Leibniz on Plurality, Dependence, and Unity (Accepted Manuscript)

Leibniz on Plurality, Dependence, and Unity1 Adam Harmer Abstract: Leibniz argues that Cartesian extension lacks the unity required to be a substance. A key premise of Leibniz’s argument is that matter is a collection or aggregation. I consider an objection to this premise raised by Leibniz’s correspondent Burchard de Volder and consider a variety of ways that Leibniz might be able to respond to De Volder’s objection. I argue that it is not easy for Leibniz to provide a dialectically relevant response, and further, that the difficulty arises from Leibniz’s commitment to part-whole priority in the case of material wholes, a commitment not shared by De Volder. One major implication is that Leibniz relies on a bottom-up conception of material things, which makes his argument vulnerable to objections stemming from certain types of monist positions. 1. Introduction According to Descartes, material substance consists in extension alone. Leibniz argues against this conception of material substance based on considerations of unity. In particular, he argues that merely extended matter cannot have the unity required to be a substance (i.e., unum per se). At best, it can be an accidental unity (i.e., unum per accidens). As such, matter can never be, strictly speaking, one thing; it always remains many things.2 In the New System (1695), Leibniz presents a concise version of this argument, which I will call the “Argument from Unity”: After much reflection, I perceived that it is impossible to find the principles of true unity in matter alone [la matiere seule], or in what is only passive, since everything in it is only a collection or aggregation [collection ou amas] of parts to infinity. Now, a multitude can derive its reality only from true unities, which have some other origin and are considerably different from points, which all agree cannot make up the continuum. Therefore, in order to find these real entities I was forced to have 1 I would like to thank Marleen Rozemond, Karolina Hübner, and the participants of the Berlin-Toronto Workshops in Early Modern, the South Central Seminar in Early Modern Philosophy, the Finnish-Hungarian Seminar in Early Modern Philosophy, and the UCLA Early Modern Conference for helpful comments on previous versions of this paper. 2 Of course, Leibniz has other lines of argument against merely extended substance. He also argues that matter cannot be a substance because it is merely passive and thus cannot explain the presence of forces in bodies. See, e.g., “On the Nature of Body and the Laws of Motion” (A 6.4, 1976-1980 = AG 245-250). For discussion of this line of argument, see, e.g., Garber 2009, chs. 3-4. This line of argument is also present in the correspondence with De Volder, though I will not address it directly. recourse to a formal atom, since a material thing cannot be both material and, at the same time, perfectly indivisible, that is, endowed with a true unity. (GP IV, 478-479 = AG 139)3 There are a variety of intersecting lines of thought in this passage. Let me extract the main components of the Argument from Unity as I see it. (1) Matter alone is only a collection or aggregation of parts to infinity. (2) A collection or aggregation of parts cannot be endowed with a true unity. (3) To be a real entity is to be endowed with a true unity. (4) Therefore, matter alone is not (and cannot be) a real entity. Unsurprisingly, given the prominence of this line of thought in Leibniz’s theory of substance, the Argument from Unity has received a great deal of attention.4 Still, I think certain important aspects of Leibniz’s argument have been overlooked. In what follows, I will examine premise (1) of the Argument from Unity. In particular, I will consider an objection to this premise that has not received much (if any) attention in the literature. This objection is presented to Leibniz by his correspondent Burchard de Volder, and may originate with some remarks made by Spinoza.5 Considering this objection will both help to clarify the sense in which Leibniz asserts that matter is a collection or aggregation as well as illuminate a potential weak spot in Leibniz’s argument. De Volder objects that, in virtue of the fact that there is no empty space (a prevalent early modern commitment), no material part can be conceived (or exist) independently of any other. If material parts cannot be conceived (or exist) independently, then matter is not a collection or aggregation; rather, there is simply a single, material substance. Since material parts are merely modes of this single material substance, matter (i.e., the entire 3 Citations of primary sources are given by the following abbreviations: A = Leibniz. Sämtliche Schriften und Briefe. Ed. Deutsche Akademie der Wissenschaften, cited by series, volume, and page number; AT = Descartes. Œuvres de Descartes. Ed. Charles Adam and Paul Tannery, cited by volume and page number; G = Spinoza. Spinoza Opera. Ed. C. Gebhardt, cited by volume and page number. GP = Leibniz. Die Philosophischen Schriften. Ed. C. I. Gerhardt, cited by volume and page number; AG = Leibniz. Philosophical Essays. Trans. Roger Ariew and Daniel Garber; Ar = Leibniz. The Labyrinth of the Continuum: Writings on the Continuum Problem, 16721686. Trans. Richard T. W. Arthur; C = Spinoza. The Collected Works of Spinoza. Ed. E. Curley, cited by volume and page number; CSMK = Descartes. The Philosophical Writings of Descartes. Trans. John Cottingham, Robert Stoothoff, Dugald Murdock, and Anthony Kenny, cited by volume and page number; DSR = Leibniz. De Summa Rerum: Metaphysical Papers, 1675-1676. Trans. G. H. Parkinson; LC = The Leibniz-Clarke Correspondence. Trans. R. Ariew; LDV = The Leibniz-De Volder Correspondence. Trans. Paul Lodge. Ma = The Leibniz-Arnauld Correspondence. Ed. H.T. Mason; WFPT = Leibniz. Philosophical Texts. Trans. Richard Francks and R.S. Woolhouse. 4 Attention has been paid both to Leibniz’s argument that matter alone lacks unity (e.g., Garber 1985, Sleigh 1990, Ch. 6, Adams 1994, Ch. 9, Rutherford 1995, Ch. 8, Levey 2003, Garber 2009, Ch. 2, Arthur 2012) and to the sense in which a substance (simple, or perhaps even composite) is a unity on Leibniz’s positive conception of substance (e.g., Sleigh 1990, Ch. 6, Adams 1994, Ch. 10, Rutherford 1995, Ch. 10, Fichant 2003, Garber 2009, Ch. 9, Smith 2011, Ch. 3, Arthur 2011). 5 Burchard De Volder is typically thought of as sympathetic to Cartesianism. But see Klever 1988 for a case that De Volder was a “crypto-Spinozist”. See Lodge 2005 for a more recent discussion. See E1P15S for a similar line of thought developed by Spinoza. 2 material plenum) can possess the unity requisite for substance after all. Call De Volder’s objection the “Monist’s Challenge”. The Monist’s Challenge relies on a conception of the physical world that is deeply at odds with Leibniz’s conception. In fact, there is some ambiguity concerning just what conception of the physical world is implied by the Monist’s Challenge. I will develop this ambiguity below. In any case, I will argue that the Monist’s Challenge constitutes a real threat to Leibniz’s Argument from Unity. Although the Monist’s Challenge is unique to the correspondence with De Volder, the threat that it poses is much broader: it threatens to undermine a key premise of Leibniz’s Argument from Unity, and in so doing, threatens to undercut a major line of argument developed by Leibniz against merely extended substance.6 I will also argue that Leibniz has a partially viable response to the Monist’s Challenge, though providing a response is not at all straightforward. Given the stage of Leibniz’s argument at which the Monist’s Challenge applies, any response that Leibniz offers must be dialectically relevant (i.e., it cannot presume features of Leibniz’s own metaphysical system explicitly at issue in the exchange with De Volder). This is because the Argument from Unity is attempting to motivate key features of that system—namely, the inability of matter alone to constitute a substance. I will survey some unviable replies that Leibniz gives, before developing his best chance for a reply: a distinction between different types of dependence. The absence of empty space implies that the physical world is a plenum. According to Leibniz, the Monist’s Challenge relies on the claim that the plenum entails specific dependence. That is to say, any two material parts will depend on each other in particular; no other parts will do. However, Leibniz argues that the plenum entails only generic dependence. That is, any material part depends on some other parts, but no particular parts. I will develop Leibniz’s distinction between specific and generic dependence and evaluate the extent to which it allows Leibniz to respond to the Monist’s Challenge. Following this, I will consider a further reply, in which Leibniz attempts radically to break the link between dependence (even specific dependence) and unity. However, I will argue that this response relies on certain assumptions about part-whole priority not shared by De Volder. Identifying these assumptions suggests that underlying Leibniz’s Argument from Unity is a certain conception of the structure of the physical world. Thus, one important outcome of the present discussion is that it highlights the difference between what might be called bottom-up versus top-down conceptions of the physical world. Leibniz’s argument relies on a bottom-up conception, though he comes up against a fundamentally different conception in De Volder, which highlights a weak spot in his otherwise powerful Argument from Unity. 2. The Monist’s Challenge In section 2, I will examine Leibniz’s reasons for holding premise (1) of the Argument from Unity (i.e., that matter alone is a collection or aggregation to infinity). I will The Argument from Unity appears as early as 1679. See A 6.4, 1464 = Ar 257-9. There is some uncertainty concerning the date of this text. The Akademie editors put it at 1682/3, based on similarity of content, while Richard T. W. Arthur makes the case that it is likely earlier. See Ar 257 and 415, n. 1 and n. 2. 6 3 then present De Volder’s formulation of the Monist’s Challenge and consider the extent to which it undercuts Leibniz’s support for this premise. Leibniz offers support for premise (1) by claiming that matter is actually infinitely divided into parts which are moving independently of one another.7 In virtue of the actual division and independent motion of the parts of matter, Leibniz claims further that any extended body is, properly speaking, a plurality (i.e., many things).8 So, Leibniz seems to be committed to the following principle, call it “Plurality”: (Plurality) Independence (with respect to motion) entails plurality.9 Leibniz’s commitment to Plurality is best understood in very general terms. That is to say, it should be understood to apply to matter no matter what one’s take on the ontology of material objects (and their parts) happens to be. To locate this principle in a slightly broader context, Leibniz’s Argument from Unity attempts to identify a shortcoming in the Cartesian conception of extended substance: merely extended matter does not (and cannot) have the unity required to be a substance. The identification of this shortcoming is based on the claim that merely extended substance is a plurality, since it is actually divided into parts. The question I will examine below is whether Leibniz is entitled to this characterization of the Cartesian conception or not. De Volder presents some reason to think that he is not. The question at issue in the following discussion, then, is not what the ultimate units of matter are—for Leibniz there are no ultimate material units at all but ultimate substantial units, which are partless, unextended substances from which matter results. Rather, the question at issue is whether or not Leibniz legitimately construes the Cartesian conception of extended substance (or, in particular, De Volder’s version of it) as being committed to the plurality of matter, from which Leibniz aims to infer the need for these ultimate substantial units. For Leibniz, as I will discuss further below, to be a plurality entails a certain partwhole priority relation. That is, the parts need to be prior to the wholes they compose.10 Leibniz appears to think that this is an uncontroversial commitment. De Volder, however, does not accept Leibniz’s commitment on this point. He argues for a reduction of Plurality I cannot fully present this view here, but will concentrate on certain texts from the Leibniz-De Volder correspondence. For broader discussion of Leibniz’s commitment to the actually infinite division of matter and its relation to his theory of substance, see, e.g., Arthur 2012 and Levey 1998. 8 There is potential for confusion here, since on Leibniz’s considered view, matter turns out to be an aggregate (or to result from an aggregate) of immaterial substances (see, e.g., Leibniz to Bernoulli, 1 September 1698 = LDV 9). As I am interpreting it here, premise (1) of the Argument from Unity is neutral with respect to what matter is a plurality of. 9 I am using “plurality” to signify that matter is, strictly speaking, many things. I intend this term to be equivalent to Leibniz’s terms “aggregation” and “collection”. Being, strictly speaking, many things is compatible with having accidental unity, since accidental unity is supplied by the mind of some perceiver. 10 If we move outside of the correspondence to De Volder, we can see Leibniz making this point frequently. One familiar expression of this commitment is in his 30 April 1687 Letter to Arnauld: “…for every entity through aggregation presupposes entities endowed with a true unity, because it obtains its reality from nowhere but that of its constituents, so that it will have no reality at all if each constituent entity is still an entity through aggregation…” (A 2.2, 184 = Ma 120). Thus, if material aggregates have only material constituents all the way down, they will have no reality at all. Leibniz, of course, leverages this claim to argue that immaterial constituents are needed in order to explain how matter can have any reality whatsoever. For further discussion of Leibniz’s so-called “borrowed reality argument”, see Levey 2012. 7 4 to the claim that matter is a plurality of modes. He does so by noting a crucial sense in which material parts fail to be independent: even if they are independent with respect to motion, they are not independently conceivable.11 Further, if they are not independently conceivable, they are not truly many. That is, according to De Volder, material parts are mere ways of being of a single, material substance. In Leibniz’s sense of “part” as something prior to the whole, they fail to be parts at all. So, De Volder seems to be committed to the following principle, which is opposed to Plurality—call it “Unity”: (Unity) Dependence (with respect to conception) entails unity. Unity is consistent with Plurality, so long as Plurality is reduced to the claim that independence entails a plurality of modes: even if material parts are independent with respect to motion, they will not be truly many unless they are also independently conceivable. With this background in mind, I will now turn to some of the particulars of Leibniz’s exchange with De Volder. Early in the correspondence, Leibniz makes the argument that the very notion of extension involves plurality. He writes, I do not think that there is a substance constituted from extension alone, since the concept of extension is incomplete. Nor do I think that extension is conceived through itself, but that it is a resolvable and relative notion. For it is resolved into plurality, continuity, and coexistence, i.e., the existence of parts at one and the same time. (3 April 1699; A 2.3, 546 = LDV 73) Leibniz then explains why extension is partially resolved into plurality: I think that that which is extended has no unity except in the abstract, namely when we divert the mind from the internal motion of the parts by which each and every part of matter is, in turn, actually subdivided into different parts, something that plenitude does not prevent. (3 April 1699, A 2.3, 546 = LDV 73) Leibniz provides a distinction between abstract extension and concrete extension. While abstract extension may have unity, concrete extension (i.e., matter), is, properly speaking, a plurality. So, Leibniz’s rationale for including plurality in the very notion of extension is that each and every part of matter (i.e., concrete extension) is subdivided by motion. This situation is, according to Leibniz, consistent with a physical plenum. These texts express a clear commitment to Plurality as formulated above. Here is a rendering of Leibniz’s argument on this point. (P1) Matter is actually infinitely divided by motion. De Volder formulates the challenge both in terms of independent conceivability and independent existence. For ease of expression, I will formulate the challenge in terms of conception in what follows, though it should be understood that, according to De Volder, material parts cannot exist independently either. 11 5 (P2) (P3) If matter is actually infinitely divided by motion, each and every part of matter is moving independently. Independence (with respect to motion) entails plurality. (P4) So, matter is a plurality. De Volder attempts to block Leibniz’s appeal to Plurality by means of the Monist’s Challenge. He writes, For if there is indeed no empty space, as you submit, it will not be possible for one part, which anyone might imagine for themselves, to be conceived without the others. From this it seems to follow that there is no real distinction [reale discrimen] between them, but that the distinction [discrimen] between parts that is imagined in these things consists not so much in a difference of substance as in a difference of modes [quam in modum varietate consistere]. (18 Feb 1699; A 2.3, 530 = LDV 61)12 Here is a rendering of De Volder’s reasoning: (MC1) (MC2) (MC3) (MC4) (MC5) There cannot be any empty space. If there cannot be any empty space, then one material part cannot be conceived without the others. If one material part cannot be conceived without the others, then the parts of matter are not really distinct. (I.e., dependence [with respect to conception and/or existence] entails unity.) If the parts of matter are not really distinct, then they are only modally distinct. So, material parts are only modally distinct from one another. Though not drawn explicitly in the passage quoted, there is a further conclusion that clearly follows from this line of reasoning, and that will be relevant below: So (MC6) The physical plenum has no really distinct parts, (i.e., it is a single substance). There is some ambiguity concerning how De Volder understands the commitment expressed by (MC6). I will return to this ambiguity below. De Volder provides a series of formulations of the Challenge. See, e.g., A 2.3, 562 = LDV 91. Also, as mentioned above, De Volder’s reasoning here is reminiscent of Spinoza in E1P15S, though De Volder does not mention Spinoza in this connection: “For if corporeal substance could be so divided that its parts were really distinct [realiter distinctae], why, then, could one part not be annihilated, the rest remaining connected with one another [inter se connexis] as before? And why must they all be so fitted together that there is no vacuum? Truly, of things which are really distinct from one another, one can be, and remain in its condition, without the other. Since, therefore, there is no vacuum in nature (a subject I discuss elsewhere), but all its parts must so concur that there is no vacuum, it follows also that they cannot be really distinguished [realiter distingui], i.e., that corporeal substance, insofar as it is a substance, cannot be divided” (G 2, 59 = C 423). 12 6 De Volder’s contention is that (MC5) demands the following revision to (P3) of Leibniz’s argument for Plurality: (P3*) Independence (with respect to motion) entails a plurality of modes. With (P3) replaced with (P3*), only a much weaker conclusion will follow: (P4*) So, matter is a plurality of modes. I think it is clear that if Leibniz’s argument for Plurality proceeds by way of (P3*) to arrive at (P4*), it will not establish that matter is truly many. The significance of Leibniz’s claim that matter alone is a collection or aggregation is that, given the plurality of matter, some mechanism needs to be provided by which to unify those parts—the contention that no such mechanism can be provided is premise (2) of Leibniz’s Argument from Unity. If it turns out that the parts of matter are merely modes (i.e., ways of being) of a single, material substance, then they do not constitute the right kind of plurality, and, it seems, the need for a unifying mechanism has been bypassed. It is worth pausing to ask whether the Monist’s Challenge can really be used against Leibniz’s argument for Plurality. There are two ways in which it might seem to falter. First of all, insofar as Leibniz denies that material parts are substances in their own right, doesn’t he also deny that there is a real distinction between any two parts of matter? If Leibniz denies that there is a real distinction between any two parts of matter, why should this line of reasoning apply?13 Second, although Leibniz denies empty space, one plausible interpretation of this denial is that empty space is morally impossible.14 That is, God’s wisdom leads God to create a world in which there is no empty space, even though empty space may figure in other uncreated (though possible) worlds.15 Does the moral impossibility of empty space entail the inability to conceive one material part without the 13 Descartes writes that “[s]trictly speaking, a real distinction exists only between two or more substances; and we can perceive that two substances are really distinct simply from the fact that we can clearly and distinctly understand one apart from the other” (AT VIII, 29 = CSMK 1, 213). Though it may seem as though Descartes is here inferring the real distinction from the independent conceivability of each part, it is not clear that independent conceivability is constitutive of real distinction; it may simply be a sign or mark of it. For discussion see, e.g., Rozemond 2011, D. Brown 2011, and Hoffman 2002. 14 Descartes’s view of empty space is somewhat different: “The impossibility of a vacuum, in the philosophical sense of that in which there is no substance whatsoever, is clear from the fact that there is no difference between the extension of a space, or internal place, and the extension of a body” (AT VIII, 49 = CSMK I, 229230). Thus, according to Descartes, empty space is metaphysically impossible. For further discussion of Descartes’s argument against empty space, see, e.g., Bennett 2001, 32. Bennett cautions that although we might provide a neat argument straight from the identification of body and extension to the identification of space and body, this is not the argument that Descartes gives. Rather Descartes’s argument proceeds by noting that the extension of space needs a subject and thus space must be filled with substance. This fits with Descartes’s formulations in earlier articles, see, e.g., Principles II.8 (AT VIII, 44-45 = CSMK I, 226). In the passage quoted, however, Descartes relies on the identity of the “extension of space” and the “extension of a body”. 15 He asserts something close to this view in, e.g., his 4th letter to Clarke: “to admit a vacuum in nature is ascribing to God a very imperfect work” (GP 7, 378 = LC 28). For discussion of Leibniz’s rejection of empty space, see, e.g., G. Brown 2011. 7 others? If not, then Leibniz’s view that space is morally impossible might be sufficient to avoid the Monist’s Challenge altogether. Although these observations do track actual commitments of Leibniz’s metaphysical system, these commitments are not available to serve as dialectically relevant responses to the Monist’s Challenge. First, although Leibniz denies that the parts of matter are substances in their own right, he still needs certain features of Descartes’s real distinction to apply to material parts (for dialectical reasons); it is just that he will refuse to draw the further conclusion that those features entail the substantiality of the parts of matter. In particular, Leibniz is motivated to uphold the independent conceivability of material parts from one another even though he denies their independent conceivability per se (i.e., without a foundation in immaterial substances). Second, although Leibniz may hold the view that empty space is only morally impossible, this observation will not dull the force of the Monist’s Challenge. A simple reformulation of (MC1) will address this concern: (MC1*) In the actual world, there cannot be any empty space.16 Even if empty space is only morally impossible, it is still the case that the actual world cannot have any, which is all that the Monist’s Challenge needs to rely on.17 The modal status of the rejection of empty space is a red herring (although it will resurface to some extent in section 5 below). So, the Monist’s Challenge is a real objection to Leibniz’s commitment to Plurality and needs to be addressed. 3. Leibniz’s Response: Dependence The core of the Monist’s Challenge, then, is the attempt to reduce the plurality of matter to a plurality of modes. Leibniz is, not surprisingly, unwilling to accept this reduction.18 But his initial attempts to respond miss the mark. These misses, however, help to clarify certain features of the Monist’s Challenge, and also help us to understand what a dialectically relevant response will look like. In the passage quoted above, De Volder formulates (MC1) as the claim that “there is indeed no empty space”. However, subsequent formulations of the Monist’s Challenge as well as Leibniz’s recapitulations of it employ the stronger claim that there cannot be any empty space (i.e., that empty space is impossible). 17 One could press the point further by attempting to argue that the conceivability claim in (MC2) will only be true if empty space is absolutely impossible. However, this is not how either De Volder or Leibniz understands the argument. Furthermore, if Leibniz gives this response, it would mean that his Argument from Unity relies on his arguments against the absolute impossibility of empty space. This would significantly reduce the power of Leibniz’s Argument from Unity, which is due (in part) to its generality: it is designed to apply to any view which cedes that matter has parts. 18 Interestingly, in early texts, c. 1676, Leibniz uses the failure of real distinction to argue for a type of monism. See, e.g., Quod ens perfectissimum sit possibile (A 6.3, 573 = DSR 93-95). In this text, however, Leibniz is appealing to the fact that it is difficult to maintain a real distinction between God and creatures. His engagement, therefore, is with a type of substance monism, rather than the material monism at issue in the current discussion. For discussion of this text and to what extent Leibniz accepted substance monism at this stage, see Laerke 2009. 16 8 Leibniz’s first misguided response attempts to maintain that matter is more than a plurality of modes by appealing to the presence of entelechies in matter. Call it the “Entelechy Response”: Entelechy Response: There are entelechies in matter, which provide more than a modal difference between the parts. ⁠ Leibniz’s formulation of the Entelechy Response follows on the heels of a passage we have already seen. He writes, I think that that which is extended has no unity except in the abstract, namely when we divert the mind from the internal motion of the parts by which each and every part of matter is, in turn, actually subdivided into different parts, something that plenitude does not prevent. Nor do the parts of matter differ only modally if they are divided by souls and entelechies, which always persist. (3 April 1699, A 2.3, 546 = LDV 73; emphasis added) Without going into too much detail concerning Leibniz’s metaphysics of substance, we might at least say this: entelechies are primitive forces of immaterial substances, from which the derivative forces operative within the phenomena result. We can observe the effects of these derivative forces when we see, e.g., the motion of bodies. There is, therefore, a sense in which, according to Leibniz’s considered view, the division, and thus the plurality of matter is explained by the presence of entelechies.19 If viable, the Entelechy Response would revise Leibniz’s argument for Plurality as follows: (P*1) (P*2) (P*2.1) (P*3) Matter is actually infinitely divided by motion. If matter is actually infinitely divided by motion, each and every part of matter is moving independently. Entelechies account for the motion that divides matter. Independence (with respect to motion) entails plurality. (P*4) So, matter is a plurality. De Volder’s conclusion (MC5) would then not be able to weaken (P*3) because (P*3) is now bolstered by (P*2.1). Though the Entelechy Response may express a clear commitment of Leibniz’s philosophical system, it does not constitute a dialectically relevant response. As I intend the term “dialectically relevant” here, in order for Leibniz’s response to be dialectically relevant, he cannot rely on the truth of any claim that is explicitly at issue (i.e., in this case, the claim that matter requires a foundation in immaterial, active substances). This is not to See Arthur 2012, 153 for an explicit development of the suggestion that the activity of substances is responsible for the division of bodies. See also GP 2, 268 = LDV 303: “…although these divisions proceed to infinity, nonetheless they all result from certain primary constituents, i.e. from real unities, though infinite in number.” 19 9 say that Leibniz cannot appeal to any claims that De Volder does not take to be true (of course, he would need to provide independent argument for these claims in order to convince De Volder), but it does prevent Leibniz from appealing to claims that assume the truth of the conclusion he is attempting to reach. In his exchange with De Volder (as in other iterations of the Argument from Unity), Leibniz is trying to argue for the view that simple, active substances underlie matter. One of the key premises in this argument is that matter is a plurality. Thus, the existence of active substances cannot be relied on to establish that matter is a plurality in the first place.20 What Leibniz needs, then, is a way to maintain the plurality of matter that does not rely on the presence of entelechies in matter, or on his considered conception of substance at all. Leibniz’s second attempt to respond consists in emphasizing the fact that the parts of matter are actually infinitely divided and, therefore, many. Call this the “Division Response”: Division Response: Material things are actually infinitely divided. If material things are actually infinitely divided, matter is a plurality. Leibniz attempts to maintain this line of defense after De Volder’s refusal to accept the Entelechy Response. He writes, I certainly had not believed that plurality could be denied in that which is extended, especially if we admit actual parts, as you do—unless we were to deny plurality even in a herd and an army, i.e. everywhere. (6 July 1699; A 2.3 576 = LDV 99) The problem with this response is that the Monist’s Challenge can cede the actually infinite division of matter while simultaneously denying the independence of the divided parts. De Volder’s response highlights this: I acknowledge plurality in a herd and in an army because they have parts joined together by a connection that is not necessary. The connection in that which is extended, where I certainly think that one part of it is necessary for another, is different. I do not admit a substantial distinction between the parts of extension, but only a modal one. In this I think I am like most, though not all, of those who ascribe all the variety in bodies to motion alone, seeing that it produces only a difference in modes. (1 August 1699; A 2.3, 586 = LDV 115) De Volder makes this point rather explicitly at A 2.3, 563 = LDV 93. He expresses frustration both about the fact that Leibniz has not given a demonstration that “every substance is active by nature” and about the fact that Leibniz has not explained exactly what an active principle is: “Is the active principle extension itself, a mode of extension, or, in fact, some other substance distinct from extension and therefore having nothing in common with it? If it is either extension or a mode of extension, extension will not be a merely passive principle. If it is another substance, how can it act on extension?” This is precisely the issue that motivates the correspondence in the first place. See, e.g., Bernoulli’s 2 August 1698 letter to Leibniz: LDV 5. (I do not believe this letter is part of any volume yet edited, besides LDV.) See Lodge 1998 & 2001 for development of the view that the Leibniz-De Volder correspondence was a failure in this respect. 20 10 According to De Volder, even if matter has actual parts, this does not entail that matter is a plurality in the relevant sense. De Volder’s reply to the Division Response signals that, in his view, the commitment to Unity is consistent with a deflationary reading of Plurality, according to which matter is a plurality of modes. It also highlights the fact that De Volder is willing to draw the conclusion (MC6) above: (MC6) So, the physical plenum has no really distinct parts (i.e., it is a single substance).21 Leibniz’s best prospects for a defense of Plurality against the Monist’s Challenge are found in a 6 July 1699 letter to De Volder—call it the “Dependence Response”. This response is given rather tersely in the letter itself, though elaborated in a draft. Here is the passage from the letter: “[n]or is any one part of matter <absolutely> necessary for another, and, even if it were, this connection would not produce the unity of substances. (A 2.3, 576 = LDV 99).22 As I said, this response is terse. From this statement alone it is not clear in what way the parts of matter fail to be absolutely necessary for one another. In fact, given a certain familiarity with Leibniz’s background commitments, it would be natural to read this response as the claim that since empty space is only morally impossible, the parts of matter depend on one another morally, though not absolutely. (This response would then track the second potential way—outlined above—that the Monist’s Challenge might not engage Leibniz’s commitments.) However, in a draft of this letter Leibniz elaborates in a surprising way. He writes, You say that the unity of that which is extended is perceived even if it is divided into parts moving around in different ways, because given parts can neither exist nor be conceived without the others. And so you assume two things that I could not bring myself to concede: that one part of what is extended cannot exist or be conceived of without the others, and that things of this sort are one. From this you show that a vacuum is impossible. But your arguments did not accomplish this. If it is conceded that a vacuum is impossible, it indeed follows that one part of matter cannot exist without some other part, but it does not follow at all that it cannot exist without this part or that part [si concederetur, sequitur quidem materiae unam partem non posse esse sine aliqua alia, sed minime sequitur non esse posse sine hac aut his]. Besides, unless I am mistaken, this argument proves too much. For according to it, things that are scattered here and there will also be one thing. As I understand unity, such things are more properly called many and do not constitute one thing except as an aggregate when they are grasped with one thought. In a substance that is truly one 21 De Volder’s view is similar to certain so-called “monist” readings of Descartes, according to which Descartes is committed to the existence of only a single material substance. De Volder’s thought here most closely resembles the argument in Lennon (2007): bodies are individuated by motion; motion is a mode; so, bodies are only modes. For other monist readings of Descartes, see, e.g., Gueroult 1984, Nelson & Smith 2010, and Sowaal 2004; for pluralist readings, see, e.g., Rozemond 2011, Normore 2008, and Kaufman 2014. However, there is an ambiguity in De Volder’s commitment to monism that prevents him from being straightforwardly placed in the monist camp. More on this in the next section. 22 I have inserted the angle brackets around “absolutely” because Lodge notes that this word was not included in Leibniz’s copy of the letter, though it was included in the letter as sent. 11 there are not many substances. (draft of 6 July 1699; A 2.3, 572 = LDV 107; emphasis added)23 The thought driving Leibniz’s response, then, is not whether empty space is morally or absolutely impossible. Rather, he is considering different types of dependence between material parts that could follow from the impossibility of empty space (whether absolute or moral). Leibniz is making the point that although the plenum entails some sort of dependence between material parts, the dependence is not as strong as De Volder takes it to be. Though one part of matter depends on some other part—aliqua alia—it does not depend on any particular part—hac aut his. I will formulate Leibniz’s distinction in terms of “generic” versus “specific” dependence: Generic Dependence: For every part of matter x and every part of matter y, x different from y, the conception of x entails the conception of y, or some other part, call it z, ⁠ that occupies the space of y.24 Specific Dependence: For every part of matter x and every part of matter y, x different from y, the existence or conception of x entails the existence or conception of y.⁠ Let me illustrate this by an example: if two things, say, my left ear and my nose, generically depend on one another, then my nose can be annihilated without issue, so long as it is replaced with some other material thing—my left ear does not require my nose in particular, but just something or other occupying that space.⁠ If the same two things—my left ear and my nose—specifically depend on one another, then the annihilation of my nose is ipso facto the annihilation of my left ear, since in virtue of the specific dependence between them, they stand or fall together, so to speak. The Dependence Response can be formulated as follows: Dependence Response: The plenum entails only generic dependence between material parts. Generic dependence is consistent with (specifically) independent conceivability. How does this address the Monist’s Challenge? It complicates De Volder’s argument by demanding a revision to (MC2) as follows: (MC2*) If there is no empty space, then one material part cannot be conceived without some other parts, but no parts in particular. The only other article I know of that mentions this passage is Rozemond 2011, 255. Rozemond’s focus, however, is on Descartes’s conception of real distinction and whether Descartes can maintain a commitment to a plurality of material substances. Rozemond finds a similar distinction in Descartes’s Principles II.18 (AT VIII, 50). 24 I borrow the term “generic dependence” from Simons 1987, 294-304. He develops a distinction between generic and rigid dependence that is very much like Leibniz’s. Thanks to Stephan Schmid for alerting me to this similarity. 23 12 This revision prevents the move to (MC3). That is, generic dependence does not imply a failure of real distinction. This is because the parts of matter remain specifically independent. So, the Dependence Response is able to block the Monist’s Challenge and reinstate Leibniz’s original argument for Plurality—in particular, the following premise: (P3) Independence (with respect to motion) entails plurality. This permits the inference to the original conclusion: (P4) So, matter is a plurality. 4. Leibniz’s Response: Unity While Leibniz’s distinction between generic and specific dependence provides an initially viable response to the Monist’s Challenge, there are certain complications that will be taken up below. However, before I turn to those complications there is a further reply present in the same passage that should also be considered. While the Dependence Response resists (MC2) of the Monist’s Challenge, the alternate reply—call it the Scattered Object Response—attempts to resist (MC3), namely, (MC3) If one material part cannot be conceived without the others, then the parts of matter are not really distinct. It is irrelevant here whether the antecedent is formulated in terms of generic or specific dependence. Leibniz, in fact, argues against the harder case, namely when the antecedent is formulated in terms of specific dependence. As I mentioned above, (MC3) is a version of De Volder’s commitment to Unity, namely that dependence (with respect to conception) entails unity. Thus, the Scattered Object Response resists a different aspect of De Volder’s argument from the Dependence Response. Here is the relevant portion of the passage from above: …[Y]ou assume two things that I could not bring myself to concede: that one part of what is extended cannot exist or be conceived of without the others, and that things of this sort are one…. Besides, unless I am mistaken, this argument proves too much. For according to it, things that are scattered here and there will also be one thing. As I understand unity, such things are more properly called many and do not constitute one thing except as an aggregate when they are grasped with one thought. In a substance that is truly one there are not many substances. (Draft of 6 July 1699; A 2.3, 572 = LDV 107; emphasis added)25 This response is included in the final version of the letter in more or less the same form. See, e.g., A 2.3, 576 = LDV 99, which continues from the portion quoted above: “Nor is any part of matter absolutely necessary for another, and, even if it were, this connection would not produce the unity of substances. In a substance that is 25 13 Leibniz’s argument proceeds by reductio ad absurdum. He claims that if dependence (with respect to conception and/or existence) did in fact entail the unity of the things that so depend, this would entail the unity of any scattered object (i.e., an object with spatially disjoint parts). For example, my little finger cannot be conceived without the Eiffel Tower (by MC2). And if dependence entails unity, then the aggregate of my little finger and the Eiffel Tower will be one thing (by MC3). If this reductio goes through, it is the basis for rejecting (MC3) of the Monist’s Challenge: Scattered Object Response: (MC3) entails scattered objects. Scattered objects are absurd. So, (MC3) is false. IF (MC3) is rejected, this will prevent both the main conclusion that the parts of matter differ only modally and the further conclusion that the physical plenum is a single substance. Though scattered objects would appear to be an unwelcome implication, it is not clear that De Volder needs to accept Leibniz’s reasoning. The relevant question is this: does the Monist’s Challenge, (MC3) in particular, entail scattered objects? Although there is some initial reason to think so, I do not think that (MC3) needs to have this implication in order for the Monist’s Challenge to work, and can be reformulated to avoid it. To be explicit, the reason to think that the Monist’s Challenge does entail scattered objects is that, according to De Volder, wherever there is a “necessary and reciprocal connection” between some things, there is, strictly speaking, only one thing. Here is De Volder: I would not so readily say that they are many things, since, on the definition just given, there is a necessary and reciprocal connection between these things [res] (if you wish to speak of them as things). For whatever plurality you suppose here, it is certain that part A of the extension cannot be conceived and cannot exist without part B, and vice versa. (7 October 1701; GP 2, 231 = LDV 219-221) Passages such as this one appear to entail that any arbitrary collection of material parts will be a unity. Since it is true that for any collection of parts we choose, there will be a necessary and reciprocal connection between those parts, it seems to follow that the collection will be one thing. But I think there is room for De Volder to resist this implication. One option is to revise Unity as follows: (Unity*) Maximal dependence (with respect to conception and/or existence) entails unity. truly one in my sense there are not many substances. And where there are many substances they do not constitute one substance but an aggregate.” 14 By “maximal dependence” I mean that some things depend on each other such that there are no further things on which they also depend. So, the only thing that meets the condition of maximal dependence is the entire plenum. In this way, De Volder can resist that “things scattered here and there will also be one thing” because, although those things depend on one another, they do not maximally depend. This fits with De Volder’s larger commitment, since, on his view, any two material parts are merely modes of a single material substance. Thus, unity is properly located only at the level of the entire plenum. 5. Material Monism and Ontological Priority At this stage, characterizing De Volder’s larger commitment to what I have called “material monism”, becomes relevant. At the heart of the Monist’s Challenge is the idea that the entire plenum is ontologically prior to individual material things—a sign of this priority is the maximal dependence that holds between all the material parts. According to De Volder, if material parts so depend, it follows that they are simply ways of being (i.e., modes) of a single material substance.26 This commitment explicitly inverts Leibniz’s conception of the physical world, according to which material parts are prior to any actual wholes that they might compose. In Leibniz’s view, whole-part priority cannot apply to actually existing things, but only to ideal things or abstracta. This distinction is pervasive in Leibniz’s texts, and presented in a 1706 letter to De Volder: Actual things are composed as a number is composed from unities, ideal things as a number is composed from fractions. There are actual [actu] parts in a real whole, but not in an ideal whole. Indeed, when we—confusing ideal things with real substances—seek actual parts [partes actuales] in the order of possible things and indeterminate parts in an aggregate of actual things, we entangle ourselves in the labyrinth of the continuum and in inexplicable contradictions. (GP 2, 282-283 = LDV 333) When a number is composed from unities, the unities—or units—are prior to the number and the number is an aggregate of those units. When a number is composed from fractions, the number is prior to the fractions, since there is no way to decompose the number into basic fractional elements; rather, the fractions result from dividing the number.27 There is, therefore, a clear connection between part-whole priority and actual parts on the one hand, and whole-part priority and potential (or indeterminate) parts on the other hand. Existing things, according to Leibniz, insofar as they are existing things, must exhibit part-whole priority and must have actual parts. Otherwise, their structure (and therefore their existence) becomes dependent on some perceiver. Leibniz makes this point about perceiver dependence explicitly: See, e.g., Horgan & Potrč 2008 for a contemporary variant of De Volder’s view called “blobjectivism”: “The blobject has enormous spatiotemporal structural complexity and enormous local variability—even though it does not have any genuine parts” (3). 27 See, e.g., Leibniz “Remarks on M. Foucher’s Objections” for further discussion of the units vs. fractions example: GP 4, 490-493 = WFPT 184-185. 26 15 In fact, matter is not continuous but discrete and actually divided to infinity, even if no assignable part of space is devoid of matter. Yet space, like time, is not something substantial, but something ideal, and consists in possibilities, i.e. the order of possible coexistents at any given time. And so, there are no divisions in it, except those that the mind makes, and the part is posterior to the whole. (GP 2, 278 = LDV 327) The important connection made in this passage is the one between whole-part priority and having no divisions, except those that the mind makes. This, for Leibniz, is a sign of the ideality of the thing in question. This observation highlights an unstated commitment in the background of Leibniz’s argument for Plurality, and therefore, in his Argument from Unity as well: material parts must be prior to any wholes they might compose. To put it in slogan form: actual things have actual parts. Built into the notion of actual part is a commitment both to the priority of these parts and to the independence of these parts from one another. It is a short path from this general commitment about actually existing material parts to the plurality of matter. There is some potential for confusion at this point, since on Leibniz’s considered view, material things require a foundation in immaterial substances. So we might ask: what are the actual parts of material things? Smaller material things? Immaterial substances? Attempting to address these questions fully is beyond the scope of the present discussion, however some brief remarks can be made. Given the ontological priority involved, we might be tempted to think that the actual parts in question are immaterial substances. However, this would be a mistake. For one thing, Leibniz is explicit that “substantial unities are not parts, but the foundations of phenomena” (GP 2, 268 = LDV 303). So, whatever relation immaterial substances bear to material things, it is not a part-whole relation. Second, insofar as material things are pluralities, and the parts of pluralities are prior to the pluralities of which they are parts, material parts can enjoy a relative priority even if they are not fundamental. So, for example, the parts of the Eiffel Tower are more fundamental than the Eiffel Tower, even though the parts themselves are not completely fundamental. The Monist’s Challenge is especially apt as an objection to Leibniz’s argument because it denies this commitment—a material whole, according to De Volder, can be prior to its parts. But what picture of the physical world is De Volder endorsing exactly? There is, in fact, some ambiguity concerning the precise nature of De Volder’s commitment to material monism. Here is the commitment as I have stated it above: (MC6) The physical universe has no really distinct parts (i.e., it is a single substance). In the correspondence itself, however, De Volder expresses this commitment in different ways, suggesting two possible interpretations, which I will call “Number” and “Nature”: (Number) (Nature) There is only one material substance There is only one material nature 16 According to Nature, De Volder’s claim would be understood to mean that the parts of matter do not differ qua substantial nature (i.e., they all have the same nature, namely extension). This view can be characterized as type (material) monism (i.e., there is one material nature). The following text suggests this interpretation of De Volder’s commitment: I believe that those who regard every distinction between bodies as a mode of extension (as so many do today, though not everyone) will not deny that when the vacuum is excluded all bodies indeed differ only modally and are one and the same with respect to substance. (GP 2, 243 = LDV 247) When presented with this explication from De Volder, Leibniz is justifiably confused, given De Volder’s previous comments. He replies as follows: When Descartes and others say that “the substance of all corporeal things is one,” they mean by that one similar nature. They do not (I think) mean that all bodies in fact make up one substance. Certainly, reality itself shows that the world is an aggregate, like a flock or a machine. (GP 2, 271 = LDV 307) In an attempt to resolve Leibniz’s confusion, De Volder appears to slide into a more or less explicit assertion of Number. He writes, Surely those who say that the substance of all corporeal things is one, or, rather, those who think that bodies themselves are only distinguished by modes of extension, are admitting that this corporeal universe is composed of one substance affected by an infinity of different modes. But this does not really matter much. (GP 2, 272 = LDV 315) This passage suggests that De Volder’s commitment to (MC6) is best understood to assert token (material) monism (i.e., there is one material substance). Material parts are then individuated (in a weak sense) by motions, but they do not achieve any independence from the entire plenum. Which interpretation is the right one? The textual evidence is difficult to interpret conclusively; however, given the passage just cited, I incline towards the conclusion that De Volder is a token monist. Still, the ambiguity present in De Volder’s expressions of his view presents Leibniz with something of a moving target. This might explain why in many of the texts we have considered, Leibniz is found appealing to the claim that “in a substance that is truly one there are not many substances” (A 2.3, 572 = LDV 107). This remark might make sense if Leibniz is arguing against a type monist; but it misses the mark if De Volder is a token monist. Furthermore, token monism provides De Volder with a stronger objection to Leibniz’s argument for Plurality. If De Volder is a token monist, it is extremely difficult for Leibniz to motivate the plurality of matter in a dialectically relevant way, since the Monist’s Challenge fundamentally departs from Leibniz’s own conception of the physical world and what it means, in his mind, to be an actually existing material thing. 17 6. Generic Dependence and the Actual World In section 6, I will consider a potential complication for the Dependence Response as I have developed it. Although the Dependence Response is, I have argued, dialectically relevant (i.e., it does not presuppose any features of Leibniz’s metaphysical system explicitly at issue in his exchange with De Volder), there is an additional condition that should be met if it is to be a truly viable response for Leibniz. Namely, the response should be all-told consistent (i.e., it should not contravene any of Leibniz’s considered commitments). I should note that this discussion is fairly speculative, since Leibniz does not explicitly address this issue, at least not to my knowledge. However, I attempt to remain as close to Leibniz’s texts as possible; in particular, I will rely primarily on evidence from Leibniz’s exchange with De Volder. Is it consistent with Leibniz’s considered commitments to say that one part of matter generically depends on another, but does not specifically depend?28 Let me formulate the question via the following case: in the actual world, both my little finger and the Statue of Liberty exist. In what sense does my little finger depend on the Statue of Liberty? The Dependence Response says that my little finger depends on the Statue of Liberty only generically, which is to say, the Statue of Liberty could be destroyed while my little finger remains, so long as some matter or other comes to occupy the space of the Statue of Liberty. But there is at least a prima facie problem lurking here. On Leibniz’s considered view, the Statue of Liberty is a well-founded phenomenon resulting from an aggregate of substances, which occupy the actual world. But furthermore, the actual world is, for Leibniz, the best possible world. And there is one and only one collection of substances answering to the description “the best possible world”. Perhaps, then, it is not possible for the Statue of Liberty (understood to result from some particular aggregate of substances) to be replaced by some matter or other (understood to result from some aggregate of substances or other) without contradiction (i.e., without altering the identity of the actual world). If so, then it seems like my little finger depends on the Statue of Liberty in particular, which is to say that it specifically depends on the Statue of Liberty. This situation provides some reason to worry that the Dependence Response is not all-told consistent. The commitment that is causing the problem is Leibniz’s view that “all things conspire”—sympnoia panta.29 As such, any change to one substance in a given world One thing worth noting here is that Leibniz acknowledges the possibility that one substance exists on its own. This has been called Leibniz’s “World-Apart Doctrine”. The World-Apart Doctrine might appear to imply that no substance depends on any other. See, e.g., A 6.4, 1550; GP 4, 484; GP 2, 307. For critical discussion of these texts, including an assessment of the type of independence involved in World-Apart, see Harmer 2016. Though I argue that this situation is metaphysically possible, it does not speak to the question whether certain substances in the actual world could be replaced by others, but only to the question whether certain substances could be removed from the world altogether. 29 See, e.g., Monadology ¶61: “In a plenum, every motion has some effect on distant bodies, in proportion to their distance. For each body is affected, not only by those in contact with it, and in some way feels the effects of everything that happens to them, but also, through them, it feels the effects of those in contact with the bodies with which it is itself immediately in contact. From this it follows that this communication extends to any distance whatsoever. As a result, every body is affected by everything that happens in the universe, to such an extent that he who sees all can read in each thing what happens everywhere, and even what has happened or what will happen, by observing in the present what is remote in time as well as in space. ‘All things conspire [sympnoia panta],’ said Hippocrates” (GP 7, 617 = AG 221). 28 18 entails a change to all other substances as well. In Theodicy §414, Leibniz makes this point explicitly, using the voice of Athena and the example of Sextus: I have only to speak, and we shall see a whole world that my father might have produced, wherein will be represented anything that can be asked of him; and in this way one may know also what would happen if any particular possibility should attain unto existence…. I will show you some [worlds], wherein shall be found, not absolutely the same Sextus as you have seen (that is not possible, he carries with him always that which he shall be) but several Sextuses resembling him, possessing all that you know already of the true Sextus, but not all that is already in him imperceptibly, nor in consequence all that shall yet happen to him. You will find in one world a very happy and noble Sextus, in another a Sextus content with a mediocre state, a Sextus, indeed, of every kind and endless diversity of forms. (GP 6, 362-363 = H 370-371) This passage suggests that insofar as each created substance carries with it everything it will become, any changes to the world in which it resides will entail changes to the identity of the substance in question and vice versa. Can Leibniz avoid the problem suggested by this passage? A different way to put the question that needs to be answered is this: does the actual world permit some replacement of its constituent substances? When asked this way, Leibniz’s prospects do not look good. This problem can be engaged, at least partially, by the following (admittedly complex) line of thought. It starts by asking whether a substance (one particular substance) remains numerically the same through its ever-changing states.30 Writing to De Volder, Leibniz says the following: [b]ut if anyone claims other substances that succeed prior ones are always produced by God and that they do not remain the same, he would be quarreling about a word, for there will be no further principle in things for deciding the question. The substance that succeeds is taken to be the same as long as the same law of the series, i.e., of the continual simple transition, persists that gives rise to our belief in the same subject of change, i.e., the monad. (21 January 1704; GP 2, 264 = LDV 291)31 Sleigh (1990) interprets this passage as the apparent suggestion that “whether we adopt an ontology of transitory individuals or an ontology of persisting individuals is a matter of convention—a decision not grounded in the nature of things” (132).32 This is controversial, 30 See Sleigh 1990, who highlights this question as an open problem of interpretation (132-133). I know of nobody since Sleigh who has attempted to close it. 31 Lodge notes that this passage was probably not included in the version of the letter sent to De Volder (LDV 393, footnote 11). 32 Sleigh’s reading of this passage might seem to run afoul of Leibniz’s Principle of the Identity of Indiscernibles, which would be reason to resist it. However, an ontology of transitory individuals need not violate this principle. Even though two transitory individuals could be said to instantiate the same “law of the series”, these individuals would exemplify different qualities, since they would not instantiate the same segment of the series in question. Thus, the individuals would be discernible insofar as the states they exemplify are discernible even if the law of the series they instantiate can be said to be the same law. This 19 to be sure. But notice how Sleigh’s reading of this passage provides a basis for maintaining that certain replacements of constituent substances are permitted. If certain replacements are permitted, it would follow that, within a given world, one substance only generically depends on the other substances. I, for example, would only generically depend on the substances from which my desk results, since they could be replaced with other substances so long as the same “law of the series” persists.33 If this line of thought is viable, then Leibniz can maintain the view that material things (understood to result from aggregates of substances) only generically depend on one another with only slight modification to the notion of generic dependence: Generic Dependence*: For every part of matter x and every part of matter y, x different from y, the existence or conception of x entails the existence or conception of y, or some other part, call it z, that results from an aggregate of substances that have the same “laws of the series”.⁠ This modification is not objectionable in itself, since it simply tracks a change to the metaphysical status of part of matter: matter is no longer identified with extension but with a phenomenon well-founded on substances. Furthermore, Leibniz need not actually adopt an ontology of transitory individuals; he need only concede that such an ontology would not be metaphysically impossible. Still, this line of thought is not without difficulty. As Sleigh notes shortly after the passage quoted above, Leibniz appears to be of a different mind in the Theodicy. He quotes the following passage from Theodicy §393: It is well to beware, moreover, lest in confusing substances with accidents, in depriving created substances of action, one fall into Spinozism, which is an exaggerated Cartesianism. That which does not act does not merit the name of substance. If the accidents are not distinct from the substances; if the created substance is a successive being, like movement; if it does not endure beyond a moment, and does not remain the same (during some stated portion of time) any more than its accidents; if it does not operate any more than a mathematical figure or a number: why shall one not say, with Spinoza, that God is the only substance, and that creatures are only accidents or modifications? (H 359-360; qtd. in Sleigh 1990, 133) This passage speaks to a number of issues that have been salient in Leibniz’s exchange with De Volder: the activity of substance, the difference between substances and accidents (or modes), and the connection between Cartesianism and Spinozism, to name a few. It also suggests that the ontology of transitory individuals outlined above is deeply at odds with argument could certainly be developed further, and there are certainly possible objections to it, but in my view it blocks the immediate dismissal of the possibility of transitory individuals on the grounds that it violates the Principle of the Identity of Indiscernibles. 33 Another way to put this point, which might be helpful, would be to say that so long as the same forces are displayed in the world (both primitive and derivative, active and passive), then whether the subject of these forces is numerically the same over time is a matter of God’s wisdom, not a matter of metaphysical necessity. 20 Leibniz’s conception of substance. A substance, for Leibniz, is something that acts and that persists through changes—in this respect Leibniz clearly follows the Aristotelian tradition. But for the purposes of the present discussion, I am not suggesting that Leibniz in fact adopts an ontology of transitory individuals—far from it. My contention is much weaker. I am simply suggesting that if an ontology of transitory individuals is not metaphysically impossible, then the claim that material parts only generically depend on one another could be all-told consistent with Leibniz’s considered position. For this purpose, Sleigh’s (admittedly tentative) reading of this passage from the Theodicy is helpful. After noting the apparent difference between this passage and the one from the letter to De Volder quoted above, Sleigh writes, Did Leibniz take the scheme of transitory individuals to be metaphysically impossible, or did he have other grounds for favoring the scheme of created substances persisting through changes? I lean toward the latter. I believe that Leibniz’s primary intellectual motivation here was theological, since he took various theological doctrines concerning the relation of God to creatures, especially creatures who are moral agents, to require persisting individuals. (Sleigh 1990, 133) If Sleigh’s hunch is right, then the persistence of substance is a theological rather than a metaphysical requirement. This would provide a way for Leibniz to cede the metaphysical possibility of transitory individuals, which would then permit the view that material things only generically depend on one another. Of course, the path to this conclusion is rather circuitous and forces Leibniz to endorse views that seem to be deeply at odds with his own philosophical instincts. Thus, the conclusion I draw here is tentative and explicitly conditional: if an ontology of transitory individuals is metaphysically possible, then the Dependence Response is all-told consistent. 7. Conclusion The Monist’s Challenge attempts to undercut premise (1) of Leibniz’s Argument from Unity, namely the claim that matter is a collection or aggregation to infinity. It does so by blocking Leibniz’s support for premise (1), which is provided by his commitment to the actually infinite division of matter: if matter is actually infinitely divided, then matter is a plurality. But in virtue of the dependence that holds between the parts of matter in light of the plenum, the plurality of matter is at risk of collapsing into a mere plurality of modes. I have argued that the Monist’s Challenge provides a real threat to Leibniz’s Argument from Unity. I have argued further that in order to meet the Monist’s Challenge, Leibniz needs to provide a dialectically relevant response. This is not as straightforward as it seems. I have argued that the Dependence Response is a partially viable response because it weakens the type of dependence that follows from the plenum and therefore resists the further inference that material parts differ only modally. Further, it does so without presupposing any features of Leibniz’s own metaphysical system that are explicitly at issue in the exchange with De Volder. Not only does the Division Response need to be dialectically relevant, it must also be all-told consistent (i.e., it must not contravene any of Leibniz’s considered commitments). 21 Here Leibniz faces more difficulty, given his considered views that matter results from aggregates of substances, and that God creates the best possible world (i.e., one particular aggregate of substances). I have provided the sketch of an argument for the view that material parts in the best possible world (understood to result from aggregates of substances) only generically depend on each other. The argument relies on the possibility (but only the possibility) of an ontology of transitory individuals. Whether or not Leibniz is comfortable with this possibility will determine the all-told consistency of the Division Response.34 One thing that this discussion has shown is that Leibniz’s Argument from Unity faces more difficulty that previously supposed. In particular, it is difficult for Leibniz to avoid presupposing features of his own metaphysical system while convincingly making this argument. If the Dependence Response does not ultimately work—and there is certainly some, if not definitive, reason to draw this conclusion—the only option left is the Scattered Object Response. Above, I isolated one commitment that seems essential to the viability of the Scattered Object Response: the priority of material parts to actual material wholes. Insofar as this commitment is directly at odds with material monism, the Monist’s Challenge has served to highlight a major commitment driving Leibniz’s Argument from Unity: his bottom-up conception of material things. This is fundamentally different from De Volder’s conception (and, arguably, Spinoza’s too35). If Leibniz can independently motivate his own bottom-up conception, this might revitalize the Scattered Object Response to the Monist’s Challenge. As it currently stands, however, De Volder has succeeded in displaying a weak spot in one of Leibniz’s powerful arguments against merely extended substance. Adam Harmer University of California, Riverside adam.harmer@ucr.edu Bibliography Robert Adams. 1994. Leibniz: Determinist, Theist, Idealist. Oxford: OUP. Richard T. W. Arthur. 2011. “Presupposition, Aggregation, and Leibniz’s Argument for a Plurality of Substances.” Leibniz Review 21: 91-116. Richard T. W. 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