellipse), whereas the latter reflects the actual one: w . . . it is useful to have definitions involving the generation of a thing, or, if this is impossible, at least its constitution, that is, a method by which the thing appears to be producible or at least possible . . . to set w up a hypothesis or to explain the method of production is merely to demonstrate the possibility of a thing, and this is useful even though the thing in question often has not been generated in that way. The same ellipse can be thought of either as described in a plane with the aid of two foci and the motion of a thread about them or as a conic or a cylindrical section. Once a hypothesis or a manner of generation is found, one has a real definition from which others can also be derived, and from them those can be selected which match at best with other things, when a method of actually producing the thing is sought.50

At a first stage, the problem of the plurality of possible constructions can be solved by referring to the simplest ones; this does work well for providing genetic definitions of types (species) of objects (e.g., the circle, the ellipse). But when we are interested in the genesis of a certain circle, then a problem of existence arises, and the criteria of selection should be different. So, the The Synthesi et Analysi invokes the fact that a construction fits best with the whole of given circumstances, and this compatibility with a wider context is w a clue that Leibniz has in mind a problem of existence. As we shall see, this idea of the different ways of producing a thing will be expressed elsewhere in the language of requisites. Anyway, when we deal with concrete existing objects, the plurality of equivalent genetic definitions makes room for the unique way the thing has been effectively produced. This conclusion is drawn already in the De Principio individui of 1676, starting from the selfsame causal axiom that states the reciprocal involvement of cause and effect, hence the possibility of going back, at least in principle, from the latter to the former. Sometimes, however, 49 50

See a note to Spinoza’s De intellectus emendatione, A VI.4 1758. On Universal Synthesis and Analysis, or the Art of Discovery and Judgment, A VI.4, 541 (GP VII 294–295; L 230–231).

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it is by no means possible to achieve this inference, given that the data of the problem are objectively underdetermined. This is the case with a geometric figure like a square, which could have been produced equally well by different types of construction, e.g. by summing up two triangles as well as two rectangles. This seems to work as a counterexample to the general rule concerning causality. Not being prepared to give up the latter, Leibniz challenges the alleged underdetermination in the case of actual squares, those for which it makes sense to speak about numerical distinction: The effect, therefore, seems not to involve its cause. So if we are certain, from some other source, that the effect does involve its cause, then it is necessary that the method of production must always be discernible in the squares that have been produced. And so it is impossible that two squares of this kind should be perfectly similar; for they will consist of matter, but that matter will have a mind, and the mind will retain the effect of its former state.51

The topic of causality links up here with that of discernibility. If geometric objects are not able to satisfy the causal requirement, so much the worse for their ontological status: perfectly similar squares, indeed, are not possible in the nature of things, being only fictitious entities. Thinking about existing beings on the model of these abstract entities would simply be a mistake. For now, it is clear enough that an individual should bear the trace of its causal connections. Here, this requirement is met by relying on the metaphysical idea, typical of the De Summa Rerum, of the link between minds and chunks of matter. But what I am interested in is the general logic of the argument. I will return in more detail to it in the next chapter, that will be entirely devoted to the contrast between concrete particulars and abstract objects. Forty Years Later: Leibniz and de Volder on Cause, Possibility F and ‘Conceptual Need’ Once again, it is possible to find an echo of these reflections of the early Hanoverian years in the later correspondence with de Volder. Here, Leibniz criticizes the definition of substance through per se conceivability, because this would imply that a substance cannot be causally dependent. Conceptual dependence, in fact, though being not (without further specification) a sufficient condition for causal dependence, remains a necessary one. De Volder replies that their discussion does not concern the existence of a substance, but rather its essence; and efficient causality is required only for existence. So far, 51

Meditatio de Principio Individui, April 1676, A VI.3, 490–491 (SR 51).

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I have emphasized that Leibniz also recognizes a privileged link of the notion of cause with existence, and with the production of what did not exist and then is brought about. Nevertheless, he now vindicates the right to talk about a “cause of the essence”: In order to conceive of the essence of a substance, the concept of a possible cause is required; in order to conceive of its existence, an actual cause is needed.52

He himself formulates a possible rejoinder through the example of an ellipse, whose general notion does not imply a univocally determined genetic explanation. To this, however, he opposes two distinct replies: (a) one can well conceive of an ellipse without thinking of a determinate way of production, but not “without being able to know a priori its possibility through its formal cause, which is included in every particular way of production, and in order to find this, one must rely on the simplest of constructions”;53 (b) if one stays within the field of mathematical objects, one can well imagine perfectly similar objects, but this is not the case for complete beings, or true substances: I have already established the fact that incomplete things such as lines or figures can be similar to each other even if they are produced by different causes, as an ellipse made by a conic section may be similar to an ellipse made by motion in a plane. But in completely determined things this cannot happen, and so one substance is not perfectly similar to another, nor can the same substance be generated in many different ways.54

One can easiliy recognize here the results of the inquiries of thirty years earlier: solution (a) was sketched in the De Synthesi et Analysi, w whereas (b) is nothing but the discovery of the De Principio Individui: the first fitting with incomplete objects, the latter with complete ones. In the first case we can pursue the core set of conditions that are common to the different ways of production; in the latter, on the contrary, we have to individuate the unique way that has been (or that could be) actually followed. The notion of a ‘possible cause’ becomes crucial when the inquiry turns to individual things. Leibniz shifts here from a view of essence as something general, common to a class of objects, and whose internal structure is ruled by conceptual links, to one I would call a w ‘camera view of essence’, where it is conceived of as a copy, in the realm of the possibile, of an individual existing thing. If one can well conceive of 52 53 54

Leibniz to de Volder, Letter XVI, GP II 225. Ibidem. Ibidem (L 524).

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a general g essence abstracting from causal connections, this is not the case with an individual one: out of such a context, a possible individual is as little conceivable as an existing one. De Volder had given a definition of the basic ontological notions relying on the Cartesian criteria of dependent-independent conceivability. According to Leibniz, however, ‘conceptual need’ cannot give a full account of ontological foundation: if we define them [the modes] merely in terms of their needing another concept [indigentia conceptus alterius] . . . this same definition will also fit things which are not contained in something, such as effects, which need causes to be understood . . . On this basis, all effects would be modifications of their causes . . . . 55

The worry about the collapsing together of inherence and causality shows that Leibniz has continued reflecting on the problems he met within his 1676 metaphysics of conditions; but now he imputes them to the Cartesian theory of conceptual dependence. The compressed argument by which he substantiates his criticism is worth quoting at length: Who will deny, too, that one substance is modified by the intervention of another, as when a body is repelled by some obstacle in its path? In order to conceive the rebound of one of these bodies, therefore, the concept of both of them will be necessary, yet the rebound can be the modification of only one, since the other can continue in its path without rebounding. Something more is needed in the definition of a modification, therefore, than the necessity of another concept, and to be contained in (a quality which is common to both properties and modes) is more than to need something else. In my m opinion there is nothing in the whole created universe which does not need, for its perfect concept, the concept of everything else in the universality of things, since everything flows into every other thing in such a way that, if anything is removed or changed, everything in the world will be different from what it now is.56

Leibniz claims the universal interconnection of all concepts. He has in mind here, in my opinion, something different from the impossibility of isolating 55

56

Leibniz to de Volder, Letter XVI, GP II 226 (L 524). But already in his former letter he advised: “Not to say that a modification requires something more than a simple conceptual need”, GP II 221. Mates and Mugnai have stressed this important difference between ontological ‘inherence’ and conceptual ‘need’. See Mates, Leibniz’s Philosophy, 220, and Mugnai, Leibniz’s Theory of Relations, 122. GP II 226 (L 524–525). Italics mine.

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some simple general g concept we have found in the discussion about attributes in the same correspondence. The notions at stake are likely to be, instead, individual concepts. Their connection reflects—and is justified from—the connection of things. But this very aspect can raise some puzzlement. Let us see why: (1) Leibniz clearly aims here at accurately distinguishing the level of conceptual relations holding among notions from that of ontological modifications, directly concerning individuals (i.e., individual substances). This ffact is, in itself, interesting, given that he is commonly held, on the contrary, to miss or to blur the distinction between an individual thing and its corresponding concept. (2) Causal relations are included within the concept of a thing, while only individual accidents do really inhere in the thing. (3) But the ground that Leibniz invokes for (2) is precisely the source of our puzzlement. The conceptual link seems to be stated on the assumption of some universal causal influence: the English translation conceals Leibniz’s usage of the word ‘influere’—just the metaphorical terminology that he has criticized since his youth, and that he finally excludes in his mature metaphysics. (4) Causal relation is able to sustain—according to what is often required from it nowadays—counterfactual reasoning: if A causes B, the lack of A or a change in A would have as a consequence that B would be different or would not have existed at all. This has to be understood in an especially strong way: the slightest change in the world would modify the whole of things. For such a causally compact world, we could speak of “causal holism”. Now, I think that the difficulty in (3) is only apparent. First, we should bear in mind that Leibniz’s argument is framed, as far as possible, in the language of his opponent, a Cartesian physicist. The example of rebounding bodies should warn us: from his own point of view, qualifying bodies as substances is at best highly problematic. On closer inspection, the moral to be drawn from the physical example is in full agreement with his standard harmony solution. Leibniz emphasizes, indeed, that the real r modification does pertain to the single individual, whereas the intervention of the external body belongs to the conceptual space of reasons only. Therefore, the connection is a merely “ideal” one, that does not imply any physical interaction. One might rather consider it as a kind of “final” cause, provided that external things work not so much as mechanical solicitations, but as perceived reasons for the divine adjustment. The discussion on conceptual versus ontological dependence is closely bound with the topic of relations. In the same discussion with de Volder, Leibniz makes a general point concerning relations. If ontological modification (i.e., inherence) simply amounted to notional dependence, he argues, then a mode C depending (conceptually) on both A and B would turn out to inhere in both—which is absurd, given his constant rejection of an individual accident having its ‘legs’ in two distinct substances. And when de Volder objects that

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a kindred simultaneous modal dependence is not possible, Leibniz defends, on the contrary, the “mode of two substances”, clearly taking here ‘modal’ dependance as a merely conceptual one: . . . if A and B are two substances in the sense in which you define them, that is, most simple, I admit that they cannot have a common predicate; yet it does not necessarily follow from this that there cannot be some third thing C which needs both of them for its concept. For just as relations result from a plurality of absolute terms, so qualities and actions also result from a plurality of substances. And just as a relation is not compounded from as many relations as there are terms to be related, so neither are the other modes which depend upon many things resolvable into many modes.57

Leibniz is ready to distinguish relational links on the conceptual level, which are ‘modes’ in the Cartesian sense, from the corresponding monadic properties on the ontological level, which are ‘real’ modifications. To summarize the twofold result of Leibniz’s complex reflection on causal dependence and conceptual involvement: (1) his criticism of Cartesian ontology has the effect of distinguishing conceptual and ontological foundation. Causality has a conceptual nature, though based on inhering accidents. The emphasis on this point serves to detach the universal interconnection of concepts from the ontological relation of inherence. On the other hand, (2) causal relation is not captured by a generic notion of conceptual dependence, let alone if interpreted through a Cartesian style epistemic approach. In particular, it cannot be reduced to a relation of logical entailment, nor to the necessary dependence among mathematical or eidetical essences. On the contrary, it belongs to a family of relations which draw the outline of a true logic of existence, and frame a type of concepts which are quite different from general essences.

Chapter 3. Ens Completum: The Emergence of Complete Being Construing Basic Particulars. Tropes and Discernibility Leibniz’s approach to particular things within his combinatorial metaphysics is well documented in the 1679 De Cogitationum Analysi,58 where w 57 58

GP II 226 (L 525). A VI.4, 2767–2774.

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the analysis of ethical and psychological notions shifts into a foundational inquiry concerning our basic ontological framework. The subject-attribute asymmetry is at the center of attention, again. It is firstly introduced as if it were equivalent to the existence-essence polarity. The new fact, with reParis Notes, is that the subject-forms distinction is related to spect to the P the universal-particular pair, so that an account can be given of the whole traditional “ontological square”: The subject and the attribute seem to result from the fact that the concept of one individual is involved in the concept of the other. I can well conceive of heat, even if I do not conceive of any hot thing, but I cannot conceive of this heat if I do not take into account some hot thing. That is to say, I am not able to conceive of the properties that exist in nature and follow from the concept of heat, unless I take into account some subject, in which there is heat, light, etc.59

General properties (“heat”) are thought of abstractly, i.e. without taking into account their subjects. This does not mean that Leibniz adheres to a nonAristotelian view of general properties, where these do not depend on particular instances for their existence. On the contrary, only the particular side of the ontological square is real, while general properties are taken as mere concepts. Remember the parallel taking down of Cartesian attributes as abstract constructions. If one wants to pass to particular accidents (“this heat”), then properties have to refer to a subject. Moreover, the reference to a subject is needed when we no longer consider an isolated property, but the co-presence of many forms: “From these definitions one could show that the selfsame subject can have many attributes, even contradictory ones, i.e. it can change”.60 A particular thing is essentially a concrete one, whose ontological structure is built up from a subject, standing in a one-to-many relation with properties. The theme of co-presence is decisive for answering an objection one could raise against the subject-properties asymmetry: ‘Also this heat cannot be understood perfectly, nor discerned from another heat, unless the whole nature of things is understood’. This is true, and it is true of all individuals. But then, how do this hot thing and this heat differ? The answer is: this hot thing and this bright thing are the same thing, although this heat and this light are not the same. Hence, a subject is an individual item that can be expressed through many different individuals.61 59 60 61

A VI.4, 2770. A VI.4, 2769, note. A VI.4, 2770.

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Leibniz insists that both subject and property are individual, where the mark of individuality is the reference to existence: “An individual is that, whose intelligibility involves the intelligibility of the existence of things.” But, then, why h and how do we distinguish between independent particulars (substances) and dependent ones (individual attributes, or better individual accidents)? The answer is a straightfroward one: the distinguishing feature of individual substance is just the co-presence of different tropes. Despite what might seem the case, we cannot interpret the co-presence argument as the outline of a ‘bundle theory’ of tropes. Leibniz’s solution, in fact, points precisely to a concrete identical subject lying beyond the bundle of tropes. His objection, therefore, somehow envisages the possibility of a trope ontology doing without substances, only to dismiss it. Anyway, we find here a crystal-clear document of Leibniz’s adherence to individual accidents. At the same time, it incites us to further question the content of this doctrine.62 Suarez had paid a lot of attention to the problem of the individuation of accidents. Like all elements of being, they are for him per se individual. This amounts to saying that, though being ontologically dependent on substance, they are nevertheless individuated independently of it. Notice that this individuation could be a merely numerical one. Suarez admits, in fact, the possibility of indiscernible accidents, even belonging to the same substance. According to the doctrine that K. Clatterbaugh attributes to Leibniz, if I understand him correctly, accidents depend on substance, instead, for their numerical individuation, but can still be qualitatively indiscernible. Now, our text presents us with a view of individual accident which is slightly different from both readings. Differently from Suarez, the particularization of a ‘form’, or general quality, is wholly dependent on its being exemplified by a subject. But each individual accident is also qualitatively discernible from all others. One could say that the Leibnizian accident cumulates the requisites of the standard ‘Aristotelian’ view with the unorthodox view put forward by G.E. Owen, according to which ‘this red’ would be a qualitatively atomic shade of red. In Leibniz’s idea of qualitative individuality, on the other hand, there is much more. Dependent or ‘abstract’ particulars, indeed, share the features of discernibility and universal involvement with independent ones. In other words, from a single accident one could ‘read off’ the whole world, exactly as from the individual substance. Interestingly enough, the subject-properties asymmetry is also faced with an objection coming from the case of relational properties. Leibniz has suggested that a distinctive feature of subjects is that of staying in a one-many 62

The seminal work for this topic is K. Clatterbaugh, Leibniz’s Doctrine of Individual Accidents, W Wiesbaden: Steiner 1973.

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relation with respect to properties. Relational properties, however, seem to attribute many subjects to the same property: It has to be shown that the same attribute cannot also have a plurality of subjects. Therefore, our definition seems bound to be further qualified, because an attribute, say a relational property, could involve in its essence the existence of many subjects; but it will involve the one differently from the other: so paternity involves two individuals, David and Solomon, but in different ways, and more properly it involves David, because the father takes its name from him.63

In order to preserve the ‘collecting attitude’ as a distinguishing feature of individuals, Leibniz argues here for a privileged foundation of relation in one of them. “Discrimina quae ex formis non sumuntur”: A ‘Strawsonian’ Leibniz? Far from being characterless, Leibniz’s basic particulars are richly determined. In this sense, they are opposed to the ‘abstract notions’ of Cartesian essentialism. Their individuation, however, is not given by the mere copresence of many forms. Particulars as such do have some features that cannot be accounted for in terms of forms, nor of their bundles: I can well conceive of a circle, as something which is possible in itself, i.e. not implying a contradiction; if I wish to know, however, whether a circle does exist now, and if I wish to know this a priori, I am bound to assume many other items besides that essence, and among them the first one I should take into account, if I methodically advance moving from the essence of circle and from the derived properties towards those further matters, is nothing but the subject of the circle. I can easily analyze the essence of circle, considered in itself, into its causes, until the first ones are reached; but I am not able to judge from that, whether any circle does exist. There are, in fact, some differences that are not drawn from forms, such as the difference between a big and a small circle, or whether there is one circle alone or many. When I find that the circle is possible, then the question arises, whether something else is possible, that involves more ffacts, in order for its possibility to be judged . . . Universal is an item, whose notion involves only possibilities. Singular is an item, from whose w notion one can judge, whether it exists, and when and where, and whether alone or with other things, in a word the whole nature of things. From 63

Ibidem. The remark does not contrast with the acknowledgment of ‘shared’ relational properties at the conceptual level in the later argument against de Volder (see above).

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this it is clear, why it is so difficult to deal with singular things, because they involve so many facts.64

Existence (“whether some circle does exist”), numerical distinction (“whether there is one circle or many”), quantitative features (“a big and a small circle”) and spatio-temporal location (“when and where it exists”) are the aspects of particulars “which are not drawn from forms.” We could say—borrowing some terminology from the present-day ontological debate—“not drawn from suchnesses”: where a suchness is a general qualitative property, that does not contain any irreducible reference to individuals. Now, the first principle lying outside forms and determining this whole ‘existential’ sphere is the subject. It is difficult to find in Leibniz’s writings a more explicit reflection on the difference between the set of properties built up from suchnesses, on one hand, and the subject on the other—the latter being tied up with thisness and existence. We find here a cluster of interrelated ideas—subject, existence, individuality—which is opposed to the complementary one: properties, essence, generality. It is important to realize that the boundary between the two spheres (say, the essential and the existential) does not properly coincide, despite all appearances, with the one between the possible and the actual: Notice that to think of existence is one thing, to think of essence is quite another. To think of a possible existence is nothing but to simply think of existence. But to prove possibility—this is quite another thing.65

This means that, in order to simply conceive of existence, we need to go beyond the idea of a (general) essence; that is to say, a possibly existing thing falls under the rule of existential principles. Here is the seed of what I have called a “camera view of essence”, when talking about causal possibility in the later de Volder correspondence. The example of circle, finally, somehow echoes the Aristotelian approach to the topic of mathematical objects. Aristotelian tradition, in fact, systematically laid stress on the distinction between abstract mathematical objects, endowed at most with intelligible matter, and their concrete instances—e.g., the brazen circles—realized in sense-perceivable matter. From this perspective, the Leibnizian ‘subject’ plays here a metaphysical role similar to that of Aristotle’s matter. I will now show the limits of this comparison. 64 65

A VI.4, 2770. A VI.4, 2769, note.

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To those differences that are not drawn from forms, numerical diversity itself belongs. Leibniz, remember, quoted with approval Spinoza’s statement that essence in itself cannot be the principle of numerical plurality. Spatiotemporal location is another feature of the group, that cannot be accounted for by forms. At this point, one should take a step backwards, to the Confessio philosophi, an important metaphysical work of the first Paris years, where individuation is traced to spatio-temporal circumstances, in contrast with Leibniz’s later views. This discussion is not located in a context of general ontology, but of theodicy. I will return to this aspect in the final part of this book; for now, let us consider how Leibniz’s strategy is epistemologically marked. Leibniz proposes the example of two eggs conceived of as two indiscernible objects which differ only numerically, an example which sounds strikingly non-Leibnizian for those who are familiar with his later well-known statements about the impossibility of finding two leaves perfectly alike and so on: But what do we mean, when we count and say “this”? What is the “this”, or determination? Nothing but the perception of time and place, that is to say the motion of a thing with respect either to us or to another determinate thing (e.g. the hand or finger) . . . This is why the individuating principles are external to the individuated thing. Given the hypothesis of maximal similarity, neither an Angel, nor even God could discern the two eggs, if not for the fact that, at present, this egg is in a place A and that in a place B . . . 66

Leibniz goes on: if they change their place, the only way for keeping them distinct will be to continuously follow their respective paths. As a consequence, individual identity is bound to some spatio-temporal path. The metaphysical problem of individuation is reduced to the epistemic one of identification—and this move, notice, is consciously presented as decisive progress with respect to the Scholastic disputes on individuation. This text is sometimes taken as an episode in Leibniz’s career, he would later leave behind. Also some years later in the P Paris Notes, however, we have found the suggestion that numerical distinction is not given by ‘forms’, but by something added, qualified as ‘matter’ or ‘point of view’. Finally, this ‘haecceitistic strand’ seems to be still at work in our 1679 essay on particularity—although in a somewhat different way. Surprising as it may be, the ontological intuition that emerges so far from the study of Leibniz’s drafts is to a large extent a ‘Strawsonian’ one. Leibniz, in fact, insists on the ontological value of the subject-predicate asymmetry—his ‘wonderful discovery’ of 1676. Moreover, he combines the 66

Confessio Philosophi, A VI.3, 147. Leibniz uses here the term of “haecceity” (haecceitas), just to indicate the principle of a purely numerical distinction.

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substance-properties distinction with the particular-general one, rejecting the possibility of construing substance as a bundle of general forms; and epistemic considerations are far from foreign to his approach. Nor does he limit himself to laying at the bottom of his ontological framework a set of basic particulars. He goes on to point out the irreducibility of existence and the role of spatio-temporal location in our referring practices. To sum up, he is willing to stress that individuation cannot be accounted for in terms of a combination of suchnesses. On the whole, this shift from the conceptual atomism of combinatorics towards an ontology of particulars can be seen as a rediscovery of the antiPlatonistic ontology of the Categories, centered around individual substance as the ultimate subject. Leibniz is probably led by some powerful intuition going back to his nominalistic training, which interacts with the constructivistqualitativist approach starting from forms. Maybe as a result of nominalistic influence, an important feature of the venerable Categories model, the topic of ‘second substances’ i.e. of sortal terms, is definitively left out by him. This is why a point of divergence of Leibniz’s framework from present-day neo-Aristotelian ontologies like Strawson’s lies in his weaker commitment to essences. Aristotelian essentialism was based, indeed, on the metaphysical relevance of natural kinds designated by sortal terms. On the other hand, Leibniz has begun to criticize the universal notions of the moderns, whose reification is as unjustified as that of the ancient realists was. Hence, also the new Cartesian essentialism, modeled on the essences “Matter” and “Mind” and the related conceptual involvement, has been questioned. As a consequence, Leibniz’s ontology of particulars, being so far deprived of ‘essences’, seems rather to be open to the dialectic between ‘bare particulars’ and ‘bundle theories’ we are nowadays familiar with. Understanding Existence Despite all this, Strawson was well entitled to take Leibniz as his ideal opponent. The ontological framework I have traced seems to contrast, indeed, with other deep tendencies of Leibniz’s thought, documented almost everywhere in his writings. This aporia invites us to a closer inspection of our w text. The ‘haecceitistic’ traits of the theory of particulars in the De Cogitationum depend on the ‘subject’, opposed to ‘forms’ and ‘essence’, the latter providing, instead, the descriptive content. But how is this dependence to be understood? In answering this question, one realizes that the ontological subject is far from playing the role of a mere existential placeholder, or of a bare

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substratum. On the contrary, it has to work as a principle of inference, hence of intelligibility: From all this it follows clearly that every ultimate subject is a complete being, which involves the whole of nature: that is to say, from its perfect understanding—i.e., if we understand all features by which it can be distinguished from everything else—one could infer, which possible things do exist.67

The emergence of ‘complete being’ clearly announces the topic of the Discourse. In m my introduction I have guessed that the Discourse actually assumed a kind of ontological completeness in order to conceive of the ‘complete’ concept and distinguish it from the ‘full’ one. Our 1679 text can be seen as a seminal document for the formation of that ‘thick’ subject. While in 1686 the talk about notional completeness will presuppose the implicit reference to complete being, in 1679, conversely, a reference to knowledge is already present in the definition of ontological completeness. The subject is complete, indeed, because it has to work as an inference principle, on the assumption that it is ‘perfectly understood’. Far from corresponding to a conceptual atom, an individual—that is, a “substantial atom”, to use an expression Leibniz will adopt in the later expositions of his philosophy—is conceptually related to every other. Leibniz’s definition of ‘individual’ embraces both the reference to existence and the intelligibility requirement. Combining this with the fact of being an ultimate subject—to the exclusion of individual accidents—an individual assumes the dignity of substance: An individual is that, whose intelligibility involves the intelligibility of the existence of things. An ultimate subject is what can be expressed by different individuals, while it cannot serve to express in its turn any other individual. Such a subject is labeled “substance”.68

Beyond the Thisness-Suchness Polarity One might be tempted to think that the individuating features are extrinsically ‘attached’, so to speak, to the particular thing; this would be misleading, however, insofar as Leibniz specifies that the subject provides an a priori justification of them: “If I wish to know whether a circle does exist, and if I wish to know it a priori . . . ”. ‘A priori’ is the knowledge of a fact, or phenomenon, which is not merely ‘by acquaintance’, but is deduced from its causes, hence w 67 68

A VI.4, 2770. Ibidem.

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has an explanatory value. Considering the subject as a bare individuator, itself individuated by some extrinsic relation, maybe to other ‘bare data’ like spaces and times, would simply amount to reversing the order of inference and treating the subject itself as a piece of matter or an atom. I have stressed how Leibniz’s opposition of concrete circles to the abstract one ideally prolongs Aristotle’s anti-Platonic challenge to the substantial status of mathematical objects. Here is the point, however, where the analogy of Leibniz’s subject with Aristotelian matter breaks down. According to Aristotle, matter works as a principle of indetermination and vagueness in contrast with the exactitude of the ideal model. On the contrary, the subject of the De Cogitationum is a principle of complete determination, supplying an answer for all questions that are not answered by the information contained within the general form or shape (the eidos) of an object, say, of a circle. As a principle of intelligibility, the subject has to be endowed in its turn with some intelligible content. What this means exactly, is hard to say. We should imagine a sort of qualitative feature, which has to be counted, however, in the category of substance—Schoolmen would say, that is predicated in quid, and not in quale—and (differently from traditional sortals) is proper to the individual. We could speak, a little paradoxically, of a non-general suchness, or of a qualitative thisness. This could work as an ontological interpretation of the point of view metaphor, by which Leibniz tried to obtain numerical difference from the same intelligible content. In this way, he escapes the dialectic between bare particulars and bundles of qualities. Moreover, he rediscovers in an original way the ancient idea that substance is a τodε d ti i, or a ‘thissuch’. This intuition is a seminal one for the attribution to it of an essence, going beyond the dimension of bare subjecthood. In the next part we shall see how all these intuitions are built into the theory of complete concept, a true ‘conceptualizing’ of the subject. Connection and Genetic Thisness We could put into correspondence the properties of particulars that cannot be accounted for in terms of ‘forms’ with some more basic properties that explain them and define the completeness of the individual subject. The features on the left side, insofar as they have explanatory power, should work as conceptual grounds. compossibility discernibility universal connection

— — —

existence numerical distinction spatio-temporal location

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The point of view metaphor warns us that the irreducible individuating feature is originally bound to a world. Connectedness is, indeed, the true key for completeness; and discernibility and connectedness are closely bound in Leibniz’s intuition about individuality. In my scheme, connectedness provides the deep explanation for spatio-temporal location. Already in this stage of his thought, I think, Leibniz does not consider individual spaces and times as irreducible. Spatio-temporal position is likely to be a function of the universal connection of the individual with all other individuals in its world. Connectedness does not have only a ‘horizontal’ dimension, so to speak, which underlies spatial location, but also a ‘vertical’ one, underpinning temw poral location. To see this, let me go back again to the haecceitistic episode of the Confessio, at the beginning of the Paris period. Interpreters have emphasized its contrast with both Leibniz’s earlier individuation theory (the 1663 Disputatio) and the later one (at least from the Discourse on). So far so good; but the contrast also conceals some important elements of continuity. It is important to bear in mind that the theory of spatio-temporal individuation put forward in the Confessio was aimed at a theodicy argument: if individuality is wholly constituted by external circumstances, then the complaint about circumstances and the desire to change them simply amount to the absurd desire to change one’s own identity. Now, this argumentative pattern, extended to all predicates, will be taken up again in 1686; and the special type of predicate at hand (the relational one) will characterize individuality, as we shall see in the third part of this work. Only, these predicates will be thought of as based on some internal features. Thus, in the De Cogitationum, the individual is still characterized, as in the Confessio, by “the when, and where”; but its position in time and place is now deduced from the subject itself. On the path that ideally connects this stance with the earlier one of the Confessio, a decisive step is taken in the De Principio individui, the Paris note on the genetic application of the causal axiom: And indeed, unless we admit that it is impossible that there should be two things which are perfectly similar, it will follow that the principle of individuation is outside the thing, in its cause. It will also follow that the effect does not involve the cause in accordance with its specific reason, but in accordance with its individual reason, and therefore that one thing does not differ from another in itself. But if we admit that two different things always differ in themselves in some respect as well, it follows that there is present in any matter something which retains the effect of what precedes it, namely a mind.69 69

A VI.3, 491 (SR 51).

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If, on one hand, the causal axiom has to be preserved at all costs and, on the other, indiscernible things are assumed, then the axiom will be satisfied only by shifting to external causes. This alternative clearly presents the same situation as the Confessio, w where the two eggs were individuated only by tracing their respective spatio-temporal tracks. This, however, is felt to be deeply unsatisfactory now. Causal or genetic discernibility, i.e. discernibility through a whole story, has to be embodied in the present effect itself. Under the rule of causal axiom, the individuation of a thing remains tied to its origin and its spatio-temporal path; only, this is no longer seen as the external determination of an indiscernible thing, but it has to be grounded within the thing itself. The theodicy move of the Confessio was already directed towards including the origin and relational features in the individuating concept of a person. Far from rejecting this, Leibniz looks now for a stronger de re embodiment, for which he also has a concrete model, the mind. As we shall see better in the next section, indeed, at least since the Hypothesis Physica Nova of 1670, he attributes to mind, in contrast with body, the power of retaining all its past impressions. In any case, the reflection documented in the 1676 De principio individui is absolutely decisive, in my opinion, for the constitution of Leibniz’s idea of a complete being, such as it appears some years later in the De Cogitationum, to arrive at the 1686 metaphysics. Another draft of December, 1676, provides us with a textual confirmation of this connection: In my view a substance, or a complete being, is that which by itself involves all things, or, for the perfect understanding of which the understanding of nothing else is required. A shape is not of this kind; for in order to understand from what a shape of such and such a kind has arisen, we need to have recourse to motion. Each complete being can be produced in only one way; the fact that figures can be produced in various ways a is sufficient indication that they are not complete beings.70

To sum up: what prevents Leibniz from embracing an ontology of bare particulars, perhaps individuated through their spatio-temporal position? I would answer, two powerful requirements concerning discernibility and explanation, that express the content of his well-known ‘principle of reason’, as formulated already from the Paris years. The decisive role that causal and temporal considerations have begun to play in the construction of complete being invites us to a closer look into the internal causal-temporal structure of individual things. 70

A VI.3, 400.

Section 3 Series Rerum The Causal-Temporal Structure of Things: Model Metaphysics1 and Philosophy of Mind

Chapter 1. De affectibus: From the Dynamics of Passions to the Series of Substance States The Chain of Thoughts as a Series The scientific handling of human passions—a true psychology in ‘geometric’ clothes—is a typical piece of seventeenth-century philosophical systems, lying at the core of Hobbes’s, Descartes’ and Spinoza’s research programs in ethics and anthropology. This was also one of the fields to which Leibniz’s search for simple basic concepts was intensively applied, especially towards the end of the seventies. One of his ‘tables of definitions’, dated April 16792 (hence contemporaneous with his first essays on logical calculus), takes the form of a remaking of Descartes’ treatise on the P Passions of Soul. Behind this, the privileged interlocutor seems to be Spinoza, again. Exactly as happens with the cognate draft De Cogitationum Analysi, however, the analysis of the basic concepts of psychology and ethics shifts more and more into a study of general ontological structures. The successive stages of this long draft show this 1

2

I borrow this expression from E.M. Curley, Spinoza’s Metaphysics, Cambridge MA: Harvard Un. Press, 1969, where it designates a Tractarian style model of world as a chain of statesof-affairs which Curley employs to understand Spinoza’s ontology. De Affectibus, A VI.4, 1410–1441 (G 512–537). The editors of A VI.4 have labeled the different layers in the redaction of the draft by the letters (A–J). H. Schepers has vigorously called attention in some unpublished contributions to the relevance of this draft for the elaboration of Leibniz’s substance metaphysics.

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shift of the focus of interest from the psychological density of the ‘series of thoughts’ (series cogitationum)—the continuous chain of ideas and affections in a human mind—to an abstract model of a ‘series of things’ (series rerum), or better a series of determinations. The unfolding of the mind’s life makes room here for a kind of ‘logical’ self-constitution of substance. This is why I will consider attentively this text, starting from its opening psychological remarks, which might appear far from the main subject of this inquiry. The continuous stream of consciousness finds a model in the Spinozian chain of modes as a discrete series of states. Within each of Spinoza’s ‘attributes’, the modes—that is to say, a particular thought, or a particular piece of matter—follow each other in an infinite uninterrupted causal chain, each finite mode being caused by another finite mode, and so on. Spinoza recognizes a double level of causality: besides the transitive one, linking each mode to the following, there is the immanent one, according to which the whole of the chain is produced by God, or the Substance. Spinoza passes from the abstract ontological model of the chain of modes (Ethics ( , part 1) to the specific handling of the modes of thought, and especially of affections (parts 2 and 3). Leibniz rather goes the other way around, or better, he goes on and back from the concrete psychological level to the study of the general structure. At the beginning, ‘affection’ is defined as an ‘occupation of soul’: that is to say, an emotional state which inclines the mind to pass to a different thought, or better to enter a whole train of thoughts. The developing of serial dimension marks a first implementation of the Spinozian chain of modes.3 At a first stage of analysis, series are individuated directly through a kind of phenomenological inspection. A series is a sequence of thoughts, cut off from the continuum of the mind’s life. What confers unity on it is just the opening thought or affection, playing the role of determinatio. This starting impulse differs from a mechanical solicitation from a double point of view: firstly, because its effect does not stop at the next state, as is the case with the mechanical collision of a body, but it prolongs into a whole series of changes. Secondly, because the unity of the series is an intentional one, hence it is teleologically oriented, affections arising from some perception of what is 3

“We can be caused (determinati esse) to think not by some [particular] previous thought, but by the series or order of thoughts we have followed so far. A thought is the cause of another thought either because there is no reason which contrasts it (then, indeed, the selfsame thought endures, as happens when we come across something singular . . . ) or because one thought involves another, or finally because it involves some ordered progression of thoughts and, among many thoughts or trains of thoughts which are involved, the mind is inclined beforehand more to one than to another.” A VI.4, 1424. In this way, Leibniz goes beyond the model of Ethics I 28, of a relation from a particular thought to the following one (a relation that could, to be sure, be extended through transitivity).

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good or bad for us: some perceived and desired good is the moving cause, and also its endpoint. The unfolding of a series, indeed, finishes either when that goal is reached, or when it turns out to be out of our reach. When one enters such a series, this unfolds almost automatically, while the remaining content of thought is put on the backdrop, in the margin of the area of consciousness. This is why Leibniz compares the emerging from an affective series to the wakening from a dream.4 This comparison with dream experience has to be understood in the background of the phenomenistic approach which is typical of our text, where all contents of inner experience are taken ontologically on a par, and w different series of thoughts are distinguished only by virtue of their respective coherence or of their capacity to be integrated into a most comprehensive w whole. To the series circumscribed in this phenomenological way, Leibniz applies a definition that echoes his Paris studies in algebra and analysis: “A series is a multitude with a rule of order.”5 A set of elements becomes a series when they are submitted to some lawlike order relation. For a present-day reader, it is interesting to observe that Leibniz introduces here the idea of law, or of ‘following a rule’, to describe a wholly ‘private’ (methodically solipsistic) experience. The Morphology of Series: Figures of Order Already at this psychological level, it is possible to apprehend a lot of things about the different types of series. One might think that a series of thoughts is an open-ended sequence of different states, ordered by a transitive, irreflexive and asymmetrical relation. This would be misleading, however. First, we have the case of reiterated thought, or of persistence in the same mental state. On the psychological level, the study of this possibility is bound to the Cartesian topic of admiration, hence to the experience of an exceptional object of thought that cannot be compared with anything similar.6 Contrary to appearance, also in those cases we have a progression: thinking does not dwell on the selfsame 4

5 6

“The wakening of our mind happens when we come to consider the end or the cause for whose sake we entered the series. And this happens either because we have found what we looked for, or because the series finished before we find it (in this case, indeed, while the series stops we remember the state before, that is the state for the sake of which we started with the series itself ), or because we have grasped the difficulty of going further, and hence we come back on our steps, or we imitate those who escape bad dreams by wakening themselves, rubbing their eyes with their hands.”A VI.4, 1425–1426. A VI.4, 1426. While Descartes, however, emphasizes the dignity of such an object, hence of the related cognitive experience, Leibniz is more sensitive to the negative aspect of the lack of connections, which blocks further progress of our experience. w

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step, but moves over a small range, coming back again and again to its starting point. This amounts to saying that we are left with a cyclical series.7 But also the open progression presents a plurality of figures. Sometimes we construe a series of series, being engaged in a new series in order to find what we have not found in the preceding one: in this way, partial series tend to be integrated into a more comprehensive one. On other occasions, a train of thought is abandoned because, while following it, we come across something which imposes itself and involves us in another series: w If, in following a series of thoughts, we come across a thought that belongs also to another series, and the latter has more force than the former, then we abandon the former and follow the new series. Such a thought is an intersection point, or a knot, which is common to both series.8

In this presentation, the series and their crossing retain some of the impersonality of Spinoza’s chains of modes of thought. Elsewhere the same situation of crossing is considered, rather, from the point of view of the subject moving along a series, and the image of ‘branching’ [Y] replaces that of ‘knot’ [X]: We are caused (determinati sumus) to pursue some series of thoughts, either because we are already in it, nor is there a reason for changing; or because we come to a crossroads where many series of thoughts meet, one of them being the strongest of all.9

In this way, different experiences suggest different forms of series: cyclical, linear, crossing and branching. The inner experience of the mind is immersed in time. The temporal dimension was important for the analysis of affections, both in Descartes’ and Spinoza’s models. For instance, fear and hope—two decisive affections for a theory of human action—are nothing but the perception of some future good or evil. For the quality of affections, it is absolutely decisive that their objects are viewed as future or past with respect to one’s location in the flux of time. This means that the relevant temporalization has to be expressed by a tensed language; in present-day terms, the series cogitationum presents itself 7

8 9

“Sometimes a series returns to its own path, and it can keep man captured for a long time, while the former thoughts come back again, as if in a circle. One is never caught, indeed, w by the selfsame thought; when we say that one is fixedly intent on the same thought, one is going in fact along a recurring series whose period is short; and this happens especially when the same thing shows a lot of confused (or also distinct) aspects, that are different or strange with respect to anything that has been experienced so far.” A VI.4, 1425. A VI.4, 1424. A VI.4, 1434.

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as an A-series. The different figures of the series of thoughts can be viewed, instead, as a first drawing of the topological varieties of time series. This is truer, as for Leibniz the order of the time series will be determined by the order of the history series—that is, of the contents of temporal unfolding. What about the possibility of a branching? In the early Hanoverian years, Leibniz applied the Hobbes-style logic of conditions in order to dispel the idea of the ‘freedom of indifference’, that would involve the absurd notion of an effect that is not univocally determined. This makes it hard to conceive of the effective possibility of a branching in a series. All this is the subject of the second half of the De Affectibus, taking directly into account the nature of determination. The Dynamics of Series: Potentiality The ethical treatises of seventeenth-century rationalist thinkers share the assumption that the successive mental states are causally connected. In the De affectibus, the nature of this connection (determinatio) is questioned. Different approaches are tested in the several layers of the text. We can distinguish a dynamic, a metaphysical and a logical one, that are not so much stratified as rather interwoven. A first explanation, or better illustration, of mental determination relies on the analogy with the dynamic case. Earlier on, Leibniz had sharply opposed the behavior of mind to that of body—the paradigmatic case of this opposition being offered by his early physical treatise Hypothesis physica nova (1670). I for my part have emphasized above that the determination proper to affection is an intentional one, wholly different from mechanical shock. The point isthat Leibniz’s science of bodies and motion is no longer that of 1670. As M. Fichant has shown,10 already in 1678 Leibniz achieved his discovery of force, the basic concept of the new science he will later call ‘dynamics’ and is labeled, at the beginning, as the science of ‘power and action’. The same where they are notions, notice, occur in the heading of our De Affectibus, w meant in a psychological sense. What is relevant for the parallel is the fact that body ceases to behave as a ‘momentary mind’, the ‘force’ already taking into account the unfolding of future effect. This is why dynamics comes to reinforce the persistence model. Leibniz’s analogy stresses the points that psychical determination has in common with dynamical solicitation: a) they persist, even if an obstacle prevents their effect from being produced; b) they do not limit themselves to a starting impulse, but again, they persist along the unfolding of the corresponding series (of thoughts or motions); c) far 10

See G.W. Leibniz, La reforme ´ de la dynamique. De corporum concursu (1678) et d’autres texts in´e´ dits. Ed. and transl. by Michel Fichant. Paris: Vrin 1994.

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from being effaced by further solicitations, they add to them. Point (a) is illustrated by the example of a balance, where two weights happen to be perfectly balanced.11 Each of them will exert a ‘determination’, though neither effect is produced because it is hindered by the other. Effects E1 and E2 (the going down of each of two plates, respectively) are mutually exclusive because of their incompatibility, while the respective determinations D1 and D2, though being really opposed, are both present and active. In the same lines where the psycho-dynamic analogy is advanced, Leibniz puts forward a general definition of ‘determination’, embracing both fields: “Determination is a state from which something does follow [sequitur], provided that nothing else prevents it.”12 Or, equivalently: “determined for something is that from whose state something follows, the former being considered in itself.”13 We meet here the central polarity between a thing considered in itself ( per se spectata) on one hand, and an impediment (impedimentum) on the other. In the absence of the latter, “a determination allows for a preview of future behavior.”14 This concept of determination captures the fact of ‘inclination’: in modern terms, dispositional facts, be they found in the dynamic or psychological field. In a sense, the whole draft can be seen as a re-thinking of the ancient ‘logic of virtuality’. The dispositional view of causal powers was a central piece in the traditional framework. In Metaphysics, Book 10 Aristotle introduced modal concepts starting precisely from that of ‘power’ (both active and passive), conceived of as a kind of dispositional fact. Analogously, the De Affectibus presents, after the definition of determination, a slightly different one of ‘power’ ( potentia) as a ‘status from which something can follow’ [sequi]. The connection between disposition and power, however, seems to work the other way around, insofar as Leibniz’s potentiality is led back, rightly from the start, to his ‘logical’ view of possibility ( possibilitas): ‘being able to follow (sequi posse) from’ coincides here with the fact that “from something considered in itself the possibility of something else is demonstrated.” The Metaphysics of Series: The Logic of Perfection One might suspect that the shift from ‘determination’ (as simply ‘following from’, provided there is no impediment) to ‘power’ (as ‘being able to follow’) aims at capturing the situation of ‘knots’ or ‘branchings’, that is the possibility 11 12 13 14

A VI.4, 1428. A VI. 4, 1426. A VI.4, 1427. A VI.4, 1426.

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of alternative developments in the unfolding of a series. In the De affectibus, indeed, intensive effort is made to explain why we follow one series rather than another. This inquiry is displayed in parallel on the double level we are familiar with. The first one is that of concrete psychological description, where we are told how the ‘strongest’ series, or the richest in content, imposes w itself, and which properties it possesses. On a second level, such psychological considerations become nothing but a special case for a general mechanism of determination. The notion of perfection15 allows Leibniz to pass to a metaphysical language, very general (both dynamic and psychological concepts can count as its specifications), though less formal than the ‘logical’ one that will prevail in the last part of the draft. Here, the metaphysical element of perfection progressively disappears, making room for a study of determination at its most abstract level, whose key notion is that of ‘consequent’ as “that which does follow from something else considered in itself.” Within this conceptual frame, two theorems are proved: (TL1) “If many similar effects can follow together from something, and one of them does effectively follow, then necessarily all of them follow, caeteris paribus.” (TL2) “If many effects, that are similar but not equal, can follow disjunctively from something, then necessarily the greatest of them does effectively follow, caeteris paribus.”16

Taken together, (TL1) and (TL2) justify the general claim (TL3) that “From each thing the effect does follow which is, if considered in itself, the most perfect among those that can follow.”17 The holding of some conflict among different sets of possible effects is assumed. The prevalence of the most perfect set—or better, series—is simply due to the fact that the only reason that can prevent the production of an effect is its being annulled by a contrasting and more powerful one, on the model of the dynamic composition of forces. The result of (TL1-3) is expressed in a modal theorem (TL4) that a marginal note hails as an “admirable passage [from power] to act”: All things that, insofar as they are considered in themselves, can follow from something else, insofar as also the latter is considered in itself—they all actually follow, as far as they can.18 15

16 17 18

A VI.4, 1431. The equivalence of ‘reality’ (realitas r ) and ‘perfection’ ( perfectio) is taken for granted, and the further Spinozian equivalence of reality and ‘power’ is somehow argued for. A VI.4, 1433. A VI.4, 1431. A VI.4, 1432.

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Leibniz tries to further clarify and confirm the underlying logic in a group of theorems which use the notion of ‘consequent’, and are again framed around the polarity between the “following from something considered in itself ” and the “impediment”: if, on the assumption of the holding of a kindred consequence, together with the absence of further impediments, the effect were not to follow, then the assumption would be contradicted. But this was precisely the point of the Hobbesian proof for (TH1): provided that the set S of conditions {C 1, C2, C3, . . . Cn} is sufficient to bring about the effect E, then, if S obtains, E necessarily also does, unless it is prevented by something else. Let me then go back for a moment to the De Corpore, to consider the modal implications of Hobbes’s theory of requisites and compare them to the analysis of the De Affectibus. The Ghost of Plenitude and the Metamorphoses of Impediment Also the chapters of the De Corpore devoted to cause and power could be read as a reshaping, in a logically minded deterministic setting, of the traditional theory of causal dispositions: the latter working as actual conditions, that bring about their effect, as soon as they are not prevented by some contrasting factor. On this basis, the Aristotelian idea of ‘power’ as rooted in a real disposition received a radical interpretation. After having sketched his causal determinism, in fact, Hobbes used it, in the following chapter 10 on ‘Power and Act’, in order to reinterpret the notion of possibility. According to him, causal conditions and the dispositions called ‘powers’ are really one and the same thing, being different only according to the way they are considered: “Something is called a cause, having respect to the effect as already produced, and a power insofar as the selfsame effect is considered as still to be produced; so that cause refers to the past, while power refers to the future.”19 From this perspective, it is quite natural to define possibility in causal terms: the possible will be that for which sufficient causal conditions hold at some time. I call this thesis (TH2). We know, however, that the holding of sufficient causal conditions necessarily determines the existence of the related effect (TH1). Hence, from the conjuction of (TH1) and (TH2) we derive that (TH3) the possible coincides with what does actually exist at some time. And this is nothing but the Hobbesian form of the venerable Principle of Plenitude. Leibniz is famous for having rejected this principle, and imputed to its acceptance the most dangerous consequences. We have seen, however, that he does accept the first step (TH1) of Hobbes’s argument—that is to say, the 19

OL I 113.

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deterministic reading of causality, or the theory of causal conditions as being both necessary and sufficient. What he vigorously rejects, on the contrary, is the causal definition of possibility (TH2) which, together with (TH1), does entail plenitude. The seminal intuition that allows for this denial is that of the possibility of alternative series of things, that never pass, or have passed, or will pass into existence. In a well-known autobiographical reconstruction, Leibniz will indicate in that idea the way out from the incumbent fatalistic result of his robust (Hobbesian-style) determinism. The texts from the last period in Paris and the early Hanoverian years seem indeed to confirm his later narrative. Thus, the short metaphysical treatise of the end of 1677 Elementa verae pietatis—whose ‘great axiom’ is nothing but the principle of reason—already presents divine creation as a choice among several possible courses of things. What determines the choice of one of them to be actualized is its perfection: all the leading ideas of Leibniz’s mature theodicy are already in place. Also the ‘novel argument’ in its standard form is there: Surely, many different series can be imagined, and one cannot think that all possible things do actually exist. Or should we think that we cannot imagine any tale, without the latter being actual somewhere in the past or in the future?20

The thought experiment of the alternative stories has its counterpart in the neat adoption of a logical definition of possibility through non-contradiction. In order to appreciate the echo of these reflections in the context of the De Affectibus theory of dispositional conditions, we have to consider more closely the role of impediment. Also this notion, after being introduced rather intuitively on the basis of dynamic analogy, is submitted to a process of logical clarification, whose final result in the semi-formalized language of the last part of the draft is the notion of ‘pertinens ‘ ad rem’, i.e. a relevant factor in a negative sense: ‘B impedes A’ means that B is the antecedent of A’s negation, i.e. its consequent is incompatible with A. This type of relation was already documented in the logical tradition and in the books of the age.21 Closer to 20 21

A VI.4, 1363. See, for instance, this quotation from Hotman, taken up by Keckermann: “Which are the r ]? They are those which do not directly contrast one things that repel one another [repugnantia another, but rather are in a kind of cross-opposition. One of them, in fact, is a term of a pair of contraries; the other, however, is not its contrary, but the consequent of the contrary . . . Thus, the repugnans r is the consequent of the contrary term.” Quoted in G. Roncaglia, Historical Remarks on the Theory of Oppositions, in I. Marchlewitz, A. Heinekamp (eds.), Leibniz’s Auseinanderstzung mit Vorg¨ gangern und Zeitgenossen, Stuttgart, Steiner 1990, 173–183. g¨

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us, let us recall the situation of balance I have considered above. The case of determinations D1 and D2 (the solicitation exerted by the equal weights) is not one of logical contradiction, but of real opposition, to use a well-known later Kantian distinction. As such, they are both present. Their effects, i.e. the actions A1 and A2 (the going down of the plates), however, are incompatible, hence they exclude one another. If this dynamic situation is translated into the vocabulary of the logical theory of oppositions, we could say that A1 and A2 behave as contrary terms, which cannot both be true. Instead, they can both be false: neither of them does obtain, indeed.22 We have seen in the De Affectibus the Hobbesian logic of determination at play: the effect does infallibly follow, provided the impediment is removed. This logic does not capture, however, the whole of Leibniz’s intuition. The ‘impediment’, in fact, can receive a double reading: on the level of actuality on one hand, as an opposing force or inclination, acting in the same spatiotemporal framework (as in the case of balance); on the level of pure possibility on the other, as a logically possible but incompatible alternative. This doubling is what allows Leibniz to maintain his view of modality, though sharing a Hobbesian conception of dispositional powers and determination. Thus, every reader familiar with Leibniz’s writings will easily recognize in T1-T2 the fundamental principles governing what he will later call ‘metaphysical mechanism’: that is, the proceeding of evaluation of the compossibility sets that determines the divine choice of a world. Leibniz already masters these ideas when writing the De Affectibus. w True, the psychological treatise of 1679 is not written from the point of view of God, but of the unfolding of a finite mind, so that it seems to apply the mechanism only to the struggle among actual contrasting psychological inclinations. Also from this point of view, however, the text could conceal some clues for an original approach to the idea of purely possible series. We need only to reflect on the competing series of thoughts that conflict in the common space of mind. The philosophy of mind of the De Affectibus tries to make sense of reality claims from within a methodically phenomenistic perspective. Like in Spinoza’s theory of mind, every mode of thought—be it a perception, or a mere imagination—is endowed with a conatus, i.e. with self-affirmation, or a claim for reality, which can be suppressed only by a more powerful (and incompatible) content.23 Thus, some series of thoughts reveal themselves as mere imaginations; other ones, on the contrary, have a justified 22

23

In section [J], the impedimentum is defined as what cannot be “true-together-with”. It does not exclude directly, however, but through its consequent: in the example of balance, the impedimentum for A1 would properly be determination D2, having action A2 as its consequent. See the example of winged horse in Ethica II Pr. 49 Scholion.

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claim for reality, insofar as they exhibit the most wide-ranging coherence and practical interest. This consideration could represent a coupling ring between the two interpretations of the opposition model: that of dynamic interaction working within actual reality, on the one hand; and that of ideal alternativeness on the other, where the unactualized series are located in the realm of the possible. Developing in the De Summa rerum the topic of the difference between dreams and reality into the nutshell of the idea of possible worlds, Leibniz observed that dream-worlds have no spatio-temporal (let alone, causal) relation with our actual world. In the De Affectibus such ‘dream-sets’—i.e., locally coherent sets of mental contents—receive a serial dimension. In this way, a the psychological study of imagination meets the intuition lying behind the ‘novel-argument’ for unactualized possibles. At this juncture, a decisive step can be taken: the alternative series are separated from the common world and constituted as purely possible ones. This move of idealization is closely bound with one of totalization, insofar as each set, or series, is conceived of as maximal. Their conflict displays itself in a common logical space that is no longer human mind, but God’s mind. Possibles as such compete as motives for creation in God’s intellect, and each of their series excludes the actualization of the others. Leibniz changes a real opposition among competing dynamic or psychological solicitations into an ideal opposition among possible series. Through this extrusion of purely possible series from the actual world and the idealization of impediment, the logic of plenitude is blocked. It continues working, however, within a single compatibility set (or better, series). Obviously, one is still left with the task of giving an account of the incompossibility among sets: a task whose difficulty Leibniz is well aware of. Alternatives without Branching. The Core Inference Leibniz devotes a great deal of his efforts in section [J] to proving the following theorem: “What can be the consequent of something else, it is indeed, if considered in itself, the consequent of the latter.”24 The demostration is as much detailed as involved. What is the aim of this complex proof? It seems to me that Leibniz wants to eliminate the apparent difference between the logic of determination and that of ‘power’ that section [H] could be understood to maintain, with its distinction between the ‘sequi’ on one hand, and the ‘sequi posse’ on the other. All is reduced here to one opposition pair only, between the consequence [consequens esse] as a possibility of following, and the fact of actually following—where the latter does infallibly 24

A VI.4, 1437.

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obtain, provided it is not blocked by an impediment. We know that in this frame plenitude is avoided through the further ‘idealized’ interpretation of ‘impediment’. The theorems of ‘metaphysical mechanism’ made the assumption that different and incompatible sets of consequences could follow from one and the same thing. On the assumption of the (proved) transitivity of the relation of consequence, however, Leibniz proves in the last section the following theorem (TL5): “What is incompatible with the consequent, is also incompatible with its antecedent.”25 Now, disjunctively possible sets of things are incompatible among themselves. But then, for (TL5) they simply cannot follow from the selfsame antecedent—that is to say, from the selfsame thing, or state-of-affairs, or hypothesis. And this amounts to saying that properly there is no branching; hence, the formulation of (TL1) and (TL2) in section (H) was ffar from accurate and potentially misleading. More correctly, already in section [G] Leibniz avoided speaking of incompatible consequents flowing from the same antecedents, saying instead: “If from two things, considered in themselves, incompatible effects follow, then . . .”26 The moral to be drawn from these (to some extent conjectural) remarks is this: the possibility of the alternative unfolding of a series of determinations does not coincide with the possibility of some branchings in the series itself, but rather with the parallel possibility of a whole and relatively autonomous series. It hardly needs to be stressed how relevant these aspects of the conditional structure of series are in order to understand Leibniz’s later theses about individual histories and counterfactual non-identity. Whereas the dynamic model was introduced by way of analogy, the ‘logical’ language in which the final account of determination is framed seems to present itself as a true explanatory account of what determination means. ‘To be determined’ is taken as synonymous with ‘to follow from”. Leibniz goes further: “Something B follows from something else A, iff the existence of B can be derived [concludi potest] from the existence of A, and B is posterior in nature to A.”27 Derivation is finally expressed by a pure inferential scheme: “B can be derived from A means that: if A obtains, B also does.”28 Precisely in this last formulation, the study of consequences reduces to the conceptual frame of the logic of conditions we are familiar with. But the same schema 25 26 27

28

Ibidem. A VI.4, 1429. A VI.4, 1427. This corresponds to the definition of consequent: “A consequent is that, whose existence can be derived from the existence of something else, which is prior in nature to it.” A VI.4, 1436. A VI.4, 1439.

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appears earlier in the De Affectibus, w where it is used for defining the relation of cause and effect: Let there be two things A and B, of which the former is prior in nature, the latter posterior; and assume that, if A obtains, B also does: then B will follow from A, i.e. A will be the cause, B the effect.29

It is not easy to provide a clear logical reading of the implication to hand. Surely, it is stronger than a material one. In any case, variables do not stand here for propositions, but for things or states of things. At least two elements of the definition indicate its extra-logical import. The first one is the explicit reference to the existence of things, as the proper term of the inference. The second is the order of nature. I will return to both, when considering the logical theory of conditions of some years later. It is clear from now, that conditional logic gives the logical syntax of determination, but the related semantics is still presupposed, and it is open to us to clarify its positive content. We will get some further clarity from the consideration of what corresponds, in Leibniz’s model, to the immanent (or ‘vertical’) dimension of Spinozian causality.

Chapter 2. Subject of Action Conditions for Action: The Mind as a Subject Action was a guiding concept for Leibniz’s theory of conditions from its origins. This had developed, in fact, from the first juristic studies to the reflections on the principle of reason, mainly with the aim of dealing with ethics and theodicy. In this context, the problem of causality appears essentially as one of imputability.30 The requisita r are as much conditions for action, as for existence. Where the analysis is pursued in this direction, the problem of subject emerges behind the quest for conditions. This is the case with the De Cogitationum Analysi, w which studies, like the De Affectibus, the disposition to act (inclinatio, or determinatio). The line of inquiry diverges, however: 29

30

A VI.4, 1429. Prior in nature is “that, whose possibility can be demostrated more easily.” A VI.4, 1427. This was, notice, the original sense of the notion of ‘cause’ (atA t a), according to reliable reconstructions. See M. Frede, The Original Notion of Cause in M. Schofield, M. Burnyeat, J. Barnes, eds., Doubt and Dogmatism. Oxford, Clarendon Press, 1980, 217–249.

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the quest for requisites is not pursued back towards the preceding states, but ‘vertically’, so to speak, towards the underlying subject: Determinate is what possesses all requisites, i.e. all absolute requisites . . . it possesses all requisites that, if they are supposed to exist, do not involve any further ultimate subject.31

The ultimate subject is the one to which action can be imputed. The idea that substantiality is connected with action, notice, is a very old entrenched one for Leibniz, going back at least to the Mainz period. There we find, in a theological context, that the power to act is essentially constitutive of a substance: “Substance is what has its principle of action within itself ”.32 We can better understand what is at stake in the need to identify the ultimate subject, however, if we consider the Spinozist model for ethics, where ‘my’ (desiring, willing, acting) mind is only a part of a more comprehensive system, insofar as the modifications that constitute it do inhere in an underlying substance, God. Conversely, for Leibniz to defend the substantiality of mind amounts to showing how the latter has a justified claim to be considered as the subject of ‘its’ actions. Spinoza’s ‘ideas’ connect themselves in chains with the impersonality of a logical system. They are related, to be sure, to individual bodies, and form some sub-systems (called ‘minds’) that work as partial perspectives on the world. Individual bodies, however, are composite aggregates, endowed only with a relatively stable connection. Correspondingly, minds have parts and are considered in their turn as parts of more comprehensive wholes—ultimately, of the all-embracing system of God’s attribute of Thought. Moreover consciousness, which Descartes took as the fundamental characteristic of mental reality, does not seem to be a qualifying feature for Spinoza’s modes of thought. So, the latter do not belong exclusively to some conscious subject as its ‘private’ contents. Leibniz’s approach is quite different: exactly as the emergence of the ontological subject of predication subverted the conceptual atomism of suchnesses, the ‘model metaphysics’ of the chain of states is profoundly reshaped by reference to active and conscious mind-like subjects. Whereas Spinoza considered ideas as self-asserting modes of thought, whose active force brought about a kind of automatic enchainment, Leibniz objects that “ideas do not act, only minds do.”33 The De Affectibus opens with a definition of the conscious mind as something able to act on itself. Directly from the start, the chain of thoughts 31 32 33

A VI.4, 2769. De Transubstantiatione, A VI. 1, 511. Notes to Spinoza’s Ethica, A VI.4, 1713 (GP I 150).

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has a focal point, the conscious mind. Consciousness, in its turn, is defined as a kind of action. Mind is not only active, however, but also passive: the concept of determination, at its first appearance in the De Affectibus, is immediately split into the action-passion pair. This was the fundamental polarity for all seventeenthcentury theories of affections, whose usual aim was that of extending human activity and of reducing merely passive affections as far as possible. Although human subjecthood and human imputability do not have an absolute ontological consistence for him, also Spinoza’s aim is that of expanding and reinforcing our activity. At the beginning of part III of the Ethics, he defines the action-passion pair through the opposition of adequate and inadequate cause. A cause is adequate when ‘through it one can conceive clearly and distinctly of its effect’, inadequate if one cannot explain the effect through it alone. Correspondingly, “we are said to act, when we are the adequate cause of something that happens in or outside ourselves: that is to say, when from our nature something does follow, that can be clearly and distinctly understood through this nature alone.”34 Spinoza makes a further connection of ‘adequate causality’ with adequate knowledge—one that has strategical relevance for his ethical project of optimization of our affective life. For his part, Leibniz does not accept the last equivalence, while concentrating on the first pair. So, the corresponding De Affectibus definitions read: An action is the state of a thing according to which something does follow, arising from its nature . . . A passion is the state of a thing, according to which something is prevented from following from its nature.35 w

The action-passion pair, so defined, strongly recalls the dialectic between the ffact of following from something ‘considered in itself’ on one hand, and the ‘impediment’ on the other, which already structured the modal framework of the De Affectibus. The ‘external’ factor, notice, could also be a help (adjumentum). “Following from Its Own Nature”: Law and Spontaneity The illustrations of the notion of “deriving from a nature” in the De Affectibus—the balance and the falling body—are drawn from the field of 34 35

Ethics III Def. 2 (GEBH II 139). A VI.4, 1428–29. See on these definitions M. Kneale, Leibniz and Spinoza on Activity, in H.G. Frankfurt (ed.), Leibniz: A Collection of Critical Essays, New Y York 1972, 215–237.

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dynamics. The latter allows Leibniz to introduce the notion of ‘spontaneity’: This action will be most spontaneous, whose pattern [species] will not be changed, but only its grade [quantity]: e.g., if we imagine that a body ffalls towards the center of the earth always on a straight path, though it is slowed down by the resistance of the medium. The situation closest to spontaneity is when the body does stop for some time because of an obstacle; then, once the obstacle is taken away, it goes on falling along its path. In this case, in fact, one will be able to go back by inference to the earlier state, without assuming any additional datum; only one will be wrong about the time employed, because the period at rest will depend on the external obstacle. But if meanwhile the body has been thrown up by some external agent, in this case we are not able to go back by our inference, if we are not acquainted with the interfering action. In this also, however, we will have different grades of facility, e.g. if the external mover pushes the body along the selfsame path it was following before, so that the path never changes.36

The path of the falling body is determined both by its initial position and the assumption (hypothesis h ) of a certain physical law. The necessity of this development is clearly a nomological one. Nomological facts have, as their ontological correlates, some corresponding dispositional facts—coinciding with physical ‘impetus’, or mental ‘inclination’. Now, insofar as a falling body follows the pattern of motion that is prescribed by the law, it is said to act ‘spontaneously’. This notion receives a markedly epistemological interpretation: a behavior or a development is spontaneous, insofar as it can be reconstructed and made understandable according to simple and homogeneous rules. All this is clearly inspired by the experience of mathematical physics, with its efforts at reducing the variety of phenomena to the unity of simple, elegant equations. Bear in mind that the formulation of equations presupposed a procedure of idealization, leaving aside for the sake of simplicity a lot of concurring conditions, in order to isolate the essence of the phenomenon studied—e.g., making abstraction from resistance. In Leibniz’s analogy, air resistance or other external impulses play the role of the impediment, interfering with the development prescribed by law. On the whole, however, Leibniz’s example shows a very characteristic feature of his approach: I mean, the attitude to use the conceptual resources of the new science, and of his own physico-mathematical studies, to rethink the old Aristotelian paradigm. In this case, the Galileian law of the fall of bodies seems to be used to give an updated version to the old idea of ‘natural motion’, 36

A VI.4, 1428–29.

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hence to the ‘internalization’ of cause, so that the philosophical impact of the new paradigm is profoundly modified. In order to delineate the traditional view, one scholar has written: at the root of the internality of Aristotelian cause . . . there is the unification of the whole physical world under the categories that provide the conceptual framework for action: if the world is an irreducible plurality of individual objects, this is because processes are imputable to things themselves, the latter being conceived of as the first sources of activity.37

The invention of dynamics is used by Leibniz exactly to recover an internal principle for physical becoming. So, whereas in Spinoza ‘our’ nature is only a fragment of the ‘Nature’ as a whole causal system, Leibniz uses that notion to give a stable and autonomous principle of action to each particular thing. There is a connection, notice, between this train of thought and his criticism to the scientific ontology of moderns: Leibniz realizes that the abstractness he imputes to the Cartesian/Spinozian view of substance and attribute—especially of ‘Extension’—is not only the product of a categorial/semantic mistake, but also the ontological projection of the new scientific image of the world as a system of homogeneous matter where mechanical interactions are subjected to global conservation principles (of motion, or force). His defence of internal causation is directed against this ontological view. Differently from ancient essentialism, however, in Leibniz also external circumstances tend to be somehow ‘internalized’. In order to see this, we should consider how the philosophy of mind of the De Affectibus contains the seed for two different levels in the analysis of causality, that are more complementary than alternative. The Expansion of Spontaneity The Spinoza style reinterpretation of the action-passion pair is the model for the standard Leibnizian reading of phenomenal (intersubstantial) causality, to be found in § 15 of the Discourse and in his Correspondence with Arnauld. According to this view, we are entitled to attribute active causality to the object that provides the most distinct explanation for a given change. For a state S2, to be caused by a state S1 (of the same or of another thing) amounts to being intelligible from the latter according to the simplest rule. The ontological dimension of subjecthood, however, opens up to a more radical sense of activity, going beyond the psychological and epistemological reading of the action-passion pair, typical of the theory of affections. The 37

M. Messeri, I corpi e le menti. Saggio sull’epistemologia di Spinoza, Saggiatore, Milano 1992, p. 115, translation mine.

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central role action or causal efficacy play in making sense of subjecthood marks the decisive step towards the well-known ‘windowlessness’ of individual substances. Leibniz is unable, I mean, to make sense of a property attribution to a subject S, that falls outside the scope of the causality of S itself. The substantiality of finite beings—hence, their being subjects of inherence for changing properties—stands or falls together with their capacity to be principles of action. As is well known, the Discourse doctrine will firmly establish that, ‘dans la rigueur m´e´ taphysique’, all that happens to a substance arises ‘from its own depth’. Maybe, already in the De Affectibus we can find some clues for this ontological sense of activity and spontaneity. First of all, spontaneity expands, insofar as we are able to include the partial trains of thoughts in a single unified development: If we consider a series of successive determinations that follow each other according to a determinate law, and the determination to enter this series has been, in its turn, a pure action; then, all actions during the unfolding of this series will be said to be spontaneous or natural, and this more so as we go back more towards the first state of the series. Bear in mind that the determination to enter a series can be found, in its turn, in a former series; and the less, in following this regress, we come across a passive state, the more spontaneous or natural we consider a process.38

The idea of a ‘series of series’, or of the progressive enchainment of series— bringing about the view of a unified one embracing the whole life of the mind— coincides with this expansion of spontaneity. Secondly, the definitions of the action-passion pair in the De Affectibus seem to presuppose interaction with external factors. In the last of these definitions, however, one could divine the clue to an interiorization of the external obstacle, insofar as explicit reference to an external agent is left behind: “A passion is the state of a thing, according to which something is prevented from following from its nature.”39 It is only a suggestion, of course; but it is far from unlikely that Leibniz, while drawing the outline for his mature theory of phenomenal causality, is already aware also of its metaphysical counterpart. Once again, a transvaluation in the way of conceiving the ontological status of impediment has to be assumed. In the case of alternative possible series, we have an idealization move, coinciding with the extrusion of some series from the realm of really interacting actual objects. Now, we would have the interiorization of the interacting factors (within the same actual world) into 38

39

A VI.4, 1430. In the margin Leibniz observes that “from this one can understand that, God excepted, the whole state of nothing is entirely natural or spontaneous.” A VI.4, 1429.

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a single series. Exactly as the actual series presupposed, in the ‘prologue in heaven’ of divine choice, the comparison with alternative possible series, the unfolding of the individual program presupposes the ideal reference to all other actual series (or substances): according to Leibniz’s warning to de Volder, the concept of a substance involves all other concepts, although substance itself is ontologically independent. Commenting on Leibniz’s criticism to Spinoza and de Volder, I have stressed the divorce between inherence and causal dependence. The first relation claimed a robust ontological import, while the latter was confined at a merely conceptual level. This is true, however, only as regards phenomenal, or intersubstantial causation—this not being a true causation at all. Immanent causality, however, i.e. the capacity of a substance to produce its own states, will be emphasized by the thesis of absolute spontaneity. So, Leibniz’s warning about distinguishing inherence from conceptual dependence does not conflict with the fact that the key for his understanding of inherence seems to be, ultimately, immanent causality. I will return to this problem when dealing with Leibniz’s mature containment theory.

Chapter 3. Subject and Time: The Birth of a Continuant Persisting r Subjects: The Matter and Form Models Making individual substances the subjects of action implies the possibility of distinguishing, and also of re-identifying them. Most of all, they have to be re-identified over time and change. Action itself, in fact, is defined with reference to change. The new ontologies of Hobbes and Spinoza, on one hand, do recognize transtemporal sameness as the key for individual identity; on the other, they tend to treat substance somehow as a ‘mass term’, and hence they ffail to provide a firm ground for this identity. Individuals, in fact, turn out to be only transient modifications of a kindred substance and their boundaries seem to a large extent relative. De Corpore 11 takes the identity problem essentially as a temporal one.40 It expounds three types of solutions, according to which the diachronic 40

“The selfsame thing can be compared with itself, I mean at a different time; hence the big dispute among philosophers about the principle of individuation: i.e., in which sense some body has to be held now as the same, now as different from what it was earlier . . . ”, OL I § 7, 120).

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individuation principle would be, respectively, (1) matter, (2) form or (3) the whole of accidents. Solution (3) alludes to the ancient Isagoge suggestion, that answered, however, the different problem of synchronic (or better, a-temporal) individuation within a hierarchy of classifying concepts. Hobbes considers the accidents of a determinate time-slice: but then, the continuous change of accidents would simply destroy identity at each moment. (1) and (2) are the two solutions old Aristotelian hylemorphism could offer. Although Aristotle did not deal expressly with the problem of temporal identity, his substance is, in present-day terms, a ‘continuant’ that endures through time and change, being wholly present at each moment of time. It hardly needs to be remarked, how this idea expresses our experience of ordinary objects and is tied to a ‘tensed’ view of time. It remains to be seen, however, whether the candidate for playing the role of continuant is matter or form. The notion of matter had been originally conceived of in the Physics as the underlying substratum that makes change intelligible. This substratum, however, was not enough to account for substantiality, as the mature substance theory of the Metaphysics pointed out. Form emerged, rather, as the constitutive element of substance, giving it its essence, hence its identity. Consequently, form could appear as the best candidate to explain temporal identity. Bear in mind that the paradigm of Aristotelian substances was biological beings, whose identity is reasonably independent of the continuous flux of their material parts. For Hobbes, however (as for the young Leibniz, at least after 1666), hylemorphism is definitively out, and the matter-form pair has to be reinterpreted in the new mechanist framework. The role of material substratum can well be fulfilled by the Hobbesian ‘body’, persisting through all changes. Matter, however, does not provide any manageable criterion for the identity of particular bodies, insofar as it behaves as a mass-term. For its own part, ‘form’ is translated into the configuration of parts and the “principle of motion”. This reinterpretation, however, leaves identity open to the aporia of Theseus’s ship, of which De Corpore 11 gives a classic exposition: on one hand, all pieces of a ship are gradually substituted by brand new ones; on the other, the rejected pieces are put in the same arrangement they had earlier: but then, which of the two ships is the same as the original one? Finally, Hobbes embraces an idea of relative identity, according to which some bodies can be considered as identical or non-identical depending on the descriptions (“names”) under which we refer to them. In Spinoza also, individual sameness amounts to the w relative stability of an aggregate of parts unified by some pattern of motion. The notion of ‘individual’, in fact, is introduced by him at the level of physical theory and is defined as a system of parts, whose identity is given by the conservation of some proportion of motion and rest.41 41

Ethica II, Lemma 7 (GEBH II 101–102).

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Matter, Memory and Mind-Body Asymmetry For the young Leibniz also, the problem of identity is chiefly conceived of as one of transtemporal sameness—what is well understandable, moving from the problems of moral and juridical imputability, as is the case in the Philosophical Questions from Law (1664). Of the two available models of persistence—matter and form—Leibniz, still moving within the Scholastic framework, prefers the second, this being also in tune with Thomasius’s negative attitude towards material individuation. Thus, the Philosophical Questions indicate substantial form as the key for transtemporal sameness, according to a tradition coming back at least to Averroes.42 Also in the De Transubstantiatione r —the text quoted above, where substantiality is identified with the power to act—Leibniz goes on to establish the further connection of substantial form and transtemporal identity: I prove the numerical identiy of substance moving from the numerical identity of substantial form, according to the principles of the best of Schoolmen and Aristotelian philosophers, who take substantial form as the principle of individuation.43

After wiping out hylemorphism, however, Leibniz also is bound to reinterpret these notions. De Corpore 11 can well represent the framework in which the problem of temporal identity poses itself for him at this juncture. w In any case, persistence over time and power to survive change—better, to dominate it as a principle of action—remain two requirements that have to be met to be a substance. Now, of the two types of substances that the “new philosophy” offered—extended matter and mind—the first one (the only one taken into account by Hobbes) seemed to be incapable of satisfying those requirements. As we have seen, the Hobbesian body could well figure as an intuitive prolongation of Aristotelian matter, working more as a bare substratum or a mass-term than as a true continuant capable of giving an account of identity. And the physicalist reinterpretation of the model of form—i.e., form as arrangement of parts—did not ensure that identity either. Leibniz, however, already during the early seventies, tried to integrate a Hobbesian style “philosophy of body” with a “philosophy of mind”, where the requirements that cannot be satisfied by matter within mechanist physics are systematically transferred to mind. A paradigmatic example of this attitude is the well-known passage of the 1670 scientific treatise Hypothesis Physica Nova, w where the mind is presented as capable of conserving (“recollecting”) 42 43

Specimen Quaestionum Philosophicarum ex Jure Collectarum, A VI.1, 90–91. A VI.1, 511.

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the antecedent conatus—hence, its temporal path—while the body is suggestively marked as a ‘momentary mind’.44 Although the physical theory of this work is far from Leibniz’s mature views, the metaphysical suggestion seems to be nevertheless a durable one, if Leibniz some decades later will still refer to it in order to illustrate his ‘new system’.45 The outcome of Leibniz’s discovery is the splitting of temporal ontology according to the two great regions of being. In the case of bodies—even if they are relatively organized—he adopts a ‘sequentialist’ view: that is to say, he frankly recognizes them as ‘entia successiva,’ though conceding to them identity in a ‘loose’ sense. Self-awareness and memory, on the contrary, make us sure that the mind possesses a true and strict identity, being a continuant that remains numerically one and the same despite its changes. Eternity and the Endless Duration of the Mind It is far from surprising that Leibniz’s further inquiry into transtemporal identity is pursued on the terrain of his philosophy of mind. This is the case within some drafts of the 1676 De Summa Rerum. Two T mutually interconnected trains of thought underlie these reflections: on one hand, the direct elaboration of a theory of temporal notions; on the other, the confrontation with Spinoza’s theory of the temporal life of the mind. In the On Forms, remember, duration was counted among “simple forms” as a common one, shared both by extended and thinking things. This consideration is in tune with Descartes’ approach, where we discover duration in the inner life of the mind, and the same type of duration is attributed both to incorporeal and corporeal beings: which is not obvious at all with respect to the tradition. More traditional, instead, is the Cartesian identification of duration with existence, or better with its continuity, whereas time is distinguished from duration as an abstract device aimed at measuring it. Also Leibniz’s remarks on duration and time in the P Paris Notes conform to this conceptual setting. Analogously to his coeval treatment of extension, they suggest a relationship of eminence between the Form in God (eternity) and its countepart at the level of creatures (duration). The notion of eternity traditionally oscillated between sempiternity (being in all times) and being timeless. Spinoza agrees with the tradition by emphasizing the contrast between eternity as necessary existence on one side, and duration on the other. Given that for him, however, 44

45

Theoria motus abstracti, Fundamenta Praedemonstrabilia, § 17, A VI.2, 266 (GP IV 230). See on this, M. Capek, Leibniz on Matter and Memory, in I. Leclerc, The Philosophy of Leibniz and the Modern World, 78–113. See Leibniz’s Remarks on Bayle’s Rorarius, GP IV 543.

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all existence is objectively necessary, what aboout his claimed distinction between these two ways of existence? Nor can we simply attribute eternity to the “things” whose necessity does not come from an external cause, because also some modes are said to be eternal. A straightforward answer seems to hand: eternity is the way of being of immutable things, whereas transient things, whose necessary existence is limited, are said to endure. So far so good; an imw portant Spinozist thesis, however, is that also singular enduring things can be known “sub specie aeternitatis”. What does this mean? Here is a persuasive interpretation46 : a thing or an event have a transient (though necessary) existence in time, and are experienced by us according to our perspectival knowledge, as objects that are situated in the A-series; hence, as something which is future, and then becomes present and more and more past. For example, “tomorrow there will be a battle at Waterloo”; “a hundred and ninty years ago there was a battle at Waterloo”. But the corrresponding fact—embodying a date—holds tenselessly at all times: “There is [tenselessly] a battle at Waterloo, at June 18, 1815”. It possesses an objective position within the world history chain (e.g., after Napoleon’s escape from Elba and before his death in Saint Helen) and can be, as such, the object of a non-perspectival knowledge (say, the divine one). Be that as it may, the knowledge of singular facts sub specie aeternitatis is decisive for the last stage of Spinoza’s ethical project. His ‘intuitive science’ is precisely this necessary and tenseless knowledge of individual things; as such, it might be seen as an objective antecedent of the Leibnizian topic of individual notion. Now, Ethics Book 5 tries to establish that our mind, insofar as it takes part (both as object and subject) in that knowledge, contains something eternal that does actually survive its body’s destruction. Being detached from body, however, this survival has nothing to do with memory, nor with our standard way of conceiving immortality as the sempiternal duration of the mind’s life. On the other hand, the asymmetry in the mind-body destiny seems to be in striking contrast with Spinoza’s idea, that our mind is nothing but the counterpart of the related body in the attribute of Thought. For this and other aspects, it is a highly difficult task to make sense of Spinoza’s fascinating idea; but of course, it is not my job here. What is certain to me, Leibniz has somehow in mind this complex of Spinozian ideas (though filtered in a scattered way, because he is not yet directly acquainted with his work), when dealing with the problem of transtemporal identity within his Paris philosophy of mind. In the On the Secrets of Sublime, he states that “every mind is of endless duration [durationis interminatae].”47 This unending existence is clearly 46

47

For this reading, see Messeri, I corpi e le menti, 66–72. See also on this M. Kneale, Eternity and Sempiternity, in Proceedings of the Aristotelian Society, 69 (1968), 223–238. A VI.3, 476 (SR 31).

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intended by him as sempiternity, or existence at all times, neatly distinguished from timeless eternity, but also from the necessary possession of existence. In order to understand what is at stake here, one has to consider another theme intensively debated in the age, that of “continuous creation”. Descartes and his followers did emphasize this traditional topic in a new way, by stressing the radical contingency of finite existence, hence its need of being re-created at each moment. Spinoza put forward a quite contrary view: analogously to the physical law of inertia, each thing tends to persist in existence, unless it is destroyed by an external obstacle48 —and this is, actually, the destiny of all finite things, involved in the spatio-temporal series, whose necessity is only an external one. Accordingly, their duration is only indefinite, insofar as it is undetermined in its own source, and can be suppressed only by external causes. We see at work here that metaphysics of self-expanding being, whose logic had been spelt out in the theorems of the De Affectibus. In one sense, Leibniz goes further than Spinoza: according to him, in fact, the mind’s existence cannot be destroyed by any external obstacle, hence it is positively unlimited. To be sure, this positive endurance is not independent of divine will, nor is it marked by necessity; anyway, it is something ‘natural’ (by the way, this will remain Leibniz’s constant attitude towards the metaphysical thesis of continuous creation). Once again, the guarantee for this type of endurance has to be found on the terrain of the philosophy of mind: the notion itself of ‘the same’ is tied to self-knowledge, and cannot be derived from corporeal reality. This irreducibility is stressed by Leibniz, to counter Spinoza’s equation of mind with the “idea of (a) body”. We are on the same line inaugurated by the Hypothesis physica nova, one that attributes quite different persistence conditions for material and immaterial beings, respectively. Anyway, in the P Paris Notes the sameness of mind is accompanied by the numerical persistence of a piece of matter, a small body that entertains a privileged relationship with mind itself.49 The Recollecting Identity and the Essence of Mind The point I wish to insist on here, is that the act of self-consciousness is interpreted as a memory act: In our mind there is a perception or sense of itself, as of a certain particular thing. This is always in us, for as often as we use a word, we recognize 48

49

See on this H.G. Frankfurt, Cr´e´ ation continuee, ´ inertie ontologique et discontinuit´e temporelle, in Revue de m´e´ taphysique et de morale, 92, 1987, 455–72. This also is a persisting theme in Leibniz. In the correspondence with Arnauld, he will claim that also some small body, strictly united with soul, survives death. See also NE II. 27 with the reference to the Rabbinic “luz” (A VI.6, 232–233, GP V 216).

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that immediately. As often as we wish, we recognize that we perceive our thoughts; that is, we recognize that we thought a short time ago. Therefore intellectual memory consists in this: not what we have perceived, but that we have perceived—that we are those who have sensed. And this is what we commonly call “the same”, this faculty in us which is independent from external things. I do not see how a man, or a mind, can die or be estinguished as long as these reflections endure. Something remains in its modifications—not as extension per se remains in space, but as a particular endowed with certain modifications, which has perceived this or that. This particular sense of oneself is without other signs, as I have noted well; when I think and reflect on myself for a long time, with continuous reflections on a reflection, there is, as it were, a kind of amazement, and a wondering at this reciprocation. It seems that this sense of oneself always exists . . . If this is the nature of the mind, and it consists in the sense of itself, then I do not see how that sense can be impeded or destroyed. Furthermore, since (as I said a little before) the identity of the mind is not destroyed by some modifications, it cannot therefore be destroyed by any, as can easily be shown.50

Tradition used to distinguish corporeal and intellectual memory for their difT ferent objects and Descartes elaborated on this. The memory which constitutes self-knowledge is intellectual, insofar as it has no empirical contents (what we perceived), but its object is a mental act, again (that we perceived). The ffascinating draft On Reminiscence51 presents in a more detailed manner this experience of self-knowledge, that is conceived of as an indefinitely iterated reflection on his own thought. This text makes evident the experimental character, so to speak, of Leibniz’s inquiries into the philosophy of mind. While in the De Affectibus the phenomenon of ‘admiration’ is interpreted as the cyclical falling back into the same state of thought—so that serial progress is blocked—here, instead, Leibniz observes that in every point of the chain of thoughtsa vertical ascent to higher and higher levels of reflection can open up. In any case, the psychological phenomenon of the possibility of indefinite iteration is for Leibniz the factual proof of the ‘endless’ or ‘indestructible’ character of mind. Leibniz insists that this type of memory needs not signs (also images are signs): this is a relevant exception to the general conditions of our knowledge he is reflecting on in this period. If, on one hand, this disproves Spinoza’s view of the mind as “idea of body,” it represents, on the other, a problem for Leibniz 50

51

On Truths, the Mind, God, and the Universe, A VI.3, 509 (SR 58–60). On these texts, see M. Wilson, Leibniz: Self-Consciousness and Immortality in the Paris Notes and After (Summary), in Leibniz a` Paris. Studia Leibn. Suppl. 18 (1978), 149–150. On Reminiscence and on the Mind’s Self-reflection, A VI.3, 515–517 (SR 71–75).

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himself, insofar as there is no human memory without images. But then, the mind’s self-knowledge would amount to nothing very different from the experience of Spinoza’s ‘eternal’ mind, deprived of any particular reminiscence.52 The passage quoted above, however, insists that the recollecting memory takes as its object a particular self, “endowed with this or that modification”. This seems to mean that the inner core of intellectual memory should be accompanied by its various (imaginative) contents. As a consequence, the continuant is not a kind of transcendental subject (an abstract ‘I’), nor a substratum on the model of matter (“not as extension per se”); it is, instead, a fully concrete subject. We can recognize here another seminal idea of the Hypothesis Physica Nova—that a mind is capable of conserving the traces of all its past impressions. And these traces, Leibniz insists, cannot vanish. Mind appears, therefore, as a continuant moving indefinitely forward along the A-series and continuously increasing its content by integrating cumulatively its former experience. This is why, Leibniz is eager to distinguish its persistence from the eternity which would belong to a tenseless essence— which Spinoza’s “eternity” would amount to: w So I do not accept Spinoza’s view that the individual mind is extinguished with the body; that the mind in no way remembers what has gone before; that there remains only that which is eternal in the mind, i.e., the idea or essence of the body—namely, of this body—and is this what survives in the mind. For if this is assumed, then first, once a particular mind is extinct nothing new will come to be, for this essence already exists; then again, now this and now that extinct mind will at each moment end in now this and now that essence, nor will the residue of the latest extinction belong to us any more than the residue of the intermediate extinctions. But consider especially: what will survive, then, will in no way belong to us, for it will not be remembered, nor shall we have any sensation of it, and we labor in vain to perfect our mind on behalf of its state after death. For that ultimate perfect essence, which is all that survive when we die, is nothing to us. For even if we do not labor for the sake of our perfection, none the less that essence already has existed and now exists, since it is eternal.53

Clearly, Leibniz is interested here in what he will later call personal or moral identity. This type of identity will be constantly associated by him with memory and self-knowledge; and he will be eager to distinguish it from metaphysical identity—as his example of the King of China in the Discourse54 52 53 54

See ibidem, A VI.3, 516 (SR 71). On Truths, the Mind, God and the Universe, A VI.3, 510 (SR 61–63). See DM § 34, A VI.4, 1584.

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shows—though later defending their harmony in the NE against Locke’s attempt at divorcing one from the other.55 We have seen, however, how the experience of memory is absolutely seminal in order to make us sure of metaphysical sameness itself and even to articulate its basic structure. I have dwelt on these studies of philosophy of mind, indeed, just because they offer material for some deep-rooted intuitons concerning the temporal nature of substance and its sameness. In the next part I shall consider how these intuitions are articulated in the logical structure of substance. Before going further, however, I wish to observe how the limits of matter suggest the elaboration of another abstract model for change. The Transproduction Model When crossing the sea from England to Holland in 1676, Leibniz wrote his great dialogue P Pacidius Philaleti, w which is devoted to the “labyrinth of continuum”. One of the characters in the dialogue, Theophilus, puts forward a radical solution to escape Zenonian apories. According to this solution, there is properly no continuous motion from points A to B, but a “jump” from the first to the second, as if a body were annihilated in A and re-created in B. Leibniz speaks of “transproduction” or “transcreation.”56 Now, also in the case of the P Pacidius Philaleti, its mathematical and physical treatment of the “labyrinth” is far from representing Leibniz’s last word on the matter. Here, however, I am interested only in a model that can mantain its interest outside its physical origin. As it was rather common in the philosophy of the age, Theophilus gives this idea, indeed, a general metaphysical and theological import, connecting it to the topic of continuous creation. In this context we find, beyond the physico-mathematical problems of local motion, a general approach to the problem of “change”, which is said to occur between two contradictory states A and not-A, which do not admit, as such, of any middle term. This definition of change as a discrete succession of contradictory states will become a classic one, that we find in the De Affectibus, applied to the model of the mind’s life, and then (as we shall see) in the “categorial tables” of the eighties, to the world’s becoming in general: “Change is an aggregate of two contradictory states.” The “transproduction” hypothesis, then, is felt as an alternative to the traditional idea of substratum, that can be used to make sense of the “loose identity” of matter. In a 1676 draft on some basic concepts of mathematics

55 56

See J. Locke, Essay, B. II, Ch. 27; NE, B. II Ch. 27. A VI.3, 560.

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we read: That something comes from something else, this means that something does remain, that belongs to the latter more than to the former. This persisting element is not always matter; it can be the mind itself, which conceives of some relationship, as it is the case with the transproduction: although all items are new, nevertheless, by the very fact that this transproduction follows a determinate rule, it imitates somehow a continuous motion, like polygons approximating a circle. Hence, we say that one comes from the other, with a similar licence of our imagination.57

This transproduction model will continue to represent an alternative to the standard continuant view embodying the idea of substratum. Coda on Truth: The Predicate-in-Notion Principle in the De Affectibus Of these inquiries into the philosophy of mind the De Affectibus represents a mature achievement. I have already observed how the series of affections possesses the temporal character of an A-series and the mind works as a classic continuant underlying the series of changing states. The De Affectibus, however, does not occupy itself with transtemporal identity, but rather seems to take it for granted. Or at most, this is considered indirectly from the point of view of the nomological unity of mental series. In the final part, however, the temporal topic comes to the fore in the context of one of the earliest statements of the ‘predicate-in-notion’ principle, which is introduced, notice, starting from the embarrassing modal consequence Arnauld will fear: . . . what w actually is, this is somehow necessary, because the predicate is always somehow contained within the nature of its subject . . . A real [a parte rei] true predicate is always contained in the nature of its subject: e.g., A is B, i.e. B is in A. Accordingly, if one understood A perfectly, one would understand that B is in it, i.e. that the concept of the existence of A does involve this notion, that what exists as A is B.58

The idea of conceptual containment does somehow prolong and achieve the process of expanding and reinterpreting spontaneity I have traced above. Passing from the dynamical model to the logical one, the ‘following from its own nature’ finally embraces all predicates, i.e. all states, or properties 57 58

Numeri infiniti, A VI.3, 503. A VI. 4, 1440–1441.

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or events that can be ascribed to a thing. In the language of the theorems of consequences, the nature of subject gives an account of all its consequents. In this way, the dichotomy between ‘following from the nature considered in itself’ and ‘absolutely following’ disappears. This could reflect the interiorization of impediment into the individual law-of-the-series, that is probably already alluded to in our text. But perhaps some tension will survive between the dynamical model of ‘nature’ on one hand, and the ‘logical’ one on the other. I shall show this gap and the related stratification within the complete concept in discussing the relationship between this concept and the law in the Discourse metaphysics. Coming to the formulation of the principle, the reference to existence strikes the eye, insinuating that there should be something more than a standard conceptual inclusion here. Immediately thereafter, indeed, the modal impact of the rule of truth is attenuated, by distinguishing two ways of involvement: (1) ‘A is B’ does follow from the concept alone of A, i.e. from its essence; in this case the truth is eternal and necessary; (2) ‘A is B’ does follow from the concept of A plus “the concept of time”, and then the truth is contingent. The notion of time, in fact, “does involve the whole series of things and the will of God and of all free agents.” In (1), therefore, the copula is wholly timeless, whereas in (2) it is tensed, or at least time-indexed.59 I will return to these aspects of temporal dimension. For now, we have to better understand this conceptual containment theory of truth that has finally emerged at the end of the De Affectibus. In order to do this, however, I have to reconsider the different stages of my inquiry and look for the elements for a theory of truth that can be found in each of them. 59

A VI.4, 1441.

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Chapter 1. The Double Root of Truth Prologue in Heaven: Eternal Truths in God’s Mind The ‘conceptual containment theory of truth’ of the Discourse—far from being a common good for the preceding philosophical tradition, as is commonly held and Leibniz himself is eager to insinuate—is something largely unheard of. In particular, it is somehow foreign to the spirit of the Aristotelian view on truth, which presents itself, especially through the Thomistic mediation, as a ‘correspondence theory’: that is to say, a theory where the truth of a proposition depends on its matching with things (or, if we prefer, facts) “out in the world”. The containment theory, instead, appears as wholly closed within the sphere of “concepts”. Saying that the conceptual containment theory contrasts with a standard view does not mean that Leibniz’s idea is entirely new, and deprived of antecedents. On the contrary, it marks the full deployment of some important philosophical tendencies of the age. In order to verify this, I wish to return to that important § 83 of the DAC, with its neat separation between eternal truths on one hand and singular or historical ones on the other. Starting from this point, I have concentrated my attention on the excluded singular propositions, where the roots of conceptual science hook onto the reality of individuals. Now, I wish to turn to the so-called “eternal truths”, to which the combinatorial treatment of the DAC did apply. w The topic, a bit exotic for us, of “eternal truths” is a central one in seventeenth-century metaphysics and epistemology; moreover, it is one that occupies both theologians in the Scholastic tradition and the pioneers of new science. Of course, the particular content assigned to these truths depends on the brand of theory of essences one is committed to: thus, it is hardly surprising that thinkers in the Aristotelian tradition (like Suarez) usually give examples of propositions concerning Porphyrian-style essences—e.g. “man is an animal”—while thinkers more interested in the mathematical science of nature (like Descartes) mainly refer to mathematical truths—e.g. “the sum of the angles of a triangle is 180◦ ”. In any case, there is large agreement upon the distinctive features of this type of truth: they are universal and necessary propositions, as the proper object of science should be according to the Aristotelian tradition. They are not only independent of time: moreover, they seem to hold also independently of the existence of the individuals that exemplify them. Precisely this last feature raised problems, however, concerning the need to give an adequate account of their truth-makers. The answer to hand was: eternal truths are about some essences that somehow subsist, even

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if they do not actually exist as created things do. But, then, the difficult problem arose, of reconciling such eternal essences with the absolute primacy of God’s creative will. The Thomist solution—where necessary truths do hold eternally, but only insofar as they are thought of by God himself (i.e., insofar as they are objects of the divine intellect)—aimed at making any too strong ontological commitment to essences superfluous. Suarez’s aim of establishing, in his classic discussion of this topic in Disputation XXXI, that essence and existence do not really differ, surely is an anti-Thomistic one. A standard objection he is faced with is based precisely on the fact that eternal truths hold independently of the existence of their objects, and consequently they seem to provide strong support for unactualized essences. As a consequence, he also is interested in a moderately deflationary reading of essences. He feels Aquinas’s solution unsatisfying, however: once conceded that eternal truths hold insofar as they are thought of by God, one is still left with the task of explaining the difference between the eternal truths and the contingent ones, both being objects of divine knowledge. Moreover, Suarez emphasizes the need, for God’s knowledge, of being grounded on some feature of its object. Suarez’s own solution points to the distinction of two senses—the existential and the essential one, respectively—of the copula “est”: whereas the former affirms the existence of the subject, the latter limits itself to stating that “the predicate belongs to the concept of subject ( praedicatum esse de ratione subjecti), be the latter existent or not.” Suarez, notice, associates a temporal value with the existential copula. As concerns eternal truths, he relies instead on the traditional idea of their equivalence to conditional propositions: Propositions, if they are read in this [second, or “essential”] sense, are reducible to hypothetical, or conditional ones; when we say, in fact, that “man is an animal”, abstracting from time, we do not say anything but this: “the man’s nature is such that one cannot make a man, without making by this very fact an animal”.1

The Jesuit thinker insists that the truth of conditional propositions does not need any cause, and goes as far as to say that they would turn out to be true, also if there were no creative cause. He has in mind, of course, the “efficient cause”, commonly associated with the production of existence. One is still bound to explain, however, where, in its turn, conditional connection is founded. This is Suarez’s answer: 1

Suarez, Disp. Met. XXXI, Sect. 12, § 45, 297.

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We must say that this connection amounts to nothing but the identity of terms, that occur in affirmative universal propositions . . . Every truth of an affirmative proposition, in fact, is grounded upon some unity or identity of its terms. This identity, although conceived by compounding the predicate- and the subject term, nevertheless really coincides with the self-same entity of the thing . . . 2

To sum up: eternal truths are said to be equivalent to conditional propositions, in order to neutralize the problem of their existential import; conditional connection, in its turn, is justified on the basis of the identity relation between the terms of the proposition. This theological model is an important root for the semantic side of Leibniz’s later conceptual containment theory. Eternal Truths within Human Language As a matter of fact, Suarez’s solution ended up giving eternal truths considerable autonomy with respect to God’s creative decision. Outside the School, on the contrary, important attempts were made at challenging the ontological privilege of these truths, while maintaining their epistemological status. Thus, an empiricistically minded author like Gassendi made ‘essential’ truths dependent on the existence of their objects. But the most revolutionary theories were put forward by Hobbes and Descartes: both making the audacious attempt to assign to eternal truths a foundation in will, in contrast with the traditional partition echoed by DAC § 83, though preserving at the same time their necessity and independence from existential commitments. Descartes links great ontological appreciation of mathematical essences with the assertion of their being created, so that their foundation lies in divine will and power. Hobbes for his part, by giving to eternal truths a linguistic (hence conventional) status, locates their ground in human will. Thus, even his conventionalist theory of truth can be seen as a (radically anti-metaphysical) contribution to the great debate on eternal truths. Necessary truths are removed by him from the divine mind and consigned to human language. Hobbes’s standard example—“man is an animal”—is exactly the same as Suarez’s. Unlike for Suarez, however, the (partial) identity of subject and predicate terms, relying not on a real essence, but on a definition that has been stipulated, will possess at most a linguistic necessity, induced by meaning. On this basis, Hobbes grounds his theory that demonstration is a chain of definitions. Though criticizing the conventionalist reading, Leibniz will never abandon the idea that definition occupies a basic role in proof. This approach 2

Ibidem, Sect. XII § 46, Viv´e´ s 298.

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gives him a first hint towards the understanding of the syntactic dimension of truth. It is important also to consider the influence of Hobbes’s semantic ideas. As we have seen, he gives the truth conditions for the universal proposition “man is an animal” in terms of containment, in the sense of extensional inclusion. The conceptualist strand of his semantics—framed in the linguistic terms of a kind of meaning postulate—emerges in the fact that a corresponding intensional “composition of names” is assumed: in every necessary proposition, either the predicate is equivalent to the subject—e.g. “man is a rational animal”—or is equivalent to part of it– e.g., “man is an animal”. The noun “rational animal” or “man”, in fact, is made up of two nouns, “animal” and “rational”.3

The reversal of the extensionalist account is evident. From this perspective, Hobbes also endorses the assimilation of hypothetical proposition with the corresponding necessary categorical one: Whenever a hypothetical proposition is true, the corresponding categorical turns out to be not only true, but also necessary. And I remark on this to the effect that philosophers can better use hypothetical propositions than categorical ones.4

Despite their opposite metaphysical insights, Suarez’s and Hobbes’s theories about necessary truths present strong structural similarities. Their double heritage provides some seminal ideas that are already present in the DAC and will later determine, respectively, the semantic and syntactic sides of Leibniz’s mature conceptual containment theory of truth. On the other hand, Leibniz will devote great effort to answering Hobbes’s and Descartes’ challenge. His denial of their creationist and conventionalist interpretations is closely bound with his fidelity to the foundation of truths in the mind of God. With regard to Descartes, Leibniz’s critical assessment of his “creation of eternal truths” begins in the early Hanoverian years; it will be exemplarily stated at the opening of Discourse. For Hobbes’s conventionalism, the confrontation goes back earlier, at least to Nizolius’ Preface. In keeping with his quite different ideal of science, Nizolius held an empiricistically minded view, making truths simply dependent on the existence of their subjects. In his notes on Nizolius’s book, Leibniz rejects this move. His 3 4

OL I 134. OL I 35.

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rejoinder shows that he also is familiar with the strategy of making universal categorical propositions equivalent to conditional ones: Nizolius is wrong [in saying that the species perishes when all individuals perish]. Even if all singular things are taken away, nevertheless a universal proposition maintains its truth, insofar as it concerns possible things. Although all elephants are suppressed, nevertheless the following sentence turns out to be true: “Every elephant is an animal”, insofar as it can be reduced to the conditional: “If something is an elephant (be it existent, or not), then it is an animal”.5

The same is said in the case of the genus ‘man’.6 According to Nizolius, giving up real universals involves the downfall of the universality claim of scientific knowledge; to this, Leibniz objects: This does not follow. Science, in effect, is not only about existing things, but also about possible ones. It does not matter whether a triangle exists in nature, but what follows from it if it does exist, e.g. how its angles are. Science, therefore, does not concern real universals, but all singular things, possible ones included.7

The truth of the consequence is not explained, as it was by Suarez and Hobbes himself, with reference to concept identity, but to possible individuals. Thus, in one of the most anti-realistic of Leibniz’s writings, universal truths are framed not so much in the frankly intensionalist language of conceptual inclusion, but in the quasi-extensionalist one of possible individuals. To be sure, a present-day reader could be perplexed by an anti-realistic move made at the cost of a luxuriant ontology of possibles; but one should not forget that a Christian nominalist like Leibniz could avail himself of some resources of Platonism, by shifting them into God’s mind. Also in God’s intellect, indeed, we do not find the universal idea ‘humanity’, but the ideas of possible individuals; better, these possible individuals are nothing but these ideas. The general outlines of such a view had been sketched in Ockham’s or Biel’s theory of divine ideas. Elsewhere in the same notes, however, Leibniz claims that science cannot be ultimately based on the inspection of singular instances, the latter being infinite. But then, the extensionalist approach to truth, both in the realm of the actual and possible, would presuppose an intensional grasp of properties. 5 6 7

A VI.2, 448. A VI.2, 451. A VI.2, 461.

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Only, the latter are ideal patterns that do not exist as real constituents of beings. Observe that in the same notes Leibniz is eager to subtract Plato’s ideas from Nizolius’s attacks on the universals of School. “Perceiving Truth” So far, Leibniz’s remarks on the truth conditions of necessary propositions and the related status of essences. In his Preface to Nizolius, however, a more general definition of truth is given: “A true sentence (oratio) is one whose content is perceived, provided that the perceiver and the medium are well disposed (the understanding is the criterion of clarity, indeed, but sense is the criterion of truth).”8 The crude empiricistic sound of Leibniz’s definition is likely to surprise the reader. The first example given is clearly a case of those ffactual truths that were excluded from the scope of combinatorial science: The sentence “Rome is on the Tiber” is true . . . If I am in Rome or near Rome, I will see by the same glance the town and the river, hence I will see that this town is near this river; and I shall hear that this town is called “Rome” and the river “Tiber”.9

More surprisingly, the same criterion is applied to more abstract truths, e.g. a simple mathematical one like “every multiple of two is even”. Here also we are said to have a perception of truth, according to the model of “seeing”! Leibniz seems to have in mind not so much a kind of intellectual intuition, but the usage of sensible characters in a Hobbesian style proof based on definitions: In the same way, in the field of abstract truths, this sentence: “every multiple of two is even” [is true], because if I see (hear, touch, think of) “a multiple of two”, I see “one plus one” (for the definition of “a multiple of two” that I have perceived from hearing or from reading) and nothing else.10

On the level of human knowledge (and bearing in mind that Leibniz gives here a definition of truth referring to our verification procedures), the usage of sense can cover two fields that remain well distinct: factual truths on one hand, where the adequacy of our sentences is verified through acts of sense acquaintance; abstract truths on the other, where senses provide us the signs 8

A VI.2, 409 (GP IV 138). Ibidem. 10 Ibidem. 9

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we need in order to grasp them. In any case, also Leibniz’s first thoughts about truth (like his analysis of predication) come to confirm some split into two relatively independent spheres: the truths based on purely ideal connections (or, in the more terrestrial version, on signs) on one hand, and those based on empirical facts, on the other.

Chapter 2. Fundamentum Veritatis Truth as a Concatenation of Natures T An interesting draft of December 1675 puts in parallel conceptual analysis concerning ‘ideas’ ((processum per ideas) and definitional analysis managing names or signs ((processum per definitiones, vel characteres).11 Leibniz wants to do justice to both dimensions, each one one-sidedly emphasized by the Cartesian and the Hobbesian approaches, respectively. His understanding of both sides has decidedly improved: on one hand, the Platonist penchant of his view on eternal truths is reinforced by his direct acquaintance with Plato’s Dialogues and the Cartesian philosophy of mathematics. On the other, Hobbes’s suggestions about the constitutive value of signs for our thinking are far from abandoned. While emphasizing the irreducibility of meaning, the De Summa Rerum develops intensive reflection about the human need for signs in order to grasp and express it. Both lines of thought find their full expression in the well-known 1677 Dialogue,12 w where the confrontation with Hobbes’s conventionalist challenge comes to a turning point, and in some closely related drafts. It is worth considering these writings together, insofar as they show how a Platonist ontology of truth coexists with the acknowledgment of the linguistic character of human thought. Both dimensions, notice, are still investigated especially in relation to necessary truths, such as mathematical ones. I cannot exhaustively analyze here the Dialogue, a small masterpiece of Leibniz’s semantics, and the best introduction to his central notion of expression. In the first part of it, where the example of a mathematical truth is given, propositions, conceived of in anti-psychologistic manner as objects of possible acts of thought, are recognized as the proper truth-bearers, independent of both our mental acts and the existence of their subject matter. Two short drafts 11

12

A VI.3, 462 (SR 3). For a penetrating account of Leibniz’s reflection on the topic of definition in the Paris years and his answer to Hobbes’s challenge, see M. Dascal, Leibniz’s Early Views on Definition. Studia Leibn. Suppl. 21 (1980), 33–50. Dialogue, August, 1677, A VI.4, 20–25 (GP VII 190–193; L 278–283).

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in the immediate surroundings of the Dialogue, starting like the latter with the independence of truth from both our thought and existent material beings, go on to inquire its ontological foundation in the divine mind.13 Leibniz concludes from the eternity of truths to the eternity of the essences that enter to constitute them: Truths arise from natures, or essences. Therefore, natures and essences also are realities that always exist. The selfsame nature contributes to the constitution of a lot of others and it can be combined with anyone of them. Realities that are in the natures a parte rei or, as usually said, in an objective way, are not spatio-temporally distinguished, because they all combine. The objective realities of conceivable natures and truths are simultaneously present in several others, remaining the same. These realities are not substances.14

Suarez’s nuanced treatment of the reality of essences is replaced here by the blunt claim of their eternity. They go on to constitute the selfsame essence of God, or at least the object of His intellect. Language and content are not as much those of Schoolmen, as of mathematical Platonism. The vocabulary of “natures” strongly recalls Descartes’ “natures simplex”; or better, the “true and immutable natures” of the “objects of pure mathesis”, to which his Meditation V accorded an ontological status wholly independent of physical existence. From innate ideas like these, many properties are deduced; hence, one is allowed to state many propositions about them, independently of any existential commitment. Leibniz also moves from geometric examples to show how ‘natures’ connect each other according to their relations of mutual involvement, with a result of growing complexity. It is important to observe that the natures that generate truths by their combinations are unequivocally presented as universal (not in the Scholastic sense, but in that of mathematical notions). The same nature, in fact, occurs in many different complexes and these natures do not possess spatio-temporal location. We are at a wholly different level from that of particularized forms, which do require such location. Trouble about causes emerges, “insofar as one and the same proposition can be proved in many ways, but of one and the same thing there are not many causes.”15 But if natures are 13

14 15

De veritatibus necessariis seu aeternis, A VI.4, 17; De veritatis realitate, A VI.4, 18–19. For a thorough analysis of the ontological status of ideas in God’s mind, see M. Mugnai, Leibniz’s Nominalism and the Reality of Ideas in the Mind of God, in A. Heinekamp, W. Lenzen, M. Schneider (eds.), Mathesis rationis, M¨u¨ nster: Nodus, 1990, 153–167. A VI.4, 19. Ibidem.

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meant as universal items, the difficulty vanishes: for such realities, differently from individual essences, we can well imagine a plurality of causes, as we already know from the De Principio Individui. All this clearly confirms that Leibniz is consciously sketching here an ontology for mathematical truths, bearing on abstract objects. Proposition as an Image of World In the Dialogue Leibniz, after having identified truth bearers (propositions) and established their objective status, turns his attention to our access to truth. With regard to the content of human thought, he rejects a naive Platonism of W meaning, as much as its modern counterpart, the Cartesian claim of having an intuitive intellectual access to “ideas”. Against this, he stresses our need to use signs, which constitutes the premise of an interesting reformulation of Hobbes’s thesis about the conventional character of truths: (1) in order to grasp propositions, we are bound to frame the related sentences, i.e. to make use of signs; but (2) signs are a matter of convention; hence (3) truth depends on our act of fixing the meaning of signs. Conclusion (3), however, contrasts with the indisputable fact that (4) mathematical truths are clearly independent of the linguistic system in which they are expressed, insofar as they are the same, be they expressed in Latin or French. But where is, then, the flaw in the argument? The difficulty lies in the fact that Leibniz, differently from Cartesian intuitionism, that does not endorse (1), accepts both (1) and (2). Nevertheless, he is able to avoid (3), by emphasizing the fact that sentences in different languages, though conventionally framed, do preserve a common structure. Given premise (2), i.e. the conventionalist view about linguistic signs, one cannot (but also need not) assume the holding of a similarity relation between the single sign and the signified thing. Despite this, a well-suited system of signs represents reality through the form of their mutual arrangement, a form that is common to other systems. This constant “proportion”, Leibniz says, is the “foundation of truth”. More explicitly: the structures of languages L1, L2, . . . correspond to each other (and as a consequence, L1, L2 . . . can be mutually translated) insofar as they all correspond to a common archetype— the structure of reality. “Correspondence according to a rule” is Leibniz’s definition for this concept, to which he will give the label of “expression”. Commentators did not fail to remark the analogy with the Tractarian Satz, working as a picture of world through sharing its “logical form”. In any case, the “logical realism” of the Dialogue provides the terrain for an original rethinking of the correspondence theory of truth. Dealing with truth as a property of sentences, we have left the heaven of “eternal natures” to turn to its image in human knowledge. Human sentences

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are a variety of expression—a central one, indeed, insofar as the expression theory is put forward in order to give an account of them. But how is the world-sentence correspondence to be concretely understood, or what do the signs that constitute a sentence stand for? Like theTractatus r , Leibniz’s Dialogue does nothing more or less than posit a very general constraint on every language (and theory of language) that claims to have sense or tell about the world. Once this is assumed, the problem of identifying the type of basic objects is still open. Ways of Language-World Correspondence: (1) Conceptual Inclusion W We have already found a kind of “family air” with modern logical atomism, in Leibniz’s 1676 reflection on the combinatorial view of “Socrates’ Dream”. At the same time, the problem did arise there of explaining the unity of the proposition. Working on the construction of God’s concept, Leibniz drew a distinction between two different ontological roles—those of subject and property (or form), respectively. Once having presupposed the original reference of “forms” to the ontological subject, however, he went on interpreting the subject and predicate terms of proposition as standing for entities of the same ontological type—forms, maybe as in the original Theaetetus model. Differently from Theaetetus, however (and also from Tractatus r ), these forms are no longer simple elements: a decisive premise in the 1676 compatibility argument stated that only propositions having complex logical subjects can be proved. If one accepts this reading, the configuration of a standard sentence will reproduce the inclusion among complex forms (concepts)—we would say, among sets of concepts: Name 1 Concept 1

Copula Conceptual Inclusion

Name 2 Concept 2

(Sentence) (Proposition)

A proposition is built up of constituents of the same ontological type—just concepts—the only difference among them lying in their grade of complexity. This interpretation induces an analytical reading, hence a divorce from the spirit of standard correspondence theories, that made the truth dependent on how things are “out in the world”. Obviously, this reading is well-suited to give an account of the adequacy of our language to express the Platonic world of ‘ideal’ connections that structure mathematical or, in general, conceptual truths. A good model for this is given by the concatenation of ‘natures’ as presented in the drafts of the Dialogue group. The extension of this model outside the scope of mathematics could be fav a ored by Descartes’ example, whose ontology of mathematics, though radically rejecting Suarez’s view on uncreated truths, maintains the idea of a

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field of essential truths, free from existential presuppositions. Moreover, he generalizes this approach, by putting forward an image of human knowledge that methodically sets aside the original dependence on extra-mental existing things. As a consequence the Aristotelian rule, according to which the inquiry into the inner content of an essence must presuppose its existence, is radically overturned.16 Only in this context can we wholly appreciate Descartes’ claim, that we discover the properties of things through inspection of the properties implied by the corresponding “ideas.” In the Axioms of the Geometrical Exposition, this principle is stated in a manner that is very close to Leibniz’s later conceptual containment explanation of truth: Whenever we say that something is involved in the concept or nature of something else, this amounts to saying that it is true of that thing, i.e. that it can be said of it.17

Ways of Language-World Correspondence: (2) Denomination W and Inherence The P Paris Notes give us also some clues towards a different way of interpreting the language/world isomorphism. Consider the second argument for genetic individuation put forward in the De principio individui: from this it is also proved that the effect involves the cause. For it is true of it that it was produced by such a cause; therefore right up to the present there is in it a quality of such a kind as to bring this about, and this quality, even though it is relative, has about it something that is real [a parte rei].18

“Verum V de eo”: true predication is directly about a particular and has to satisfy the requirement of an ontological correlate. Talking about a “quality being present” in the thing is talking the vocabulary of ontological inherence. The idea is meant in a typically strong way: if it is now true that “p was the case in a past time”, then there must be a trace now of that past fact. Compared to present-day discussion on realism and truth, the move looks interesting: on one hand, the claim is raised of absolute truth value for propositions about the past, quite independently of our ability to know it. On the other, a present ground is required for the assertion of such propositions, that is to say a 16

17 18

See First Replies: ““According to the rule of a sound logic, one should not ask about anything whether it exists, before understanding what it is”, AT VII 107–108. w Second Replies, AT VII 162. A VI.3, 491 (SR 51).

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present feature from which one could in principle go back to connect to a past f fact. The semantic thesis of expression, according to which true sentences reflect the inclusion relations among concepts, is accompanied by a metaphysical thesis, according to which every true predication has a real correlate within the thing. In this interpretation, the language-reality isomorphism is granted by a direct correspondence between elements of language and reality. But the elements of reality belong to different ontological types; in practice, the complex structure of the proposition will directly express the ontological dualism that was focused on in the On Forms. From this perspective, ‘names’ stand for things and for the properties belonging to things: Name 1 Thing

Copula Inesse Relation

Name 2 Property

(Sentence) (World)

More precisely, the correlate in the world of a noun in the predicative role is likely to be not a general property, but a particular accident: something like ‘this heat’ of the De Cogitationum. The two interpretations of the Isomorphism Postulate seem to arise from the consideration of two different types of truths—purely conceptual on one hand, and concerning individual things on the other—but they are not alternative: on the contrary, they constitute two dimensions that are both present also in all applications of the conceptual containment theory of truth, such as it will be stated a few years later. The second reading is more faithful to the spirit of the traditional correspondence; but the crucial point is, where does the basis of truth ultimately lie, according to the explanatory and foundational order. One can ask, in fact, whether the need to affirm real foundation depends on conceptual inclusion, or does the reverse hold. Although an extra-conceptual dimension of truth is maintained, nevertheless the pivotal role is certainly played by the conceptual interpretation. Coda: “All Things Are Contained in All other Things.” Inherence and Plato’s Puzzles on Relations Also the second interpretation can be traced to the 1676 reflection on Plato’s combinatorial attempts, in particular on some aporias concerning relational predicates and change, translated or annotated by Leibniz. One is to be found again in the Theaetetus: 1) as long as something is equal to itself, it does not come to be greater or smaller (in size or number); 2) if something has nothing added to it or subtracted from it, it is equal to itself; 3) nothing is what it previously was not, without having come to be so. Now, Socrates at time t1 is taller than Theaetetus; at time t2 he remained equal, and nothing

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has been subtracted from him; nevertheless, he is now smaller than Theaetetus, because the latter has grown up; and this simple fact seems to contradict premises (1–3). From the Categories on, it was a standard thesis to affirm that a relation can change, provided that only one of its relata has changed. The Theaetetus aporia, on the other hand, shows that at the very origins of the ontological tradition this phenomenon appears as a puzzling one. Leibniz’s annotation in the margin of his translation shares this philosophical puzzlement: “This aporia is worth noticing, and is also relevant for other matters.”19 There is more: he finally gives the aporia a solution that flies in the face of the standard (and commonsense) view. In a draft of the same month, devoted to the metaphysics of forms, he writes: It is undeniable that, when the mind perceives something in matter, whilst it perceives various things there is also a change in it. While 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.20

Thus, when a change of any kind occurs, all relata do change (I will call this ‘thesis of Changing Relata’). Here, the inference to a real inner change is introduced as a generalization of the case of perception. It is quite reasonable, in fact, to observe that mind does change while perceiving change. But the generalization still perplexes us. This counter-intuitive statement anticipates a well-known later thesis that will be grounded directly on the complete concept. Already here, the modification of each relatum r is inferred from the linguistic ffact of predication: “a denomination of mine has changed”, exactly as in the De principio individui. Just in the case of relational predicates, however, Leibniz should be far from purporting an immediate one-to-one correspondence of linguistic elements, concepts and reality. We know, in fact, that he is well aware early of the need to distinguish, in this case, conceptual modifications from the ontological ones of the corresponding individuals. Thus, we could well have a conceptual variation (in relational properties) with no need for a real change in each of the corresponding accidents. I think indeed that, to make sense of the 1676 opposite conclusion, we need a further assumption: the basic ontological 19

20

A VI.3, 301. A similar aporia occurs in the other dialogue translated by Leibniz, the Phaedo. Here, notice, Forms in themselves (Tallness in general) and “forms within the individual” (the tallness-of-Socrates) are accurately distinguished. See Phaedo 102 b3-c4; Hector-Neri Castaneda, ˜ Leibniz and Plato’s Phaedo Theory of Relations and Predication, in Hooker (ed.), Leibniz, 124–159. A VI.3, 523 (SR 83–85).

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ffacts expressed by relational predicates—hence, the individual objects-withaccidents—stand in their turn in a relation of reciprocal expression, which justifies the thesis of Changing Relata. But this new application of the idea of expression is a logically independent metaphysical postulate. In any case, it allows Leibniz to recover a perfect isomorphism even on the ontological level and in the relational case. This is why he ends up with a strong ‘internalization’ of relations, though sharply distinguishing conceptual connection and ontological inherence.

Chapter 3. Conceptual Containment From r Concepts to Truths: The Primacy of Predication and Proposition In the 1677 Dialogue, Leibniz has shifted his attention from simple elements—simple forms, or natures—to the way of their connection. I have suggested two possible ways of reading the world-language correspondence: conceptual inclusion and ontological correlatedness. We should consider both from the point of view of a powerful Gestalt shift, whose sides are the rediscovery of ontological asymmetry on one hand, and the central role of proposition on the other. The primacy of predication, on both the ontological and semantic levels, seems to be the central intuition marking a decisive turning point in the Leibnizian project of conceptual analysis in the years 1677–79. Leibniz points out, indeed, the opportunity to shift the scope of inquiry from the arduous analysis of concepts into primitive ones to the relatively more accessible analysis of truths. Many truths, he observes, can be completely analyzed also without going to primitive notions, provided one is able to pursue the analysis until the identity of subject and predicate terms is reached. Far from expressing a contingent lack of information or analytical sharpness, our incapacity to grasp the simple has a more structural nature, awareness of which lurks in some interesting remarks between the Dialogue and the De Affectibus. Thus, a note of September 1677 radically questions the conceivability of simple terms, insofar as they should have something in common (reality), and be at the same time irreducibly different. It seems that, reality being absolutely common, the distinguishing feature (differentia) of each intelligible item should not participate in it. This would be absurd, however, provided that the difference also has to be real, or a possible object of thought (cogitabile): From this it follows that nothing absolutely simple can be thought of by us; every item which we think of, in fact, presents us at least with two aspects,

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conceivability and the kind of conceivability, i.e. something common and something peculiar to it. But conceivability is also in this peculiar element: otherwise this could not be thought of. Therefore, it results that those two aspects cannot be separated, nor can they be conceived of by us except by one and the same act.21

Immediately after showing this original co-presence of identity and difference, Leibniz applies to the subject-predicate structure a similar remark, which is clearly connected to his former metaphysical reflection about the w “origins of things from forms”: Also about the subject and the adjunct there is something very subtle to be noted. We are conceiving the subject, or substance, whenever we are saying: “I”, “he”, “this”; in fact, through these utterances we are thinking of something in common, that is the idea of a subject, lying within bodies themselves quasi according to the rhetorical figure of prosopopoeia. Every conceivable quality is composed from conceivability and a subject of conceivability. Conceivability is inherent in this subject; one thing is conceivability, however, and quite another is the fact that it is referred to a subject. Therefore this reference to the subject, as such, cannot be thought of.22

This primitive structure is presupposed by the notion of possibility itself. At the end of the De affectibus, we read: The definition of Possibility has to be analyzed into the simpler one of the “to-be-something”; this in its turn has to be explained by what we have said above [in the preceding lines Leibniz had illustrated his containment theory of true predication].23

And in the margin he annotates: From this it is clear that one cannot grasp simple notions, unless one takes into account some proposition, at least considered in a reflexive way a [reflexive].24

By “reflexive r ”, Leibniz usually means a usage of terms (or of statements) not directed to things, but to our ways of expressing things, i.e. to our concepts themselves (we would say, an “intensional” usage). Remember that a quality 21 22 23 24

De iis quae per se concipiuntur, A VI.4, 26. Ibidem. A VI.4, 1441. Ibidem.

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like “White” as such, or better “Whiteness,” corresponds to a predication of the “X being white” type. This priority of predication on the notion of possibility will be reflected in those tables of definitions where the notion of Possible or Ens is introduced as “Something is A, B and so on . . . ” and contrasted with “Nothing”, the latter being equivalent to “having no properties.”25 The Subject-Predicate Structure: Phenomenology and Pragmatics of Judgment In the crucial period around 1679, we also find some attempts at grounding the subject-predicate structure of proposition on some aspects of our cognitive procedures. The opening of the De Affectibus distinguishes the “concept” as an imaginative apprehension from the judgment (sententia), that adds to imagination a striving (conatus) to act. The distinction between the apprehension of a content on one hand, and the act of asserting (or denying) the same content on the other, was a standard one in the Scholastic theories of knowledge and proposition, and was also important for Descartes and the post-Cartesian debate. While accepting the distinction, Leibniz originally connotates judgment through further reference to action. In the Scholastic tradition, the content apprehended assumed a propositional structure; whereas in the post-Cartesian counterpart of this theory— where an “idea” is asserted—this aspect had somehow been lost. Now, let w me consider another Leibnizian text which starts with the familiar distinction between “to conceive” (concipere) and “to assert” (statuere), the latter being marked, exactly as in the De Affectibus, by a conatus to act. The new fact is the acknowledgment of the complex (i.e. propositional) character of the content apprehended. Also this internal structure is explained by reference to a conatus to act. Whenever, because of some phenomenon, we strive to act as if from it, if we were not to prevent it, another one would follow, together with some benefit or damage to ourselves, then we are judging that the first phenomenon does exist. And, if we are in such a mental state that we are thinking of some phenomenon (that we do not hold to actually exist, but we only imagine, or conceive of ), and we are aware that, in the case we were actually perceiving it now (i.e., if we were to imagine it with a conatus to act, as if it were actually there), we would be at the same time acting as if some other phenomenon were to happen—then, we are asserting some consequence, that is to say we are believing some proposition.26 25 26

See for instance VI.4, 146; GI, A VI.4, 740. Enumeratio terminorum simplicium, A VI.4, 394.

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While the first assertion (“phenomenon A exists”) remains confined to an antepredicative level, the complex content of the second statement is originally structured according to an inferential pattern, immediate as its apprehension may be from a psychological point of view. Some lines below, this inference (consequentia) is confirmed as the core of the standard categorical proposition: To assert (i.e. to believe, or to know that A is B) amounts to imagining together A and B, and by the same fact to conceive that, if you were now to conceive A, you would strive in order to produce or prevent the same things that you would strive to produce or prevent, if you were to perceive B: hence, if you actually perceive A, and by this very fact you are acting to produce or prevent the same things, as if you would perceive B, then you are asserting that A is B.27

We should bear in mind this phenomenologico-pragmatic foundation of a topic—the equivalence of categorical propositions with the hypothetical ones—that we will consider later (and is usually considered only) on a strictly logical level. On the whole, these scattered remarks converge to indicate a kind of phenomenological approach. Though more suggested than achieved, this strand of Leibniz’s inquiry shows that also the logical structure of propositions, on which the objective notion of truth is based, is grasped by our mind as a w function of its cognitive and practical needs and structures. Bearing in mind this interesting and less known side, let me turn now to the treatment of propositional structure on the properly logico-conceptual level. I will only summarize the main traits of the well-known theory of conceptual containment, that achieves the interpretation (1) of isomorphism and provides the general background where the theory of individual concept is located. The Logic of Truth: Conceptual Containment and the Interpretation of Calculi In the same weeks as he writes the De Affectibus, Leibniz drafts the first group of logical calculi (April, 1679), which are accompanied by some drafts meant to provide a semantic reading of them.28 Terms stand for concepts; and the connecting element (normally expressed by the copula) is interpreted as conceptual inclusion, the latter being meant in an intensional way. Leibniz explicitly argues for his choice of the intensional point of view (the so-called 27 28

A VI.4, 395. A paradigmatic example is offered by the Elementa calculi (A VI.4, 195–205; C 49–56).

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methodus per ideas, as opposed to the methodus per individua), on the ground that it would be free from existence presuppositions.29 The interpretation of proposition as a kind of conceptual inclusion has its syntactic counterpart in the manipulation of symbols (definitions), where substitution is the basic transformation rule. Here we find a hint to the formal definition of a proof as a procedure that in a finite number of steps does lead to “express identity”. On the whole, the theory of truth of these drafts takes up the double approach through conceptual analysis and the chain of definitions, whose application to necessary or conceptual truths Leibniz had envisaged in the earlier years. Here also, notice, only general g propositions, be they universal or particular, are dealt with (at least explicitly), from which syllogisms were built up. Capacity to provide a satisfactory formal treatment of their four types is a good test for the new logic, without preventing an extension of its scope. As a matter of fact, in the De Affectibus the conceptual containment theory of truth is explicitly applied to the case of contingent singular propositions, as we have seen. In this way, the limit imposed by the DAC is broken. But then, one is left with the question: what did happen, in order to infringe the old prohibition and allow for the extension of conceptual containment to singular propositions? One is tempted to answer: well, we are simply faced with the extension of a model that Leibniz successfully applied to the semantics of calculi. I do not believe, however, that his move amounts to the mechanical extension of the truth definition for general propositions. One has to consider, rather, the epistemological dimension of the topic of truth on one hand, and the central role that individual has assumed within Leibniz’s categorial framework, on the other. Two other areas of his “general science” correspond to this: the encyclopedic project and the categorial one. Elementa Veritatis: Conceptual Containment and Principle of Reason within the System of Truth From 1679 the notion of truth begins to work as the guiding thread for Leibniz’s reorganization of science. This is evident in the encyclopedic project, aimed at ordering the whole of our knowledge as an axiomatic-deductive system. The foundational part of this project, concerning the basic principles and the outline of a system of truth, receives in some drafts of the early eighties the label of “elements of truth” ((Elementa veritatis). Interestingly enough, in Leibniz’s view Descartes’ Cogito is included as the first factual truth in the empirical or factual side of science, intended in 29

Elementa calculi, § 12, A VI.4, 200 (C 53).

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a phenomenistic way. This side has to be integrated with the demonstrative one, grounded on definitions. According to this dichotomy, Leibniz goes on to formulate that hierarchy of general principles, variously subordinated or coordinated, that has been much discussed in the literature. The text Definitiones Cogitationesque Metaphysicae30 presents an interesting essay of articulation: the phenomenistic side is ruled by the “principles of senses,” that are furnished by our primitive experiences. “Intellectual principles,” for their part, are split into those which govern the essence and the existence of things, respectively. Independently of the epistemological splitting of truths with regard to our knowledge, truth in itself—truth from the point of view of God, so to speak—presents a structural dichotomy, insofar as truths having existential import presuppose a divine choice (the old idea of DAC § 83, again). In this way, a the system of principles on one hand confirms the double root of truth. On the other, a strong tendency towards a unitary definition of truth emerges within this project for a unified science; let us see how it does. The intellectual principle that determines existence is one of perfection. Among the principles that determine essence we find the basic rules for a classic logic of truth: bivalence and non-contradiction, first of all. It is important to notice that primitive truths (in practice, identities) are formally expressed by the axioms of the calculi that Leibniz construes. Also the principle of reason, however, is counted here among those “of essence”; and its statement is equivalent to that of the conceptual containment theory of truth: One can give a reason for every truth, first ones being excluded, where the same is said of the same, or denied of its opposite, e.g. A is A, A is not non-A . . . That is to say, the connection of the predicate with the subject, i.e. the ground for truth (connexio praedicati et subjecti quae fundamentum est veritatis) is either immediate or mediate, and in the latter case can be reduced to the immediate one through analysis: and precisely this means to prove a priori, or to give the reason.31

At least since 1670, remember, the “principle of reason” (from now also, PR) was considered by Leibniz the “great principle” for the construction of a metaphysical system. Certainly, it is conceptually independent of and historically antecedent to the elaboration of the conceptual containment theory of truth.32 During the seventies, its logical structure was spelt out rather in r ). In this context, the principle of terms of the theory of conditions (requisita 30 31 32

A VI.4, 1393–1405. A VI.4, 1395 See on this R. Sleigh, T Truth and Sufficient Reason in the Philosophy of Leibniz, in Hooker (ed.), Leibniz, 209–242.

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reason typically ruled the field of existences; and it assumed, ultimately, the form of a principle of perfection, that is of selection among different sets of possibles according to their content. In the text I am considering, it is not applied directly to things or events, but to truths. Moreover, it is shifted to the field of essential truths (more precisely, of those necessary truths that are not explicit identities), and is equated to conceptual containment. The dichotomy stated here has not to be taken in an absolute sense, however. On the existential side, in fact, perfection works as a reason r for existence, in continuity with the first historical setting of the principle. As a consequence, the principle of perfection can be, in its turn, easily subsumed under the idea of conceptual containment. The cause of existence is properly a “reason”, that is to say, it is not a brute fact, e.g. a mere decision of will, but is located in a conceptual space. Back Again: From Proposition to Concept Both lines of thought I have evoked so far, i.e. the logic of truth as it is developed in the calculi, and the epistemology of the system of truth, find their highest achievement in the great 1686 study Generales Inquisitiones33 (from now, the GI). One of the leading ideas of the GI is to show that the terms of the calculi can be indifferently interpreted both as concepts and propositions. If “A” and “B” stand for propositions, then the “est” in “A “ est B” stands for the logical relation of entailment. Leibniz does not limit himself to stating the possibility of this double reading, but he aims at showing the full equivalence of the two interpretations. Concepts can be reduced to propositions, and propositions to concepts. As a matter of fact, his main efforts are devoted to the latter reduction. All this is in tune with the whole logical project of the GI, that prefigures a true algebra of concepts, hence a logical system whose basic ingredients are concepts, and whose basic relation is containment. One might feel some tension with the so-called “propositional turn” I have insisted on above (we will find a similar tension in the case of the definition of identity). But this is not the case, I mean. The primacy of the propositional structure, and the shift from the analysis of concepts into the analysis of truths depended on the impossibility of grasping isolated concepts. But truths and concepts belong to the same ontological type, truths being nothing but complex concepts. Neither is the reference to things—the other dimension of 33

Generales Inquisitiones de Analysi Notionum et Veritatum, A VI 739–788 (C 356–399; transl. LP 47–87). For a helpful introduction to this text, see the edition of F. Schupp, Hamburg, Meiner, 1982.

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the predicative structure—eliminated. On the contrary, it is presupposed by this “general analysis of concepts and truths” (and the related construction of calculi) which is pursued wholly at the conceptual level. A clue to this is the emphasis put, at the opening of the GI, on the fact that terms are always taken in concreto.34 Conceptual and Physical Analysis The scientific system of truth is oriented to promote and organize human knowledge of the world. In this context it is interesting to observe how the leading idea of conceptual analysis tends to incorporate some proceedings and results which are specifically physical. If the Leibnizian theory of conceptual inclusion prolongs the Hobbesian model of demonstrative knowledge based on definitions, it embodies also the different model of genetic definition. A real definition, we know, makes us sure of the possibility of its definiendum by showing its way of production. In the case of mathematical objects, we furnish such definitions by constructing the corresponding object. When we have to do with the definitions of natural kinds or stuffs, however, the possibility of such beings is given by experience; and our analysis will consist in physical manipulation, aiming at discovering their properties. Thus, the definition of gold, unlike that of a geometrical figure, is construed in a Kripkian way, through inquiry into a given natural kind.35 In our conceptual analysis, which is bound to presuppose the divine creative synthesis, lexicographic and encyclopedic competence cannot be sharply separated. Also in the GI, conceptual analysis aiming at establishing the possibility of some notions needs to rely on experimental knowledge. I want to emphasize this fact here, where Leibniz tries to construe a unified system of science, hence a unified notion of truth. But the conceptual containment model, the only one able to be translated into the language of the characteristica, originally worked only for some types of truths. The tendency to extend it to empirical truths goes on a par with a refinement (one could say, a weakening) of the model itself. Nevertheless, the application to the case of singular proposition, announced in the De Affectibus, is still beyond our horizon. In order to understand it, we have to consider two other interests: firstly, the ontological centrality of individual, that already emerged in the “genesis of things from forms”; secondly, 34

35

The text opens with the advice: “Let us, for the present at any rate, omit all abstract terms, so that all terms are understood to refer to concrete things alone . . .”, A VI.4, 740 (C 356; LP 47 ). See the De notionibus empiricis, A VI.4, 16.

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the developing of the topic of scientia Dei with regard, this time, to contingent futures and possible individuals. I will consider this second aspect in the last part of this book, when dealing with the role of complete concept in the Discourse metaphysics. Now, I turn to the categorial project, where Leibniz gives a mature form to the outcomes of the two great ontological researches I have reconstructed in the first part: the emergence of concrete particulars from the metaphysics of forms and the causal structure of the metaphysics of conditions. These two topics are bound in a strong categorial framework that provides the ontological counterpart to the application of conceptual containment to individual substances.

Part II A Logico-Ontological Framework for Substances

Section 4 Categories (1) Concepts, Things and the Reform of the Category Table

0. Introduction to the Category Tables Categorial Turn and Linguistic Turn During the decade 1679–89 we find a new flourishing of Leibnizian drafts devoted to conceptual analyses and the search for primitive terms. Most of them were left out of Couturat’s edition, more interested in the calculi, while these drafts pursue the ‘material’ side of the characteristica. This type of text presents us with a markedly different scenario from the lists of ‘forms’ of the Paris Notes or the essays in conceptual analysis of the early Hanoverian period. P They mainly appear as attempts at an original reworking of the categorial table. The shift from conceptual atomism to the central role of predication has its ontological counterpart in this new interest in categorial articulation. The subject-forms asymmetry suggested taking into account also some distinctions of ontological types in mapping concepts. The De Cogitationum Analysi and the De Affectibus could well represent the passage from an inquiry into the basic notions of a given field (psychology, or ethics and so on), pursued by the method of the chains of definitions, to a general categorial inquiry. By the same move, the study of the notion of substance is displaced from the regional ontologies of mind and body, as was the case in Descartes’ or Hobbes’s ‘first philosophy’, to the terrain of a general ontology. But Leibniz’s attention is directed also to the categorial articulation of the different types of predicates, in Scholastic language to ‘accidental categories’.

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From the methodological viewpoint, the ‘way of ideas’ appeared to Leibniz increasingly unsatisfying as the basis for a reform of ontology. His approach to things will no longer pursue the direct inspection of the mind’s contents, but the guiding thread of (logico-) linguistic structures: Given that words [vocabula] have been invented in order to signify thoughts [ad cogitationum designationem], we can follow them as our guide; we cannot, indeed, directly describe ideas, but only their signs on paper.1

In this context, a highly relevant fact is the emergence of the new project which is variously presented and labeled as ‘analysis linguarum’ or ‘charw acteristica verbalis’ or ‘grammatica rationalis’.2 It appears in 1678 within Leibniz’s efforts towards a symbolic language which should be able to express our thoughts in a crystal-clear manner for the pursuit and check of truth. Linguistic analysis should represent an intermediate stage between the complexity of natural languages on one hand and artificial ones on the other. Starting from Latin grammar and submitting it to a procedure of rational simplification, Leibniz aims at individuating a ‘universal grammar’ common to all natural languages, beyond their idiosyncrasies and accidental features. Finding this deep structure amounts to individuating the true ‘logical form’ which is somehow concealed in ordinary language. This is why this type of w philosophical analysis of language is preliminary to the study of formal logic and the construction of a suitable symbolic language. Studying the true logic of language, however, becomes also a privileged way of exploring the categorial structure of things. In particular, the study of the syntactic-semantic roles of terms within a proposition, hence of the subject-predicate distinction, can introduce the topic of substance and inherence better than the Cartesian account based on conceptual (un)saturation. This linguistic approach is prevalent, in effect, in the section of Leibniz’s tables devoted to substance. Before concentrating on this aspect, however, I want to spend some words to better evoke the whole historical and textual setting of the ‘category tables’.3 1 2

3

De totae cogitabilium varietatis uno obtutu complexione, A VI.4, 595. For an interesting exposition of this research program, see Analysis linguarum, A VI.4, 102– ¨ Sprache und Allgemeine Characteristk bei 105. See on this topic A. Heinekamp, Naturliche Leibniz, in Akten des II. Int. Leibniz-Kongr., Studia Leibn. Suppl. 15, 1975, vol. 4, 257–86; B. Mates, The Lingua Philosophica, in Studia Leibn. Sonderheft 8, 1978, 59–66; D. Rutherford, Philosophy and Language in Leibniz, in N. Jolley, The Cambridge Companion to Leibniz, Cambridge Un. Press, 1994, 22–69. The first identification of this type of text is due to H. Schepers, who coined the label ‘Kategorialsynthese’ in order to stress their difference with respect to the usual procedures of

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For a History of the Categorial Project: An Ontology for Scientia Generalis It is arduous to trace any line of development within scattered material, almost entirely deprived of steadfast chronological landmarks. Nevertheless, I will try to individuate some finer-grained textual typologies, that could give some coordinates to the categorial project and even suggest a kind of main line of development. The first textual layer for categorial inquiry is represented by those studies that are meant to provide a semantic interpretation of the first logical calculi. I have referred to them, talking about the containment theory of truth. But some of these drafts present also a family of other ideas, almost all connected to the theory of definition. This is far from unexpected, given the central role definition plays in Leibniz’s account of formal proof and truth. Some problems come to the fore: first of all, that of introducing a hierarchy into the plurality of equivalent definitions, which is solved by the “order of nature”. Attempts are also made to reformulate the old theory of predicables in the new combinatorial setting.4 While this approach will be later abandoned, the notion of order of nature, that we have already met in the study of causation in the De Affectibus, will play an important role in the category tables. It is worth noting that the theory of definition is spelt out in the language of requisites: “A requisite is what can enter into a definition, like g, n, s . . . The requisite, therefore, is to the definition as the part is to the whole, or the prime number is to the product.”5 Clearly, “requisitum r ” is meant here in its analytical sense, in line with the “requisites of essence.” The analogies that Leibniz puts forward are important: as regards the arithmetical one with prime numbers, we are already familiar with its metaphysical application to the combination of simple forms. In the first calculi, to which the present text is closely related, it receives a well-known logical application. Leibniz tries to construe, in fact, a numerical model for propositions, where simple concepts are symbolized precisely by prime numbers. With regard to the part-whole relation, special attention is devoted to it in this type of text, where Leibniz tries to give the basic definitions for a mereology. To sum up, he identifies ‘requisite’ with

4 5

conceptual analysis (‘Begriffsanalyse’) of the tables of definitions. See H. Schepers, Leibniz’ Arbeiten zu einer Reformation der Kategorien, Zeitschrift f¨ ffur philosophische Forschung 20, 1966, 539–567; Idem, Begriffsanalyse und Kategorialsynthese. Zur Verflechtung von Logik und Metaphysik bei Leibniz, in Akten des I. Leibniz-Kongresses, Band III, Steiner, Wiesbaden 1969, pp. 34–49. See also the valuable remarks in D. Rutherford, Leibniz and the Rational Order of Nature, Cambridge, Cambridge Un. Pr., 1995, 99–124. See Ad Specimen Calculi universalis addenda, A VI.4, 295–296. Elementa ad calculum condendum, A VI.4, 153.

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the element of combinatorial analysis and synthesis, being aware that it can be interpreted according to a plurality of notions or relations. Conceptual containment is the basic one, the part-whole relation can be another. Also the dynamic sense of requisite is taken into account—the requisite for existence, prevailing in the old reflections on conditions. In the same lines, Leibniz gives a definition of “causa” in the framework of the combinatorial theory of conditions: if all ingredients taken together bring the whole (totum) immediately into existence, all causal conditions together bring the effect into existence by way of inference. This shows that the ambiguity of requisita r is far from abandoned. On the contrary, it is confirmed as a deeply entrenched intuition, that will be articulated in the tables, however, taking into account the need to draw due distinctions among different interpretations. It is important to recognize here—besides the logical calculi, that promote the conceptual interpretation—the influence of another important specimen of the scientia generalis. I am thinking of the inquiry into the “initia mathematicarum” i.e. into the primitive notions that furnish the axiomatic basis for the different fields of mathesis. Besides mereological notions, this research deals with the mathematical relations of similarity, equality and congruence. On this terrain, Leibniz is constantly working on the double tune of a logical and phenomenological approach. We have here a sketch of formal ontology, the ontological counterpart to the variety of inquiries and calculi Leibniz works out in the fruitful period 1678–79: logical calculi, geometric characteristics and so on. In the slightly later drafts of the eighties, these ideas are integrated into the plan of a reformed categorial table. Let me pass to this stage of Leibniz’s conceptual inquiry. A Standard Table of Categories The group of drafts which properly deserve the label of ‘tables of categories’ is not so large and they present relevant differences one from fanother.6 Nevertheless, they stand out clearly from the mere lists of definitions, insofar 6

I refer to the following texts: Definitiones: Aliquid, nihil (N. 76), A VI.4, 306–310; Enumeratio terminorum simpliciorum (N. 97), A VI.4, 388–397; De Notionibus omnia quae cogitamus continentibus (N. 98), A VI.4, 398–405; Notationes Genarales (N. 131), A VI.4, 550–557; Divisio terminorum ac enumeratio attributorum (N. 132), A VI.4, 558–566; Genera terminorum. Substantiae (N. 133), A VI.4, 566–569; De abstracto, concreto, substantia, accidente, substantivo, adjectivo et similibus (N. 134), A VI.4, 569–573; De abstractis (N. 135), A VI.4, 573–574; Divisiones (N. 136), A VI.4, 574–576; De totae cogitabilium varietatis uno obtutu complexione (N. 143), A VI.4, 594–604; Definitiones notionum metaphysicarum atque logicarum (N. 147), A VI.4, 624–630; Tabula notionum praeparanda (N. 148), A VI.4, 630– 635; Catalogus notionum primariarum, ex quibus caeterae pleraeque omnes componuntur (N. 149), A VI.4, 635–639; Inquirenda logico-metaphysica (N. 210), A VI.4, 997–1000. Some of these drafts (especially, N. 97, 98, 132) offer a view of the whole categorial system.

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as they exhibit relative homogeneity in their contents and also a kind of standard order of exposition, at least in the case of the richest and most developed ones. Perhaps the best example of this standard setting is offered by a text like the De notionibus omnia quae cogitamus continentibus.7 The concepts listed are distributed in different and relatively independent groups, each referring to a kind of super-category, according to the following scheme: Possible Impossible

Reality

Positive Negative Complete Incomplete Absolute Limited Same

Variety

One/Many Different Incompatibilia Inconnegabilia

Most General

Opposita Consequences Conditio Conditionatum Inferens Illatum

Cause/Effect

Prior Order (of Nature)

Posterior Time

Change Active/Passive

7

Others deal only with parts of the project; for instance with the theory of conditions or the ontological-linguistic inquiry into abstract reference. A group of texts is especially interested in the topic of substance; in particular, the Notationes Generales, though having many points of contact with the categorial tables, develops a theory of individual substance which anticipates the central themes of the Discourse. On the contrary, other drafts study the other categories without considering substance. Finally, some texts prolong the categorial analysis into a classification of the various types of substances: see for instance, Genera terminorum (N. 133) and De totae cogitabilium etc. (N. 143). N. 98, A VI.4, 398–405. The text should be considered together with its twin Enumeratio terminorum simpliciorum (N. 97), A VI.4, 388–397, a rich analysis of which the former represents a sort of schematizing result.

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More Special

Quantity Position Thought

Most Special

Extension

Substance and the accidental categories are inserted in the wider context of seventeenth century Scholastic ontology centered around the notion of being (ens) and its general properties. Thus, the first conceptual group, labeled under the heading of ‘Reality’ ((Realitas), moves from Being, passing through the dichotomy of Possibility and Existence, to the substance-accident structure (under the heading of the complete-incomplete pair). The super-category of Variety (Varietas V ) follows, embracing the basic relations of identity and diversity and the notions of unity and number. On one hand, Leibniz’s disposition of the subject recalls the study of the formal properties of being, such as can be found in the handling of Unity in Suarez’s Disputationes. Contrary to this model, however, logical priority is accorded to the relation of identity, while the concepts of One and Many are logically posterior to it. Moreover, the style of analysis is vastly different from Scholastic models, dialectic distinctions being replaced by the clear-cut definitions of a mathesis universalis. Thus, the notion of identity is introduced by the well-known definition through substitutibility salva veritate, and on this basis a suggestive attempt is made to define natural numbers in a spirit close to our ‘logicism’. A new type of Variety is considered later, when passing to the conceptual family of Change ((Mutatio). The next section on ‘Consequences’ (Consequentiae) studies the formal properties of inference relations. If reinforced by the notion of Order of nature, this logical framework is suitable to express many important ontological relations, first of all that of causality; it takes up again, of course, the topic of requisites. So far we have the groups of notions that are to be considered as the ‘most general’ (Generalissima), i.e. the set of transcategorial properties of being that are absolutely pervasive with respect to all categorial specifications. The study of the old classic (accidental) categories of Quality, Quantity, Relation and Position, instead, already pertains to the level of the ‘More Special Predicates’ (Specialiora), by which we are able to distinguish things. As I will show in the next chapter, the different categories are nothing but different ways of specifying the fundamental logical relations of identity-diversity according

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to our cognitive devices, hence to the functions of perceiving and conceiving and the related ability to discern objects they make possible. As a matter of ffact, this analysis represents the ideal prosecution of the ontological side of the mathesis universalis, as it was delineated in the 1678–79 drafts. Finally, the most special determinations (Maxime ( Specialia) introduce some irreducibly different types of contents, such as the perception of Thought and Extension: practically, what determined the two ontic regions of the moderns. A Cartesian style ontology of mind and matter can find here its place within the wider categorial inquiry, provided we bear in mind that the basic meaning of substance has been grounded on the different level of the general subject-predicate structure. As I have anticipated, the analysis of language is largely applied to this topic. In the context of categorial tables, however, the direct analysis of notions is far from being abandoned and totally replaced by the analysis of linguistic devices. On the contrary, the tables exhibit a basic parallelism between a phenomenological approach and a (logico-) linguistic one. This is particularly clear, for example, in a text labeled Divisio Terminorum, where w the list of the different types of ‘attributes’ is introduced by the words: “At first reality presents itself to mind . . .”8 and the study is further pursued following the guiding thread of a phenomenological recognition of our mind’s contents and operations: “we perceive . . . we observe . . . ”. This double approach is especially evident in the topic of identity, that I will consider firstly, because it provides a general conceptual framework for the problems of individual identity.

1. Varietas. Identity for Concepts and Things: The General Framework 1.1. Substitution and Concept Identity At the Origins of Sameness: Predicative Structure and the Phenomenological Approach In the category tables, identity is usually defined through the well-known Substitutivity Rule (from now on, SUBST): “eadem sunt quorum unum alteri 8

Divisio terminorum ac Enumeratio Attributorum: “It seems that, first of all, some positively conceivable matter presents itself to mind . . . ”, A VI.4, 561.

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substitui potest salva veritate”. The primitive character of the predicative structure, on which Leibniz was reflecting in the early Hanoverian years, is absolutely central for understanding his approach to identity. The formulation itself of SUBST already presupposes a predicative structure, which in its turn implies a kind of primitive identity, insofar as many predicates are referred to the same subject. Besides the canonical ‘logical’ approach of SUBST, a ‘phenomenological’ one sometimes emerges, where identity and difference are met within the experience of “perceiving-together” (comperceptio): In the things that are present, we observe some variety. And in this way we grasp the notions of “different,” of “many” and of “together.” So, when I perceive a horse and an ox, I observe that the ox is not the same [as the horse], but they are different; but, insofar as they agree in some respect, they are many, I mean many animals or many beings. The same is that which can be substituted for the other salva veritate.9 w

This double approach is deeply rooted in Leibniz’s reflection. Already in the final part of the De Affectibus he relies, surprisingly enough, on our experience in order to introduce the principle of non-contradiction: Let us imagine that something is perceived and not perceived at the same time: we shall say that we are dealing with two different things, not with one and the same.10

A ffew lines below, the traditional ‘inference from being to possibility’ (ab esse ad posse) is justified in a similar way: What actually does exist, is also possible. This principle can be proved by us through experience only. It depends indeed on the nature of actual existence, where we can never detect any contradiction. It could be proved perhaps in the following manner: “Let the same actually be and not be. How could we know that it is one and the same?”11

This amounts to saying that we never experience contradiction, just because there is no possible experience of a contradictory state of affairs. The argument somehow recalls Aristotle’s defence of the principle of non-contradiction in the lεgxoς of Metaphysics, Book
. The impossibility of a contradictory 9 10 11

A VI.4, 561. A VI.4, 1439. A VI.4, 1439–1440.

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experience is linked, in its turn, to a Verificationist Claim, which is often neglected by Leibniz’s interpreters: we must always be able to give a perceptible or intelligible content to both our identity and diversity statements.12 In the same lines of the De Affectibus we already find a definition of identity through substitution, with no mention of truth but with a phenomenological nuance: “Identical are those items, of which one can be substituted for the other, so that no contradiction does appear.”13 The same criterion is applied in an important text of the Discourse period, the Notationes Generales, when w arguing for the IdInd: It is enough that there cannot be two singular beings that are absolutely similar, e.g. two eggs. Necessarily, in fact, some properties can be said of one and not of the other; otherwise, they could be mutually substituted, and there would be no reason why they are not said rather to be one and the same.14

Here, we find the lexicon of ‘being said of’, but objects are directly substituted one for another. I suspect that the idea of substitution has, originally, an ante-predicative model in the intuitive (and idealized) operation of replacing some object (or in general, some perceivable content) with another one. Even the replacing of an individual with his/her perfectly similar twin within a given environment, as was envisaged in the Confessio, worked as a kindred substitution test. Moreover, also the linguistic dimension of substitution seems to be originally rooted in perceptual experience. So, the De Affectibus gives a purely syntactic characterization of conceptual truths, ultimately relying on the perceptual indiscernibility of signs: A = A. Already in the P Paris Notes Leibniz elaborated a similar idea of substitution, in the draft entitled De Elementis Cogitandi; in this case, the non-formal identity A = B is concerned. This interesting draft pursues a linguistic version of that εlεnxos strategy for the foundation of first principles, of which I have shown a phenomenological version. Non-contradiction is introduced as the condition for the institution of a meaningful language, reliable both for private discourse and intersubjective 12

13 14

When diversity is stated, the claim assumes the form of a Discernibility requirement: “I define as distinct or different those items, that are capable of having contradictory predicates, from which we are able to understand that they are not one and the same, but different.” Notes to w T Temmik , VE 1082. Temmik’s text Philosophia vera Theologiae et Medicinae Ministra (K¨o¨ ln 1706) has been published with Leibniz’s notes by Mugnai as an appendix to his Leibniz’s Theory of Relations. A VI.4, 1439. A VI.4, 554.

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communication. To this end, once the meaning of a word is fixed, one is bound to allow constantly for certain substitutions of signs. Coherent substitution is truth-preserving by definition: true is what is derived coherently with the stipulated substitutions. Finally, substitution is constitutive of the idea of proposition (or better, of sentence) itself: When we experience that ourselves or others connect the words in use in a certain way, and substitute them one for another, then we call this a Proposition: to say that “A is B,” indeed, is nothing but to say: “I permit that B be substituted for A.”15

The operation of substitution on signs becomes the key for the sentence structure, quasi as a counterpart of the phenomenologico-pragmatic approach I have illustrated in the previous section (‘Conceiving A, I tend to act as if I were expecting B’). Logic and Substitution The substitution test assumes its well-known propositional form in the drafts devoted to the semantic interpretation of the 1679 calculi. In this context, it is quite reasonable to interpret the salva veritate substitution rule as an identity criterion for concepts.16 The close connection of sign and concept in the Leibnizian usage of ‘term’ should be taken into account to understand Leibniz’s formulation without being too eager to charge him with a use-mention confusion. I will only sketch some coordinates of the salva veritate substitution as applied to concepts, in order to provide a framework for discussing its controversial application to individual objects. Interpreting his calculi, Leibniz firstly approaches identity starting from the basic relation of conceptual containment, intended in an intensional way. Two concepts A and B coincide when they contain one another: A = B iff ((A est B) and (B est A)). But Leibniz is able to demonstrate the equivalence of this 15 16

A VI.3, 506. On Leibniz’s substitutivity rule, its interpretation and its controversial relationship with our so-called “Leibniz Law”, see A. Angelelli, On Identity and Interchangeability in Leibniz and Frege. Notre Dame Journal of Formal Logic, VIII (1967), 94–100; R. Kauppi, Substitutivity Salva Veritate in Leibniz and in Modern Logic. Ratio 10 (1968), 141–149; F. Feldman, Leibniz and Leibniz’ Law, The Philosophical Review (1970), 510–52; E. Curley, Did leibniz state ‘Leibniz’ Law’? The Philosophical Review (1971), 497–501; H. Ishiguro, Leibniz’s Philosophy of Logic and Language (1972), Ch. 2.; B. Mates, The Philosophy of Leibniz (1986), 123–32.

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definition with that through substitutivity,17 that is soon preferred.18 The role of the salva veritate criterion can be related to the primacy of the predicative structure, hence of the proposition. It is quite reasonable to read into Leibniz’s strategy the intuition that we can grasp concepts and fix their boundaries and reciprocal relations only considering their use, i.e. their occurring as constituents of propositions: That A is the same as B means that one can be substituted for the other in any proposition without loss of truth [salva veritate]. For those relations are explained through propositions or truths.19

In this vein, Hid´e Ishiguro is well entitled to consider SUBST as if it were a kind of Leibnizian “Principle of Context.”20 On the other hand, one should not forget that Leibniz’s doctrine emerges within a wholly intensional interpretation of concepts and truth. The link of identity definition with concept analysis is confirmed in the clearest way in the selfsame passage quoted from the GI: That these coincide can always be shown by an analysis: namely, if they are analyzed until it appears a priori that they are possible, and if the same terms appear formally, then different terms are the same.21

So, we can well say that the identity of Leibniz’s concepts does depend on the truth conditions of the propositions where they occur; truth conditions, however, depend in their turn on the containment relations among concepts. If we want to insist on the Fregean comparison, we are faced here with a tension similar to that between the Principle of Context and the Compositional Principle. We are concerned, however, not so much with a vicious circle, as 17 18

19 20

21

See Ad specimen calculi universalis addenda, VI.4, 294. The salva veritate formulation arises quite naturally from the circumstance that definitional substitution is the main truth-preserving rule of calculus: “‘A coincides with B’ if the one can be substituted in place for the other without loss of truth [salva veritate], or if, on analyzing each of the two by substitution of their values (i.e., of their definitions) in place of the terms, the same terms appear on both sides: the same, I mean, formally—for example, if L, M and N appear on both sides. For those changes are made without loss of truth which are made by substituting a definition in place of a defined term, or conversely.” GI, A VI.4, 746 (C 362; LP 53). The remark on the ‘formal’ character of substitution aims at stressing the mechanical (syntactic) aspect of the perfect coincidence of signs. Ibidem (LP 52). See H. Ishiguro, Leibniz’s Philosophy of Logic and Language, Ch. 2. London, Duckworth, 1972, 2nd ed. Cambridge, Cambridge Un. Press 1990. A VI. 4, 746 (C 362, LP 53).

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with the fact that a cluster of notions—identity, truth, substitution—are inseparably interdefined. Maybe, the notion of truth is privileged in the expression of the criterion, insofar as it plays a leading role in our heuristic and cognitive practice. But conceptual containment, which is brought to light through conceptual analysis, remains the logico-ontological basis of truth. Failures of Substitution F A much debated issue in the recent studies on Leibniz’s philosophy of language has been his treatment of the apparent exceptions to the “salva veritate” rule.22 Leibniz, in fact, is well aware of the fact that substitution ffails in the contexts that we nowadays label “intensional”. In the GI, we find one of the often quoted passages on the failure of substitutivity: SUBST, Leibniz observes, holds true, except in the case of those propositions that you could label as “formal”— where one of the terms that coincide is taken in such a formal way, that it w maintains a distinction from the other (admittedly) coincident term. Now, these propositions are reflexive and they do not bear on things, but rather on our way of conceiving them—where there is a distinction, indeed.23

The ‘formal’ consideration that creates problems to SUBST alludes to the sense of ‘formal’ according to which a formal identity (of the type A = A) is opposed to a coincidence (like A = B). This means that, applying some devices (typically, intensional or ‘reduplicative’ operators) to coincident terms, we can concentrate our attention precisely on this or that way of expressing the same notion. In the passage quoted, no example is given. Elsewhere, one of Leibniz’s cherished examples of exceptions to SUBST is that of “triangle” and “trilateral”. We found it in connection with Trinitarian aporias and their Raue style solution. Sometimes however, also in the GI, triangle and trilateral, far from being presented as an exception to the Substitution law, are taken as a standard example for it: clearly, when they are not considered in the “reflexive” way. a The choice is not accidental: in the occurrences of the substitutivity rule in the 1679 drafts, indeed, the examples are normally drawn from geometry, 22

23

See B. Mates, The Philosophy of Leibniz, 130–132; M. Mugnai, Intensionale Kontexte und ‘Termini reduplicativi’ in der Grammatica rationalis von Leibniz. In Intensionale Logik St. Leibnitiana Sonderheft 8, 82–92 (1978); G. Nuchelmans, JJudgment and Proposition, 225–230. GI, § 19, A VI.4, 752 (C 366–67).

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hence from general properties or abstract objects.24 This can reinforce the idea that the criterion is originally formulated for concepts, bearing in view the exigences of an idealized language, a kind of Begriffsschrift fit to express mathematical knowledge and necessary relations among ideas. This is why I have talked about A and B being the same ‘notion,’ and not simply the same ‘thing’, as the letter of the text suggested. Even if considered as a possible exception to the substitution test, the triangle-trilateral example would confirm that we are dealing with the identity of intensional objects. It is not in ffact a case of a simply “intensional” context, but rather of an hyperintensional h one.25 The identity of triangle and trilateral, in fact, is a necessary one, that can be established demonstratively through conceptual analysis only. According to the definitions of the GI, both concepts can be reduced to the same constituents. In the GI, however, the triangle-trilateral pair appears together with ‘Alexander the Great’ and ‘the king of Macedonia, conqueror of Darius’, hence with two designations (a proper name and a definite description, we would say) of the same concrete individual.26 Also the Notationes Generales gives an example of failure of SUBST that is no longer drawn from general concepts that are necessarily equivalent, such as triangle and trilateral, but from two designations of the same individual, that turn out to be only contingently coextensive: So, “Peter” and “the apostle who denied Christ” are one and the same and one term can be substituted for the other; unless I consider precisely this way of conceiving that is labeled as “reflexive”, e.g. when I say: “Peter, insofar as he was the apostle who denied Christ, sinned”, I cannot substitute here “Peter”, i.e. I cannot say: “Peter, insofar as he was Peter, sinned”.27

Here, we are not faced with a hyperintensional, but with a classic intensional context of the kind we are nowadays familiar with: the common reference of our distinct ‘ways of considering’ is properly a thing in flesh and blood. The new examples of exceptions to SUBST in the GI and the Notationes Generales are the clues of an implicit extension of the rule to individuals—or better to individual concepts. 24 25

26 27

See Calculus ratiocinator, A VI.4, 275; Specimen calculi universalis, A VI.4, 282. I take this terminology from G. Bealer, ‘Concept’ in J. Kim, E. Sosa, A Companion to Metaphysics, Oxford- Cambridge Mass., Blackwell, 1995, p. 89. A VI.4, 746 (C 362). A VI.4, 552.

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To sum up: it seems that SUBST is firstly and basically formulated, in the field of the semantics for logical calculi, as a definition for conceptual identity. From this perspective, ‘triangle’ and ‘trilateral’ are different designations for the same ‘idea’;28 and the failures of SUBST reveal some finer-grained difference in the objective ways of conceiving the idea. Later on, however, ‘things’ in flesh and blood are considered (admittedly, always via the corresponding concepts): so, the examples are interpreted this time according to a true thing-concept dichotomy. A link between the two different perspectives is represented, probably, by the fact that Leibniz, at the stage of the GI, is eager to insist on the need to take all concepts in concreto: so, the term T will not stand for ‘triangularity’, but for ‘triangle’: more precisely, for ‘triangular’ (thing). This way of conceiving surely favors the move to an extensional view of identity. We can also put the matter in this way: we meet again, in a context of conceptual analysis, an idea that already emerged with the Raue style solution to Trinitarian problems. I mean, that there are two quite different types of predication, related to two different ways of connecting concepts: a necessary one, determined by their internal content (which defines their logical space), and a contingent one, mediated by their common reference to objects, i.e. by their extensions. Anyway, surrounding the GI the problem of handling individuals within a conceptual science is at the center of attention. The example of substitution failure from the Notationes, then, is all the more intriguing, as it touches a leading problem in our research, i.e. the relationship of individual identity to accidental features. One could think that, from the point of view of strict ‘superessentialist’ logic, the forbidden substitution of “Peter” to “the apostle who denied Christ” would be quite correct, even in the intensional context. In this sense, assuming this as a counterexample to SUBST seems foreign to a superessentialist approach. I leave this problem open, to limit myself to some general considerations on the application of SUBST to individuals. 28

Maybe this label is more appropriate than that of ‘concept’, which is sometimes used by Leibniz for the psychological side in the apprehension of an intelligible content: in Fregean terminology, a Vorstellung r . The different ways of grasping it are, instead, objective Sinne. In this work, however, I normally use ‘concept’ (corresponding to ‘term’), in the objective sense. The ‘hyperintensional’ approach is confirmed by an interesting draft [LH IV 7C Bl. 76 vs.] edited by Mugnai, where ‘triangular’ and ‘trilateral’ are taken as ‘different ways of conceiving’ the same ‘notion’. But this distinction is preceded by the main dichotomy between ‘real’ and ‘formal’ (i.e. conceptual) distinction, which reflects the thing/terms polarity. See An Unpublished Latin Text on Terms and w Relations. Transcribed and translated by M. Mugnai. The Leibniz Society Review, 7, 1997, 125–127.

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1.2. Sameness and Change: The Phenomenological Approach What Counts as One and the Same Thing? Given the role of SUBST, it is tempting to explain Leibniz’s theses about individual identity, i.e. his intransigent version of both IndId and IdInd, as simply being the application to individuals of the left-right, respectively right-left side of what we call nowadays ‘Leibniz’s Law’. It will not be hard to see, however, how SUBST in itself could scarcely decide our identity questions concerning individuals, without assuming some previous ontological intuition. Thus, the left-right side of the Substitution Law, i.e. the Indiscernibility of Identicals, states a necessary condition for individual identity, to be sure. But the hard thing is to give the conditions for its application. We are bound to a previous intuition of what being an individual entity means. In his late notes to Temmik’s book, Leibniz observes: Socrates-the-white and Socrates-the-musician are one and the same. Although, in fact, Socrates sings well, insofar as he is a musician, and he does not sing, insofar as he is white; nevertheless it is true that Socratesthe-white does sing, and whatever can be said of Socrates-the-musician is also true of Socrates-the-white, except for “reduplicative” predications, by w which the formal concepts of the respective predicates—i.e. “whiteness” and “musical ability”—are distinguished.29

‘Socrates-the-musician’ or ‘Socrates-the-white’ are typical cases of ‘accidental compounds’, which Aristotle already took into account in close connection with the apparent failures of SUBST. The substitution test is applied here by Leibniz in order to neutralize difference and to restate identity—the identity of a thing which simultaneously underlies different properties. It supports sameness, contrasted with the diversity that prevails (with the failure of substitutivity) from the intensional viewpoint. Thus, the application of SUBST must presuppose some intuition about the different aspects of a concrete thing or the different descriptions it can fall under. But our ordinary intuitions are prepared to accept a more radical difference within the same thing. The text Leibniz annotates deals with the traditional theory of change, which contrasted the same underlying subject with the forms it can successively assume. This was the origin of the idea of matter as a persisting substratum. But also primary substance, remember, was conceived of 29

VE 1082.

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as a ‘power of contraries’. This amounts to saying that the same ontological subject cannot only sustain different predicates simultaneously, but even contradictory ones, successively. A suitable weakening of the Indiscernibility of Identicals appears as the natural correlate to this idea. A kindred intuition— whose basic model is provided by ordinary spatio-temporal objects—is also w presupposed by Leibniz’s application of SUBST to individuals. Already in the De Cogitationum, the one-many structure of subject and properties embraces not only difference, but also contradiction: “From these definitions one could show that the same subject can possess many attributes, even contradictory, that is to say it can change.”30 And against de Volder, abstract properties are opposed to the concrete changing subject.31 Change, therefore, is originally part of the Leibnizian idea of a concrete subject or of a thing. It appears, however, more puzzling than the mere co-presence of properties, just insofar as it implies that contradictory properties, such as A and not-A, are attributed to the same subject. On the other hand, notice, reference to the same subject is required in order to have a contradiction; otherwise, we would simply be left with a succession of different states, as was the case in the transproduction model. Between Logic and Phenomenology: Two Models for Change Leibniz’s intuition about sameness through change comes under the pressure of the Verificationist Claim, according to which we are bound to exhibit an indiscernible element when stating identity. This becomes clear within the phenomenological account of identity in the Divisio terminorum, where w change is introduced by “observing”, or “perceiving”: Then, we observe also Novelty or Change, i.e. we observe that one and the same thing has contradictory properties. E.g., two objects that are contiguous then are separated, while all other properties of them remain, except their contact; and this is why we are inclined to conceive that the same things become separated from being contiguous, rather than those contiguous things are destroyed and other separated ones are substituted for them. But it is impossible that two absolutely contradictory predicates are said of one and the same thing. Now, the difference that does hold while all other properties are the same, and in this way makes true that w we are not faced with an absolute contradiction, is precisely temporal difference.32 30 31 32

A VI.4, 2770. See the criticism to de Volder (GP II 249) discussed above (Section 2). A VI.4, 561–562.

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The succession of opposite states (aggregatum g statuum contradictoriorum), elaborated in the P Pacidius Philaleti, is the standard way of defining Change in the categorial tables, where it usually works as an abstract model applied both to physical phenomena and the succession of states of a substance and is still neutral with respect to further metaphysical interpretations. The Divisio, however, occupies itself precisely with the ontological interpretation of the scheme. Are we truly faced with the same underlying subject, or not? The statement of sameness turns out to be puzzling, insofar as Leibniz shifts it here beyond the properly phenomenological level. Pure perception simply exhibits to the mind two different states-of-affairs. Saying that the successive states belong to the same thing is already an interpretation, or the content of a judgment. But an alternative interpretation is possible, corresponding to the transproduction model, hence to an ontology of entia successiva, w where the different states hold as different objects and sameness is at most a loose one. The language of substitution adopted here could reveal some connection with SUBST, not taken in its propositional version, but rather in the phenomenological one. But the substitution test does not purport indiscernibility here. On the other hand, the interpretation which endorses sameness is a deep intuition of ours, whose suitability can be also argued for by relying on a qualitative view of identity: the states of affairs S1 and S2 share all their properties, one excepted (remember, we are dealing with a highly idealized example, drawn from abstract extended objects). So, we are well entitled to the identity statement we are strongly inclined to. The temporal difference is invoked at this juncture, just to dispel the threat of contradiction. It is not seen as a further different property, but as a kind of parameter that neutralizes the other differences. So, the temporal modification seems to have parametric or adverbial nature, that can be further interpreted as applied either to the predicate or directly to the copula of the corresponding judgment. Experimentum Sui The Divisio terminorum has suggested a rationale for our preference for the sameness model. Leibniz points out, however, that we are bound to verify in each case, which of the two models of temporal ontology (the continuant or the ens successivum) matches better with the way things are. And he also indicates a case—the Self—where the presence of a continuant should be taken for granted. All this is far from unexpected: since its origins Leibniz’s ontology of change was split into two different models, according to whether we are dealing with minds or bodies, respectively. The relatively new fact is that in the same lines Leibniz takes seriously into account, although finally rejecting it, the possibility of applying the transproduction model to mind itself.

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So, he construes a rreductio ad absurdum of the attempt to extend the sequentialist interpretation to the temporal existence of mind. The argument runs as follows:33 (1) Every perception of ours needs time to be performed. (2) I know my own existence through a perception. Hence, (3) either (3a) I do persist beyond the limits of a moment or (3b) I cannot perceive myself, because (for 1) my perception necessarily extends itself beyond the moment. The same argument is repeated starting directly from the notion of selfknowledge (or apperception) as memory: (1’) Every consciousness of my perceptions is an act of memory, hence it refers to an object (i.e., the perception) that is already past. (2’) I know myself by becoming conscious of my perceptions. Hence, (3’) either (3a’) I do persist beyond the limits of a moment or (3b’) my self-knowledge is illusory and erroneous, because the conscious Self, which is present now, and the perceived one, which is past (for 1’) would be different. But if (3b-b’) is true, then I cannot simply know anything, because I would be committed to giving up the basic certainty of my own existence, i.e. the first factual truth. The key premise (1–1’) for the double reductio r is a discovery of Leibniz’s philosophy of mind, already documented in the 1676 writings: every action of mind has a temporal extension. In the 1676 remarks, this structural condition appeared mainly as a limit to our cognitive means; now, it becomes a resource for establishing real sameness, which cannot be assured by a compelling ontological interpretation of the “logical” model of change. The premise (1’), then, is nothing but the explicit application of (1) to the crucial case of self-knowledge. It expresses quasi-axiomatically what already emerged in the concrete analyses of the De Summa Rerum, where w memory appeared as essentially constitutive of the phenomenon of self-knowledge. But the topic is located here in the context of a phenomenological-categorial approach which is brought about in competition with the Cartesian foundational project. Also on this point, notice, Leibniz develops a Hobbesian hint: in his Objections to Descartes, Hobbes raised against the Cogito some aporias based on the 33

A VI.4, 562–563. See on this S. Di Bella, Zeit- und Identit¨ tats-Modelle bei Leibniz: zwischen t¨ Logik und Ph¨a¨ nomenologie, in Leibniz und Europa, Akten des VI Internationalen LeibnizK Kongresses , Hannover 1994, pp. 48–56. The same argument is alluded to in a compressed manner in the Definitiones Notionum Metaphysic. atque Logicarum (N. 147), A VI.4, 627– 628.

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temporal dimension of inner knowledge. Far from being destructive, however, Leibniz’s remark assumes the significance of a critical implementation of the Cogito. Against the alleged “atomistic” character of Cartesian selfknowledge—and regardless of whether this reading actually corresponds to Descartes’ historical Cogito (I think this is not the case)—Leibniz puts forward a Cogito that includes not only the synchronic variety of its inner object, but also the temporal multiplicity and variety of its history. In any case, the argument of the Divisio terminorum reintroduces the basic experience of self-knowledge at the core of the categorial analysis of identity. As we will see, in some of his 1686 writings, on the contrary, Leibniz tries to displace the foundation of transtemporal identity of substance from the terrain of the philosophy of mind to that of logic. Nevertheless, he will always make a similar move towards the inner experience of mind, whenever temporal identity is radically challenged.

1.3. Discernibility and Categorization: Identity for Abstract Objects Mathesis and Categories In the extremely creative 1678–1679 period Leibniz is producing, beside logical calculi, several other essays in semi-formal language and other types of calculi. In particular, he tries to lay down, within his studies for a characteristica geometrica, the basic notions of geometry, we could better say of topology. While identity was a basic relation for logical calculi, this role in the field of mathesis is played by the relations of equality, similarity and congruence concerning geometric objects. Leibniz adopts the Euclidean strategy of defining ‘equal things’ rather than the abstract property of equality. For a present-day reader, his procedure announces the classic Fregean move of defining properties and relations by construing some classes of equivalence. I wish to call attention, however, to two further features of this approach: firstly, the reference to our cognitive abilities, secondly and above all, the results on categorial inquiry. In some of the oldest drafts, similarity and equality are introduced as types of identity: we could say, as ways of weakening identity, insofar as they relativize it to a determinate category. So, “similar is a thing that is the same as far as quality is concerned (eadem qualitate).”34 By a corresponding specification, Leibniz obtains the varieties of SUBST: 34

A VI.4, 154.

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Equal are those things that . . . can be mutually substituted without loss of quantity (salva quantitate). Similar are those things that can be mutually substituted without loss of quality (salva qualitate).35

So far, the different relations are defined as equivalence relations modulo the corresponding categories. The following step Leibniz takes is the attempt at contextually defining the category itself: quality is what similar things have in common, quantity what equal things do. This move does not fall into circularity, insofar as the different categories are related to different cognitive functions; more precisely, to the epistemic conditions of our discernibility statements. Following this line, Leibniz elaborates some ways of characterizing the different categories that become standard for him. So, a Quality is a feature that “can be retained per se by memory”, i.e. that makes us able to distinguish two things even if only one of them is present now: Quality is a property according to which we distinguish things by using memory: that is to say, we can distinguish two things, of which one only is present now, while the other is not.36

When two objects cannot be distinguished in this way—that is to say, when they are the same according to quality, or similar—then they can be distinguished only if they are both present and we compare them. This amounts to saying that they need to be perceived together, in order to be distinguished.37 Thus, we can distinguish different species of geometric figures (e.g. a square and a triangle) by considering their different properties in themselves, but we distinguish two squares or two similar triangles only by their size, hence by comparing them together, or to a common measure. Finally, it can happen that two objects are not only similar, but also equal; in this case, we are still able to distinguish them, but only by comparing them to a third item, and this situation defines the category of Position, which is further specified as spatial and temporal location: In this way those things are distinguished, that cannot be distinguished if they are considered each for itself ( per se), nor if they are considered 35

36 37

Definitiones, A VI.4, 406. See also the Demonstratio axiomatum Euclidis: “Equal are those things that . . . can be mutually substituted without loss of size (salva magnitudine)”, A VI.4, 165. A VI.4, 308 (N 76). “Those things are distinguished only for their quantity, that cannot be distinguished if they are taken separately; nevertheless they can be distinguished if they are considered together”, A VI.4, 393.

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together (simul spectata). They are distinguished by assuming a third thing, and considering the three things together . . . 38

This standard articulation of accidental categories according to our discernibility procedures is developed in the drafts devoted to the basic notions of mathematics ((Initia mathematica), as I have said; on the other hand, this ffamily of concepts is included in the category tables.39 As a result, the ontology of substance and that of abstract objects are integrated into a unitary framework around the basic relation of identity and its further specifications. At the same time, accidental categories as a whole are contrasted with substance, and a principle for their hierarchical classification is given. In this way, a Leibniz achieves an ontological program, echoing the Ockhamist one, that contemplates the reduction of the traditional categories to some basic ones (Quality-Quantity-Relation-Position) and the ontological weakening of some of them (e.g. Quantity), insofar as they are related to abstract objects or to the phenomenal level. The category of Quality occupies a crucial role in this context: if Quantity is decidedly confined to the phenomenal level, Quality cannot help receiving a stronger ontological import. On one hand, “qualities” or “forms” are the basis for similitude, on the other they are, as intelligible differences, the cornerstone for discernibility. A Phenomenal Order for Individuals Also the ontological significance of Position is not easy to determine. It is explicitly connected to existence: What has a position, that is to say what has an existence relation to other things, while the relations above—i.e. quality and quantity—concern essence, or formality.40

38 39

40

Ibidem. For this integration, see the draft “De divisione praedicati” (N. 195), in A VI.4, 926–930, where Leibniz is clearly interested in reconstructing the traditional division of accidental w predicates (‘accidental’ in categorial sense, referring to all categories except substance). But the merging of the categorial inquiry on complete and mathematical beings is even more interesting in the draft Definitiones notionum metaphysicarum atque logicarum, A VI.4, 624–30. A VI.4, 393. For the Position-Existence link, see the T Tentamina de definitione quantitatis: “[Position] is a relation with other things insofar as existence is concerned, i.e. the existingtogether [coexistentia] of things.” A VI.4, 164.

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Remember the passage of the De Cogitationum Analysi about the differences not drawn from forms (but there, notice, both quantitative and positional differences were counted together, and opposed to qualitative or conceptual ones). Leibniz now pursues a similar train of thought on the phenomenological level. True, I have suggested that the De Cogitationum Analysi alluded to some deeper foundation for spatio-temporal individuation; but the matter was still far from clear. The problem is a classic one for the evaluation of Leibniz’s philosophy. As is well known, Kant (and Strawson as well) will charge Leibniz—in the Anphiboly of Concepts of the Critique of Pure Reason—with having blurred the discernibility conditions holding for concepts within an intelligible world (i.e., within a system of concepts) for the ones holding for existing things within our actual physical world (i.e., within a system of objects). This could be finally true, but the quotation above should warn us that Leibniz’s way is in any case more complex, and he is not unaware of some of the intuitions that Kant will emphasize. It seems that for Leibniz the conceivability of the relations of position presupposes, indeed, a common spatio-temporal framework, hence our referring practices to existing things—be this existence actual, or at least possible. Conversely, in identifying and distinguishing existent objects we are bound to make great use of position. As concerns our ordinary experience and also scientific knowledge, in fact, Leibniz continues to put forward spatio-temporal individuation as the viable one, perfectly in tune with the old Confessio strategy: We distinguish also individuals by referring to times and places; and in this way a we judge which things are the same and which are different; e.g., if I see two eggs completely similar and equal, and I wish to distinguish them, I should either mark them, so that they become dissimilar, or put them in a fixed place . . . or finally, if they . . . can move, then there is nothing left to do but follow their motion with my eyes, in order to see how they change their place over time . . . 41

We individuate things in this way in the world of phenomena. It is worth noting that in this text the notion of “Individual” is counted—together with Space, Time and World - among the basic notions of empirical-phenomenal knowledge, providing the conceptual framework for a coherent science of the actual world.42 Thus, the ‘numerical’ distinction based on Position seems 41 42

Definitiones Cogitationesque Met., A VI.4, 1397. See A VI.4, 1396. Also the categorial scheme of the De divisione praedicati presents the following box: “Individual [differences] i.e. haecceities, where place and time are dealt with.” A VI.4, 927.

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to confirm its privileged link with the conceivability conditions for existent objects. Leibniz is speaking on the level of phenomena, however. Let me consider this difference of levels further. Similarity and Abstract Objects. From Mathesis to Metaphysics Leibniz attributes explicitly this handling of Quality, Quantity and spatiotemporal Position to the field of mathesis, considered as a “logic of imagination”;43 and he is eager to stress the difference from metaphysics, which is concerned, instead, with purely intelligible objects. It is interesting to remark that the universal and abstract character of mathematical knowledge is not tied to intellect, but to imagination. This faculty turns the limited sharpness of our sense perception into a resource for construing a simplified and economical image of world. In this way, imagination plays in Leibniz a central epistemological role, insofar as it makes the construction of our general concepts possible. Accordingly, he is well aware that the construction of indiscernible objects is the outcome of an abstraction move and that mathematical objects, in particular, are abstract beings.44 Hence, the warning: Whether it is possible, then, that there are in nature two things that differ only numerically, i.e. only by the fact that they are not one and the same, but many: this question does not pertain to the present topic, but to Metaphysics; for our present purpose it is enough that such things can be found that cannot be distinguished according to imagination, or to sense appearance.45

On the metaphysical level, Leibniz’s answer to this question turns out to be unequivocally negative. This is clearly stated in a draft of the end of 43

44

45

See Elementa nova matheseos universalis: “The Universal Mathesis should give a method of exact determination for those things that are subjected to imagination, that is to say a kind of Logic of Imagination. Thus, Metaphisics is excluded here, which deals with purely intelligible things . . .” A VI.4, 513–514. So, in the Elementa ad Calculum Condenda, after one of the first occurrences of his celebrated definition of identity, he writes: “Similar are those objects, whose diversity cannot be proved a priori, insofar as they are what they are said to be. So, those figures are similar, whose diversity cannot be proved insofar as they are figures, i.e. can be proved through situs w and magnitude”, A VI.4, 154–155. The use of ‘quatenus’ signals that perfect similarity—i.e. indiscernibility as far as Quality or ‘Such’ is considered—is a typical feature of abstract objects. The qualification ‘insofar as they are what they are said to be’ is also interesting: the abstractive, or intensional approach is related to a kind of ‘de dicto’ consideration, which we can imagine as opposed to the ‘de re’ transparent consideration of concrete objects. A VI.4, 514.

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the eighties, where similarity is defined through a narrowing of SUBST to the “propositions in which things are considered per se, i.e. according to the properties that really inhere in them.” But then, “only incomplete Beings are similar, nor are two complete beings of the same species infima to be found.”46 Finally, First T Truths draws the same consequence from the statement of the IdInd: A perfect similarity, therefore, is found only among incomplete or abstract notions, where things are taken into account not according to their whole being, but insofar as they are considered under certain aspects; w e.g., when we consider figures alone, leaving aside the figured matter: so two triangles are rightly held to be similar, although two perfectly similar material triangles are never to be found.47

A neat opposition is drawn, which is expressed in the Discourse by the examples of Polycrates’ golden ring as opposed to an abstract circle, or of the sphere on Archimedes’ tomb as opposed to the geometric solid studied by the great mathematician. Contrasting the general triangle with particular material ones, Leibniz echoes the example of circles in the De Cogitationum; but now it is quite clear, that the distinction of material instances cannot be a merely numerical, or spatio-temporal one. It is also clear that the need to rely on the weaker forms of discernibility (quantitative, and finally spatio-temporal, which is considered as solo numero) is just relative to abstract and phenomenal objects. This seems to contrast, however, with the privileged link that positional difference is said to have with existing objects in general. Could a solution be found in a hierarchy of basic and derived types of predicates? Surely, the categorial framework outlined here will turn out to be decisive in order to understand the exact import of the mature IdInd. The converse IndId, I have said, cannot be simply considered as the left-right side of SUBST, insofar as it presupposes an intuition concerning what means to be an identical individual. Similarly, neither is the Leibnizian IdInd simply the right-left side of SUBST, but some further restriction on the range of the relevant properties has to be assumed. In order to finally verify these hypotheses, we have to consider the final configuration of the concept-thing relationship in the 1686 writings.

46 47

Definitiones (N. 196), A VI.4, 932. A VI.4, 1645.

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2. Concepts, Things and the Grammar of Substance 2.1. Things and Terms From r Forms to Terms: Ontological Asymmetry and Semantics At the beginning of the Characteristica verbalis,48 one of his first attempts at tracing a semantic analysis of the main categories of linguistic items, Leibniz draws a division between ‘names’ (nomina) on one hand and the other parts of speech (later called ‘‘particulae’) on the other, which echoes the medieval one between categorematic and syncategorematic terms. The first stand for “concepts”, the others express “ways of conceiving”. Categorematic ‘terms’ (expressing ‘concepts’) are semantically saturated. Here we meet a first type of ‘completeness’ which can be attributed to a category of linguistic items and to their related meaning. Later, it will be labeled by Leibniz as ‘integrity’ and handled extensively in the first part of the GI.49 This feature is bound to the topic of direct-oblique predication: ‘integral terms’ in the nominative case can be reciprocally connected by the copula ‘est’, without any further device, hence by ‘direct predication’ (in recto). They are therefore the semantic units that can figure as the subject or predicate term in a proposition. One can easily see how far the “integrity” of Leibniz’s “terms” is from Frege’s view on saturated expressions. The Leibnizian “integrity” matches well with a logic of terms, where the same terms can play the logical role both of subject and predicate. An asymmetry in the role of terms, however, immediately comes to light also in our text, as soon as it passes to the further attempt at classifying ‘nouns’ [nomina], the linguistic items expressing ‘concepts’, according to the different a they signify: ways Concepts are considered either per se (as they are as such) or per accidens. Per se, that is to say according to formalities themselves, like humanity, beauty, three-footedness, and not considering metaphysical matter, or the subject—hence t leaving aside also time, place and inflection. Per accidens, on the contrary, if we consider the going together of many formalities within one and the same subject; in this manner, poetical ability and 48 49

Characteristica verbalis (N. 80), A VI.4, 333–337. AVI.4, 740–743 (C 356–359). A

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jurisprudence happen to be in the same subject. Hence abstract nouns are coined, such as “humanity” and “heat”; and concrete ones, such as “Man” and “hot.”50

A former version reads: Concepts are either abstract or concrete. Concrete concepts involve the subject-with-formality. Abstract ones, on the contrary, consider formalities themselves, or essences as such, independently of their case, that is to say without considering subject, place, time, matter, individual. This is why formalities cannot be reciprocally predicated, unless in necessary propositions, which make abstraction from metaphysical matter (i.e. from subject).51

One can immediately recognize here the echo of the De Cogitationum Analysi, where ‘forms’ as such (here, transformed into ‘formalities’) were excluded w from the possibility of giving an account of location, numerical distinction and so on. The approach of characteristica verbalis appears as the linguistic counterpart of Leibniz’s inquiry into the field of combinatorial metaphysics. More precisely, the semantic analysis sketched here works as the inverse of the ontological synthesis delineated in the texts on the ‘origins of things from forms’. The language of ‘formalities’ ( formalitates f )—here connected by Leibniz with Lullus’s heritage—seems to have an unmistakable Scotistic flavor. One should be very cautious, however, in inferring from these lexical clues any commitment to a realistic attitude. The ontological subject-forms polarity is translated into a semantic distinction in the way of signifying of terms. In this way, a the ontological import of ‘forms’ is clearly diminished to the rank of ‘concepts’, while ‘formality’ is used to indicate a concept as such, and not a strange quasi-thing: Some terms signify things, others the objects of our concepts, i.e. . . . the objective concepts.52 E.g., ‘wise A’, ‘rich B’ are terms that signify a 50 51

52

Characteristica verbalis, A VI.4, 333–334. A VI.4, 334. For the usage of the terminology of ‘formalities’, see NE IV ch.17, VI.6, 489 (GP V 469) and the notes to Temmik, VE 1084. The topic of the objective concept (i.e. what is grasped by our act of knowledge) had been developed within the Scholastic theory of knoweldge, especially by Suarez. Another important source of these reflections should be looked for in the “logic of concepts” (logica de notionibus) that Leibniz finds in Jungius’s legacy. See his extraits and notes from Jung’s Logica de notionibus, A VI.4, 1211–1299. In this context also ‘abstract notions’ are handled.

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concept, and it does not follow that, if they are given, two different things are given . . . 53

In the combinatorial metaphysics of the Mira res, subject and properties appeared as two different types of ontological items; from the point of view of the traditional logic of terms, but also of the new calculi, subject and predicate are both concepts, whose role is interchangeable. This aspect is reflected in their integrity, or semantic completeness. Leibniz’s linguistic-categorial inquiry attributes them, instead, to two different levels: the ontological and the conceptual, respectively. This is only half the truth, however. Also the dimension of ‘thing’ finds expression within our linguistic and conceptual framework. While the original subject-forms distinction apparently left the possibility open of thinking of the subject as separated from forms, we now have a “subject-with-formality”. And in the new res-termini r opposition, the ‘thing’ does not figure as an X deprived of any descriptive content: on the contrary, its content is richer than every single concept referring to it; concepts being seen as partial perspectives on the concrete thing. The problem will be that of indentifying the type of concepts that are fit to capture (i.e. to adequately express) that dimension. Multum interest inter terminos et res Before going further, I want to briefly verify my interpretation of the Characteristica verbalis by comparing it with some texts of categorial inquiry, where Leibniz is willing to systematically emphasize the difference in the way w of identifying (or counting) concepts (or properties) on one hand, and things (or substances, in a rather loose sense) on the other. In particular, a late group of texts, probably dated to the first decade of the eighteenth century, hence in the period of the exchanges with de Volder and des Bosses, takes as a leitmotiv the dictum: “There is a great difference between concepts on one hand and things on the other” (‘multum interest inter terminos et res’). Also these texts present themselves as an essay in categorial inquiry which is carried out following the line of semantic analysis. From this perspective, the well-known ambiguity of the Leibnizian ‘term’—which oscillates between ‘word’ and ‘concept’—ceases to be simply the clue to an incurable terminological inaccuracy, to become a sign of his attempt at reforming conceptual analysis by following the thread of language. Leibniz’s terms are, right from 53

Inquirenda Logico-Metaphysica, A VI.4, 999. For the passage from ‘forms’ to ‘terms’, compare the De Cogitationum Analysi, A VI.4, 2767–2774, with the Characteristica Verbalis, A VI.4, 333–334.

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the start, intepreted signs, something like ‘semantic units’ of language. More properly, they are categorematic expressions, with the capacity of playing the roles of subject and predicate in a proposition, exactly as the ‘integral terms’ of the GI: “The term is a conceivable item that can figure as the subject of a true proposition.”54 This is perfectly in tune with the well-known Leibnizian theory of truth as conceptual containment. The logical or conceptual subject, however, does not always and immediately coincide with the ontological one, the ‘thing’—or better, not all terms are able to adequately express the latter. Leibniz is fully aware of this distinction, which was presupposed by the formulation of DM 8. I report here some of his insistent remarks; sometimes, they present a thing-term opposition, sometimes a similar being-term one: (1) An ens per accidens is a Term such that, while it perishes, the Being does remain, like “hot Man”: the same being does remain, no matter whether he is hot or not. So is the case with poet or musician. Poet is not w a Being in a proper sense; the Being that is a poet does remain, while being no longer a poet. Or, the poet does remain, but not insofar as he is a poet. One has to distinguish, in effect, between Beings and terms.55 (2) There is a great difference between terms on one hand, and things on the other; the terms “man” and “poet” are attributed to the same thing. Now, a poet is not different from a man, but being-a-poet is different from being-a-man.56 (3) Things are distinguished (counted) in one way, terms in quite another.57 (4) Because of the concrete terms corresponding to the names of accidents, it happens that terms are more than things. The abstract of a term, in fact, counts as a thing, but the term itself is not a thing.58 (5) Beings, e.g. Man, Heat, Wise, great, do not coincide with Terms, e.g. t`o Man, t`o Hot. Different terms, in fact, often signify the same Being . . . In 54 55

56

57

58

LH IV 7C Bl. 76 vs. “Ens per accidens terminus quo non manente licet, Ens tamen manet, ut Homo calidus; idem enim Ens manet sive sit calidum sive non calidum. Tale Ens est poeta, Musicus; itaque proprie poeta non est Ens, nam Ens quod est poeta manet, etsi non amplius sit poeta. Revera ergo distinguendum inter Entia et terminos.” (LH IV 7C Bl. 75 recto). “Multum interest inter terminos et res, homo et poeta sunt ejusdem rei, poeta non aliud est ab homine, sed aliud est esse hominem aliud esse poetam.” (LH IV 7C Bl. 76 recto). ““Alia est rerum alia est terminorum divisio” (LH IV 7C Bl. 76 vs.). This text has been recently edited by Mugnai. See An Unpublished Latin Text on Terms and Relations, Leibniz Society Review, 7, 1997, 125–127. “Per concreta Accidentium fit ut plures sint termini quam res, ibi nempe abstractum termini est res cum terminus ipse non sit res.” (LH IV 7C Bl. 77 recto).

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ffact, different terms have their respective foundations or reasons within the same thing.59

The basic intuition is that we can conceive the same thing under different aspects, according to a semantic one-to-many structure. Sometimes, we have simply the co-presence of different properties (‘man’ and ‘poet’ in text 2); sometimes, the distinction between a thing and a merely attributive term is led back to change, hence to the idea that the latter can arise and disappear, while the former remains the same (see the definition of ens per accidens in text 1). It is important to remark that in any case terms are taken in concreto. Hence, the distinction is internal to concrete talk, and precedes the operation of reification expressed by abstract nouns: “the abstract counterpart of a term counts as a thing, but the term is not a thing” (text 4). The one-to-one correspondence concepts-things is restored at the level of complete concepts.60 Abstract Terms The termini-res polarity is seen by Leibniz as the root of the linguistic distinction between abstract and concrete talk. The formation of an abstract term is nothing but the nominalization of one of these attributive devices, hence it expresses the attitude of taking it as if it were a thing. On this basis, he tries to formally define the abstract-concrete pair. An abstract expression is wholly synonymous with the corresponding concrete one, except for the fact w that it represents a different principle of counting: So far I am not able to explain the abstract and the concrete other than in the following manner. Suppose A and B are one and the same thing; then consider two items L and M, which do differ from A and B respectively only for the fact that L and M are (contrary to A and B) two different things. Then I call L and M abstract items and A and B concrete ones. E.g., let something be hot and dry; now, heat and dryness do not differ from “the hot” and “the dry”, respectively, if not because what is hot and what is dry are one and the same thing (which is said to be a subject), w 59

60

“ “Alia sunt Entia, v.g. Homo, Calor, doctus, magnus; aliud Termini, nempe t`o Homo, t`o calidus. Nam diversi termini saepe significant idem Ens . . . nam diversi termini habent sua fundamenta vel rationes in eadem re.” (LH IV 7C Bl. 89 recto). The draft Inquirenda Logico-Metaphysica, quoted above, continues: “It can happen that YA is ∞ YB [YA is identical with YB], e.g. that some wise is identical with some rich. If A, however, signifies Alexander the Great, B Caesar the dictator, then this cannot happen. When A and B are things, in fact, given that not (A∞B), it follows that not even (YA ∞ XB) is true. And the reason for this is that A and B are complete terms, that already contain all that one could add to them, so that YA∞A.” A VI.4, 999.

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w whereas heat and dryness are two different things which are said to be inherent in the subject. This is why, “hot” is called concrete, and “heat” abstract; “dry” concrete, “dryness” abstract.61

As a matter of fact, this analysis takes up again the reductionist attitude of Nizolius’s Preface, hence Hobbes’s heritage. In the same period, indeed, Leibniz is pursuing anew the aim of excluding, as far as possible, abstract terms from the ‘lingua philosophica’. The selfsame Characteristica verbalis offers one of the first statements of this program,62 w which is confirmed also at the opening of the GI and in several other places. Bear in mind that the project of ‘philosophical language’, in general, presents a double aim: on one hand, to give to natural language a canonical, logically transparent form which is well-suited to be translated into the artificial language of calculi; on the other, to shed light on the ontological commitments of ordinary language. Accordingly, the study of the abstractconcrete dichotomy presents a double interest: on one hand, the strategies for paraphrasing abstract terms serve to simplify the interpretation of calculi and to free it from the problems of abstract reference; in particular, the preference for concrete talk is bound to the attempt at reducing, as far as possible, the reciprocal relationship of terms to the canonical form of a predication in r recto of the ‘A is B’ type. On the other hand, the ‘parsing away’ of abstract talk is part of an analysis which aims at—or, at least, indirectly contributes to—identifying what our language is ultimately about, the ‘furniture of the world’ or the ‘basic particulars’. In practice, the task will be to identify the terms that are able to capture the dimension of ‘thing’.

2.2. The Grammar of Substance: From Abstract Terms to Complete Being Towards d the Complete: The Linguistic Way In the 1641 Arnauld–Descartes discussion, remember, ‘completeness’— intended as a necessary and sufficient condition for substancehood—had been separated from ‘adequacy’ or predicative completeness (C1) and equated to 61 62

De Notionibus omnia quae cogitamus continentibus, A VI.4, 400. “We can do without abstract terms in the lingua philosophica . . . ”, A VI.4, p. 337. The themes of the Preface to Nizolius are taken up again here. On Leibniz’s treatment of abstract terms in his philosophy of language, see M. Mugnai, Astrazione e realta. t Saggio su Leibniz, t` Milano, Feltrinelli 1976; J.B. Rauzy, Leibniz et les termes abstraits: Un nominalisme par provision, Philosophie, vol. 39, 1993, 108–128; S. Di Bella, L’astratto e il concreto. Hobbes, Leibniz e la riforma dell’ontologia, in Rivista di storia della filosofia, 1998/2, 235–266.

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the property of ‘being the notion of a non abstract thing’ (C2). As a matter of fact, the ‘thinghood’ requisite provided by Descartes’ C2 amounted to autonomous conceivability. For Leibniz, however, the Cartesian interpretation does not meet the decisive concreteness requirement. In his 1686 discussion with the by now Cartesian Arnauld, he will claim that, in order to satisfy it, a concept needs to possess the predicative completeness C1. Thus, he joins together again the two senses of completeness separated by Descartes. We well know that he ultimately refers to the definition of truth in order to challenge the Cartesian intuition about completeness and support his own. Right from the start, however, I have observed that the truth criterion alone is at pains to ground ontological completeness, just because it applies to abstract subjects as well, where at most full notions can be obtained. The linguistic-ontological analysis of the categorial texts is likely to provide a justification for that idea of concrete subject to which the truth criterion is applied. As a matter of fact, the analysis of the characteristica verbalis on these topics is usually recorded in the section of categorial tables devoted to substance, where it delineates an apparently linear path going from concrete to complete terms. This attempt to identify a framework for basic particulars in the medium of language coincides with the search for substance terms and for the rules of their introduction and usage. This might recall to a present-day reader a Strawsonian-style ‘essay in descriptive metaphysics’. This seemingly‘descriptive’ approach, however, will conclude with a sharply ‘revisionary’ solution about substance terms: as we know from the debate with Arnauld, true substance terms express infinitely rich, exhaustive descriptions of the corresponding individuals. The Substantive-Adjective Distinction According to the preliminary decision to use only concrete terms in rational language, several texts of categorial analysis do not further dwell on the concrete-abstract distinction, but pursue their analysis on the supposition of taking into account only concrete terms. Their next step is to assume that “in concrete talk, every substantival term signifies a substance.”63 Now, in ordinary language the names for individual substances—which are ultimately acknowledged by Leibniz as being the true substance-terms—are only a subset of (concrete) substantives. First of all, we find concrete general g terms, like ‘man’. For them, Leibniz is prepared to give an explanation in a purely nominalist style, not so far from the old Nizolian analysis of general terms. They simply

63

Divisiones (N. 136), A VI.4, 574.

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stand, indeed, for every singular substance of a certain kind.64 Interestingly enough, other drafts label the reference of general terms as a ‘vague’ one.65 What about the further distinction into substantives and adjectives? The Notationes Generales raises the question: It remains to be explained, why “Man” is held to be a substance term, whereas “hot” is taken as an accidental one; nevertheless, nothing prevents w us from taking “hot” as standing for any singular substance which is hot.66

Remember how in the Hobbesian analysis, names like ‘man’ were actually handled on a par with accidental ones like ‘hot’. Leibniz’s answer should be ffamiliar to us from the time of his notes on Nizolius’s book: I admit that these inquiries are reflexive [we would say, “metalinguistic”] and not very relevant for philosophical purposes. Anyway, if one accepts that these second order concepts (notiones secundas) are worth rigorously establishing, then I shall say that “hot” is, indeed, an adjective term, that is to say it needs to be supplemented by something else, in order to make complete sense: I mean, “hot subject”, or “hot substance”. “Man”, on the contrary, is a substantive term and when we say “man”, by this very fact the subject is already involved, nor can it be added to without a repetition of the same; so, we would say uselessly “subject man,” whereas we will say quite correctly “human subject” or “endowed with humanity”.67

Terms in concrete talk—be they, from a grammatical point of view, in the substantive or adjective form—always imply a primitive composition of an underlying being/thing (ens) and a properly descriptive term, according to a remark that is common in the drafts on philosophical grammar.68 It is the same 64

65

66 67 68

“What I have said is meant first and foremost of singular substances; because universal substances signify nothing but any singular substance whatever, so they create no problem.”Definitiones. Aliquid. Nihil (N. 76), A VI.4, 307. Thus, the Definitiones notionum metaphysicarum atque logicarum: “If A is B, and B is a complete term, then A will be a singular substance, i.e. a determinate subject [subjectum certum] . . . Not every substantive term designates a singular substance, i.e. a certain and definite one, although it always signifies [involvat] some vague substance, i.e.some undeterminate subject [subjectum incertum]”, A VI.4, 626. Notationes Generales, A VI.4, 554. Ibidem. In the De termino praedicato relatione (N. 201), what is implied is labeled not as ‘being’, but as ‘substance’: “It seems that there is this difference between a substantival and an adjectival predicate: who says ‘Peter is a man,’ says: ‘Peter is a rational substance,’ while who says ‘Peter is rational’ does not mention substance, though it is implied.” A VI.4, 943. Notice that also the substantive term is labeled here as ‘predicate’.

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‘ens’ w which worked as a subject in the Raue style theory of predication. We are not faced, however, with a non-conceptualized ‘bare substratum’ (say, a Subject 1), but with a ‘subject-with-predicate’,69 the “subject-with-formality” of the Characteristica vebalis (say, a Subject 2). Anyway, the very fact that substantival terms include (involvunt) the reference to the ‘ens’, whereas adjectival ones imply it as something to be added (subintelligunt),70 is interpreted in the sense of a fundamental semantic equivalence. Leibniz, therefore, is well entitled to confirm that the substantive-adjective difference is ultimately superfluous in rational grammar and has no philosophical relevance.71 In the type of text we are dealing with, however, the substantive-adjective distinction does acquire philosophical relevance. Concrete substantival terms appear as an intermediate step on the way towards the complete, being the point where language attains substances; or at least, where it comes in touch with w “things”. Sometimes Leibniz goes as far as to talk about ‘complete terms’ in this sense, without any further addition; in any case without implying any commitment to predicative completeness: “Concrete or complete [terms] are those which do not need any subject to which they are attributed”;72 “A substantival w term is that which contains a complete term, that is to say involves the subject, such as ‘king’, that means ‘a reigning subject”;73 and finally, in the GI: “We take here every term as complete, or substantive.”74 Leibniz relies on this type of completeness when he takes ‘thing’ in a rather loose and non-committal sense and is not interested in circumscribing basic particulars in a strict metaphysical sense. In practice, when he is about to construe a transparent language, without committing himself to identify true substances. So, opening the GI, he observes that “all terms are understood to refer to concrete things alone—whether these are substances, like the Ego, or phenomena, like the rainbow.”75 In some later categorial texts, he will indicate “substantial things” 69

70

71

72

73

74 75

The locution ‘Subjectum-cum-praedicato’ occurs in the important text Divisio terminorum: “The concrete is either substantive or adjective . . . The substantive only involves the subject with the predicate . . . ” A VI.4, 559. As it was already the case in the Nizolius notes, and contrary to ancient Ockhamist tradition, Leibniz does consider the thing, and not the quality, as the item which is “connoted”. See Characteristica verbalis, A VI.4, 334–335; De lingua philosophica: “The difference between adjective and substantive terms in rational language is not so relevant.” A VI.4, 885. De totae cogitabilium varietatis uno obtutu complexione (N. 143), A VI.4, 595. And below: “Notions can be conceived of by us as being complete, like things . . . ” A VI.4, 596. Definitiones Not. Metaph. atque Logic. (N. 147), 625. A few lines above, however, the complete term has been defined as that from which all predicates of the thing are derived. Clearly, we have here two senses of completeness which are quite different. A VI.4, 740 (C 356, LP 47). Ibidem.

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(substantiata) as the reference of concrete substantival terms in ordinary language: practically, the “things” of our phenomenal and ordinary experience. Sometimes other intuitions come to reinforce these grammatical distinctions. Thus, a term like ‘man’ is taken as expressing what a thing cannot cease to be, whereas others express properties that can be acquired and lost.76 The criterion of change, notice, does not cover all substantival terms, because they often designate roles (‘king’) or non-persisting or phasal sortals (‘boy’) which are not inseparable from the subject. Anyway, all this shows that when Leibniz advances closer to ordinary language, the traditional framework for substances tends to come to the fore. Accordingly, a later remark in a draft for a letter to des Bosses develops the semantic analysis of substantive terms (Ens ( + quality) together with the privilege accorded to substance terms. The return to the traditional usage of ‘connotative’ is worth noting, where the quality and not the being/thing is ‘connotated’ by a term: Terms are simply real or connoting. Real terms are those for things, when nothing else is expressed besides the thing itself; connoting terms are terms for things plus some addition, e.g. “Man” is a mere real term, “rational Man” is a connoting essential term, and it contains something superfluous, because one part of the term follows from the other. “Wise man” is a connoting accidental term; the same, in fact, is now wise, now non-wise, while the same thing remains by changing its accidents . . . 77

Mass Terms and Natural Kinds Also texts which stress how the substantive-adjective distinction is superfluous from a logico-semantic point of view feel the need to explain how this 76

77

See GI, A VI 740: “An entity [Ens] is either in itself [ per se] or accidental [ per accidens]; or, a term is either necessary or mutable. Thus, ‘man’ is an entity in itself, but ‘learned man’ or ‘king’ are accidental entities. For that thing which is called ‘a man’ cannot cease to be a man except by annihilation; but someone can begin or cease to be a king, or learned, though he himself remains the same.” A VI.4, 740 (C 356–357; LP 47). See also Divisiones (N. 136), A VI.4 575; De terminis singularibus vel universalibus (N. 182.3): “The term which involves all essential predicates is the lowest species (species infima) . . . Of concrete terms, the ones are essential, the others accidental.” A VI.4 866. When Leibniz uses this criterion for essence, contingent predicates are intended to be accidental, though being associated with the complete or individual term. The species infima is here a general notion. In a late ‘table of predicates’ Leibniz annotates: “A substantive name is that which contains all necessary predicates of its subject.” De divisione praedicati, A VI.4, 928. GP II 471. If we apply the same logic to complete concept, every predicate becomes a ‘connoting essential’ one, insofar as it is superfluous (e.g., ‘Alexander king’, or ‘winner’).

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distinction arose. The Characteristica verbalis provides us with an interesting suggestion, pointing decidedly to the privilege of sortal terms: We can do without the difference between substantive and adjective terms. Between “body” and “extended” [extensum], in fact, there is no difference, except that “body” seems to signify: “extended subject”; this, however, is already implied by “extended”. Analogously, “man” is nothing but People, however, are used to “human subject” or “subject of humanity”. P coining such substantive names involving reference to the subject for those things they are usually dealing with. The aggregate of extended things, in fact, is one whose parts have not only common characteristics, but also a connection. The set of hot things, on the contrary, is highly scattered. Similarly, all the gold in the world is considered as a whole (hence we do not use the plural form “golds”, but we say “a quantity of gold”, “de l’or”, “gold g d”); and all men are meant to be a unique class, especially if we consider their parental relationships. Hence comes the question, whether things specifically differ. Men, in fact, think as if some seeds were present even in inanimate things, like metals; chemists especially are inclined to this idea: they attribute even to all qualities some sort of radical subjects. So they believe that substantial forms are concealed in seeds, colors in some pigments, odors in some sulphides, savors in some salts; so that forms [i.e. qualities] together with their bearers could be extracted from some subjects and applied to others.78

Mass terms like ‘gold’, and count nouns like ‘man’ are handled on a par here. More interestingly, the explanation Leibniz suggests for the privilege accorded to sortal terms is modeled precisely on the behavior of mass terms: it appears, in fact, as a kind of mereological interpretation of universal reference, which is held to work for substance terms. Things that are referred to through these terms could be considered as the parts of a unique physical whole. A slightly different (but partially overlapping) explanation emphasizes w the fact that golden as well as human particulars are reciprocally tied by relationships which are of a different type than those of resemblance: relations of ‘connection’, rather than of ‘comparison’. Presumably, Leibniz has in mind ffactual or causal relationships in a spatio-temporal order. Obviously this works well especially with organic beings, reproductive capacity being the strongest mark for a biological species concept. On the other hand, this train of thought is balanced by the constant Leibnizian stances on this matter: from a logical point of view, the reluctance of the characteristica to privilege some terms with respect to others; from 78

Characteristica verbalis , italics mine, A VI.4, 334–335. Leibniz quotes the German form ‘Gold’. In English, we would say ‘some gold’.

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an ontological one, the nominalistically-minded weakening of “second substances”. Thus the selfsame Characteristica Verbalis, after having illustrated the empirical presupposition of the usage of substance terms—i.e., that there are natural kinds underlying observable regularities in natural phenomena— concludes a bit skeptically: Because all this is less certain, however, and it is not clear enough, what people mean exactly when they look for specific difference—for all this, we will put aside also these qualifications in our characteristics, until they are established in a more distinct way.79

Our classifying concepts admit different degrees of vagueness, and the ordinary concepts of natural kinds, though based on ‘natural’ collecting criteria such as mutual reproduction, are also vague. Leibniz’s final stance seems to be an intermediate one between the acknowledgment of natural value to some substantial terms and the relativity of their actual specification. We privilege some features for our practical needs, anyway, some natural features.80 Moreover, in Leibniz’s lingua philosophica it is always possible to substantivate every adjective and to obtain terms which are wholly on a par with our alleged ‘substance terms’: I do not see what could prevent us from saying “calorio” in the sense of “warm thing”, analogously as we usually say “man” in the sense of “thing endowed with humanity”, or “capito” in the sense of “thing having a great head”, if the usage and analogic application of the formation rules of language (analogia linguae) were leading us to this. And “calorio”, “mugil”, “capito”, “naso” are substances as much as “man” is a substance, although there is no genus or species capable of reproduction of “thingswith-a-great-nose”, in the way there is a species of men. But here we take the species not in a physical, but in a more general way.81 79 80

81

Characteristica verbalis, A VI.4, 335. It would be interesting to compare these private Leibnizian reflections with his later criticism to the Lockean doctrine of substance terms. As is well-known, in the NE Leibniz will be eager to contrast the pragmatic conventionalist drift of that doctrine, and to defend the ontological import of those terms. Now, also the earlier writing recognizes a non-arbitrary basis which could justify the later emphasis on naturalness. Conversely, in the NE he will maintain some relativity to our needs and interests of our naturally based classifications, and different degrees in the logico-ontological import of them. See NE III.6; N. Jolley, Leibniz and Locke. A Study of the New Essays Concerning Human Understanding. Oxford, Clarendon Press 1984, ch. V, 74–101. Notationes Generales, A VI.4, 554. The items like ‘calorio’ occupy the last place in the table of the De abstracto etc.

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The last remark could be seen simply as the clue to a persisting divorce between logico-semantic considerations on one hand and ontological ones on the other. Analogously, Nizolius contrasted the logical approach to species with the physical one. In Leibniz, however, physical species are far from being ontologically privileged, given that sortal terms for natural kinds are considered as somehow ‘vague’, and to some extent arbitrary. As a result, the only clear-cut ontological hierarchy within concrete terms will be that between individual substances (and individual terms) on one hand and general kinds (be they terms for natural kinds, or simple general terms for qualified things) on the other. From r Concrete to Complete Terms Starting from the familiar dichotomies of abstract-concrete and adjectivesubstantive, several drafts prolong their analysis towards the complete: where “complete”, finally, is intended in the sense of predicative completeness: The term that expresses a singular substance involves all predicates of its subject, i.e. is a complete term. If we were to use in our reasoning only concrete terms, leaving aside all abstract ones (which is possible), then every substantive term—that is every term which does not need anything else, or in which the subject is not elliptically implied [non subintelligitur] would express a substance; so “man”, i.e. “a thing endowed with humanity”, or “the headed”, i.e. “a thing endowed with a head”. But every term that involves all predicates of its subject, i.e. all the properties that are predicated together with it [omnia sua compraedicata]—that is to say, every complete term, will express a singular substance.82

The further requirement singles out the subset of individual terms which are, finally, the true substance terms. It is interesting to observe how the De Notionibus construes a kind of ‘ontological square’ based on the concreteabstract and complete-incomplete dichotomies:83

82 83

Concrete complete Substance (A particular man, e.g. Caesar)

Abstract complete Essence of the Substance (Lentuleity)

Concrete incomplete Mathematical Being (Space, Time)

Abstract incomplete Accident (Heat)

De abstracto concreto substantia etc. (N. 134/2), A VI.4, 572. A VI.4, 400.

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Two places in the square are rather unusual in linguistic-ontological analyses: I mean, the Abstract complete, which embraces names for individual essences, and the Concrete incomplete, which is the label for names of mathematical beings. Abstract complete terms could be identified as the output of applying abstraction-operators to proper names. They could scarcely be found in ordinary language, nor in philosophical jargon. They are relevant for Leibniz, however, given that in this period he is strongly interested in individual essences. Notice that when he talks about complete concepts, he always talks in concrete terms: “Alexander “ is strong, and king and so on . . . ”. Anyway, ‘Alexandreity’, or ‘Lentuleity’ are names for the corresponding haecceities. Under the heading of ‘Concrete incomplete’, Leibniz places some mathematical constructions which are the objects of undue reification in the philosophies influenced by the new mathematical science of nature. It is clear, however, that the criticism of the ontological status of space or time is not so much the outcome of linguistic analysis (from a strictly linguistic viewpoint ‘space’ and ‘time’ behave precisely as concrete substantive terms, i.e. as terms fit to designate things), as of a properly conceptual one.84 We might rather expect that the concrete incomplete counterpart of the abstract incomplete ‘heat’ were something like ‘hot’. But this type of term is absent from the square, which is entirely construed from substantive terms. Also concrete substantive w terms like ‘man’ are difficult to be inserted, given that only concrete complete terms, corresponding to proper names, are considered. The intermediate step of concrete general substance terms is simply left out here. Coda: Proper Names and Descriptions Ordinary language supports the identification of substance terms with terms designating basic particulars or individuals. But the attribution to these terms of C1 completeness can hardly be justified on the basis of a semantic analysis of ordinary language. When speaking about complete concepts, Leibniz is not giving a plausible theory of meaning for our proper names. Two questions are at stake here: the status of a complete concept, and Leibniz’s semantic considerations on proper names. 84

Already the Divisio terminorum considered the case of the reification of mathematical entities: “Similarly [to the case of bodies as phenomena] Mathematical beings [Res Mathematicae] such as space, time, sphere, hour, are only phenomena that we conceive as if they were substances. Therefore, there is no real substance, which is not individual.” A VI.4, 559–560. For a deconstruction of ‘mathematical bodies’ as abstract beings, see Leibniz to de Volder, letter XXXI (June 1704), GP II 268–69. Interestingly enough, Leibniz confutes here the Cartesian inference—going back to Meditation V V—from the attribution of many properties to mathematical beings to the reality of the latter.

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As concerns the first, we should bear in mind that Leibniz’s semantic analysis moves at the objective level of ‘ideas’, the constituents of propositions or truths according to the Dialogue theory, and something corresponding to Fregean Sinne. They are some innate intelligible patterns in our mind, basically grounded in God’s ideas. In some context Leibniz, while reserving the label of ‘ideas’ to these intelligible contents, employs ‘concepts’ to label our psychological acts of grasping them, or their corresponding images. But when usually speaking about ‘concepts’ in semantic analysis, objective notions are meant: be they ideas as such or the different objective aspects they exhibit. Also abstract ideas (e.g. ‘a circle’, or ‘a triangle’), in fact, present different aspects and a rich content we do not exhaustively understand when grasping one of their aspects, or ‘Sinne’. This is all the truer for complete concepts, of course. Complete concepts are ideas in God’s mind and they are properly known by God only. This does not exclude, however, that human mind comes somehow in touch with them. Our incomplete concepts of an individual are the objective intelligible devices by which we refer to that individual; and they are the ways of exhibiting the complete concept, in principle deducible from it. In this way, our names for individuals—while directly expressing our incomplete concepts and singling out their reference—indirectly express the corresponding complete concept. Matters are more complex when we take into account the indexical aspects which emerge if we go on to consider Leibniz’s concrete analyses of our linguistic means to refer to individuals. The devices that are used in our language to single out individuals are proper names, indexical expressions (typically, demonstratives) and definite descriptions. Leibniz is well aware of this. In the GI we find the notion of ‘individual’ among the primitive ones. As a matter of fact, all things are individual (the old Particularist Claim, that is well present behind the antirealistic semantics of the GI), while terms have either multiple or singular reference. This sense of individuality is basically captured by demonstrative devices or uniquely identifying descriptions: . . . a certain individual is this one, whom I designate either by pointing it or by adding some distinguishing marks. For although we cannot have marks which distinguish it perfectly from every other possible individual, nevertheless we have marks which distinguish it from other individuals we meet.85

Indexicals do not identify their reference through descriptive traits, but through ostension (“by showing it”), hence taking into account the context of their 85

A VI.4, 744 (C 360, LP 51, modified).

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utterance. They seem not to be dispensable from ordinary (or better, from human) language, exactly like the term ‘I’. Besides ostension, we refer to individuals by way of description (“adding some distinguishing traits”). According to Leibniz, we are able, in principle, to provide definite descriptions which succeed in identifying individuals in the actual world, but not in disw tinguishing them from their possible counterparts. The latter work is made precisely by complete concepts. One might think that indexical strategies do reflect our approach to individuals, while the absolute semantics of complete concept is framed in purely descriptive terms. Also in our language, only definite descriptions would provide the objective sense of a proper name, while indexical reference would simply express our subjective ways of grasping it. The result would be a division of labor, envisaging elements of direct reference for the semantics of ordinary language, and a purely descriptive reference for the logical meaning of proper names. This model could be rather misleading, however. To see why, let me consider some Leibnizian remarks on the proper names of grammarians. Leibniz seems to be inclined to keep apart the proper names in the logical sense considered above—indexicals and definite descriptions—from “proper names” as a grammatical category. In the Characteristica verbalis, he affirms that the true difference between ‘appellative’ and ‘proper names’ does not lie so much in their respective generality (this being an accidental feature), as in the connotative vs. denotative character of the first vs. the second ones: We could neglect also the difference between proper names and appellative ones. Not only, in fact, were the names of individuals originally appellative (descriptive) insofar as they were derived from some distinguishing feature; moreover, it is unimportant, whether we say that what we talk about is alone in nature or there is something else similar to it. Rather we should trace another distinction among names, which is similar to the first. I mean, we should distinguish the case when we name things through some features taken from their qualities, and the case when we name them through some sign given arbitrarily to them. In this sense, “quadrilateral” is an appellative name for the thing to which it is applied, and “rhombus” a proper one.86

‘Appellative’ and ‘proper’ do not coincide, respectively, with ‘general’ and ‘individual’: a general name can be a purely denotative expression, whereas on the contrary names for individuals can have a descriptive (connotative) 86

Characteristica verbalis, A VI.4, 335.

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content. The denotative sense of ‘proper’ is quite different from the sense of ‘proper’ of both grammarians and logicians: A noun which is proper of a thing is not what logicians label as “proper” (i.e., a predicate that is attributed to all the individuals of a class, and to them alone); it is, instead, what one is not in need of looking for a reason, why h it is attributed to the thing; etymology, indeed, does pertain to the history of language, rather than to its semantics [philosophiam [ ]. So, “Peter”, “John”, but also “Man”, “Horse” are proper nouns for things; those, instead, that are to be demonstrated of the thing are called “appellative” and by them attributes are designated.87

The sharp distinction between genetic and semantic considerations alludes to the fact that, if one considers their etymology, most denotative names do reveal a connotative origin. On the other hand, this type of historical consideration has a semantic impact, insofar as it reveals a non-accidental feature of our approach to things. In the NE, Leibniz observes that proper names in the sense of grammarians and logicians—i.e., names for individuals—derive as a matter of fact from general connotative names.88 This circumstance does not only reflect the genetical order of our knowledge—that, contrary to the ontological primacy of particulars, goes from general to particular—but also a structural constraint on our epistemic access to substances. We do not directly grasp individuals as such, but their general properties. The Divisio Terminorum— while it documents the irreducible indexical nature of the knowledge of at least w one substance, the Ego—does confirm that we grasp other substances through their attributes.89 In this sense, the descriptivist approach to substance, with its bundle theoretical resonances, is also bound up with the structural limitations of our knowledge. When Locke in the NE puts forward a view of the idea of substance as a bundle of ‘ideas’, and attacks the idea of a ‘bare substratum’, Leibniz replies by stressing (besides the need to distinguish ideas from qualities) the abstract character of Locke’s qualities: On the contrary, what comes into our mind is the concretum conceived as wise, warm, shining, rather than abstractions or qualities such as wisdom, warmth, light etc., which are much harder to grasp . . . It can even be 87 88 89

Definitiones Notionum Metaph et Logic., A VI.4, 625. See NE III, Ch.3, A VI.6, 288 (GP V 267). “Because the supposita are known through their attributes, it is worth listing the types of attributes.” A VI.4, 560.

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doubted whether these accidents are genuine entities at all, and indeed many of them are only relations.90

In this way, Lebniz’s criticism to the reification of abstractions meets the rejection of a bundle theoretical view of substance. In an unpublished manuscript belonging to the group centered around the thing/terms polarity, he writes: Because Beings are known by their predicates, Abstract items are known prior to concrete ones. In a concrete thing we can conceive now the mere subject, which presents itself in the same way in many things, now abstract beings, by which one concrete thing is distinguished from another. Although in God there is no room for this composition from a subject and some abstract items, and He has no subject which is common to other concrete things. Subject, however, cannot be conceived, but only perceived. And this is what is said, in the case of bodies, prime matter . . . 91

This remark is intriguing from different aspects. Abstract beings, which are posterior to concrete ones from an ontological point of view, are prior to them from the cognitive point of view. It is also worth noting that the subject appears here as a bare substratum, so that qualities work as distinguishing factors; and this subject is properly perceived. Finally the link between the ontological framework for subjecthood and the hylemorphic framework for matter clearly emerges. We should bear in mind, however, that these considerations are put forward from the point of view of our cognitive approach. The true dimension of subjecthood is hardly captured by this idea of bare substratum. At the same time, the polarity between descriptivist and haecceitistic elements seems constitutive of the knowledge of individual not only from the human viewpoint, but also in the absolute semantics of complete concepts. This amounts to saying, that also from God’s viewpoint the descriptive knowledge should capture a dimension of ‘thisness’. In order to see this, let me further pursue Leibniz’s theory of complete concepts, which no longer follows the semantics of ordinary language. 90 91

NE II. 23, A VI.6, 217 (GP V 202; transl. Remnant-Bennett). LH IV 7C Bl. 89 r. The remark on God has to be compared with the reflection of On Forms. It further weakens the seemingly realistic approach of the Paris text.

Section 5 Complete Concept and Substance The New Alliance of Concept and Thing

Chapter 1. Complete Concepts Ultimate Subjects and Truth Linguistic analysis circumscribes the terms for basic particulars; but it is not enough to take steps to C1 predicative completeness. To do so, the drafts which are the closest to the Discourse framework point directly to the role w that basic particulars play as ultimate subjects in predication: (1) A substantive (term) is either complete—and we call it a Suppositum— or incomplete, say, an Attribute. Complete is a being, whose concept involves all predicates of one and the same subject, hence it is just the concept of the ultimate subject, or suppositum. Thus, the concept of Alexander, or of Bucephalus involves all that can be predicated of that subject, to which the name “Alexander” is given; whoever perfectly knows Alexanw der, in fact, knows his whole nature and story. The names “man,” “king,” “conqueror,” on the contrary, do not involve all predicates (of the suppositum) and hence they do not circumscribe a thing in such a manner, that there could not be anything else to which the same properties could be attributed.1 (2) In order to inquire into the nature of a substance, or of a subsisting thing, one should consider that, if many different attributes are said of the 1

Divisio terminorum ac enumeratio attributorum. A VI.4, 559. See also the definition of “complete term” as the one which “expresses the whole nature of its subject” in the Def. Notionum Metaph. Atque Logic., A VI.4, 625.

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same subject, then none of them is something subsistent: so “hot” and “bright”, and “located here, or today” are said of this one and the same fire. The concept of a subsisting thing, however, e.g. of this fire, is that which includes all the attributes, that can be said of the same subject, of w which itself can be said. Therefore, a subsisting thing is nothing but a w complete term, that is a concept in which all properties inhere, which can be attributed to it or to the subject to which itself can be attributed.2

The presence of the two dimensions (ontological and propositional) of predication can be recognized even more clearly than in DM 8. The complete term, or substance term (sometimes, directly, ‘the substance’), plays the role of ultimate logical subject, and at the same time it is ‘said of ’ the ultimately underlying ontological subject (‘suppositum’ or ‘subsistens’). I would say, it expresses it, because they are really identical. To find the concept adequate to express a substance, therefore, amounts to finding the ultimate subject of predication, that is a term which cannot but play the role of subject. So far, Leibniz does nothing but repeat Aristotle’s move in the Categories, by using predication in order to make sense of substancehood. Ordinary language could still work as our guide: the criterion of predication leads us beyond substance kinds, towards particular objects. ‘This man’ or ‘this fire’, at the bottom of the predicative chain, are appropriate examples for ultimate subjects, corresponding to the ‘primary substances’ of the Categories. We well know, however, that in the Aristotelian framework individual substances as such somehow remain outside the scope of conceptual knowledge. And we have seen that ordinary language could offer only demonstrative devices in a Strawsonian vein or, at most, descriptions (or their abbreviations) that are only accidentally identifying. What is new in Leibniz compared to Aristotle, and what allows him to go beyond the data of ordinary language, is the fact that predication is interpreted by him as conceptual inclusion, and that this reading is applied even at the level of the individual subject. It is precisely at this juncture that the study of referring expressions meets the theory of truth. This link is made explicit, in the Notationes Generales, in the context of a possibility proof for complete concepts, which are defined relying on identity and predicative maximality: If the same thing [eadem res] is B, and it is also C, D and so on, because it is A; in other words, if the concept A involves all concepts B, C, D etc. which can be said of the selfsame thing; then the concept A will express a w singular substance. This amounts to saying that the concept of a singular 2

Definitiones. Aliquid, Nihil (N 76), A VI.4, 306. This approach strongly recalls that of the De Cogitationum Analysi, also in the choice of examples.

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substance is a complete concept, which includes all that can be said of the substance.3

The complete concept of Alexander, or Caesar, however, is not at our disposal; nor can we give a distinctly conceived model of it. In order to prove that this type of concept is not an arbitrary fancy, therefore, we have to provide somehow a proof of its possibility. In the language of DM 8: ‘individual concept’ is a purely nominal definition. To have a real definition of it, one has to take into account its role in making sense of what it is for a singular proposition to be true: Now, it is clear that there is such a kind of concept, according to the definition of a true proposition which I have explained. When we utter ““Alexander is strong”, indeed, we do not mean anything but that “strong” is contained in the concept of Alexander, and the same for all predicates.4

Descartes justified the intuitionist approach to his C2 completeness through the transcendental reference to our epistemic way of access to substance. Leibniz’s strategy for the rehabilitation of C1 completeness relies on our need to assume it in order to make sense of the basic notion of truth. We conceive of truth and utter true propositions about individuals, i.e.wholly determinate basic particulars; but the conditions for making sense of our statements concerning individuals, i.e. of singular statements, where our talk comes into touch with things, involve the subsistence of individual concepts. This amounts to saying that the ontological subject, as such, does possess a concept. The Construction of a Complete Term Sometimes, Leibniz sketches a construction of complete concept from the viewpoint of the thing-concepts polarity.5 In this view, concepts are partial perspectives on a thing, which never exhaust its descriptive content; every further determination of a concept is seen as an approximation to it. Now, 3

4 5

Notationes Generales, A VI.4, 553. This text present a significant inversion in the order of appearance of the topics of substance and identity, with respect to the standard categorial scheme. Ibidem. Another draft makes it explicit: “Let the proposition be true: ‘Y is B’, and let Y be any subject of which B can be said, and let Z be any attribute of Y whatever. Now, I say that, if we can demonstrate that Y is Z from the fact that Y is B, then B will be the complete term which expresses the substance.” Enumeratio terminorum, A VI.4, 389.

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the complete concept is the limit of this progression, the locus w where the two worlds of ‘concepts’ and ‘things’ find their perfect correspondence. The requisite for this adequacy is the maximality of the descriptive content. This can be formally expressed by stating that a certain concept does not suffer any further addition; the latter would entail a contradiction. By contraposition, the possibility of being positively increased by some conceptual addition is the sign of the (more or less) abstract character of a concept. We find this formal definition of completeness within the general theory of concepts of the GI: Take BY, and let any indefinite Y be superfluous; i.e. “a certain Alexander the Great” and “Alexander the Great” be the same; then, B is an individual concept. If BA is a concept, and B is an individual, A will be redundant, i.e. if BA = C, then B = C.6

A text from the end of the eighties traces in an exemplary way the path from the termini-res distinction of the Characteristica verbalis to this definition of completeness: Some terms signify things, some signify the objects of our concepts or notions or, as some people call them, the objective concepts. So “wise A”, “rich B” are terms each of which signifies a concept; and if they are given, it does not follow that two things are given; it could happen that YA∞XB, i.e. that some wise be the same as some rich. If A signifies Alexander the Great, however, or Caesar the dictator, this cannot happen: in fact, when A and B are things, provided that not (A∞B), then neither XB is, or not (YA∞XB); and this because A and B are complete terms, which already contain all that could be added to them, and YA∞A.7 w

The complete concept obtained through this sort of ‘a priori deduction’ could well be compared with the ideal of complete conceptual determination which Kant will apply in the Critique of Pure Reason to God’s idea.8 From this, the uniqueness of the designatum of a complete term follows: . . . in the former sense, A and B are universal terms, in this present sense they are singular. From this I conclude that each singular term is a complete Being. And it seems to follow, that singular terms only are things; in the former sense in fact, though A and B are different, nevertheless 6 7 8

GI sect. 72, A VI.4, 762 (C 375). Inquirenda logico-metaphysica (N. 210), A VI.4, 999. Critique of Pure Reason. Transcendental r Dialectic, II, Ch. 3, Sect. 2: On Transcendental Ideal.

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they are not two things, I mean numerically different things. Surely, one could say: the wise is a “wise thing”; but in this case “thing” itself is the “Y” which fulfils the term.9

While text (2) above started from an idea of ultimate subject to arrive at a complete concept, the texts quoted somehow proceed in the opposite way: starting directly from the construction of a complete term, they go on to prove that it coincides with that of an ultimate subject.10 In the former case, complete notion is implicitly modeled on the intuitive idea of a fully determinate thing; whereas in the latter it is obtained through a purely combinatorial construction. w According to the formal requisite for completeness, for each pair of contradictory predicates, one predicate belongs to the subject. I suspect, however, that a metaphysically relevant application of this principle does presuppose some categorial articulation and hierarchy of predicates and some previous intuition about the determined mode of existence of a ‘concrete thing.’ I wish to call attention to another slightly different, though related, opposition between two ways of conceiving the construction of a complete concept. If this is built up simply by increasing the content of a notion as far as possible by way a of conjunction, then we finally obtain a maximally consistent conjunctive predicate. This logico-combinatorial characterization can easily agree with an epistemic approach to individuality through discernibility, where only the exhaustive description contained in a complete concept could provide the means for identifying an individual among all possible ones. The construction of a complete concept, however, can hardly be reduced to this cumulative procedure. The ‘predicative formula’ “if X is A, then X is B, C, D and so on . . . ” presents the complete concept more as a principle of deduction than as a ‘list’. A comparison with the De Cogitationum might help us. The ‘subject’—being distinct from the bundle of properties, according to ontological asymmetry—figured there as a true principle of explanation, hence as a ‘nature’, to be expressed in conceptual terms. This matches well with the view of predication as conceptual containment, where the subject concept provides a reason r , or a justification for all its predicates: Given the fact that from the notion of the subject a rreason for its attributes can always be drawn, it follows that every notion from which one can draw 9 10

A VI.4, 999. “Moreover, a singular substance is that which cannot be said of anything else. That is to say, if a singular substance is said of something else, then they will be one and the same. Hence, if from the sole fact that A is B, one could conclude that B is A, i.e. that A and B are the same, then A or B will be a singular substance, or a thing subsisting per se . . . ”, A VI.4, 554–555.

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a reason for all attributes of the same subject is the notion of substance itself; and a complete term expresses the substance.11

Finally, such a reading could make sense of the strong ontological interpretation given to complete concept in the Notationes passage. According to this interpretation, the complete concept will express nothing less than the individual essence of a person, embracing his/her whole history: So, if someone is strong, vehement, educated, and a king, and the general of an army, and the winner in the battle of Arbela, and so on for all the predicates which are said of Alexander the Great; then God, who is intuitively acquainted with Alexander the Great’s singular essence, will see some complete concept, in which all those predicates are virtually contained, or from which they all follow. From “strong” one cannot infer “king”, nor from “general” “winner”; on the contrary, from Alexander’s concept “strong”, “king”, “general” and “winner” are all deduced.12

Commenting on the De Cogitationum Analysi, I had guessed that in order to work as a principle of intelligibility, the subject has to be considered as a tode ti and an essence. But insofar as both the (specific) Aristotelian eidos and the (mathematical) Cartesian one are largely bypassed, we are faced with a new type of essence, which is located at the individual’s level—a haecceity. A general remark is in order, however. The two ways of construing the complete concept—as an identifying property, from which the others can be deduced, or as a set of predicates simply built up by the logical operation of conjunction—remain as two possibilities both documented in Leibniz’s text.13 The first surfaces where Leibniz makes the notion adhere to the inner metaphysical structure of an individual, but it is never explicitly and fully spelt out. The second is put forward when he deals with individual concepts, in logical contexts, as a limiting case in the general manipulation of concepts, availing himself of the standard resources of their combinatorial treatment. Moreover, also in metaphysical contexts like the debate with Arnauld, as we shall see, Leibniz uses one or the other of the two approaches, according to his will to emphasize more or less the ontological import and inner compactness of the notion 11 12 13

Enumeratio (N. 97), A VI.4, 388–389. A VI.4, 553. See on this Mates, The Philosophy of Leibniz, 87–88.

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Complete and Incomplete Beings Coherently with the general style of mid-eighties texts, the examples of both complete and incomplete terms are given in concreto: ‘Alexander’ on one hand, ‘man’, or ‘king’ (rex), or ‘ruler’ (regnans e ), or ‘strong’ on the other. Using terms in concreto, one has only in recto predications. This allows Leibniz to eliminate the double predication of the Categories by reducing all predication to the ‘being-said-of’ that is handled, in its turn, through conceptual inclusion. Consider the class of incomplete terms, that are opposed as a whole to the complete concept and involved in the latter. General substantive terms and attributive ones are put wholly on a par. Whereas the tables closer to linguistic morphology somehow took into account the substantive-adjective distinction of grammarians, the true ontological distinction between substantial and attributive items turn out to coincide with that between individual and general terms. Though expressed by concrete substantive terms, concepts like ‘man’ and ‘king’—exactly as ‘hot’—are all incomplete: in Leibnizian jargon, they express ‘incomplete beings’, having a properly predicative role. We can call them ‘beings’ (entia), not properly ‘things’ (res), let alone ‘substances’. We could also say that they are only concepts, as opposed to the thing, which is represented by the complete concept. We can try to summarize the different types of incomplete beings we have met so far: 1) mathematical (especially geometric) objects (e.g. ‘triangle’), or constructs (e.g. ‘space’); 2) sortal terms for natural kinds or mass terms, e.g. ‘man’, ‘gold’; 3) properties, e.g. ‘strong’. In the Correspondence with Arnauld we will find 4) the (concepts of) individuals sub ratione generalitatis—i.e. definite descriptions that are not complete, e.g. ‘the first man’; but on this more later. The Notationes, as we shall see in a moment, distinguish the individual concept from specific ones, either having an empirical basis, like those of natural kinds of type (2), or being exactly defined through a finite number of concepts, like mathematical ones of type (1). Abstract talk mainly expresses the reification of items of type (3). No incomplete concept is able to completely determine (hence, to univocally identify) its bearer; it does not provide an answer to many questions one can pose about him/her/it. We could see a complete concept as the limiting point in a structure of abstract objects. Only for complete concepts the Law of Excluded Middle holds. And this, notice, is required to be considered as the notion of a possibly existent being. Talking about a “structure of abstract objects”, I mean that the abstract constituents of complete concept are ordered according to a logic of increasing specification: Animal—Man—King—King of Macedonia—Conqueror of Darius . . .. Their order has also (in part) an explicative value: Alexander is a conqueror because (or insofar as) he is the general of an army, and is strong and courageous and so on. The explicative

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force of every incomplete predicate, however, is always only a partial one. This is a capital point Leibniz insists on in order to distinguish incomplete concepts from complete ones: according to him, a predicate Sn can never be deduced either from any other predicate Sn−1 , nor from any finite series of predicates (Sm . . . Sn−1 ). The examples of historical characters make us aware of a further fact: the constituents of complete concepts that are ordered in this causal structure are not so much abstract timeless properties, but temporally ordered states. Should we consider a state a concrete or an abstract entity? Leave this question open; certainly, this approach introduces a new way of considering incompleteness and related undertermination. Having an incomplete concept of an individual will also (and especially) mean being acquainted, in a more or less detailed manner, with a partial story of it up to a fixed moment, and being faced with a range of possible branchings with regard to its further development. In this way the causal temporal dimension of substance which emerged in the De Affectibus from the abstract modeling of the life’s mind is integrated in the individual notion. The formal tool which makes this move possible is the development of conditional analysis in the categorial tables, which I will further explore in the next section. Actiones Sunt Suppositorum : Ultimate Subjects for Action At the very heart of DM8, remember, the themes of predication and individual substance were introduced by the old dictum ‘actiones sunt suppositorum,’ that was invoked against the Malebranchian idea that God only acts. In a later work—where the notion of substance is approached from dynamical considerations—Leibniz takes up again the dictum of DM 8, and emphasizes its convertibility: So far as I have made the concept of action clear to myself, I believe that there follows from it and is established by it that most widely accepted principle of philosophy—that actions belong to substances [actiones esse suppositorum]. And hence I hold it also to be true that this is a reciprocal proposition, so that not only is everything that acts an individual substance but also every individual substance acts without interruption . . . 14

Now, I have shown how the notions of subject and inherence have been actually rediscovered and reshaped by Leibniz moving from the problems of 14

On Nature Itself, or on the Inherent Forces and Actions of Created Things, GP IV 509 (L 502). In this work, Leibniz reproaches this Occasionalist view with the danger of falling into a Spinozistic-style monism. See § 15, GP IV 515 (L 507).

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action. In the Discourse exposition, he goes the other way around: conceptual containment provides a precise meaning and an explanatory ground for the notion of substantial action itself, which is ‘derived’ from the complete concept as a corollary, a derivation which takes the aspect of a bold rehabilitation of ‘substantial forms’ in section 10 and following. In this context even Leibniz’s dynamic discoveries find their place among the consequences of the complete concept view. It is worth noting that the rehabilitation of substantial forms is grounded a priori on the concept in sections 10–12, without mentioning the discoveries in the field of dynamics that are introduced later. Section 12 stresses the link between this aspect and the possibility of stating transtemporal identity.15 Around the Discourse, Leibniz makes explicit what has already emerged in the De affectibus: his (logico-) ontology of action works as a true rediscovery of the ancient theme of physis, the subject-matter of Aristotelian physical science, whose classic definition, in fact, is that of ‘principle of action’. An interesting draft of the mid-eighties documents Leibniz’s conscious connection to this idea: . . . [according to Aristotle] nature is the principle or cause, for which the thing, in which this nature itself inheres immediately and per se, i.e. not accidentally, does move and rest. This statement seems to be absurd and meaningless, were it not clarified through my discoveries: I have proved, indeed, that each Being per se, or truly one, brings in itself some principle from which all that happens naturally and per se to it does follow, and this is an analogon of soul, and of what Aristotle labeled as “nature” . . . It is true that from the nature of each individual thing all its predicates do follow, even those that simply happen to it; that is to say, nothing happens accidentally with respect to an individual . . . 16

If this is the idea lying behind the “actiones sunt suppositorum”, we have a new confirmation that the suppositum that Leibniz has in mind is far from working as a bare substratum. In a sense, essentialism appears in Leibniz properly at this level, when he comes to consider essence no longer as a principle of classification, but of action: hence, when he deals with the temporal development of an individual thing. Exactly as in the case of descriptive and classificatory devices, however, Leibniz exceeds the boundaries of ancient 15

16

“ “And if there is no other principle of identity in body than those we have just mentioned [i.e. extension , figure, motion, which are abstract notions], no body can ever subsist longer than a moment.” A VI.4, 1545 (GP IV 436; L 309–310). De natura sive analogo animae, A VI.4, 1505. This idea, notice, is explicitly applied here by Leibniz to “corporeal substance”. For the link between complete concept and substantial form, see the remarks in R. Adams, Leibniz, 315.

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essentialism. Aristotle’s physis, in ffact, concerned only the general g patterns of development that are implied by natural kinds and determine the successive phases of the life of each individual instance. Leibniz’s encoded program, on the contrary, reaches individuality.

Chapter 2. Conceptual Individuation: Complete Concept and the Identity of Indiscernibles 2.1. The “Paradoxes” of IdInd Substitution and Conceptual Containment, or: IdInd without Bundles Leibniz’s mature theses about individual identity are presented as corollaries of the complete concept view. This is the case with the well-known IdInd.17 Let me give a sample of formulations: (I) From these considerations a number of important paradoxes follows; among others, that it is not true that two substances can resemble each other completely and differ only in number and that what St. Thomas says on this point about angels or intelligences (quod ibi omne individuum sit species infima) is true of all substances, provided we take the specific difference as geometricians understand it in their figures.18 (II) Moreover, from this it follows that Singular beings are truly the lowest species, and that no two individuals can be given that are wholly similar to one another; hence, the principle of individuation always lies in some specific difference; Aquinas stated this for pure spirits, but it is true for whichever individual.19 w (III) It follows also from that [the PR] that there cannot be two individual things in nature which differ only numerically. For surely it must be 17

18 19

The literature on Leibniz’s IdInd is massive. Here, I recall only—besides the classic expositions of Russell and Mates in their Leibnizian monographies—K. Lorenz, Die Begr¨u¨ ndung des principium identitatis indiscernibilium. St. Leibn. Suppl. III (1969), 149-59; K. Clatterbaugh, Leibniz’s Principle of the Identity of Indiscernibles. Studia Leibnitiana, 1972, 241–252; R. Kauppi, Einige Bemerkungen zum Principium Identitatis Indiscernibilium in Leibniz. Zeitschrift f¨ ffur philosophische Forschung, 1966, 497–506. Other papers focus attention on the statement of IdInd in the late correspondence with Clarke. DM 9, A VI.4, 1541 (GP IV 433). Notationes Generales, A VI.4, 553.

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possible to give a reason why they are different; and this must be sought in some differences within themselves.20 (IV) It follows also that there can be as many singular substances as there are different ways of combining all mutually compatible attributes. From this a principle of individuation clearly results, about which Schoolmen entertained a great deal of useless disputations.21 Remember that to differ for spatio-temporal predicates is the classic way of differring solo numero. This amounts to saying that the difference should be an intelligible one, belonging to the category of Quality. What is the ground for Leibniz’s thesis? How is it exactly connected to the complete concept view? The texts suggest different answers, related to the different interpretations one could give to the structure of complete concept. The severe judgment on Scholastic discussions in (IV), which is presented as an immediate corollary of the complete concept theory, recalls the dissolving of the individuation problem through the tota entitate thesis in the youthful De principio individui; and the solution does realize the combinatorial principle once expressed by the dictum ‘the essences of things are like numbers’. The IdInd seems here to be bound to a combinatorial construction of complete concepts and their corresponding individuals, starting from a common set of properties. From this perspective, the only difference to be conceived can be qualitative, i.e. a difference in the constituents of the set itself. So, the passage offers a strong suggestion for a universalist and descriptivist (if not bundle-theoretical) interpretation of Leibnizian individuals. In (III), the thesis appears, instead, as a consequence of the PR or, if one prefers, of Conceptual Containment. Text (II) from the Notationes is followed by a more articulated argument, making room for SUBST: . . . there can be no two individuals wholly similar, e.g. two eggs. Necessarily, in fact, one could say of one of them some predicates which cannot be said of the other one; otherwise, they could be mutually substituted, hence there should no longer be any reason, why they are not said to be one and the same. But then, if they have different predicates, by this very ffact their concepts also differ, in which these predicates are inherent. From this simple remark many consequences follow of the most importance, even in physical science, which are likely to be unexpected.22 20

21 22

First Truths T , A VI.4, 1645 (L 268). Here also, the usual reference to Aquinas’s thesis follows. Moreover, the principle is empirically applied: “Never are two eggs, two leaves, or two blades of grass in a garden to be found exactly similar to each other.” (ibidem). Definitiones (N 76), A VI.4, 306. A VI.4, 554.

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We are faced here with a patent case of application of the ‘substitutability law’ directly to individuals: two eggs, as in the Confessio of more than ten years earlier. Eggs were invoked there, however, in order to establish a haecceitistic conclusion; now, on the contrary, they serve to make clear the need for conceptual individuation. The reasoning can be roughly schematized in the following manner: [1] Two items having all properties in common are mutually substitutable, and hence [2] they are one and the same, according to the substitutability law. By contraposition, [3] if two objects a and b are different, then they will differ at least in some of their properties. Now, [4] all predicates of aand b are implied by their respective (individual) concepts. But then, if [3] is true—i.e. if (Pa & ∼Pb)—also [5] the concept of awill differ from the concept of b : C(a) = C (b). One can easily see that, at step (3), discernibility is deduced directly from the SUBST. The further conclusion [5], however, is reached through the appeal to [4] the Concept-containment principle. Making explicit the inference already suggested by the De Cogitationum Analysi, predicative discernibility comes back to the fact of being drawn from different basic concepts. A trivial reading could be given of this ‘being contained’. But it is also (and more) plausible to give it an explanatory value. One might even guess that the discernibility established in (3) would be assured by any type of predicate, even extrinsic (such as was the case with spatio-temporal paths in the Confessio); whereas coming back to the individual concept would provide the basis for a stronger Discernibility Claim, which has to be satisfied by some intrinsic qualitative features. Usually, the necessity of the IdInd, i.e., its holding in all possible worlds, is held to stay or fall with a qualitativist and bundle-theoretical approach to substance. By stressing the thing-properties distinction, Leibniz would be committed, therefore, to a contingent version of the principle. I hope to have shown, however, that he locates himself beyond the substratum-properties polarity that constitutes the framework for present-day debates on the IdInd. Thus, Leibnizian individuals do not amount to the bundle of their qualities, to be sure. Their reciprocal distinction, however, is not a barely numerical one, nor is it originally given by the sets of qualities themselves, but by the identifying core working as a principle of deduction. Given, then, that all qualities are deduced from it, it follows that no two individuals can share all of them. If we admit, therefore, that Leibniz has in mind a principle of deduction that lies beyond the set of predicates, then he is not necessarily committed to a bundle-theoretical interpretation of the IdInd. Seneca’s Wisdom, Or: IdInd and the Ontology of Properties It remains to be clarified which ontology of properties is assumed by Leibniz’s IdInd. Even if a bundle theoretical view is not in sight, the IdInd

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appears as the most important piece of evidence for Leibniz’s commitment to a qualitative theory of individuation. According to a standard interpretation of the principle, in fact, individual concepts are sets built up from the same stock of general Qualities, hence they can differ only if their constituents differ. Our text (IV), as I have hinted above, could support a kindred reading. In the last decades this interpretation has been challenged on the basis of the ontology of individual accidents that Leibniz actually endorses, according to which no two individuals share the same qualities. It seems to me, however, that a Trope theory and a universalist Bundletheory are both somehow inadequate to capture Leibniz’s intuitions. In order to see this, let me reconsider more closely the ontological nature of his individual accidents. Commenting on the De Cogitationum, I have insisted on the co-presence of properties. Now, I suspect that the role of co-presence in their particularization is far more important: a trope of a single quality properly cannot be conceived of. Every quality, insofar as it is conceived of in isolation from others (and from its bearer) is conceived of in a general manner. In this respect—and, notice, only in this—it can be seen as indistinguishable from other tokens of the same quality. In other words, an expression like ‘this red’,which aims at capturing precisely a particular instance of redr ness, far f from grasping the most concrete element of being, still designates an abstract concept. This idea, which in my opinion already underlies the theory of particularization in the De Cogitationum, is to be explicitly found in the later De Abstracto et concreto, an important ontological text to which I will return in the next section. I anticipate here the passage on individual accidents: It is very doubtful whether abstract items are true real Beings. If they are, they are never complete even within a single individual. If this wisdom, which is in Seneca, involves a relation to his riches, by the very fact w it does not involve the formal concept of wisdom only, that has been brought to our attention when we have coined such an abstract term. If, then, we were to abstain from accidental considerations, in this case it would not be clear at all how two individual wisdoms of the same grade, or two equally intense heats, or two numbers “two” differ. Or better still, we shall compare these Metaphysical Beings with Mathematical ones, e.g. the Circle insofar as it is abstracted from matter, or the parts of time insofar as they are separated from their contents; exactly as we cannot explain how two equal circles differ, which are separated from matter, or two hours—so we cannot explain how two similar and equal instances of wisdom, or two instances of heat having the same nature and grade differ.23 23

De abstracto et concreto, A VI.4, 991.

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The assimilation of predicative (here, ‘metaphysical’) beings with mathematical ones is explicitly confirmed. Above all, this long quotation shows that we should be more cautious in transferring directly to Leibniz the traditional ontological square, having items such as ‘this white’ or ‘this wisdom’ as basic individuals among accidents; and even more, in attributing to him a kind of tropetheory in present-day fashion. Roughly speaking, I think that in Leibniz’s view the only individual accident is a whole ‘state’ of a substance—hence, an infinitely complex whole, resulting from the complication of infinite qualities.24 What I have observed about individual accidents could help in some way the standard interpretation of the IdInd under pressure. Surely, no shared entity corresponds to common predication and no bundle theory is in view; in spite of the underlying particularist ontology, however, we are able to know individuals and talk about them only by using the alphabet of general qualities. This constraint is rooted on one hand in the limits of our senses: we cannot perceive differences under a certain level, and this amounts to saying that we have a confused knowledge of the individual. The difference on this point from the epistemological tenets of the tradition of particularist ontology has not been fully appreciated: in the nominalistic tradition of the late Middle Ages, ontological particularism presupposed an intuitive knowledge of the individual as such. For Leibniz, instead, intellectual knowledge and language are bound to manage only general concepts. As a consequence, he is not liable to the objection that comes to the trope theory from the semantics of predication: when I say that Socrates is wise and Plato is wise, I am not attributing to them two different items (wise1 and wise2 ). The De Abstracto et Concreto advises us, indeed, that focusing our attention on the property expressed by ‘wise’ amounts to grasping something which is predicable both of Socrates and Plato. The correct stance is to distinguish the level of individual accident, which inheres in an individual thing, from that of general property, which belongs to the individual concept and is predicated of the thing on the basis of the accident. Hence, the constituents of our concepts are general, while the corresponding accidents are particular. Anyway, the Discernibility Claim implied by the IdInd is ultimately satisfied just at the level of accidents; only, their differences can transcend our cognitive and expressive ability. But they should be reflected in the (i.e. God’s) individual concept—whose ingredients would turn out to be particular. Our way of conceptualizing—hence, the language of predication itself—is bound to operate, instead, with general terms and abstract suchnesses. Thus, when talking about conceptual individuation, we have to bear in mind that it is somehow located beyond our conceptual framework. 24

K. Clatterbaugh indicates quite correctly the perceptions of a monad as proper instances of Leibnizian accidents.

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Connexa: Influence and Position At this point, one might think that individuation is made possible through a qualitative structure, only much finer-grained than general suchnesses are: something like Owen’s ‘atomic shades’ of a quality, provided they can lie beyond our perceptual powers, and each of them is individuated through the co-presence of other qualities belonging to the same individual. There is more, however: passing from general suchnesses to ‘individual’ qualities, we are taking a step into another categorial type. In combinatorial metaphysics, remember, absolute forms were not only particularized, but also transformed into ‘requisites’: a language that is tied to that of connection. In the De Cogitationum, finite subjects and their properties were qualified as “connexa.” In Leibniz’s theory of relations, we constantly find a distinction between ‘relations of comparison’ on one hand and ‘relations of connection’ on the other. Relations of connection are mainly asymmetrical ones (the most resistant to reductionist attempts, both semantic and ontological) expressing factual interactions (e.g. loving one another) or origin (e.g. being-son-of). A draft of the eighties on semantics and ontology, the De Termino, Praedicato, Relatione, after dealing with the comparison-connection distinction, introduces a slightly different one: The relations between two things seem to be either rational r [conceptual] or real r , i.e. of essence or of existence. Real relations are of Position (i.e. of time and place), or of Influence: the latter occur, when by one thing a change is made or prevented to happen to another one . . . 25

A ffew lines above, notice, Leibniz has stressed the fact that the terms A and B of a relation are to be taken not as concepts, but as things or individuals. The label of ‘real’, embracing both Influence and Position, in my view alludes to a type of relations that involve possibly existing things. This is confirmed by a similar remark in a categorial list: What has position; that is to say, what is in a relation of existence with other things, while the other categories, i.e. quality and quantity, are relations of essence or formality.26 25 26

A VI.4, 944. Enumeratio terminorum, A VI.4 (N 97), 393. The opposition of existence relations to the distinctions drawn from ‘formalities’ recalls the topic of the De cogitationum. In the latter, however, quantity was associated with position.

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Let me first consider Position, hence spatio-temporal relations, whose categorial place raised some puzzlement in the former section. The De Termino confirms its ambiguous nature. Leibniz is uncertain whether to assign it to comparison or connection relations. At the same time, he considers it as a ‘real’ relation and this does confirm its privileged tie to existence. But it behaves differently from the relations of influence. The relations of position, in fact, exactly as the conceptual ones, bring about only “extrinsic denominations” i.e. predicates that do not necessarily correspond to any inner modification (always, “except the general connection of things”). The IdInd surely excludes that spatio-temporal position alone suffices to distinguish real individuals. This does not exclude, however, that concrete objects do have predicates of position, and even less that these are, in the phenomenal world, the most apt for us to identify things, maybe the only ones we have at our disposal for distinguishing small bodies or parts of homogeneous matter, given the limited resolution power of our senses. Stating that individual substances must differ for inner qualities, the IdInd does not deny that spatio-temporal predicates (or at least temporal ones) are typical of them, and also that they must accompany the more basic individuating features. Only, it states that they are to be grounded on a set of more basic properties. It is quite plausible that in Leibniz’s intuition positional properties are dependent on influence relations. In the next section we will see, how temporal relations are actually grounded on casual ones. Differently from Position, Leibniz says, influence relations bring about a real change, i.e. a change in internal properties. We know from elsewhere that this influence need not be—and as a matter of fact is not—a physical one. In a Leibnizian world, intersubstantial causality has an ideal character, i.e. it amounts to a correspondence according to a rule between the states of different substances. But the concrete nature of the causal link is not at stake here. What matters is that there must be, in each of the substances involved, some internal modifications of a certain type that ground influence relations. Some accuracy is required, as regards the categorial place of these basic intrinsic features: maybe, it is not enough to say that they belong to the category of Quality. The emphasis laid by Leibniz on the relations by connection—and, derivatively, on those of position—as distinguished from those by comparison, does circumscribe a special class of accidents that are typical of possible individuals. It is quite plausible, indeed, that relational properties like “sonof” or “lover-of”—though having only a conceptual status, too—require some appropriate fundamenta, having a some stronger ‘towardness’ than that required to ground, say, a similarity relation . In this way, Leibniz’s particulars would not be built up from a set of general properties, but rather of characters similar to Strawson’s ‘placed

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features’—though being different because their particularization would not be given by the relation with particular times or places, but by some primitive order relations holding among them, by which times and places themselves are identified. Besides this, Leibniz’s qualia are also dependent on the ‘basic quality’ or point of view of the individual thing, playing the role of thisness. The First T Truths presents, immediately after the IdInd, another consequence of the doctrine of the complete concept: It follows further that there are no purely extrinsic denominations which have no basis at all in the denominated thing itself. For the concept of the denominated subject necessarily involves the concept of the predicate. Likewise, whenever the denomination of a thing is changed, some variation has to occur in the thing itself.27

Clarification is in order: Leibniz’s thesis does not simply coincide with the ontological doctrine that every relation needs some foundation in related things. This is an ontological truism that is part of the common framework of the discussions on relations, as Mugnai’s studies have shown; so, it could hardly be argued for as a new “paradoxical” consequence of Leibniz’s doctrine. Rather, the content of the statement is the stronger Thesis of the Changing Relata. We have met it in the1676 comments on Plato’s Dialogues, w where it revealed a further metaphysical dimension of the notion of ‘expression.’ Now, it is no longer juxtaposed to conceptual containment as its ontological counterpart, but directly grounded on it. Anyway, the reservation about the ‘general connexion of things’, which induces some real change also in the case of extrinsic relations like Position, alludes precisely to this thesis. But then, what would an influence relation add to the real change which is induced also in the case of more extrinsic relations, in virtue of the ‘general connection of things’? I can only advance a conjecture. Mugnai points out that, when the relation aRb changes for a change in its fundamentum in b, not necessarily the corresponding intrinsic change in a concerns precisely the individual accident which is its fundamentum in a. It could concern, istead, another aspect of a. On the basis of the De termino passage, the difference between influence relations and extrinsic relations like Position might lie in the fact that in the former’s case the change does concern exactly the relevant individual accident. One might object that some of Leibniz’s classic examples of extrinsic relation—accompanied by real change, but only in virtue of the ‘general connection of things’—are just of the 27

A VI.4, 1645–1646. (L 268).

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connecting type (e.g. a man becoming father, or widower when he is in India). But in these cases, relations are not perceivably relevant, as Leibniz specifies also in this piece.

2.2. Individuals as Infimae Species Individuals, Natural Kinds and Geometric Species The IdInd is equated to the statement that “individuals are the lowest species” (species infimae). That is to say, the qualitative difference needed is labelled a specific one. Why? The question is all the more urgent, as Leibniz had fundamentally ignored, in the earlier years, some historical antecedents of this statement, to be found in Nizolius or Gassendi. It seems that it has now assumed a new pregnant value for him. Now, the sense of ‘species’ relevant here is quite different from that related to natural kinds. Leibniz does not refrain from insinuating that the ‘natural’ or ‘physical’ sense is far from being privileged by any absolute ground. Our exploration of the topic of sortal terms for natural kinds in the characteristica verbalis and of their vagueness can help us to understand this point: Be careful, however: when I say that men differ one from another as lowest species, I do not take the term “species”, as usual, in the sense of some progeny of beings which are able to generate somebody similar to them, such as is the case for the species of men, dogs, roses (although this notion of species is not clear enough, and one could doubt, whether wolves and dogs, Molossians and little Maltese dogs rather differ for their species). Nor do I mean a universal notion, i.e. a concept constructed from a finite number of simpler concepts taken together; on the contrary, I mean a term which has a quite peculiar concept, distinct from all others. And surely, w nobody can deny that the concept of Alexander the Great is different from that of Julius Caesar, and we are able to draw much information from the concept of the one or the other. If, however, one is eager to define the concept of “species” in such a way, that it could not fit for individuals, I do not want to argue with him about terminology.28

In order to better understand what the species infima thesis positively means, we are left to consider the two suggestions Leibniz has given us. According to DM 9, ‘specific difference’ has to be understood here in the sense “of the geometers”; in several places, this advice is illustrated by a standard example: individual substances will differ exactly as two ellipses do. Now, in 28

A VI.4, 553–554.

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geometric objects the relevant differences are those which determine a dissimilarity in the mathematical sense we already know. There is a marked shift w the with respect to the haecceitistic passage of the De Cogitationum, where distinction provided by the ‘subject’ was assimilated to a difference in size and contrasted with the intelligible traits framing the definition of a circle. Here, on the contrary, it is assimilated exactly to these defining features. In a draft, we find an interesting variation on Leibniz’s current definition of similarity: Similar are those things that cannot be mutually distinguished, if they are taken separately [so far, we have the usual phenomenological qualification], by virtue of some property that is necessarily bound [to them], i.e. of some demonstrable truth about them; that is to say, similar are those to which no different demonstrable predicates can be assigned. So, every parabola is similar to every other, and every circle to every other; but not every Ellipse is similar to every other: on the contrary, there are properties that are peculiar to some types of Ellipses, e.g. the Ellipse that has its two axes equal is very different from the other ones.29

The properties of figures that count for similarity-dissimilarity are the relevant ones for demonstration. The special case of the Ellipse to hand is a geometric species, precisely because it has demonstrable properties derived from its notion. Analogously, each individual is a different species, insofar as its properties can be drawn, or deduced, from its concept. Maybe we have got, however, something too strong. The language of demonstration is for Leibniz a very precise and strong one, indeed; and he is eager to reserve it for incomplete concepts. This is why, I think that the simile, when applied to real individuals, has only an analogical force. It warns us that some kind of conceptual derivation should be possible; but this does not mean it works like in geometry. Thus, the passage from the Notationes Generales, after separating the metaphysical sense of species infima from the physical one, hence from the Aristotelian model of natural kind, goes on to separate it also from mathematical species, hence from the model of geometric essentialism. We are advised that a metaphysical species is not a universal constituted by a finite number of concepts. The compressed allusion can be enlightened by reference to Lebniz’s concept of demonstration as a proof that can be performed in a finite number of steps, hence assuming finite conceptual analysis. As is well known, Leibniz will ground here his proof-theoretical approach to the difference between contingent and necessary truths. From a terminological point of view he will usually reserve the venerable lexicon of 29

Definitiones (N 196), A VI.4, 931. Similar considerations are developed in NE III, 6, where Leibniz distinguishes the mathematical sense of species from the physical one.

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“essence, essential” to this type of conceptual containment, which is bound to incomplete concepts. Anyway, this terminological usage is not without exceptions. Thus in the very late Notes to Temmik, in the context of a remark on the status of relational properties, all properties of an individual, contingent ones included, are explicitly said to be essential to him: We can draw a distinction between the predicates which add something to a subject, and those which do not. . . . Does paternity add something to Philip? If individuals are taken as complete concepts, it adds nothing. Contingent properties can be said to be essential with respect to individuals, insofar as it is proper to the notion of individual things that it includes all contingent predicates. But contingent properties are not essential if taken with respect to whatever property of individual not able to express exhaustively the content of it.30

Needless to say, the italicized sense of ‘essential’ is the relevant one for the superessentialist debate. Another text, while confirming that the inclusion in a geometric concept is a demonstrative one, contrasts it with the weaker “saying of”, to specify the type of derivation made possible by a complete concept: The one able to perfectly understand the concept of a singular substance would know from it all its predicates. So, God can conceive within the concept of Peter the Apostle all that has happened or will happen to this Peter, as he conceives in the concept of a circular thing all that geometers can demonstrate of it. In the concept of a circular thing, however, he does not conceive all that can be said of (enuntiari) a circular thing, because he does not conceive the subject that can be thought of as circular.31

On the other hand, this “saying of” has to be understood in the peculiar (and strong enough) sense of the conceptual theory of truth. The classic brands of essentialism—the Aristotelian one, inspired by natural kinds, as well as the Cartesian one, inspired by mathematical essences—assigned to accidental predication all those predicates that are not derived from the essential core, and hence fall out of the scope of the concept of a thing; for Leibniz, on the 30

31

VE 1084. Italics mine Also quoted in Mondadori, On some disputed questions. Attention to this passage has been drawn by Mugnai. It is the more interesting as a further confirmation of the persistence of Leibniz’s view about complete concept until the end of his career. Leibniz’s last remark alludes to the fact that from an incomplete predicate (e.g. ‘king’) not all contingent predicates (e.g. ‘winner’) can be drawn. A VI.4, 575 (N 136).

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contrary, claiming that P is said of a would make no sense, if it were to mean that P is attached to a without any conceptual link. Essential predicates in the sense of old essentialism are included as a subset of the all-including set of intrinsic ones. Leibniz himself literally states the equivalence of predication and per se predication as the first corollary of the complete concept view: From this it follows that nothing inheres per accidens to a complete term. That is to say all its predicates can be demonstrated from its own nature.32

Admittedly, there are remarkable terminological oscillations, like the occurrence of “to demonstrate” here. But the point is sufficiently clear: contingent predicates, although they cannot be demonstrated in the proper sense, do belong per se in a relevant sense to complete being, insofar as they are conceptually involved. Leibniz always feels the need, however, to draw a distinction between this “involution” and related derivation, and the strictly essential implication which corresponds to the classic forms of essentialism and is accompanied by demonstrative derivation. The real discrimen between essential predicates and those that are included in the complete concept but are not essential, is explained by him in a twofold manner: a) mainly, the non-demonstrative character of the connection is stressed; b) sometimes the difference lies in the fact that contingent ‘accidental’ predicates do suppose relational properties, hence the inclusion of the individual in a wider context.33 Angelic Individuation or: Against Bare Substrata In order to illustrate what it means for an individual to be an infima species, Leibniz uses the theological simile of the Thomistic individuation of spiritual substances, much more than the geometrical one. I have already talked about that doctrine in the first chapter of this book. When professing the tota entitate solution Leibniz, not being interested, as Suarez was, to show any Thomistic fidelity, did not make any reference to the doctrine. If he rediscovers it (of course, in the usual highly stylized manner) in 1686, and only then, this is because he takes it, contrary to Suarez, in its original Thomistic sense, according to which angelic individuation, having a conceptual nature, is quite different from a merely numerical one. Unlike Aquinas, Leibniz does qualify this thesis exactly as one about individuation, w while extending it to all individuals; unlike Suraez, he subordinates the numerical sense of identity to the specific one. 32 33

A VI.4, 306. This is the case in the interesting N 136, where we find the distinction between ‘saying’ and ‘demonstrating’. See A VI.4, 575.

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The main ground for Aquinas’s thesis was the fact that, for him, individuation is linked to matter: hence, immaterial beings, which mutually differ only by virtue of their form, can differ only specifically. One might suppose that Leibniz comes to Aquinas’s conclusion by the same route, given that all his individual substances are, in effect, immaterial beings. This would be too hasty an inference, however. Leibniz is constantly willing to introduce something analogous to matter in the individuation process. I have shown traces of this idea in the Paris notes or in the De Cogitationum, but it is present also in the late monadology, where confused perception works as an idealistic counterpart of matter, to justify the splitting into particular and limited perspectives of the same intelligible content which all monads represent. What Leibniz cannot accept are not so much the suggestions of the hylemorphic model, as rather the logical implications traditionally associated with the idea of matter. The traditional (logico-) ontological subject was indeed somehow analogous to matter, insofar as it worked as an underlying substratum to which changes and properties happen, or are extrinsically attached to. Leibniz’s conceptual view of individuation excludes exactly this image of subject. It does work as an individuator just insofar as it works as a formal f principle, exactly as Scotus’s haecceity did. In this sense, Leibniz in DM 8 to a certain extent restores a non-generic or non-neutral meaning of “haecceity.” The substitution of the substratum model with the conceptual one is even more evident with regard to identity through change. It is time to reconsider this central dimension of complete being and see how it is integrated into the categorial framework and embodied in the structure of the complete concept.

Chapter 3. Conceptual Individuation: Complete Concept and Transtemporal Identity 3.1. A Concept Involving Change The A Priori Foundation of Sameness In his Remarques to Arnauld’s letter of May 1686, Leibniz argues that the possession of a complete concept is the basis for temporal identity: Suppose a straight line ABC representing a certain length of time. And suppose a certain individual substance, for instance me, existing or

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surviving during that length of time. Let us then first of all take me as existing during the time AB, and also as existing during the time BC. . . there must of necessity be a reason for the true statement that I continue to exist, that is to say that I who was in Paris am now in Germany. For if there is no reason, one would be as much entitled to say that it is another person. To be sure, my inner experience has convinced me a posteriori of this identity, but there must also be one a priori. Now, w it is impossible to find another reason, except that my attributes of the preceding time and state as well as those of the following time and state are predicates of one and the same subject.34

In section 3, I have tried to show that Leibniz’s categorial framework actually presupposes a rather traditional idea of continuant. This is far from being for him an unreflected assumption, however. On the contrary, he turned out to be so sensitive to the problems that the IndId raises to the continuant, as to oscillate between two contrasting models. We can even find some suggestion towards the weakening of transtemporal samemess into a similarity relation, on the basis of the ‘mathematical’ sense of species and identity we found in discussing the IdInd. Thus, in the NE he will write: “According to mathematical rigor . . . the same individual will pass from one species to a different one, because it is never entirely similar to itself, beyond a single moment.”35 So far, kindred challenges for the continuant coming from the IndId have been overcome, by relying on the inner experience of the mind. The example of the “moy” in Paris and Germany warns us, however, that temporal identity requires a foundation going far beyond and more deeply than that experience. This can well assure us of the fact of the temporal sameness of changing objects; also ordinary language accepts it as a basic feature of our conceptual scheme. But neither experience nor linguistic analysis has given us a satisfying model for this persistence. The complete concept theory can succeed in this task. The metaphysical identity, based on the complete concept, and the psychological (and moral) one, based on memory, are not only parallel, but the former is the explanatory ground for the latter, differently from the historical order of discovery or justification I have emphasized elsewhere. Of this a priori foundation, that should provide the real ground for psychological sameness, the Notationes Generales offers us a good example. Pursuing its outline of a theory of substance drawn from complete concept, it comes to discuss the problem of composite beings (entia per aggregationem). The question of diachronic identity emerges in this context as a capital point 34

35

GP II 42–43 (Mason 46, modified). See the parallel shorter passage in the July letter, GP II 53 (L 335). NE III, Ch. 6, A VI.6, 308 (GP V 288). But Leibniz refers here to physical individuals.

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in the comparison of bodies and true substances. We already know that the identity of a material being is bound to its parts and their mutual arrangement, and hence it cannot survive their changes. On the contrary, a thing can remain the same, though changed, if from its very nature it follows that the same thing must pass successively through different states. I myself am said, indeed, to be the same as I was before, because my substance involves all my past, present and future states. And it does not matter that in this way contradictory properties are predicated of me; the nature of time, in fact, amounts just to the fact that contradictory predicates can be true of one and the same thing, according to different times.36

In these few lines, some of Leibniz’s deepest insights about the temporal dimension of substance are concentrated. Remember Russell’s reduction of the complete concept view to “the assertion of permanent substances; . . . [and] the obvious fact that every proposition about the future is already determined as true or false . . . ”. The concept however, far from presupposing a reference to an underlying substratum, is the element that allows us to identify a continuant. As regards its internal structure, let me assume for a moment that it is simply an aggregate of temporal states. In this case, in the example of the ‘moy’ in Paris and in Germany, identity would be assured by the fact that there is a concept built up from two partial ones, like C1 = (S1673, S 1674 . . . S 1676) and C2 = (S1677, S1678 . . . S 1686). But it is difficult to see how the possibility of construing a unitary notion from two partial ones of this kind could have an informative, let alone a foundational role, as far as the sameness of their reference is concerned. Once again, in order to give a nontrivial sense to this derivation, one needs to admit that a complete concept expresses a principle of deduction transcending the set of predicates. To sum up, the intuition that makes change intelligible is not that of an underlying matter-like substratum accompanied by a concept/set of predicates, but of a form-like nature involving change. This temporal sense of ‘being per se’ is absolutely central in the Discourse metaphysics. It allows Leibnizian substance to overcome the “Heraclitean” challenge and it marks an important dimension of substantial unity, against Cartesian extension. After the example of ‘moy’ in Paris and Germany, Leibniz observes: Some philosophers, who have failed adequately to understand the nature of substances or of indivisible beings, or beings per se, have in ffact thought 36

A VI.4, 556.

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that nothing remains truly the same. It is for this reason, among others, that I conclude that bodies would not be substances if there were only extension in them.37

A decisive distinction between complete beings and incomplete ones like extension lies in the capacity of the former of bringing with and giving account of its own changes in time. These hints have been rather overlooked by Leibniz’s interlocutors and interpreters, who have privileged the problem of spatial parts.38 In any case, the logico-ontological structure underlying this temporal dimension suggests that we have to modify our usual way of understanding both (1) what a ‘concept,’ or an ‘essence’ is, in order to embrace temporal properties; and (2) the relationship of this concept/essence with the ontological dimension of subject. I will begin by considering (1). Leibniz and de Volder on Essence and Temporal Predicates The solution to the problem of change put forward in the Notationes is twofold, relying on (a) the notion of deriving from a nature on one hand and (b) a theory about the nature of time on the other. A part of the later debate with de Volder could shed some light on the general problem raised by (a). Once again, the discussion arises from a wider question at the boundary between metaphysics and dynamics, i.e. de Volder’s insistent request for an a priori explanation of the activity of substance. The geometric essentialism of extended substance is somehow at pains to explain change, hence the origin of modifications within the attribute ‘extension.’ At the same time, the Dutch scientist is not ready to accept Leibniz’s solution. When Leibniz claims that “finite substance essentially possesses an internal tendency to change,”39 he objects that we cannot make any sense of a nature involving change: I am firmly persuaded that all that follows from the nature of a thing always belongs to it in the same and unchangeable manner; nor can it be 37 38

39

GP II 53–54 (L 335). See also DM 12. But this strand of thought emerges in the following discussion with Arnauld on substantial forms. See the preparatory draft for letter XIII: “Extension is an attribute which cannot make up a complete entity, no action or change can be deduced from it; it expresses only a present state, not at all the future and past as the concept of a substance must do. When two triangles are found linked together, one cannot deduce therefrom how the link was made. For that can have occurred in many ways, but anything capable of having many causes is never a complete entity.”, GP II 72 (Mason 88–89). It is interesting to find here the old example of 1676 De Principio individui. GP II 252 (L 531). Here also, Leibniz contrasts this property of individual substances with incomplete i.e. abstract notions.

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subtracted from it, because it has a necessary connection with it. As a consequence, a change which is produced while nature remains the same is surely due to some external cause.40

De Volder’s statement is a good example of the classic view, according to which the essential properties of a are those which always (i.e., at all times) belong to a and cannot be lost while a still exists. In the Aristotelian tradition, largely shaped by the so-called “statistical view” on modalities, necessity de re and omnitemporality tended to coincide. In the Cartesian brand of essentialism, inspired by the conceptual necessity of mathematical essences, the omnitemporal attribution of A is no longer a sufficient condition, but it does not cease to be a necessary one for speaking of A as an essential property. Change and time-indexed predicates are excluded from the scope of essential attribution. On the other hand the Aristotelian tradition, with its idea of physis, made room for the inclusion of some general patterns of change within an essentialist epistemology. The essence of natural kinds, indeed, being embodied in individuals as their substantial form and ruling their teleological development (e.g., from the seed to the oak), involves the main lines of this development, passing regularly through some stages or phases. To this, some dispositional properties correspond, and there are also a lot of other permanent dispositions. But nature surely does not involve any particular fact actualizing these dispositions, least of all its date of occurrence: the ability to laugh is surely included in Socrates’ nature, but the fact that he laughs at March 1 of 405 B.C. does not. For its own part, Cartesian thought, being strongly committed to the criticism of Aristotelian potentiality, had great trouble in making sense of dispositional properties in general. In this framework, Leibniz’s stance is decidedly original. On one hand, the “logical” view of necessity he endorses leads him towards a sharp distinction between omnitemporality and necessity de re, and towards the strongest exclusion of transitory predicates from essence. On the other hand, he is willing to preserve a relevant sense of ‘nature’ inspired by Aristotelian essentialism, making room for change and dispositional properties. We know that the complete concept means to express precisely this idea of physis, and the program of development it imposes on a substance is not conceived of in a general way, as is the case with Aristotelian form, but it claims to determine the detail of the individual’s change. All this is the root of some radical incomprehension or misunderstanding in Leibniz’s discussions on substance and complete concept with Cartesian interlocutors like de Volder and Arnauld. They are prepared to make sense of conceptual inclusion only on the model of mathematical 40

GP II 256.

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essences. As a consequence, when faced with Leibniz’s theory of complete concept, they oscillate between the two poles of taking it as a unheard-of modal scandal or as a quite innocuous metaphor. So, let us consider Leibniz’s distinction between two levels of ‘derivation from a nature’ and de Volder’s perplexed reaction. Leibniz does accept to reinterpret the properties-modifications distinction in a temporal way, while stressing that also temporal modifications do follow from the nature of a thing: One should distinguish between the properties on one hand, which are perpetual, and the modifications on the other, which are transitory. All that does follow from the nature of a thing can follow either in a perpetual manner or at certain times; and in the latter case, it can follow either immediately, i.e. in the present, or through some preceding state, as is the case with a future modification.41

Notice that Leibniz sometimes refers to perpetual properties as the properly “essential” ones.42 In the debate on the so-called superessentialism, some scholars have tried to dispute its attribution to Leibniz by relying precisely on this temporal sense of the essential-accidental pair. The champion of superessentialist interpretation Mondadori, however, was quite right in pointing out the non-relevance of this distinction for the debate. There is in Leibniz, to be sure, such restricted sense of ‘essential’, that has to be connected with the essential predication typical of incomplete objects; nevertheless (and leaving aside terminological oscillations) the sense which is relevant to the superessentialism debate is just the one according to which also temporal modifications (or changing properties) are included in the nature of the thing. Leibniz’s idea might be expressed in our language as the tenseless predication of a series of dated properties of the type “being-in-Paris-in 1676”, “being-in-Germany-in1679”. Bear in mind, however, that the dates should be basically reduced to some non-temporal order among the states.43 Another interesting terminological variation—which does not alter, however, the gist of the argument—can be found in the exchange with the Benedictine monk Francois ¸ Lamy. As a good Cartesian, this stressed that “what is 41 42

43

GP II 258. For instance, in the selfsame de Volder correspondence, to justify the dynamico-metaphysical inference from ‘derivative forces’ to the primitive ones: “Every accidental i.e. changeable must be a modification of something essential and perpetual. . . ” GP II 270 (L 537). For the temporal meaning of “essential” and superessentialism, see Mondadori, Leibniz and the Doctrine of Inter-World Identity. For a discussion on time-indexed predicates see Mates, Philosophy of Leibniz, 88–89 and 91–92. According to him, to attach a time index to the copula captures Leibniz’s stance better than to attach it to the predicates. This matches well, indeed, with Leibniz’s way of speaking in several passages, like the end of the De Affectibus.

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drawn from the nature or essence of a thing, must endure as long as the thing itself.”44 Leibniz replies that “what is essential is commonly distinguished from what is natural. . . properties are essential and eternal, whereas modifications w can be natural, although they are changing.”45 To find a kind of conceptual inclusion different both from logical necessity and arbitrary connection does coincide, indeed, with a re-invention of the concept of ‘nature’. In order to better illustrate this type of inclusion, Leibniz does rely on two analogies we are already familiar with at least since the time of the De Affectibus: the dynamic, which is documented at the level of physical science concerning quasi-substances, and the mathematical. In the dynamic case, the future position of a body at time t1 can be now derived from the law of its motion, although the body will occupy it just only at t1 ; analogously, “all works as in the case of the laws of series or of the equations of lines, where some initial portion of the series or line is sufficient to deduce the whole of the following development.”46 Completeness, Succession and the Nature of Time De Volder’s choice of triangle as a paradigm for essence makes Leibniz’s rejoinder easy: de Volder, like Arnauld before him (we will see this in the next section), would miss the type of inclusion Leibniz has in mind, because he would not go beyond the level of abstract objects: You do not distinguish between universal natures and singular ones. From universal notions eternal properties follow, from singular notions temporal ones . . . All singular things are successive . . . nor is there anything permanent, but the law itself that involves the whole series and that corresponds within single things to the whole law of the universe.47

In the same letter, Leibniz goes on to suggest a radical sense of this ‘succession of things’, that weakens the permanence of a substratum to the advantage of the mere permanence of a law. Once again, de Volder cannot understand the ontological import that Leibniz assigns to conceptual inclusion. He is far from challenging the need individual concepts have to include temporal predicates, as a matter of fact, because the corresponding individuals do have 44

45

46 47

Addition a` l’explication du syst`e` me nouveau, a` l’occasion d’un livre intitul´e Connoissance de soy mˆme, GP IV 582. Ibidem. In the same page, Leibniz stresses that ‘natural’ is meant here in a special sense, connected to the complete concept. GP II 258. GP II 263.

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such properties. But this inclusion is for him extrinsic and deprived of any de re necessity: hence, it would be unable to account for the alleged internality of a principle of change.48 In his last counter Leibniz on one hand refers to the difficulty of accounting for change through intersubstantial causation. This is somehow a movead hominem, however: for him, spontaneity is a corollary, not a ground, for the fact of possessing a complete concept. On the other hand, he makes an interesting allusion to a deeper constitutive relation (essentialis ordinatio) of individuals to time: The essential relation of singular things to time and place has to be understood as a relation to the things that are contained in time and place, be they close or far; and these contents are to be expressed by every singular thing, so that one could read in it the whole universe, provided he is a reader of infinite penetration.49

Moving from the relation to times towards the relation to the things contained in times, Leibniz alludes in a discreet but clear manner to his theory according to which time is not an absolute thing, but a relational order among possibly existing things. The order of the temporal system is dependent on the order of the history system, i.e. on the concrete contents of time: things and their changes. De Volder’s assumptions make him highly sensitive to the difficulty of capturing the temporal dimension of development in a concept. He turns Leibniz’s examples to his own advantage: the inclusion of terms in the law of a mathematical series, he observes, is indeed a conceptual, but not a temporal one: hence, it does not involve any real change or succession, any more than any other connection of logically ordered properties does: “In the nature of a series all terms are included in one and the same way, nor can we conceive a true succession in it.”50 Leibniz seems to have missed the force of this objection, insofar as he simply relies on his own wide concept of mathematical series, to stress the non-uniformity of series itself. Finally, he admits the distinction between the general concept of series and the temporal succession, but he considers temporal order a further specification of conceptual order: 48

49 50

“To explain how singular things differ from universal ones, you say that ‘singular things are essentially related to certain parts of time and place, which universal notions disregard’. I agree. But I insist: what does this relation do, in order to explain why from singular things change follows. . . ?” GP II 274. GP II 277–278. GP II 260.

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I do not say that every series is a [temporal] succession but only that a [temporal] succession is a series, which has in common with other series the property that the law of the series shows where one must arrive in following its progress; in other words, that there is an order in which its terms will proceed, once the beginning and the rule of series are given, be this order only a natural or also a temporal one.51

Let me spend some words on the assumption (b) concerning the nature of time: “the nature of time, in fact, amounts just to the fact that contradictory predicates can be true of one and the same thing at different times.”52 We have already found this idea of time as a powerful means to neutralize contradiction, within Leibniz’s general study on identity. Now, it is directly connected to the logical structure of complete concept. Maybe this strong link between contradiction and time does prevent, in Leibniz’s mind, other forms of ‘contradiction’—or better, of weakening of the IndId—like counterfactual identity would be. The proper way for the same subject of sustaining contradictory predicates is to shift them into temporal succession. This suggestion, coming from the deep logico-ontological structure of temporal things, could shed some light on the puzzling connection, in the Arnauld correspondence, between the foundation of transtemporal identity and the denial of the counterffactual one. Surprising as it may be, Leibniz’s stance, regarding the possibility of mutually exclusive predicates for the same individual, turns out to be ultimately rather close to an idea that was typical of the ancient temporal view of modality.

3.2. Concept, Essence and the Subject of Change Essence as a Law: Doing without Substrata? In Leibniz’s mature substance theory, only the possession of a nature expressed by the complete concept, and not an underlying matter-like substratum, does allow one to talk about a true continuant. What about simply doing without the substratum, then? The formal character of the identifying element seems to contemplate the possibility of a continuant without a substratum. Commenting on the idea of substantial notion as a law, Russell observes that its coherent development would have been giving away the idea of substance as a substratum.53 Surprising as it may be, Leibniz himself does not refrain, in 51 52 53

GP II 263. A VI.4, 556. “It would have had a purely formal unity; there would not have been an actual subject, the same at all points of time.” (Crit. Expos., pp. 48–49).

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some places, from taking this step. A passage in his discussion with de Volder shows that the sequentialist alternative is quite open for him, also beyond the field of bodies or corporeal substances to which it is normally confined: If someone wants to claim that God continually recreates other substances that substitute earlier ones, so that substances do not remain the same, he will raise a purely terminological question. Nor is there any ground in the things themselves, that allows us to settle the question; but that alleged subsequent substance will be simply taken as the same, so long as the same law of series persists, i.e. a law ruling a continuous and uniform passage from one state into another one: what makes us conceive the view of one and the same changing subject. Now, the very fact that there is a permanent law, which does involve the future states of what we conceive to be the same, is just what constitutes the same substance, in my opinion.54

The verificationist postulate is at work: if the corresponding phenomena are indiscernible, the dispute between the two conceptual interpretations is undecidable, and the question turns out to be a merely linguistic one. The language of permanence or sameness has to be privileged, because it reflects the continuity of a change which accords with a rule. In this way, the sequentialist ontology is implemented by the nomological element. Surely, this and similar passages should be balanced by other ones: for example Leibniz, in discussing in the Theodicy a radical ontological interpretation of continued creation, observes that “so far, people have believed that accidents do change, while the substance remains the same; I for myself am persuaded that one should stay with this traditional doctrine.”55 His ontology cannot do without the ontological dimension of subjecthood. But the point is exactly that this dimension is no longer satisfied by the old substratum model, but by the primitive law itself. The Aristotelian Connection: Subject, Matter and Essentialism Leibniz’s way of coping with subject-essence polarity is particularly evident in an interesting and little known draft that has been published in the Vorausedition r under the title De Mutationibus.56 It belongs to the later period 54 55 56

Letter of January 21, 1704, GP II 264. Theodicy, § 393, GP VI 351. VE (N 55), 172–175. See on this Di Bella, Leibniz on the Subject of Change. On De Mutationibus (Vorausedition, N. 55), in Individuation, Sympnoia panta, Harmonia, Emanation. Festgabe f¨ F fur Heinrich Schepers zu seinem 75. Geburtstag. Hrsg. von Klaus D. Dutz, Nodus Publikationen, M¨u¨ nster, 2000, pp. 23–48.

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of the NE, hence it reflects an approach to the substance theory that, though being not contrasting with, surely is different from that of 1686 for the emphasis laid on other aspects. On the other hand, it is clearly tied to a train of thought we are well familiar with, insofar as it opens with the distinction between being (ens) and concept (terminus), to handle the semantics of abstract talk: “A Term is the predicate of a Being. If A is a Being, and we say ‘A is B,’ then B will be a term. E.g. ‘Man is honest,’ where ‘man’ is a being, B is ‘honest’.”57 Special attention is devoted to the relationship between abstract terms and the ontology of change. I will return to this topic in my next section; for the moment it is enough to say that abstract reference reveals itself intractable just in relation to the phenomenon of change. It is, indeed, the linguistic device suitable for expressing real accidents, and real accidents in their turn seem to be needed in order to give an account of change itself, by their arising and perishing. As a consequence, Leibniz can apply to the semantic analysis of abstract terms a kind of Criterion of Change one could make explicit in this way: a a concrete term T, predicated of a thing X, is allowed to have an abstract counterpart T’ iff T can cease to be true of X, being substituted by not-T, while X is still existing. But if we take together the Criterion of Change and w the traditional Essentialist Claim, we are no longer entitled to adopt the typical language of essences, or at least its abstract version: w about . . . the suggestion of not allowing for the formation of abstract what terms derived from essential concrete predicates, such as Appiety, humanity, animality? There is indeed no being which persists, while ceasing to be Appius, or to be a man, or to be an animal.58

For ‘essential properties’ here is meant the expression of what a thing properly is. Semantically, we have to do with abstract nouns derived from the names of natural kinds (genera and species) and even from proper names. As regards the latter (“Appiety”), we have already found them (“Lentuleity”) in the eighties, where Leibniz reserved to such terms a place in his categorial scheme, as w the abstract counterpart of the ‘complete being’ reflected into the individual concept. But now, all these abstract devices for referring to essence are suspect. So much the worse for abstract talk, one could say. But the semantic problem introduces us to an ontological one concerning the metaphysical structure of substance. There is historically to hand, Leibniz observes, a view which is willing to deny the Essentialist Claim: 57 58

VE 172. VE 173.

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It should be observed, that one can doubt whether there is truly no being which while subsisting in itself ceases to be Appius, or to be a man, or to be w an animal. Maybe some people will contend that such a Being, or subject, turns out to be just matter; while Appiety, humanity, animality are forms which can be taken away while the same subject persists. And in their w view Appiety, humanity and so on will be accidents of that subject . . . and this will be, I imagine, the opinion of Democriteans.59

Leibniz’s concern in contrasting ‘Aristotelians’ and ‘Democriteans’ is not an historical one; nor is he referring to the atomistic model in the strict sense. Rather, he has in mind a scientific paradigm which relies only on matter and motion. And this was nothing but the inspiring view that seventeenthcentury new science and philosophy opposed to the traditional Aristotelian one. Needless to say, it is a controversy in which he himself is deeply involved throughout his entire career, from the youthful adhesion to the mechanical explanation of nature to the 1686 philosophical rehabilitation of the ancient ‘substantial forms’. In order to understand what is at stake with the “Democritean” objection, it is worth recalling very sketchily some traits of the Aristotelian concept of substance, passing from the Categories theory to the more sophisticated one of the middle books of the Metaphysics. The true complication in respect to the ontological scheme of the Categories lies indeed in the introduction of the problem of matter, hence in considering substance no longer as a compact logical subject, but as a compound of matter and form. This leads to questioning the criterion of the ultimate subject which played the prominent role in the Categories: Metaphysics Z3 shows that, if we try to isolate the ultimate subject through a procedure of stripping away of all descriptive determinations, then we are left with bare matter, which is not a good candidate for substancehood. Leibniz goes on to explain that Aristotelians seek to avoid the unwelcome promotion of material substratum i.e. of bare matter to the dignity of substance by drawing a sharp distinction between the “subject of predication” (subjectum praedicationis) i.e. the individual on one hand, and the “subject of inhesion” (subjectum inhaesionis) or material substratum on the other, with the corresponding forms they can assume in change. Whereas an accidental form is predicated of a being which is already constituted (the individual), a substantial form gives being and identity to its subject (matter). The model of the underlying substratum, however, is extended also to substantial change. Here also, something i.e. matter survives the destruction of substance and pre-exists its generation, entering into the compound. But, then, 59

Ibidem.

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Aristotle’s distinction between substantial and accidental change is liable to the ‘Democritean’ counter: But then the Democriteans will insist: why do Aristotelians not admit that the same being persists, being now a man, now a non-man, or in other words: why what constitutes man within matter is less accidental than what constitutes honesty, knowledge, and so on? Surely, according to Democriteans, the two situations will not differ, if not for the fact that the one [form] is a bit more permanent than the other; but ultimately they all simply arise from the figures and motion of matter.60

Leibniz’s Way Out: The Unperishability of Substance Only at this point, after developing the dialectic between hylemorphism and materialism, and showing that the former has to surrender to the latter, if it takes the role of matter in the traditional way the School takes it to be, Leibniz advances his own solution as the only possibility of overcoming the aporia and avoiding the materialistic conclusion: Now, they will never be able to solve this knot by appealing to the commonly accepted philosophical principles [with this expression Scholastic principles are usually meant], nor they will provide any account for the distinction between a substantial and an accidental form. Therefore, one should rely on my thesis, according to which substantial form is something everlasting, which can never be separated from its subject.61

Leibniz holds the thesis of the ungenerability and unperishability of substance at least from the first exposition of his ‘mature’ philosophy in 1686. In DM 9 he maintains that substances can be produced and destroyed only by creation and annihilation respectively, i.e. only by a power which is reserved to God’s direct action. Also this thesis is counted among the paradoxical corollaries of the complete concept theory: “From these considerations [i.e. from the theory of individual concept] there follow a number of important paradoxes . . . it follows also that a substance cannot come into being except by creation, or perish except by annihilation. . . ”62 The rationale for this consequence, that is not argued for explicitly, seems to be that two logical subjects cannot collapse together, nor can one logical subject be split into two different ones: hence, generation and corruption cannot concern ultimate subjects, or primary substances. 60 61 62

VE 174. Ibidem. DM 9, A VI.4, 1541 (GP IV, 433; L 472).

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Now the theory of DM 8, if compared with the two stages of the Aristotelian substance theory, remains located within the horizon of the Categories model. As we have seen, the key criterion for substancehood is being an ultimate subject; and this requirement is fulfilled by ordinary individuals like ‘this man’ or ‘Caesar’: maybe better by their souls (think of the shift from the ‘haecceity of Alexander’ to his ‘soul’ in DM 8). The problem of matter remains wholly extraneous to this approach. The question whether Leibniz does seriously consider the case of composite substance in this phase of his philosophical development has been intensively debated also very recently, but I do not want to go into this. Anyway, we have seen that the conceptual interpretation of predication allows him to introduce substantial form as an immediate corollary of this theory. Now, this is an element that goes beyond the conceptual setting of the Categories ontology. As a consequence, we are faced with a slightly paradoxical situation: the ontology of the Discourse already appeared as an essentialism without secondary substances, i.e. without general essences; now, it appears as a hylemorphism without matter. We well know, however, that the dimension of the hypochemeinon h is never absent in the Discourse style expositions, which make abstraction from properly physical considerations. It is precisely the aspect for which the subject was qualified in the Characteristica verbalis as ‘metaphysical matter’. Thus, Leibniz always maintains a conceptual distinction between subjectum inhaesionis and subjectum praedicationis; but the point he wants to stress is that the two can be in no way separated, unless by an extreme abstraction act.63 Transmigration r of Souls: Appius and His Self, or Predication de re and de se The identity of the two dimensions of subjecthood is Leibniz’s way of subscribing to the Essentialist Claim. That is to say: a substance a is this X (an Ens, or a subjectum inhaesionis) that cannot cease being an a (a such-and-such, a subjectum predicationis). But this general constraint can be fulfilled by different intuitions of what counts as an essence. In the De Mutationibus Leibniz, immediately after advancing his own solution of the substratum dialectic, tests it through the thought experiment of metempsychosis: 63

“. . . substantial form cannot be separated from its subject. Hence one might wonder, whether there are truly two incomplete beings—the subject and the inhering substantial form—or not. Though lacking an apt principle to prove it [such as the principle of change did], we can anyway conceive of two items, i.e. a principle of passion as subject, and a principle of action in the role of form.” VE 175.

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. . . who w is Appius, or a man, never ceases to be Appius or to be a man, though maybe he could change his name sometimes. This, I mean, provided that for “man” is meant “rational animal”, and for “Appius”, “this individual”. If we imagine a moderate form of metempsychosis, i.e. a transmigration of the soul from one man to another man, then “Appius” will be a term per accidens, like “learned”; that is, Appiety will be an accidental form; from Appius, in fact, Valerius could have come, so that the same who once was Appius, now is Valerius. And if we were prepared to accept a radical form of metempsychosis, then even “man” will be a term per accidens; w what was once a man, indeed, will become a pig. Better: if we only concede the possibility of these transmigrations, then Appius and man will be beings per accidens. If, on the contrary, this is not possible, we shall have to say that Appius and man are beings per se.64

What might appear to us a highly extravagant fancy was seriously discussed in the European culture of the age, and more precisely by people and circles Leibniz was well acquainted with. In any case, the text has to be put in context with the seminal Chapter II.27 of Locke’s Essay, w where the same hypothesis of metempsychosis is employed by the English philosopher to weaken the link between the metaphysical identity of a substance and the moral one of a conscious person. Leibniz contemplates, though being skeptical about it, the possibility of both weak (i.e. intraspecific) and radical (i.e. interspecific) transmigration. As a result, ‘Appius’ and ‘man’, respectively, would turn out to be nothing more than ‘accidental terms’. There is, however, a real sameness which has to be preserved through any meaningful transformation, and assures w the holding of the Essentialist Claim: “although we concede that ‘Appius’ and ‘man’ are terms per accidens, nevertheless I, You will be no Beings per accidens, nor can we be produced except by creation or destroyed except by annihilation.”65 In the transmigration hypothesis, then, the proper name of an individual substance (but we, who are acquainted with Leibniz’s theory of proper names, could go a bit further and associate some description with it), could be given up, whereas the essential core which inseparably expresses the ontological dimension of the ‘subjectum inhaesionis’ would be still captured by indexical expressions like ‘I’ or ‘You’, which are found elsewhere (see the introductory section of the Generales Inquisitiones) among ‘primitive terms’. Given all this, the reader could scarcely resist the suggestion that Leibniz, moving from ‘Appius’ to ‘I’, or ‘You’, is reversing the primacy of ‘logical’ foundation on 64 65

VE 174. Ibidem.

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inner-sense experience, overtly claimed in 1686, and turning to an Arnauld style non-descriptive identification of self. Despite this fascinating appearance, I think that what Leibniz has in mind here is slightly different and can be grasped from the comparison with NE II.27. Referring there to Apuleius’s ass, he writes: I would not quarrel with someone who said that in the Golden Ass there is still the same “self ” or individual (because of the same immaterial spirit), as well as the same Lucius or person (because of his awareness of this I ); but that there is no longer a man. . . . 66

Leaving aside here the question about the essence of ‘man’, consider the pair: on one side, ‘self’ and ‘individual’ go together, and they are clearly used to express the ontological side of sameness. The indexical devices are employed to pick up the soul, or the ontological self, f as the real bearer of sameness. On the other side, the proper name ‘Lucius’ is used to express the ‘person’, who is linked (in partial agreement with Locke) to self-consciousness and memory. If we apply this interpretative key to the De Mutationibus, then, the ‘Appius,’ which could turn out to be a merely accidental term, designates (or expresses) a ‘person’, which is the object of ‘consciousness,’ while ‘I’ and ‘You’ designate the ontological Self. Leibniz has shown himself ready to treat as accidental many terms which are commonly held as essential. The unbreakable essential core, however, maintains a double objective tie: with a possible consciousness on one hand— we know from NE II.27 that every hypothetical gap between metaphysical and moral identity has to be ultimately filled—and with predicative completeness on the other: the logico-ontological subject cannot be but one and its concept embraces all its predicates. At least since 1686, this unity grounds the unperishability of substance through all its conceivable transformations. Paradoxical as this may sound: on one hand, so far as we know, even properties like ‘having a human corporeal figure’ might turn out to be accidental—in the temporal sense of “accidental”. On the other hand, from a radical metaphysical 66

NE II.27, A VI.6, 235 (GP V 218; transl. Remnant-Bennett, italics mine). Our point is confirmed below: “As far as the Self is concerned, it is good to distinguish it from the appearance of the self and from consciousness. The self makes the real or physical identity, whereas the appearance of self—when accompanied by truth—adds personal identity.” GP w V 219 (A VI.6, 237; italics mine). At the same time, Leibniz defends against Locke the ultimate harmony (hence the impossibility of an everlasting divorce) between ‘moral’ and ‘real’ sameness. Notice also: apperception effectively is the privileged way of grasping the persisting substance; but the point here is that what is grasped is something independent from our perceiving it, and this ‘thing’ is called ‘self’.

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point of view, all that does actually happen to the substance is not accidental (in the non-temporal sense), hence is part of its identity. The Thesis of Marks and Traces Another corollary of the complete concept theory concerns the temporal dimension of individual substance. According to DM 8, w when we well consider the connection of things, it can be said that there are at all times in the soul of Alexander traces of all that has happened to him and marks of all that will happen to him . . . 67

And DM 14, illustrating the spontaneity of substance: . . . all our future thoughts and perceptions are only the consequences, however contingent they may be, of our preceding ones, so that, if I were capable of considering distinctly everything that is happening to me or appearing to me at this hour, I could see in it everything which will ever happen or appear to me.68

The two statements are slightly different, insofar as the first says that future and past properties are involved ‘in the soul’ as a whole, while the second refers them to each successive state of the soul’s life as they arrive. Leibniz seems to consider them as equivalent. As usual, the idea is illustrated according to both dynamical and psychological considerations. Remember the early contrast between body and mind in the Hypothesis physica nova. The mind’s capacity to conserve its previous conatus and to plan consequently its future is the remote hint towards the idea of marks and traces. In the De Affectibus both approaches were assimilated. The correspondence with Arnauld connects the thesis to the foundation of transtemporal sameness on the complete concept: future predicates are contained by the individual substance as “laws”.69 The remark will find its full development in the NE, where marks and traces 67

68 69

A VI.4, 1541 (GP IV, 433; L 308). DM 9 confirms this implication, introducing it as the temporal aspect of the general involvement of its world by a complete concept. See A VI.4, 1542 (GP IV 434, L 308). A VI.4, 1551 (GP IV 440; L 312). Italics mine. ““And seeing that since the beginning of my existence it could truly be said of me that this or that would happen to me, one must admit that these predicates were laws contained in the subject or in the complete concept of me which makes what is called myself, which is the basis of the connexion between all my different states. . . ”, Remarques, GP II 43 (Mason 47).

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themselves are said to constitute the sameness of substance70 w while being presented as dispositional facts (the psychological interpretation of “petites perceptions” prevails here). Anyway, the thesis of marks and traces remains a constant theme for Leibniz, and the best realization of the intuition according to which a complete being is “laden with its past and big with its future”. In the last part I will test the ability of the different interpretations of complete concept to give an account of this temporal aspect of substance. Note: A Leibnizian Circle? Also in the De Mutationibus, the sameness of the changing substance has been finally anchored to the bedrock of inner experience, despite Leibniz’s claim that its ultimate basis lies in the logical structure of substance. Is there some tension between these two poles of Leibniz’s view? In a slightly neglected remark, Russell suggested that this is the case, so that Leibniz’s view on substance and time would be committed to a kind of vicious circle: Is the reality of time assumed as a premise and denied as a conclusion? A substance, we have seen, is essentially a subject persisting in time. But by the doctrine that all the states of a substance are eternally its predicates, Leibniz endeavors to eliminate dependence upon time. There is, however, no possible way, as far as I can discover, in which such an elimination can be ultimately effected.71

Russell is alluding here to the view of complete concept as a set of tenseless ffacts, and to the reduction of time to a more basic logical structure. In order to fully appreciate this aspect, we should take into account the causal aspect of the complete concept, hence the inclusion in it of the old metaphysics of conditions.

Post-Script. Twenty Years Later: De Volder (and Others) Facing Individual Concept In Section 2 I have taken into account Leibniz’s discussion with de Volder on the status of abstract concepts and their claim to express substances. The further discussion on the relationship between time and concept, referred to 70 71

See NE II, Ch. 27, A VI.6., 239 (GP V 222). Russell, Critical Exposition, p. 51.

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above, can be considered a continuation of it.72 Also in his coeval discussion with Bayle on his “new system”, Leibniz emphasizes the ‘incomplete’ i.e. abstract character of the notion of matter familiar to his interlocutor, in order to stress its contrast with substance as regards the respective capacity of accounting for change: Matter is an incomplete being, lacking in a source for its actions . . . Things are quite different for the soul or the mind. Since the latter is a true substance or a complete being, which is the source of its actions, it remembers, so to speak (admittedly, in a confused manner) all its preceding states . . . 73

Cartesian essentialism does not capture the peculiar dimension of Leibniz’s substance concept—i.e. of individual concept. Now, Leibniz does not fail to emphasize the link of this fact with the understanding of conceptual containment. He relies exactly on this to explain his rejection of the abstract view on substance of Descartes and Spinoza, and the origin of their ontological mistakes: no substance with but one attribute can be conceived, nor can we, so far as I know, conceive of an attribute or simple and absolute predicate by itself. I know that the Cartesians have felt otherwise about the former point, and Spinoza about the latter, but I know also that this resulted from a lack of adequate analysis, the touchstone of which is a demonstration of predicates from the subject. For every demonstrable proposition whose demonstration we do not have must contain an insufficiently analyzed term.74

This passage—one of the few explicit allusions to the containment theory outside the cronologico-textual context of the Discourse metaphysics of the eighties—suffices to show that this perspective is far from abandoned by Leibniz, contrary to what some scholars have suspected. De Volder for his part can well subscribe to Leibniz’s containment principle, but he cannot imagine how to pass from this logical truism to any relevant ontological claim. Or also, he can well admit that our concept of an individual 72

73

74

In the de Volder correspondence, Leibniz develops also the connection between criticism of abstract mathematical notions and IdInd, on the occasion of his criticism of the Cartesian view of bodies as modifications of extension. See Leibniz to de Volder, letter XXV, June 1703, GP II 249 (L 528–29). GP IV, 543–44. This is the place where Leibniz connects his view with the mind-body contrast of his Hypothesis physica nova. See above, sect. 3.3, note 45. Leibniz to de Volder, letter XX (April 1702), GP II 239 (L 526).

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thing does involve its connection with others in a spatio-temporal framework, but he does not succeed in understanding how this fact could be constitutive of its identity: No matter how this relation can be, a thing does not possess anything beyond its own nature . . . A spherical body is the same, no matter in which time or place it is located, and nothing follows from it, except what w is included in the nature of a sphere.75

Leibniz’s reply—where the idea of expression is taken into account— explicitly relies on the complete concept view: Singular beings do involve infinity, while by framing universal concepts we take into account only certain aspects, and leave aside innumerable others. Thus only in the case of singular things do we have a complete concept, which involves also changes.76

In this case also, we have a discreet but unmistakable allusion to the standard view of the Discourse, taken in its whole ontological import. 75

76

De Volder to Leibniz, letter XXXII, November 1704, GP II 273–74. See also letter XXX, GP II 266. Leibniz to de Volder, letter XXXIII, GP II 277. See above note 49.

Section 6 Categories (2) The Theory of Conditions in the Categorial Framework

Chapter 1. Consequentiae. A Theory of Causal Temporal Order The Square of Existential Oppositions: A Logic for Existence In his writings from the seventies, the language of requisita r was adopted by Leibniz to sketch the outline of a metaphysics of conditions. The need to distinguish inherence from causality on one hand, and notional from causal involvement on the other, provoked a general rethinking of that conceptual setting. At the same time, the study of causal determination was applied to the temporal series of substance states. Now, the materials and results of these inquiries are settled in the categorial tables of the Eighties, where an important section is devoted to the study of ‘Consequences’ (Consequentiae). This heading echoes, on one hand, a traditional and wide-ranging section of late Scholastic logic, where also some pieces of propositional logic had been preserved; on the other and more closely, the semi-formal theory that constituted the last and most abstract layer of the De Affectibus. The core notion of this section of the tables is exactly that of requisite r ; but the mature theory sketched here, besides having a markedly formal character, in the sense of a logic of conditions, or better of a formal ontology, is well aware of the critical problems Leibniz already faced in his rethinking of rationalistic causality. Let me consider again two texts that I have indicated as paradigmatic for the undertaking of categorial inquiry, the De Notionibus Omnia quae Cogitamus Continentibus and the cognate Enumeratio Terminorum Simpliciorum.1 The 1

Respectively, N 98, A VI.4, 398–405; N 97, A VI.4, 388–397.

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meta-categorial classification of the first presents a compact conceptual block of ‘Consequences,’ after those of ‘Reality’ and ‘Variation’: “Consequences, and the things among which consequences hold”: Incomponibilia (those that cannot be true together) ∼ (A  B) Inconnegabilia (those that cannot be false together) ∼ (∼A  ∼B) A v B Opposita (those that cannot be either true or false together) ∼ (A  B) & (AvB) ∼A Conditio/Conditionatum ∼B A Inferens/Illatum B Leibniz uses letters here to express his schemes of inference. How are these letters to be interpreted, that is to say: what are the items (the Latin text presents the neutral adjectival form) among which consequences hold? The Scholastic logic of consequences was about propositions. Also the De Affectibus defined ‘opposites’ as ‘those which cannot be true together’. In Leibniz’s mind, however, variable letters do not stand directly for propositions, but rather for the things (let them be individuals, or states or properties of them) whose existence is stated in the corresponding propositions: w If, given the proposition “A exists”, the proposition “B does not exist” follows, then A and B are incompatible (incomponibilia) . . . If, on the assumption of the proposition “A does not exist,” the proposition “B does not exist” follows, then A will be the condition, B the conditioned.2

Therefore, things—and the corresponding ‘terms’, or concepts—play the role of conditions, opposites and so on. Parallel texts make use of the terminology of ‘Incompatibilia’, and also—as a synonym for ‘inconnegabilia’—of ‘incontollibilia’ or ‘incondestructibilia’, the last pair being more apt for expressing mutual real r opposition, whereas the terminology of ‘inconnegabilia’ is closer to expressing propositional opposition.3 Anyway, these terms and the related propositions stand to each other exactly like the propositions of the Aristotelian syllogistic square. Incomponibilia behave as contrary, inconnegabilia as subcontrary, opposites as contradictory. While the relationships in the syllogistic square are properly logical ones among quantified sentences, 2 3

Enumeratio, A VI.4, 389. Some penetrating remarks on the origin of this terminology in Leibniz’s metaphysical drafts in G. Roncaglia, Modality in Leibniz’s essays on Logical Calculus of April 1679, St. Leibn. 20/1 (1988), 43–62.

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however, those in the Leibnizian square are ontological ones, holding true to a large extent on extra-logical grounds. The construction of an ontological opposition square, modeled on the logical one, was not a novelty. The ontological relations of opposition had been constantly studied in the tradition. From the De Affectibus, we know that Leibniz’s attention was attracted by real oppositions within the dynamic model. Accordingly, in the tables he stresses that there can be more than two incomponibilia or inconnegabilia, exactly as there can be several competing or concurring forces or sets of things. Only the case of opposite terms, a terminology which is reserved here for the contradictory pair, corresponds to that of logical contradiction. We already know, however, that precisely this case presents the greatest difficulties, when individual things are considered. The study of series in the De Affectibus, in fact, f has made clear that thinking of a true branching is at best problematic. The deterministic logic of conditions seems to make counterfactual statements literally false. In any case, it is quite clear that the opposition square expressed in the language of conditional inferences concerns existential relations: those “relations of connection” holding among (at least, possibly) existing things. It is worth noting that the version of the “square of existential oppositions” presented by the Enumeratio terminorum includes also the foundation of temporal order on incompatibility: If two incompatibles [to read: incompatible things, or states-of-affairs] do exist, then they temporally differ, and the one which is prior (resp. posterior) in nature, will also be prior (posterior) in time. And the one which is together [simul ] with something incompatible [incomponibile] w with a third thing, will be in its turn prior or posterior to this third thing. So, if A is together with B, and B and C are incomponibilia, and also C exists, then A will be prior or posterior in time to C. If two propositions are true, and they appear as mutually contradictory, except for one difference, that can be acknowledged only from some external relationship, then they have different temporal qualification.4

Propositions, notice, appear contradictory, whereas temporal difference actually prevents contradiction. We know that compatibility relations among states-of-affairs structure possible worlds. Now, we apprehend that a world can contain also contradictory states-of-affairs, provided they are distributed over different times. Temporal succession confirms itself as a way to expand the space of compatibility. Finally, temporal difference is brought back to “some external relation”: this matches well with the fact that temporal predicates in the tables are usually referred to the category of Position; and we know 4

A VI.4, 390.

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that this category is defined by its capacity to discern things in this relational way. ‘Antecedens reale or tantum logicum’: From Inference to Cause In the texts of categorial inquiry, the main attention is devoted to the two pairs conditio-conditionatum and inferens-illatum: in many drafts, they are the only fragment of the ‘square’ that is dealt with. The definition of ‘condition’ is given in the form of the logical skeleton of a scheme of inference (if not-A, then not-B), that captures exactly what we are accustomed to call a ‘necessary condition.’ Correspondingly, the inferens-illatum pair codifies the notion of a sufficient condition (if A, then B). Leibniz is wholly clear about the reciprocal relation of the two pairs: he remarks, indeed, that the necessary condition (conditio) can be in its turn inferred from the existence of its conditionatum, on the assumption that the consequence does hold. In this reversed inference, the conditionatum will play the role of inferens and the condition will be the illatum. Conversely, an inferred consequent (illatum) will work as a necessary condition (conditio) for the holding (existence) of its respective sufficient condition. Now, the requisitum r of the early theory of determination was defined exactly as a necessary condition for the existence of something. The logical scheme of the conditions, however, is not enough to capture the notion of ‘requisitum r ’ of the tables. In order to do this, it has to be implemented by the ‘order of nature’. So, Leibniz’s standard definition sounds: Requisite = A condition that is prior in nature Req (A, B) := Cond (A, B) and A