The Structure of Leibnizian Simple Substances John Whipple a a

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British Journal for the History of Philosophy 18(3) 2010: 379 410 ARTICLE THE STRUCTURE OF LEIBNIZIAN SIMPLE SUBSTANCES John Whipple 1. INTRODUCTION At its core, Leibniz s metaphysics is a metaphysics of substances. In his late or mature metaphysics he maintained that the created world consists in an infinity of mind-like substances, which he calls monads. 1 In the first three sections of the Monadology, a condensed statement of his mature metaphysics, he writes: [1] The monad, which we shall discuss here, is nothing but a simple substance that enters into composites simple, that is, without parts. And there must be simple substances, since there are composites; for the composite is nothing more than a collection, or aggregate, of simples. But where there are no parts, neither extension, nor shape, nor divisibility is possible. These monads are the true atoms of nature, and, in brief, the elements of things. 2 (G6: 607; AG: 213; emphasis Leibniz) 1 I take Leibniz s mature metaphysics to be largely in place by the time A New System of Nature is published in 1695. One important question concerning Leibniz s mature metaphysics that has been discussed in the secondary literature is whether his ontology countenances corporeal substances in addition to simple substances. I will bracket this issue in the present study, and focus exclusively on Leibnizian simple substances. See Robert Adams (1994, 262 307), Donald Rutherford (1995, 265 82), Pauline Phemister (2005) and Glenn Hartz (2006) for discussions of Leibniz s mature view on corporeal substance. 2 The following abbreviations are used in this paper: A ¼ Sa mtliche Schriften und Briefe (Darmstadt and Berlin: Berlin Academy, 1923) (cited by series, volume and page). AG ¼ Philosophical Essays, translated by R. Ariew and D. Garber (Indianapolis: Hackett, 1989). E ¼ Locke, John. An Essay Concerning Human Understanding, edited by P. Nidditch (New York: Oxford University Press, 1975) (cited by book, chapter and section). FC ¼ Lettres et opuscules inedits, edited by F. de Careil (New York: Georg Olms, 1975). G ¼ Die philosophischen Schriften von Gottfried Wilhelm Leibniz, edited by C. I. Gerhardt (Berlin: Weidman, 1875 90) (cited by volume and page). GM ¼ Leibnizens mathematische Schriften, edited by C. I. Gerhardt (Berlin: A. Asher) (cited by volume and page). HK ¼ Correspondenz von Leibniz mit der Prinzessin Sophie, edited by H. O. Klopp (New York: Georg Olms, 1973) (cited by volume and page). L ¼ Philosophical Papers and Letters, 2nd edn, translated by L. E. Loemker (Dordrecht and Boston: Reidel, 1969). NE ¼ New Essays on Human Understanding, British Journal for the History of Philosophy ISSN 0960-8788 print/issn 1469-3526 online ª 2010 BSHP http://www.informaworld.com DOI: 10.1080/09608781003779768

380 JOHN WHIPPLE This text makes it clear that if one wants to understand and evaluate Leibniz s mature metaphysics, one must understand his conception of the monad. Many commentators have hazarded this task, and although few have argued that Leibniz s theory of substance is true, it is generally taken to form the basis of a powerful and coherent metaphysical system. 3 But even this latter claim cannot be maintained, for Leibniz s theory of substance, as interpreted by recent commentators, is beset with serious internal problems, or so I intend to show. The issues that I shall discuss can be broached by considering two important claims that Leibniz makes concerning monads. On the one hand, he claims that they are real unities absolutely destitute of parts (G4: 482; AG: 142), but he also claims that each monad involves a series of successive perceptual states. 4 It is crucial to consider how these claims are supposed to fit together. Let us distinguish two closely related questions: Q1: What is the ontological relation between a substance and its successive states? Q2: What is a successive (total temporary) state? Although it has not been widely discussed, Q1 has received some attention in the secondary literature. Bertrand Russell, in his immensely influential study of Leibniz s philosophy, attributed a substratum conception of substance to him. 5 A Leibnizian substance, according to Russell, is an underlying substratum in which a series of successive perceptual states translated by P. Remnant and J. Bennett (Cambridge: Cambridge University Press, 1981) (The pagination of Remnant and Bennett corresponds to that of the Academy edition (A6: vi); therefore only one reference is required). RA ¼ The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672 1686, translated by R. T. W. Arthur (New Haven: Yale University Press, 2001). S ¼ Spinoza, Baruch. Ethics, translated by Samuel Shirley (Indianapolis: Hackett, 1992). T ¼ Theodicy (1710) (cited from G IV by section number). The English translation is by E. M. Huggard (La Salle, IL: Open Court, 1985). WF ¼ Leibniz s New System and Associated Contemporary Texts, translated by R. S. Woolhouse and R. Francks (Oxford: Clarendon Press, 1997). 3 Here I have in mind the recent book-length interpretations of Leibniz s metaphysics by Adams (1994), Jan Cover and John Hawthorne (1999), Benson Mates (1986) and Rutherford (1995). Catherine Wilson (1989) is a notable exception to this recent trend. Earlier commentators, particularly Bertrand Russell (1937), were more critical of Leibniz s account. Two of Russell s criticisms will be discussed in x2. J. E. McGuire (1976) is also critical of Leibniz s theory of substance. Nicholas Rescher takes a more nuanced position. Although Leibniz s metaphysics does not suffer from the outright inconsistencies attributed to it by Russell, it does exhibit significant gaps and weak spots. One can still say, however, that his metaphysical system is a tightly coordinated structure of conceptions and principles, devised and organized by one of the most informed, powerful, and logically sophisticated minds that the history of philosophy has to offer (1969, 159). 4 G4: 439 40; AG: 47/ G4: 484 5; AG: 143 4/ G4: 573 4; WF: 139/ G6: 567; WF: 196/ G6: 609 10/ AG: 215/ T: 65/ T: 399. 5 1937, 50.

THE STRUCTURE OF LEIBNIZIAN SUBSTANCES 381 inheres. The substratum conception of substance, however, has been effectively criticized by Locke, Hume, Kant and a number of more contemporary philosophers (including Russell himself). Given the problems attending this answer to Q1, it is not surprising that most of Leibniz s recent expositors have avoided attributing a substratum conception of substance to him. In rejecting substrata, however, some commentators have come perilously close to attributing an equally problematic view to Leibniz, namely that a substance is the sum of a series of successive states. No sympathetic commentator would explicitly attribute this conception of substance to Leibniz, and for good reason. A substance of this stripe would be essentially a plurality, while Leibnizian substances are supposed to be simple unities. The question thus becomes: is it possible to understand the ontological relation between the states of a substance and the substance itself in a way that avoids the pitfalls associated with both of these problematic accounts? I shall argue that some of these problems can be avoided, but that standard interpretations do not have the resources to provide a satisfactory answer to Q1. A number of Leibniz s central metaphysical views, such as his accounts of causation and diachronic identity, involve an appeal to the successive states of a monad. In order properly to understand these views, one must understand Leibniz s conception of a successive monadic state. This is precisely what Q2 asks. The standard answer to this largely neglected interpretive question is that successive states are instantaneous perceptual states. I shall argue, however, that a commitment to real instantaneous states would conflict with Leibniz s solution to the continuum problem a solution that he thought any solid metaphysics must respect. 6 The only alternative position that it appears Leibniz could affirm is that successive states are individuated at durational intervals of some finite length or other. However, this position runs foul of the principle of sufficient reason, which Leibniz praises as one of the two great principles upon which all our reasoning is based. 7 Leibniz thus appears to be forced to choose between two deeply problematic alternatives: the view that successive states are instantaneous, and the view that successive states are individuated at finite durational intervals. In either case the coherence of Leibniz s metaphysics would be seriously compromised. I shall refer to this dilemma as The Problem of Monadic States. The primary aim of this paper is to provide a forceful statement of The Problem of Monadic States. I will not, however, end the paper on a negative note. Although it must be conceded that the problem is extremely difficult, I am not convinced that it is insoluble. In the final section of the paper, I will sketch an alternative interpretive framework for the theory of monads. The leading idea of this interpretation is that successive states are distinguished 6 A6: iii: 54: 449, cited in RA: xxiii. 7 G6: 612; AG: 217.

382 JOHN WHIPPLE only in the realm of appearance they are not part of the deep ontological structure of the created world. Leibniz does not, to my knowledge, affirm this position in terms as unequivocal as these. Nevertheless, the position is consistent with the things that Leibniz does say on the subject. There are also powerful systematic reasons for thinking that it is his considered view. Perhaps the most significant of these is that it coheres with his resolution of the continuum problem and the principle of sufficient reason thereby absolving him of The Problem of Monadic States. It also allows for a clean account of the ontological relation between a substance and its successive states. What is more, the interpretation serves to elucidate an important but seemingly obscure aspect of Leibniz s philosophy his view that substances are neither spatial nor temporal. 8 2. RUSSELL S LEIBNIZ It can reasonably be said that Bertrand Russell s A Critical Exposition of the Philosophy of Leibniz set the agenda for contemporary interpretations of Leibniz s philosophical system. Russell is perhaps most famous for defending the thesis that Leibniz s philosophy was almost entirely derived from his logic (1937, ix). This logicist thesis, as it is often called, is controversial, and has received a great deal of attention in the secondary literature. 9 My present aim is not to discuss how Leibniz purportedly sought to derive various of his metaphysical doctrines from his logic, but to summarize briefly Russell s interpretation of Leibnizian substances, to state his answers to Q1 and Q2 and to mention two features of Leibniz s view that he thought were deeply problematic. According to Russell, a Leibnizian substance is that which can only be subject, not predicate, which has many predicates, and persists through change (1937, 43). There are two sorts of predicate, those that exist only at a particular time and those that are eternal. A predicate of the former sort is the state of a substance at a particular time, while the latter consists in the fact of its being an attribute at that time (1937, 43). A substance s eternal predicates, which are included in its complete concept, are thus temporally indexed. The totality of a substance s temporally indexed predicates specifies the state that substance will be in at each moment of time. Each state of a substance is perceptual it involves the representation of a plurality in a unity. The substance itself possesses a primitive force of action, which is manifested in a series of instantaneous states. Each state s activity consists in an element or quality of that state in virtue of which it is not permanent, but tends to pass into the next state (1937, 45). These temporary predicates 8 As we shall see in x3, however, not all commentators agree that Leibniz takes created substances to be strictly atemporal. 9 For a clear overview of the logicist strategy see Nicholas Jolley (2005, 46 55).

THE STRUCTURE OF LEIBNIZIAN SUBSTANCES 383 or states form a single causal series; each state in the series follows from its preceding state in accordance with a law. Every substance has its own law of succession, which Leibniz calls the law of the series. How does Russell answer Q1 and Q2? Let us begin with the latter question. He thinks that each successive (total temporary) state is instantaneous. He also thinks that each state follows from one preceding state and is followed by one succeeding state. In other words, there is always a next state in the series; it is not the case that between any two states there is an intermediate state. As far as the substance itself is concerned, Russell suggests that it is not an idea, or a predicate, or a collection of predicates; it is the substratum in which predicates inhere (1937, 50). Russell thus provides an explicit answer to Q1: a substance is an enduring substratum in which a series of instantaneous perceptual states inhere. Russell levies several criticisms against Leibniz s theory of substance, of which I shall presently mention two. The first criticism is aimed directly at the substratum conception of substance. A substratum is essentially a theoretical posit. It is inferred from the nature of a predicate, which must inhere in something. The fact that a series of predicates inheres in the same substratum is what is supposed to account for the identity of a substance over time. However, the notion of a substratum is philosophically problematic, and Russell wastes no time making the point: the substance remains, apart from its predicates, wholly destitute of meaning. As to the way in which a term wholly destitute of meaning can be logically employed, or can be valuable in metaphysics, I confess that I share Locke s wonder (1937, 50). 10 The second criticism concerns Leibniz s views on time. Russell s analysis of Leibnizian predicates, which interprets them as being temporally indexed, presupposes the reality of time. This is problematic because Leibniz famously maintained that time is something relational and ideal, not something actual or real. Once again, Russell does not fail to note the inconsistency: Time is necessarily presupposed in Leibniz s treatment of substance. That it is denied in the conclusion, is not a triumph, but a contradiction (1937, 53). 3. TIME Nicholas Rescher attempts to defend Leibniz s theory of time against Russell s criticism. His leading idea is that time has a dual nature for 10 It is likely that Russell is not entirely accurate in his characterization of Locke s view on the substratum conception of substance. Although Locke does think that the substratum conception of substance cannot be usefully employed in metaphysics, it does not seem that he takes the notion of a substratum to be wholly devoid of meaning. He does, after all, claim that we have an (confused) idea of substance as a (unknown) support for different collections of perceived qualities (E: 2.23.1 2). I thank Paul Hoffman and Paul Lodge for suggesting that I make this qualification.

384 JOHN WHIPPLE Leibniz. There is the essentially private, intra-monadic time of each individual substance continuing, by appetition, through its transitions from state to state, and there is the public time, which holds throughout the entire system of monads (1979, 88). Rescher suggests that when Leibniz claims that time is not a fundamental feature of reality, he is speaking only of public time. His central argument for this position is that Leibniz s standard definitions of space and time presuppose monadic time. According to these definitions, space is an order of coexistences, as time is an order of successions (G7: 363; AG: 324). One way of understanding the order of coexistences is as an order of things existing at the same time, and the order of successions as an order of things that do not exist at the same time. This is the way that Rescher understands Leibniz s definitions, the latter of which would involve a vicious circle if real intra-monadic time were not being presupposed. Thus, although public time is relational and ideal, it is well founded on intra-monadic time the continuous generation of a series of instantaneous states via appetition, which is a fundamental feature of the created world. 11 Although some influential commentators have accepted Rescher s analysis of Leibnizian time, 12 others, notably Richard Arthur and Jan Cover, have argued that Leibniz is not committed to real intra-monadic temporality. 13 Arthur and Cover suggest (in separate articles) that Leibniz offers more nuanced definitions of space and time in one of his last works, Initia Rerum Mathematicarum Metaphysica. 14 Although their respective reconstructions of this account differ on some key details, their general interpretative strategy proceeds as follows. If we assume a plurality of states, these states can be ordered depending on (a) their compatibility or incompatibility, and (b) whether or not they involve the reason for each other. Simultaneity is then defined in terms of states that are not incompatible with each other. With the appropriate qualifications (e.g. that all the states of a single substance are mutually incompatible), (a) isolates sets of compatible states such that one state of any monad is compatible with exactly one state of every other monad. An instant is then defined on the basis of a set of simultaneous states (not on the basis of a single monadic state). These sets of states are then given an order of succession through the atemporal notion of reason inclusion (b). This allows Leibniz to hold that there is only one time rather than a plurality of intra-monadic time sequences. Interpretations of Leibniz s theory of time that proceed along these lines are more satisfactory than the account Rescher and others attribute to him. 11 Russell himself hints that Leibniz might have unconsciously had two theories of time (1937, 129). 12 Benson Mates (1986, 228), for example. 13 Arthur (1985) and Cover (1997). 14 GM7: 17 29, partially translated in L: 666 73.

THE STRUCTURE OF LEIBNIZIAN SUBSTANCES 385 They preserve (or at least come closer to preserving) the analogy between space and time: both are relational, ideal and not to be found on the metaphysical ground floor. It will be noticed, however, that the theory of time, as formulated above, is essentially static. As Arthur puts it, we do not yet have any principle of change or becoming, whereby a monad, having attained a given state, passes into the next state in the series (1985, 276). Arthur suggests that Leibniz does postulate such a principle, namely appetition. The postulation of appetition thus allows for a substance to run through the series of states which, as we have seen, is determined by the atemporal notions of compatibility and reason inclusion. Several common features of the interpretations of Arthur and Cover should be emphasized. First, neither of them note that Leibniz begins the Initia Rerum the locus classicus for their respective interpretations by making an interesting qualification: If a plurality of states of things is assumed (ponantur) to exist which involve no opposition to each other, they are said to exist simultaneously (GM7: 18; L2: 1083). Leibniz does not explain why he presents the existence of a plurality of states of things as a hypothetical assumption, but this qualification could be quite significant (for example, he might be presenting this as an assumption because he thinks that there is not a plurality of states of things at the deepest level of metaphysical rigour). Second, they do not discuss the ontological relation between a substance s series of states and the substance itself. Is the substance identical with its series of states? Is it some feature or characteristic that is found in each of the states in the series? Is it a substratum-like entity that somehow underlies the series of states? Answers to these crucial questions are not forthcoming. 4. THE REJECTION OF SUBSTRATA The discussion of Leibniz s theory of time brings to the fore another aspect of Russell s interpretation from which some commentators have tried to distance themselves, namely, the view that Leibnizian substances are substrata. It will be recalled, however, that Russell appeals to the notion of a substratum to account for diachronic identity. If the appeal to substrata is dropped, then there must be another explanation of diachronic identity. Louis Loeb confronts these issues, arguing that Leibniz views on causation provide the basis for an account of diachronic identity that does not presuppose that substances are substrata. He draws on texts such as the following: [2] One particular substance never acts upon another particular substance nor is acted upon by it... nothing can happen to us except thoughts and perceptions, and all our future thoughts and perceptions are merely consequences, though contingent, of our preceding thoughts and perceptions. (G4: 440; AG: 47).

386 JOHN WHIPPLE [3] By nature every simple substance has perception, and... its individuality consists in the perpetual law which brings about the sequence of perceptions that are assigned to it. (T: 291) [4] For me nothing is permanent in things except the law itself which involves a continuous succession and which corresponds, in individual things, to that law which determines the whole world. (21 January 1704 letter to De Volder; G2: 261; L: 534) Leibniz has been traditionally interpreted as claiming at least two things about causality in these texts: first, that there is no inter-substantial causation, strictly speaking; and second, that there is real or genuine intra-substantial causation. 15 Loeb s analysis of intra-substantial causation makes use of the notion of a substance s law of the series, mentioned by Leibniz in texts [3] and [4]. Leibniz is quite explicit in stating that each substance has its own law, which Loeb takes to be something analogous to a mathematical formula. 16 Each law of the series determines a causally connected sequence of distinct total states. This causal ordering provides all that is needed to account for the identity of a substance over time: there is a remarkably simple Leibnizian causal theory or analysis of persistence: perceptual states at distinct times are states of the same monad just in case one of the states is at least a partial cause of the other (1981, 318). With this analysis in hand, Leibniz can account for diachronic identity without having to appeal to a substratum: Such substrata are at best a third wheel, and Leibniz must have perceived that they are dispensable (1981, 334). 17 Loeb s interpretation of Leibniz s account of substance seems to be a step in the right direction, at least in so far as it involves a rejection of the notion of a substratum. There is a lacuna in his argument, however, for he does not provide an account of the ontological status of a substance s law of the series. This is not a difficult question for Russell to answer, of course. Given the rather generous ontology he attributes to Leibniz, the law of the series can simply be associated with a substratum; but if substrata are going to be 15 See Sleigh (1990, 130) and Jolley (1998). Although Leibniz rejects inter-substantial causation, he does stipulate a non-rigorous sense in which one substance can be said to act on another substance. One substance acts on another substance in virtue of expressing that substance distinctly (see, e.g., G4: 440 1; AG: 48). 16 Leibniz does occasionally use mathematical analogies to illustrate his position that each substance has a law of the series (see, e.g., G2: 258 9; L: 532 3). It is important to keep in mind, however, that these are only analogies. Loeb seems to be supposing that they are something more than analogies, or at least that the analogy is too strict. I thank Paul Lodge for calling my attention to this point. 17 Other commentators have endorsed the general strategy of his analysis of diachronic identity. See, e.g., Sleigh (1990, 132) and Adams (1994, 80).

THE STRUCTURE OF LEIBNIZIAN SUBSTANCES 387 jettisoned in favour of a more parsimonious ontology, an explanation of how the law of the series fits into the resulting framework must be provided. Loeb does make one remark that might be intended to convey a position on the ontological status of the law of the series: some passages suggest that Leibniz identifies a monad s law of succession with a temporal sequence of perceptual states (1981, 317). Does Loeb mean to suggest that the law of the series just is a series of perceptual states? Such a position would be in keeping with the rejection of substrata, but is it plausible as an interpretation of Leibniz? In attempting to answer this question, it is imperative to note that Loeb assumes that each total state in a monad s series of states is rigorously individuated from all its other states. This is evident from the way he sets up the problem of diachronic identity: Of the various perceptual states which exist at different times, what reason is there to unite one pair of temporally distinct states into a sequence rather than another pair? (1981, 317). In other words, one begins with the assumption that there are a plurality of distinct total states, and then attempts to determine how these states can be organized into unique sequences. Loeb s proposed solution to this problem, taken in conjunction with his remark concerning the ontological status of the law of the series, suggests the following answer to Q1: a substance just is a series of distinct perceptual states. This conclusion is problematic, however, for it appears to make a substance into an aggregate. Leibniz considered view is that aggregates reduce to simple substances, not that simple substances themselves are aggregates: There must be simple substances, since there are composites; for the composite is nothing more than a collection, or aggregate, of simples (G6: 607; AG: 213; emphasis Leibniz). Loeb s is not the only interpretation suggestive of the conclusion that Leibnizian substances are the sum of a series of distinct states. We can find Mates, for example, writing: In the last analysis... there is only one realm; everything is reducible to the states of monads (1986, 50); and consider Rescher: There is nothing to monads except their states (and the succession thereof) (1979, 72; emphasis Rescher). Leibniz repeatedly describes his fundamental entities as simple substances, metaphysical points, and real unities absolutely destitute of parts (G4: 482; AG: 142). However, if these interpretations of Leibniz s account of substance are correct, then his so-called metaphysical atoms are in danger of fragmenting into entities more aptly described as metaphysical aggregates. 18 18 R. M. Yost provides the most explicit affirmation of the view that a substance is the sum of a series of distinct states that I have found in the secondary literature (1954, 118).

388 JOHN WHIPPLE 5. INTRA-SUBSTANTIAL CAUSATION Two unsatisfactory accounts of the relation between the states of a substance and the substance itself have been considered. There is the view that a Leibnizian substance is a substratum in which a series of successive states inhere, and the view in which a substance is the sum of a series of distinct states. Both of these accounts are problematic, and few commentators would be willing to explicitly attribute either position to Leibniz. The question that must be considered, then, is whether it is possible to understand the relation between the states of a substance and the substance itself in a way that avoids the problems attending these two views. Greater insight into this question can be gained by examining certain controversies concerning Leibniz s account of intra-substantial causation. Although there is overwhelming agreement in the secondary literature that Leibniz is committed to this doctrine, there has been significant disagreement over how it should be understood. One of the central disagreements concerns what exactly it is that Leibniz thinks causes specific states of a substance. Some commentators think that a state is always caused by its preceding state, while others claim that it is the substance itself (or the primitive force of the substance) that is causally efficacious. The former view has been termed the efficacious perception view, and the latter the monadic agency view. 19 Loeb s interpretation of intra-substantial causation, discussed above, was an example of an efficacious perception view. Interpretations along these lines rely on texts like [2], where Leibniz claims that all our future thoughts and perceptions are merely consequences, though contingent, of our preceding thoughts and perceptions. Bobro and Clatterbaugh have recently criticized the efficacious perception view and defended the monadic agency thesis. They contend that the efficacious perception view makes Leibnizian causality too Humean (1996, 414). Discrete states are not the right sorts of thing to be causally efficacious. It is only the substance itself that can adequately perform this task. The substance fits the bill, as it were, because it possesses a primitive force of action. A number of texts support this view; the following two from A New System of Nature are paradigmatic: [5] We must say that God originally created the soul (and any other real unity) in such a way that everything must arise for it from its own depths, through a perfect spontaneity relative to itself, and yet with a perfect conformity relative to external things. (G4: 484; AG: 143; emphasis Leibniz) 19 This terminology is used by Bobro and Clatterbaugh (1996). Other terminology has been used in the secondary literature, however. Rutherford, for example, prefers derivative force theory and primitive force theory (2005, 163).

THE STRUCTURE OF LEIBNIZIAN SUBSTANCES 389 [6] This hypothesis is entirely possible. For why should God be unable to give substance, from the beginning, a nature or an internal force that can produce in it, in an orderly way (as would happen in a spiritual or formal automaton, but free in the case where it has a share of reason), everything that will happen to it, that is, all the appearances or expressions it will have, without the help of any created being? (G4: 485; AG: 144; emphasis Leibniz) According to Bobro and Clatterbaugh, the primitive force of a substance plays (at least) two important roles in Leibniz s system: it is responsible for the production of each of a substance s states, and it accounts for the substance s diachronic identity. Primitive force can perform the latter task because it is imprinted upon a substance at creation, and it remains the same even though the states of a substance are continually in flux. Donald Rutherford has recently argued that it is a mistake to regard the efficacious perception view and the monadic agency view as opposed models of intra-substantial causality. 20 He suggests that these views provide different answers to different questions. The monadic agency view answers this question: why is there change in a substance at all? The answer: there is change in a substance because it possesses a primitive force. However, if one wants to explain why a substance is in one particular state rather than another, one must appeal to the prior state from which the state in question has followed. The prior state produces the later state in virtue of its derivative force, which is a determinate expression of primitive force. The primitive force is thus conceived as the ultimate ground of change, and a particular state is only causally efficacious to the extent that the substance itself is (2005, 165). Rutherford and Bobro and Clatterbaugh disagree on whether the monadic agency view and the efficacious perception view both have a place in Leibniz s account of intra-substantial causation. There is, however, one point on which they clearly agree a Leibnizian substance is not to be identified with the mere sum of its successive states. There is something more to a substance than its states, namely its primitive force of action. Many Leibniz commentators would be willing to make this claim, for it has a firm basis in the primary texts. But what, exactly, is the ontological relation between a substance s primitive force and its series of successive states? This 20 Jolley also suggests that these two models are not inconsistent, but he provides a different account of how they can be brought together: Although Leibniz may say that it is substances which produce their states, this is only a loose way of speaking; in strictness, it is perceptual states which causally produce other perceptual states of the same substance (1998, 605). While Rutherford thinks that the efficacious perception view and the monadic agency view provide different answers to different questions, Jolley claims that texts suggestive of the monadic agency view are just loose or imprecise expressions of the efficacious perception view. See also Carlin (2004, 368 9), who argues for the opposite position: texts that suggest the efficacious perception view are imprecise expressions of the monadic agency view.

390 JOHN WHIPPLE is a crucial question, but it has been little discussed. Bobro and Clatterbaugh briefly consider it and conclude that the relation is far from fully transparent. They suggest that primitive force is postulated as the ultimate metaphysical cause of monadic states, and as what accounts for the identity of a monad over time, but it is something that Leibniz talks about only metaphorically (1996, 424). Thus construed, the primitive force being attributed to substances is something closely analogous to a substratum. 21 It plays an important theoretical role in Leibniz s metaphysics, but its ontological status is not clearly explained. As an analysis of the ontological relation between a substance and its successive states, this account is hardly more satisfactory than the ontological framework that Russell attributes to Leibniz. 22 6. PRIMITIVE FORCE AND THE LAW OF THE SERIES To this point our investigation into the structure of Leibnizian substances has focused on a pair of questions, one concerning the notion of a total temporary state, and another concerning the ontological relation between a substance and its series of states. Although these are the guiding questions of the study, they are not the only questions relevant to its central theme. In this section I will raise several additional questions, which the discussions in x4 and x5 should lead one to consider. We have seen that some interpretations of Leibnizian intra-substantial causation focus on a substance s law of the series, while others focus on a substance s primitive force. The interpretations that have been discussed thus far focus primarily on the functions of the law of the series and the primitive force, rather than on characterizing their ontological status. If one is to achieve clarity on the structure of substances, the questions of ontology must be directly addressed. Let us distinguish the following questions: Q3: What is the ontological relation between a substance s law of the series and its primitive force? Q4: What is the ontological relation between a substance and its law of the series? Q5: What is the ontological relation between a substance and its primitive force? 21 It should be no surprise, then, that in a different paper Clatterbaugh explicitly attributes a substratum account of substance to Leibniz (1973, 17). 22 Rutherford does not attempt to provide a full analysis of the ontological relation between a substance s primitive force and its derivative forces (i.e., successive states). Nevertheless, his claim that the monadic agency view and the efficacious perception view are not opposed models of causality constitutes an important advance in our understanding of Leibnizian intrasubstantial causation. In x8 I will attempt to develop this insight within the context of an alternative ontological framework.

THE STRUCTURE OF LEIBNIZIAN SUBSTANCES 391 Q6: What is the ontological relation between a substance s law of the series and its successive states? Q7: What is the ontological relation between a substance s primitive force and its successive states? My strategy in this section will be to proceed through these questions in order. I will argue that the answers to Q3, Q4 and Q5 imply that Q6 and Q7 are merely reformulations of Q1: what is the ontological relation between a substance and its successive states? In order to answer Q3, one must determine whether the law of the series and the primitive force are distinct components of a substance, or merely two ways of describing the same thing. Broad affirms the former position: [7] The whole history of the monad... will be a continuous series of... total states... producing each other without any influence from outside in accordance with the law of development which God impressed on the monad at its creation, and in consequence of the active force of appetition with which he endowed it. (1975, 95) Broad comes to this conclusion, it seems, because he takes the law of the series and the primitive force to perform distinct functions. The basic idea is that the primitive force provides the power, while the law of the series provides the order. The force ensures that the substance has the power to produce a series of states; the law determines which specific series is produced. It is not clear to me, however, that the functions Leibniz attributes to primitive force and the law of the series are, in fact, different. Recall text [3], where Leibniz states that every simple substance has perception, and... its individuality consists in the perpetual law which brings about the sequence of perceptions that are assigned to it. In this text Leibniz attributes the production of a substance s states to the law of the series. Similarly, in text [6] Leibniz says that God gives a substance an internal force that can produce in it, in an orderly way... everything that will happen to it. Here Leibniz attributes the power and the order to the force, with no appeal to a developmental law. This suggests that primitive force and law of the series are merely different names that Leibniz uses to refer to one thing that is responsible for the production of a substance s modifications in an orderly way. I shall term this the Primitive Force/Law of the Series Identity Thesis. Further support for the Primitive Force/Law of the Series Identity Thesis can be garnered by returning to the issue of diachronic identity. In De Ipsa Natura Leibniz states that primitive force is what accounts for diachronic identity:

392 JOHN WHIPPLE [8] The very substance of things consists in a force for acting and being acted upon. From this it follows that persisting things cannot be produced if no force lasting through time can be imprinted on them by the divine power. Were that so, it would follow that no created substance, no soul would remain numerically the same, and thus, nothing would be conserved by God. (G4: 508; AG: 159 60) In other places, however, Leibniz appeals to the law of the series. One clear example of this is found in a 1704 letter to De Volder: [9] If it is claimed that substances do not remain the same but that different substances which follow upon prior ones are always produced by God, this would be to quarrel about a word, for there is no further principle in things by which such a controversy can be decided. The succeeding substance will be considered the same as the preceding as long as the same law of the series or of simple continual transition persists, which makes us believe in the same subject of change, or the monad. The fact that a certain law persists which involves all of the future states of that which we conceive to be the same this is the very fact, I say, which constitutes the enduring substance. (G2: 264; L: 535) This passage occurs in the context of a discussion of inter-substantial causation. As we have seen, Leibniz denies that finite substances can act upon each other, strictly speaking. There is one case in which intersubstantial causation does occur, however, and this is the action of the infinite substance on finite substances, an action which consists in continuously producing or constituting them (G 2: 264; L: 535). Leibniz does not pause to fill out the details of the continual creation doctrine in this text, but he does attempt to forestall the objection that it undermines diachronic identity. In text [8], Leibniz explains that a substance remains the same, despite being continually created by God, because the law of the series persists through change. 23 The linchpin of the argument for the Primitive Force/Law of the Series Identity Thesis is that Leibniz explicitly identifies the force with the law in this letter to De Volder and in De Ipsa Natura. First, the letter: [10] Derivative force is itself the present state when it tends toward or preinvolves a following state, as every present is great with the future. But that which persists, insofar as it involves all cases, contains primitive force, so that primitive force is the law of the series, as it were [velut], while derivative force is the determinate value which distinguishes some term in the series. (G2: 262; L: 533) 23 I provide an analysis of Leibniz s account of creation in Continual Creation and Finite Substance in Leibniz s Metaphysics. See also J. Whipple Leibniz on Divine Concurrence.

THE STRUCTURE OF LEIBNIZIAN SUBSTANCES 393 Perhaps Leibniz s identification of the primitive force with the law of the series is not perfectly explicit in this text, given the velut qualification. However, several paragraphs later, Leibniz claims that nothing is permanent in things except the law itself which involves a continuous succession (G2: 263; L: 534). If Leibniz takes the primitive force of a substance to be something over and above its law of the series, then he should certainly not be making this claim, for he is quite clear in affirming that the primitive force of a substance is enduring. This is explicit in text [8] from De Ipsa Natura. Several paragraphs later in that same work Leibniz claims that the soul is a certain urge or primitive force of acting, which itself is an inherent law, impressed by divine decree (G4: 512; AG: 162 3). This textual evidence, in conjunction with the considerations previously adduced, strongly suggests that Leibniz endorsed the Primitive Force/Law of the Series Identity Thesis. 24 Having answered Q3, let us proceed to Q4 and Q5. If Leibniz strictly identified a substance s primitive force with its developmental law, as I have argued, then these questions can be answered in tandem. What then is the ontological relation between a substance and its law/primitive force? The text from De Ipsa Natura, cited in the previous paragraph, suggests a simple answer: the substance just is a primitive force/law of the series. I shall call this the Substance/Primitive Force/Law of the Series Identity Thesis. This thesis can also be discerned in the following Theodicy passage: [11] I maintain that all the Souls, Entelechies or primitive forces, substantial forms, simple substances, or monads, whatever name one may apply to them, can neither spring up naturally nor perish. (T: 396) This text is, in my opinion, quite revealing. It suggests that primitive force, substantial form, entelechy and several other words are nothing more than different names, each of which is used to designate the fundamental entities in Leibniz s ontology. 25 Leibniz does not mention the law of the series in this text, but that should not give us pause. For one thing, there is no indication he is attempting to provide an exhaustive list of names in text [11]. More importantly, given that Leibniz identifies primitive force with the law of series, by identifying the former with the substance itself, he is, in effect, identifying the latter with the substance as well. 24 Adams (1994, 77 80) and Cover and Hawthorne (1999, 219 24) interpret Leibniz as affirming this thesis. 25 In certain contexts Leibniz gives some of these words technical meanings so that they are not strictly synonymous. For example, in the Monadology Leibniz uses soul not to designate any simple substance whatsoever, but only those where perception is more distinct and accompanied by memory (G6: 610; AG: 215). To cite another example, in some places Leibniz uses entelechy to refer to all simple substances (see G6: 609; AG: 215), while in others he uses it to refer to a substance only insofar as it is active (see, e.g., G2: 252; AG: 177).

394 JOHN WHIPPLE The Substance/Primitive Force/Law of the Series Identity Thesis renders certain issues of ontology perspicuous. It provides clear answers to Q3, Q4, and Q5, and it shows that Q6 and Q7 are merely reformulations of Q1: what is the ontological relation between a substance and its successive states? It does not, however, issue in a complete ontological framework until it is combined with an answer to Q1. Keeping this point in mind, I turn to the interpretation of Leibniz s theory of substance provided by Cover and Hawthorne. They explicitly affirm the Substance/Primitive Force/Law of the Series Identity Thesis in their important study Substance and Individuation in Leibniz. 26 Let us examine their interpretation to see if they provide a clear account of the ontological relation between a substance and its successive states. Cover and Hawthorne attempt to flesh out the details of Leibniz s theory of substance by focusing on the law of the series. The law of the series just is the substance, on their account, and they suggest that the law should be understood on the model of an immanent function, where the total temporary states of a substance are taken as arguments and values of the function. Assuming that God creates a substantial function in an initial total temporary state, that state will serve as the function s first argument. The law of the series can then generate another total state as value. The new state then serves as an argument for the generation of yet another state in accordance with the law, etc. Each successive state serves as both a value and an argument for the substantial function. 27 With this basic framework in place, Cover and Hawthorne are able to provide innovative reconstructions of Leibnizian intra-substantial causation and the doctrine of marks and traces, among other things. The first thing to note about Cover and Hawthorne s interpretation is that it relies heavily on the notion of a total temporary state. They take the duration of a substance to consist in a determinate series of causally related total temporary states. As we shall soon see, this construal of total temporary states involves deep metaphysical problems. Let us hold these problems in abeyance for a bit longer, however, and focus on Q1: what is the ontological relation between this series of states and the substance itself? Cover and Hawthorne do not emphasize this question, noting only that: Such [total temporary] states, meanwhile, being arguments and values of the function, are not the function itself, nor... is the substantial function identical with the list of arguments and values (2001, 229). This shows that they reject two possible answers to Q1: a substance cannot be identified with one of its successive states, and it is not the sum of a series of states either. This tells us two things about what a substance is not, but it does not provide us with a positive account of the ontological relation between a substance and its states. The functional relation between the substance and 26 2001, 224. 27 2001, 229.

THE STRUCTURE OF LEIBNIZIAN SUBSTANCES 395 the successive states is reasonably clear, but the ontological relation is not clearly articulated. 28 How might one attempt to provide a positive account of the ontological relation between a substance and its successive states from within the framework suggested by Cover and Hawthorne? One might claim that the substance somehow underlies the series of total temporary states. This strategy in not particularly attractive, however, for it would saddle Leibniz with a substratum-like conception of substance. A different option would be to claim that the substance is wholly present in each total temporary state. Perhaps this approach is more promising, but it raises additional questions of its own. First, something would have to be said about how each total temporary state could (in some sense) be divisible into a primitive force/ substance/law on the one hand, and a derivative force/modification/term in the series on the other. Second, one would need to explain the sense in which the law that is found in one total temporary state is the same as the law that is found in a subsequent total temporary state. Leibniz clearly thinks that each substance has (or is, according to the Substance/Primitive Force/Law of the Series Identity Thesis) one law, but could a law found in one total temporary state and a law found in another total temporary state (of a single series) be identically the same? It is not clear that adequate answers to these questions can be provided, and until they are, a satisfactory account of the ontological relation between a substance and its successive states has not been set forth. 7. THE PROBLEM OF MONADIC STATES We have examined standard interpretations of Leibniz s theory of time, his account of diachronic identity and his account of intra-substantial causation. We have also considered different interpretations of the ontological relations between a substance, its law of the series, its primitive active force, and its series of states. The accounts considered diverge with respect to some important interpretive issues, but each them utilizes the notion of a total temporary state. I have noted how this notion has been typically understood, but it has yet to be subjected to a rigorous analysis. Such is the aim of the present section. I shall argue that if recent commentators have understood this notion correctly, then Leibniz s theory of substance suffers from severe internal problems. 28 The same observation holds with respect to Stefano Di Bella s rich and detailed study of Leibniz s theory of substance. Di Bella argues that Leibniz rejects both a bundle theory of substance and a substratum theory. He avoids the bare substratum view, according to Di Bella, by identifying each substance with a primitive subsisting law. However, I do not think that Di Bella succeeds in illuminating the ontological relation between the subsisting law and the series of states. Indeed, he appears to regard the subsisting law as a somewhat mysterious entity that must be postulated (2005, 390).